From 3f5cccf6547a52b0c2c87ff818f73f381bf9b7c7 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 14 May 2012 18:11:17 +0000 Subject: [PATCH 001/115] Minor doc update. [SVN r78473] --- doc/sf_and_dist/html/index.html | 2 +- doc/sf_and_dist/html/index/s13.html | 4 ++-- doc/sf_and_dist/html/index/s14.html | 4 ++-- doc/sf_and_dist/html/index/s15.html | 4 ++-- doc/sf_and_dist/html/index/s16.html | 4 ++-- doc/sf_and_dist/html/index/s17.html | 4 ++-- .../math_toolkit/constants/constants.html | 19 +++++++++++++++++++ .../dist/dist_ref/dists/skew_normal_dist.html | 7 ++++++- .../main_overview/conventions.html | 2 +- .../main_overview/navigation.html | 2 +- 10 files changed, 38 insertions(+), 14 deletions(-) diff --git a/doc/sf_and_dist/html/index.html b/doc/sf_and_dist/html/index.html index a4af5cdd0..f0094e8cc 100644 --- a/doc/sf_and_dist/html/index.html +++ b/doc/sf_and_dist/html/index.html @@ -541,7 +541,7 @@

- +

Last revised: April 29, 2012 at 16:45:52 GMT

Last revised: May 14, 2012 at 18:06:46 GMT


diff --git a/doc/sf_and_dist/html/index/s13.html b/doc/sf_and_dist/html/index/s13.html index a55d21d3a..b73f963b6 100644 --- a/doc/sf_and_dist/html/index/s13.html +++ b/doc/sf_and_dist/html/index/s13.html @@ -22,9 +22,9 @@
PrevUpHomeNext
-
+

-Function Index

+Function Index

A B C D E F G H I K L M N O P Q R S T U V W Z

diff --git a/doc/sf_and_dist/html/index/s14.html b/doc/sf_and_dist/html/index/s14.html index f8000ff41..b6ad66578 100644 --- a/doc/sf_and_dist/html/index/s14.html +++ b/doc/sf_and_dist/html/index/s14.html @@ -22,9 +22,9 @@
PrevUpHomeNext
-
+

-Class Index

+Class Index

B C D E F G H I L M N P R S T U W

diff --git a/doc/sf_and_dist/html/index/s15.html b/doc/sf_and_dist/html/index/s15.html index d5669cac1..5c7fd584b 100644 --- a/doc/sf_and_dist/html/index/s15.html +++ b/doc/sf_and_dist/html/index/s15.html @@ -22,9 +22,9 @@
PrevUpHomeNext
-
+

-Typedef Index

+Typedef Index

A B C D E F G H I L N O P R S T U V W

diff --git a/doc/sf_and_dist/html/index/s16.html b/doc/sf_and_dist/html/index/s16.html index 6d351e63d..61968a82e 100644 --- a/doc/sf_and_dist/html/index/s16.html +++ b/doc/sf_and_dist/html/index/s16.html @@ -22,9 +22,9 @@
PrevUpHomeNext
-
+

-Macro Index

+Macro Index

B F

diff --git a/doc/sf_and_dist/html/index/s17.html b/doc/sf_and_dist/html/index/s17.html index a231c5f3a..b7344d7e3 100644 --- a/doc/sf_and_dist/html/index/s17.html +++ b/doc/sf_and_dist/html/index/s17.html @@ -21,9 +21,9 @@
PrevUpHome
-
+

-Index

+Index

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diff --git a/doc/sf_and_dist/html/math_toolkit/constants/constants.html b/doc/sf_and_dist/html/math_toolkit/constants/constants.html index fa4c6097c..e232c6618 100644 --- a/doc/sf_and_dist/html/math_toolkit/constants/constants.html +++ b/doc/sf_and_dist/html/math_toolkit/constants/constants.html @@ -241,6 +241,25 @@ + +

+ ln_ten +

+ + +

+ ln(10) +

+ + +

+ 2.30258 +

+ + + + +

ln_ln_two diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/skew_normal_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/skew_normal_dist.html index 0120c4477..73bd8b63b 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/skew_normal_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/skew_normal_dist.html @@ -233,7 +233,7 @@

- testing + Testing

The R Project for Statistical @@ -246,6 +246,11 @@ skew-t (ST) probability distributions, both for the univariate and for the the multivariate case, including regression models.

+

+ Wolfram + Mathematica was also used to generate some more accurate spot + test data. +

Accuracy diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html b/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html index 90935406f..72bbf68da 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html @@ -27,7 +27,7 @@ Document Conventions

- +

This documentation aims to use of the following naming and formatting conventions. diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html index e3642efdc..1be09a220 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html @@ -27,7 +27,7 @@ Navigation

- +

Boost.Math documentation is provided in both HTML and PDF formats. From 056745573f8f6de1da884878e321dcd505723ad0 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 17 May 2012 09:19:57 +0000 Subject: [PATCH 002/115] Add the Jacobi elliptic special functions. 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97 +- doc/sf_and_dist/html/index/s14.html | 40 +- doc/sf_and_dist/html/index/s15.html | 44 +- doc/sf_and_dist/html/index/s16.html | 10 +- doc/sf_and_dist/html/index/s17.html | 177 +- .../math_toolkit/backgrounders/lanczos.html | 4 +- .../math_toolkit/constants/constants.html | 2 +- .../main_overview/conventions.html | 2 +- .../main_overview/navigation.html | 2 +- .../math_toolkit/perf/comp_compilers.html | 2 +- .../html/math_toolkit/perf/comparisons.html | 4 +- .../html/math_toolkit/perf/getting_best.html | 2 +- .../html/math_toolkit/perf/tuning.html | 4 +- .../html/math_toolkit/special.html | 29 + .../math_toolkit/special/ellint/ellint_3.html | 6 +- .../math_toolkit/special/expint/expint_i.html | 2 +- .../math_toolkit/special/expint/expint_n.html | 2 +- .../html/math_toolkit/special/jacobi.html | 72 + .../special/jacobi/jacobi_cd.html | 87 + .../special/jacobi/jacobi_cn.html | 83 + .../special/jacobi/jacobi_cs.html | 87 + .../special/jacobi/jacobi_dc.html | 87 + .../special/jacobi/jacobi_dn.html | 83 + .../special/jacobi/jacobi_ds.html | 87 + .../special/jacobi/jacobi_elliptic.html | 301 +++ .../special/jacobi/jacobi_nc.html | 87 + .../special/jacobi/jacobi_nd.html | 87 + .../special/jacobi/jacobi_ns.html | 87 + .../special/jacobi/jacobi_sc.html | 87 + .../special/jacobi/jacobi_sd.html | 87 + .../special/jacobi/jacobi_sn.html | 83 + .../html/math_toolkit/special/zetas.html | 6 +- .../html/math_toolkit/special/zetas/zeta.html | 2 +- .../math_toolkit/utils/fp_facets/intro.html | 2 +- doc/sf_and_dist/jacobi_elliptic.qbk | 513 +++++ doc/sf_and_dist/math.qbk | 5 + include/boost/math/special_functions.hpp | 1 + .../boost/math/special_functions/hankel.hpp | 4 +- .../special_functions/jacobi_elliptic.hpp | 318 ++++ .../boost/math/special_functions/math_fwd.hpp | 134 ++ test/Jamfile.v2 | 1 + test/compile_test/instantiate.hpp | 63 + test/jacobi_elliptic.ipp | 407 ++++ test/jacobi_elliptic_small.ipp | 1688 +++++++++++++++++ test/jacobi_large_phi.ipp | 307 +++ test/jacobi_near_1.ipp | 347 ++++ test/test_instances.hpp | 28 + test/test_jacobi.cpp | 114 ++ test/test_jacobi.hpp | 182 ++ 87 files changed, 7363 insertions(+), 124 deletions(-) create mode 100644 doc/sf_and_dist/equations/jacobi1.mml create mode 100644 doc/sf_and_dist/equations/jacobi1.png create mode 100644 doc/sf_and_dist/equations/jacobi1.svg create mode 100644 doc/sf_and_dist/equations/jacobi2.mml create mode 100644 doc/sf_and_dist/equations/jacobi2.png create mode 100644 doc/sf_and_dist/equations/jacobi2.svg create mode 100644 doc/sf_and_dist/equations/jacobi3.mml create mode 100644 doc/sf_and_dist/equations/jacobi3.png create mode 100644 doc/sf_and_dist/equations/jacobi3.svg create mode 100644 doc/sf_and_dist/equations/jacobi4.mml create mode 100644 doc/sf_and_dist/equations/jacobi4.png create mode 100644 doc/sf_and_dist/equations/jacobi4.svg create mode 100644 doc/sf_and_dist/graphs/jacobi_cd.png create mode 100644 doc/sf_and_dist/graphs/jacobi_cd.svg create mode 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(*f3)(double, double, double); double (*f4)(double, double, double, double); - + f = boost::math::zeta; plot.add(f, 1 + find_end_point(f, 0.1, 40.0, false, 1.0), 10, ""); plot.add(f, -20, 1 + find_end_point(f, -0.1, -40.0, false, 1.0), ""); @@ -568,6 +568,114 @@ int main() -0.5, 4, true, 1) + 1, "n=0.75 φ=π/2"); plot.plot("Elliptic Of the Third Kind", "ellint_3.svg", "k", "ellint_3(k, n, phi)"); + f2 = boost::math::jacobi_sn; + plot.clear(); + plot.add(boost::bind(f2, 0, _1), -10, 10, "k=0"); + plot.add(boost::bind(f2, 0.5, _1), -10, 10, "k=0.5"); + plot.add(boost::bind(f2, 0.75, _1), -10, 10, "k=0.75"); + plot.add(boost::bind(f2, 0.95, _1), -10, 10, "k=0.95"); + plot.add(boost::bind(f2, 1, _1), -10, 10, "k=1"); + plot.plot("Jacobi Elliptic sn", "jacobi_sn.svg", "k", "jacobi_sn(k, phi)"); + + f2 = boost::math::jacobi_cn; + plot.clear(); + plot.add(boost::bind(f2, 0, _1), -10, 10, "k=0"); + plot.add(boost::bind(f2, 0.5, _1), -10, 10, "k=0.5"); + plot.add(boost::bind(f2, 0.75, _1), -10, 10, "k=0.75"); + plot.add(boost::bind(f2, 0.95, _1), -10, 10, "k=0.95"); + plot.add(boost::bind(f2, 1, _1), -10, 10, "k=1"); + plot.plot("Jacobi Elliptic cn", "jacobi_cn.svg", "k", "jacobi_cn(k, phi)"); + + f2 = boost::math::jacobi_dn; + plot.clear(); + plot.add(boost::bind(f2, 0, _1), -10, 10, "k=0"); + plot.add(boost::bind(f2, 0.5, _1), -10, 10, "k=0.5"); + plot.add(boost::bind(f2, 0.75, _1), -10, 10, "k=0.75"); + plot.add(boost::bind(f2, 0.95, _1), -10, 10, "k=0.95"); + plot.add(boost::bind(f2, 1, _1), -10, 10, "k=1"); + plot.plot("Jacobi Elliptic dn", "jacobi_dn.svg", "k", "jacobi_dn(k, phi)"); + + f2 = boost::math::jacobi_cd; + plot.clear(); + plot.add(boost::bind(f2, 0, _1), -10, 10, "k=0"); + plot.add(boost::bind(f2, 0.5, _1), -10, 10, "k=0.5"); + plot.add(boost::bind(f2, 0.75, _1), -10, 10, "k=0.75"); + plot.add(boost::bind(f2, 0.95, _1), -10, 10, "k=0.95"); + plot.add(boost::bind(f2, 1, _1), -10, 10, "k=1"); + plot.plot("Jacobi Elliptic cd", "jacobi_cd.svg", "k", "jacobi_cd(k, phi)"); + + f2 = boost::math::jacobi_cs; + plot.clear(); + plot.add(boost::bind(f2, 0, _1), 0.1, 3, "k=0"); + plot.add(boost::bind(f2, 0.5, _1), 0.1, 3, "k=0.5"); + plot.add(boost::bind(f2, 0.75, _1), 0.1, 3, "k=0.75"); + plot.add(boost::bind(f2, 0.95, _1), 0.1, 3, "k=0.95"); + plot.add(boost::bind(f2, 1, _1), 0.1, 3, "k=1"); + plot.plot("Jacobi Elliptic cs", "jacobi_cs.svg", "k", "jacobi_cs(k, phi)"); + + f2 = boost::math::jacobi_dc; + plot.clear(); + plot.add(boost::bind(f2, 0, _1), -10, 10, "k=0"); + plot.add(boost::bind(f2, 0.5, _1), -10, 10, "k=0.5"); + plot.add(boost::bind(f2, 0.75, _1), -10, 10, "k=0.75"); + plot.add(boost::bind(f2, 0.95, _1), -10, 10, "k=0.95"); + plot.add(boost::bind(f2, 1, _1), -10, 10, "k=1"); + plot.plot("Jacobi Elliptic dc", "jacobi_dc.svg", "k", "jacobi_dc(k, phi)"); + + f2 = boost::math::jacobi_ds; + plot.clear(); + plot.add(boost::bind(f2, 0, _1), 0.1, 3, "k=0"); + plot.add(boost::bind(f2, 0.5, _1), 0.1, 3, "k=0.5"); + plot.add(boost::bind(f2, 0.75, _1), 0.1, 3, "k=0.75"); + plot.add(boost::bind(f2, 0.95, _1), 0.1, 3, "k=0.95"); + plot.add(boost::bind(f2, 1, _1), 0.1, 3, "k=1"); + plot.plot("Jacobi Elliptic ds", "jacobi_ds.svg", "k", "jacobi_ds(k, phi)"); + + f2 = boost::math::jacobi_nc; + plot.clear(); + plot.add(boost::bind(f2, 0, _1), -5, 5, "k=0"); + plot.add(boost::bind(f2, 0.5, _1), -5, 5, "k=0.5"); + plot.add(boost::bind(f2, 0.75, _1), -5, 5, "k=0.75"); + plot.add(boost::bind(f2, 0.95, _1), -5, 5, "k=0.95"); + plot.add(boost::bind(f2, 1, _1), -5, 5, "k=1"); + plot.plot("Jacobi Elliptic nc", "jacobi_nc.svg", "k", "jacobi_nc(k, phi)"); + + f2 = boost::math::jacobi_ns; + plot.clear(); + plot.add(boost::bind(f2, 0, _1), 0.1, 4, "k=0"); + plot.add(boost::bind(f2, 0.5, _1), 0.1, 4, "k=0.5"); + plot.add(boost::bind(f2, 0.75, _1), 0.1, 4, "k=0.75"); + plot.add(boost::bind(f2, 0.95, _1), 0.1, 4, "k=0.95"); + plot.add(boost::bind(f2, 1, _1), 0.1, 4, "k=1"); + plot.plot("Jacobi Elliptic ns", "jacobi_ns.svg", "k", "jacobi_ns(k, phi)"); + + f2 = boost::math::jacobi_nd; + plot.clear(); + plot.add(boost::bind(f2, 0, _1), -2, 2, "k=0"); + plot.add(boost::bind(f2, 0.5, _1), -2, 2, "k=0.5"); + plot.add(boost::bind(f2, 0.75, _1), -2, 2, "k=0.75"); + plot.add(boost::bind(f2, 0.95, _1), -2, 2, "k=0.95"); + plot.add(boost::bind(f2, 1, _1), -2, 2, "k=1"); + plot.plot("Jacobi Elliptic nd", "jacobi_nd.svg", "k", "jacobi_nd(k, phi)"); + + f2 = boost::math::jacobi_sc; + plot.clear(); + plot.add(boost::bind(f2, 0, _1), -5, 5, "k=0"); + plot.add(boost::bind(f2, 0.5, _1), -5, 5, "k=0.5"); + plot.add(boost::bind(f2, 0.75, _1), -5, 5, "k=0.75"); + plot.add(boost::bind(f2, 0.95, _1), -5, 5, "k=0.95"); + plot.add(boost::bind(f2, 1, _1), -5, 5, "k=1"); + plot.plot("Jacobi Elliptic sc", "jacobi_sc.svg", "k", "jacobi_sc(k, phi)"); + + f2 = boost::math::jacobi_sd; + plot.clear(); + plot.add(boost::bind(f2, 0, _1), -2.5, 2.5, "k=0"); + plot.add(boost::bind(f2, 0.5, _1), -2.5, 2.5, "k=0.5"); + plot.add(boost::bind(f2, 0.75, _1), -2.5, 2.5, "k=0.75"); + plot.add(boost::bind(f2, 0.95, _1), -2.5, 2.5, "k=0.95"); + plot.add(boost::bind(f2, 1, _1), -2.5, 2.5, "k=1"); + plot.plot("Jacobi Elliptic sd", "jacobi_sd.svg", "k", "jacobi_sd(k, phi)"); + return 0; } diff --git a/doc/sf_and_dist/html/index.html b/doc/sf_and_dist/html/index.html index f0094e8cc..85dacbe28 100644 --- a/doc/sf_and_dist/html/index.html +++ b/doc/sf_and_dist/html/index.html @@ -307,6 +307,35 @@

+
Jacobi Elliptic Functions
+
+
Jacobi + Elliptic SN, CN and DN
+
Jacobi Elliptic + Function cd
+
Jacobi Elliptic + Function cn
+
Jacobi Elliptic + Function cs
+
Jacobi Elliptic + Function dc
+
Jacobi Elliptic + Function dn
+
Jacobi Elliptic + Function ds
+
Jacobi Elliptic + Function nc
+
Jacobi Elliptic + Function nd
+
Jacobi Elliptic + Function ns
+
Jacobi Elliptic + Function sc
+
Jacobi Elliptic + Function sd
+
Jacobi Elliptic + Function sn
+
Zeta Functions
Riemann Zeta Function
Exponential Integrals
@@ -541,7 +570,7 @@

- +

Last revised: May 14, 2012 at 18:06:46 GMT

Last revised: May 16, 2012 at 16:09:40 GMT


diff --git a/doc/sf_and_dist/html/index/s13.html b/doc/sf_and_dist/html/index/s13.html index b73f963b6..9e64e628d 100644 --- a/doc/sf_and_dist/html/index/s13.html +++ b/doc/sf_and_dist/html/index/s13.html @@ -22,10 +22,10 @@
PrevUpHomeNext
-
+

-Function Index

-

A B C D E F G H I K L M N O P Q R S T U V W Z

+Function Index
Elliptic Integrals of the Third Kind - Legendre Form

+

A B C D E F G H I J K L M N O P Q R S T U V W Z

A @@ -704,8 +704,8 @@
-K +J +
+
+
+K
  • @@ -1231,7 +1288,7 @@
-L +L
  • @@ -1514,7 +1571,7 @@
-M +M
  • @@ -1568,7 +1625,7 @@
-N +N
  • @@ -1675,14 +1732,14 @@
-O +O
-P +P
  • @@ -1697,7 +1754,7 @@
  • powm1

-Q +Q
  • quantile

    @@ -1716,7 +1773,7 @@
-R +R
  • @@ -1854,7 +1911,7 @@
-S +S
  • @@ -2058,7 +2115,7 @@
-T +T
  • @@ -2166,7 +2223,7 @@
-U +U
  • @@ -2228,7 +2285,7 @@
-V +V
  • @@ -2257,7 +2314,7 @@
-W +W
  • @@ -2270,12 +2327,12 @@
-Z +Z

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+

B C D E F G H I L M N P R S T U W

-B +B
-C +C
  • @@ -50,14 +50,14 @@
-D +D
-E +E
-F +F
-G +G
-H +H
-I +I
-L +L
-M +M
-N +N
-P +P
-R +R
-S +S
-T +T
  • @@ -213,7 +213,7 @@
-U +U
-W +W
diff --git a/doc/sf_and_dist/html/index/s15.html b/doc/sf_and_dist/html/index/s15.html index 5c7fd584b..d00091a6d 100644 --- a/doc/sf_and_dist/html/index/s15.html +++ b/doc/sf_and_dist/html/index/s15.html @@ -22,20 +22,20 @@
PrevUpHomeNext
-
+

-Typedef Index

-

A B C D E F G H I L N O P R S T U V W

+Typedef Index
+

A B C D E F G H I L N O P R S T U V W

-A +A
-B +B
  • @@ -52,7 +52,7 @@
-C +C
  • @@ -71,7 +71,7 @@
-D +D
  • @@ -96,7 +96,7 @@
-E +E
  • @@ -113,7 +113,7 @@
-F +F
  • @@ -133,7 +133,7 @@
-G +G
  • @@ -150,14 +150,14 @@
-H +H
-I +I
  • @@ -174,7 +174,7 @@
-L +L
  • @@ -191,7 +191,7 @@
-N +N
  • @@ -228,14 +228,14 @@
-O +O
-P +P
  • @@ -296,7 +296,7 @@
-R +R
  • @@ -309,7 +309,7 @@
-S +S
  • students_t

    @@ -319,14 +319,14 @@
-T +T
-U +U
  • @@ -339,7 +339,7 @@
-V +V
  • value_type

    @@ -380,7 +380,7 @@
-W +W
  • weibull

    diff --git a/doc/sf_and_dist/html/index/s16.html b/doc/sf_and_dist/html/index/s16.html index 61968a82e..49c699e23 100644 --- a/doc/sf_and_dist/html/index/s16.html +++ b/doc/sf_and_dist/html/index/s16.html @@ -22,13 +22,13 @@
    PrevUpHomeNext
    -
    +

    -Macro Index

    -

    B F

    +Macro Index
+

B F

-B +B
  • @@ -260,7 +260,7 @@
-F +F
  • diff --git a/doc/sf_and_dist/html/index/s17.html b/doc/sf_and_dist/html/index/s17.html index b7344d7e3..eadce3121 100644 --- a/doc/sf_and_dist/html/index/s17.html +++ b/doc/sf_and_dist/html/index/s17.html @@ -21,13 +21,13 @@
    PrevUpHome
    -
    +

    -Index

    -

    A B C D E F G H I K L M N O P Q R S T U V W Z

    +Index
+

A B C D E F G H I J K L M N O P Q R S T U V W Z

-A +A
  • @@ -166,7 +166,7 @@
-B +B
  • @@ -550,7 +550,7 @@
-C +C
  • @@ -1450,7 +1450,7 @@
-D +D
  • @@ -1525,7 +1525,7 @@
-E +E
-F +F
  • @@ -2294,7 +2295,7 @@
-G +G
  • @@ -2434,7 +2435,7 @@
-H +H
  • @@ -2560,7 +2561,7 @@
-I +I
  • @@ -2824,7 +2825,119 @@
-K +J +
+
+
+K
  • @@ -2851,7 +2964,7 @@
-L +L
  • @@ -3246,7 +3359,7 @@
-M +M
  • @@ -3326,7 +3439,7 @@
-N +N
  • @@ -3596,7 +3709,7 @@
-O +O
  • @@ -3613,7 +3726,7 @@
-P +P
  • @@ -3760,7 +3873,7 @@
-Q +Q
  • quantile

    @@ -3779,7 +3892,7 @@
-R +R
  • @@ -4008,7 +4121,7 @@
-S +S
  • @@ -4313,7 +4426,7 @@
-T +T
  • @@ -4534,7 +4647,7 @@
-U +U
  • @@ -4670,7 +4783,7 @@
-V +V
  • @@ -4737,7 +4850,7 @@
-W +W
  • @@ -4767,12 +4880,12 @@
-Z +Z
  • zeta

    diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html b/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html index c189b9485..f3ef1ee6f 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html @@ -228,7 +228,7 @@ computing to float precision with double precision arithmetic.

    -

    Table 58. Optimal choices for N and g when computing with guard digits (source: +

    Table 59. Optimal choices for N and g when computing with guard digits (source: Pugh)

    @@ -371,7 +371,7 @@ exactly matches the machine epsilon for the type in question.

    -

    Table 59. Optimum value for N and g when computing at fixed precision

    +

    Table 60. Optimum value for N and g when computing at fixed precision

    diff --git a/doc/sf_and_dist/html/math_toolkit/constants/constants.html b/doc/sf_and_dist/html/math_toolkit/constants/constants.html index e232c6618..9bb34f5bd 100644 --- a/doc/sf_and_dist/html/math_toolkit/constants/constants.html +++ b/doc/sf_and_dist/html/math_toolkit/constants/constants.html @@ -31,7 +31,7 @@ rationale for their inclusion).

    -

    Table 51. Mathematical Constants

    +

    Table 52. Mathematical Constants

    diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html b/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html index 72bbf68da..d573de825 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html @@ -27,7 +27,7 @@ Document Conventions

    - +

    This documentation aims to use of the following naming and formatting conventions. diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html index 1be09a220..32cfa7acb 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html @@ -27,7 +27,7 @@ Navigation

    - +

    Boost.Math documentation is provided in both HTML and PDF formats. diff --git a/doc/sf_and_dist/html/math_toolkit/perf/comp_compilers.html b/doc/sf_and_dist/html/math_toolkit/perf/comp_compilers.html index 734f7d1f0..2c03ba1e0 100644 --- a/doc/sf_and_dist/html/math_toolkit/perf/comp_compilers.html +++ b/doc/sf_and_dist/html/math_toolkit/perf/comp_compilers.html @@ -35,7 +35,7 @@ in this respect).

    -

    Table 53. Performance Comparison of Various Windows Compilers

    +

    Table 54. Performance Comparison of Various Windows Compilers

    diff --git a/doc/sf_and_dist/html/math_toolkit/perf/comparisons.html b/doc/sf_and_dist/html/math_toolkit/perf/comparisons.html index df7a48af5..f16e5833a 100644 --- a/doc/sf_and_dist/html/math_toolkit/perf/comparisons.html +++ b/doc/sf_and_dist/html/math_toolkit/perf/comparisons.html @@ -574,7 +574,7 @@ (R-2.9.2 appears not to be buildable with Visual C++).

    -

    Table 56. A Comparison to the R Statistical Library on Windows XP

    +

    Table 57. A Comparison to the R Statistical Library on Windows XP

    @@ -1849,7 +1849,7 @@ G++ 4.3.3 using -O3 -DNDEBUG=1.

    -

    Table 57. A Comparison to the R Statistical Library on Linux

    +

    Table 58. A Comparison to the R Statistical Library on Linux

    diff --git a/doc/sf_and_dist/html/math_toolkit/perf/getting_best.html b/doc/sf_and_dist/html/math_toolkit/perf/getting_best.html index f4a8ceaed..00838c3b5 100644 --- a/doc/sf_and_dist/html/math_toolkit/perf/getting_best.html +++ b/doc/sf_and_dist/html/math_toolkit/perf/getting_best.html @@ -33,7 +33,7 @@ penalty for using the library in debug mode can be quite large.

    -

    Table 52. Performance Comparison of Release and Debug Settings

    +

    Table 53. Performance Comparison of Release and Debug Settings

    diff --git a/doc/sf_and_dist/html/math_toolkit/perf/tuning.html b/doc/sf_and_dist/html/math_toolkit/perf/tuning.html index 86fd95053..e82a9a20d 100644 --- a/doc/sf_and_dist/html/math_toolkit/perf/tuning.html +++ b/doc/sf_and_dist/html/math_toolkit/perf/tuning.html @@ -238,7 +238,7 @@ highly vectorisable processors in the future.

    -

    Table 54. A Comparison of Polynomial Evaluation Methods

    +

    Table 55. A Comparison of Polynomial Evaluation Methods

    @@ -638,7 +638,7 @@ tutorial.

    -

    Table 55. Performance Comparison with and Without Internal Promotion to long +

    Table 56. Performance Comparison with and Without Internal Promotion to long double

    diff --git a/doc/sf_and_dist/html/math_toolkit/special.html b/doc/sf_and_dist/html/math_toolkit/special.html index e31d061be..41e84c7d6 100644 --- a/doc/sf_and_dist/html/math_toolkit/special.html +++ b/doc/sf_and_dist/html/math_toolkit/special.html @@ -110,6 +110,35 @@
    Elliptic Integrals of the Third Kind - Legendre Form
    +
    Jacobi Elliptic Functions
    +
    +
    Jacobi + Elliptic SN, CN and DN
    +
    Jacobi Elliptic + Function cd
    +
    Jacobi Elliptic + Function cn
    +
    Jacobi Elliptic + Function cs
    +
    Jacobi Elliptic + Function dc
    +
    Jacobi Elliptic + Function dn
    +
    Jacobi Elliptic + Function ds
    +
    Jacobi Elliptic + Function nc
    +
    Jacobi Elliptic + Function nd
    +
    Jacobi Elliptic + Function ns
    +
    Jacobi Elliptic + Function sc
    +
    Jacobi Elliptic + Function sd
    +
    Jacobi Elliptic + Function sn
    +
    Zeta Functions
    Riemann Zeta Function
    Exponential Integrals
    diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html index 6b6e33dcc..34c7a0039 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html +++ b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html @@ -7,7 +7,7 @@ - +
    @@ -20,7 +20,7 @@

    -PrevUpHomeNext +PrevUpHomeNext

    @@ -316,7 +316,7 @@
    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html b/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html index 79ad1377a..9ccdff164 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html +++ b/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html @@ -89,7 +89,7 @@ error.

    -

    Table 49. Errors In the Function expint(z)

    +

    Table 50. Errors In the Function expint(z)

    diff --git a/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html b/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html index bf87a9991..69a8e91c1 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html +++ b/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html @@ -88,7 +88,7 @@ the one shown will have effectively zero error.

    -

    Table 48. Errors In the Function expint(n, z)

    +

    Table 49. Errors In the Function expint(n, z)

    diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi.html new file mode 100644 index 000000000..700fa1a0e --- /dev/null +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi.html @@ -0,0 +1,72 @@ + + + +Jacobi Elliptic Functions + + + + + + + + +
    + + + + + + +
    Boost C++ LibrariesHomeLibrariesPeopleFAQMore
    +
    +
    +PrevUpHomeNext +
    + + + + +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cd.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cd.html new file mode 100644 index 000000000..4f9dd1c35 --- /dev/null +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cd.html @@ -0,0 +1,87 @@ + + + +Jacobi Elliptic Function cd + + + + + + + + + + + + + + + +
    Boost C++ LibrariesHomeLibrariesPeopleFAQMore
    +
    +
    +PrevUpHomeNext +
    +
    + +
    + + Synopsis +
    +

    +

    +
    #include <boost/math/special_functions/jacobi_elliptic.hpp>
    +
    +

    +

    +
    namespace boost { namespace math {
    +
    + template <class T, class U>
    + calculated-result-type jacobi_cd(T k, U theta);
    +
    + template <class T, class U, class Policy>
    + calculated-result-type jacobi_cd(T k, U theta, const Policy& pol);
    +
    +}} // namespaces
    +
    +
    + + Description +
    +

    + This function returns the Jacobi elliptic function cd. +

    +

    + The final Policy argument is + optional and can be used to control the behaviour of the function: how + it handles errors, what level of precision to use etc. Refer to the policy documentation for more details. +

    +

    + This function is a trivial wrapper around jacobi_elliptic, + with: +

    +

    + cd(x, k) = cn(x, k) / dn(x, k) +

    +

    + +

    +
    + + + +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cn.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cn.html new file mode 100644 index 000000000..99b359055 --- /dev/null +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cn.html @@ -0,0 +1,83 @@ + + + +Jacobi Elliptic Function cn + + + + + + + + + + + + + + + +
    Boost C++ LibrariesHomeLibrariesPeopleFAQMore
    +
    +
    +PrevUpHomeNext +
    +
    + +
    + + Synopsis +
    +

    +

    +
    #include <boost/math/special_functions/jacobi_elliptic.hpp>
    +
    +

    +

    +
    namespace boost { namespace math {
    +
    + template <class T, class U>
    + calculated-result-type jacobi_cn(T k, U theta);
    +
    + template <class T, class U, class Policy>
    + calculated-result-type jacobi_cn(T k, U theta, const Policy& pol);
    +
    +}} // namespaces
    +
    +
    + + Description +
    +

    + This function returns the Jacobi elliptic function cn. +

    +

    + The final Policy argument is + optional and can be used to control the behaviour of the function: how + it handles errors, what level of precision to use etc. Refer to the policy documentation for more details. +

    +

    + This function is a trivial wrapper around jacobi_elliptic. +

    +

    + +

    +
    + + + +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cs.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cs.html new file mode 100644 index 000000000..c3f21dd40 --- /dev/null +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cs.html @@ -0,0 +1,87 @@ + + + +Jacobi Elliptic Function cs + + + + + + + + + + + + + + + +
    Boost C++ LibrariesHomeLibrariesPeopleFAQMore
    +
    +
    +PrevUpHomeNext +
    +
    + +
    + + Synopsis +
    +

    +

    +
    #include <boost/math/special_functions/jacobi_elliptic.hpp>
    +
    +

    +

    +
    namespace boost { namespace math {
    +
    + template <class T, class U>
    + calculated-result-type jacobi_cs(T k, U theta);
    +
    + template <class T, class U, class Policy>
    + calculated-result-type jacobi_cs(T k, U theta, const Policy& pol);
    +
    +}} // namespaces
    +
    +
    + + Description +
    +

    + This function returns the Jacobi elliptic function cs. +

    +

    + The final Policy argument is + optional and can be used to control the behaviour of the function: how + it handles errors, what level of precision to use etc. Refer to the policy documentation for more details. +

    +

    + This function is a trivial wrapper around jacobi_elliptic, + with: +

    +

    + cs(x, k) = cn(x, k) / sn(x, k) +

    +

    + +

    +
    + + + +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_dc.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_dc.html new file mode 100644 index 000000000..9936e4e77 --- /dev/null +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_dc.html @@ -0,0 +1,87 @@ + + + +Jacobi Elliptic Function dc + + + + + + + + + + + + + + + +
    Boost C++ LibrariesHomeLibrariesPeopleFAQMore
    +
    +
    +PrevUpHomeNext +
    +
    + +
    + + Synopsis +
    +

    +

    +
    #include <boost/math/special_functions/jacobi_elliptic.hpp>
    +
    +

    +

    +
    namespace boost { namespace math {
    +
    + template <class T, class U>
    + calculated-result-type jacobi_dc(T k, U theta);
    +
    + template <class T, class U, class Policy>
    + calculated-result-type jacobi_dc(T k, U theta, const Policy& pol);
    +
    +}} // namespaces
    +
    +
    + + Description +
    +

    + This function returns the Jacobi elliptic function dc. +

    +

    + The final Policy argument is + optional and can be used to control the behaviour of the function: how + it handles errors, what level of precision to use etc. Refer to the policy documentation for more details. +

    +

    + This function is a trivial wrapper around jacobi_elliptic, + with: +

    +

    + dc(x, k) = dn(x, k) / cn(x, k) +

    +

    + +

    +
    + + + +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_dn.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_dn.html new file mode 100644 index 000000000..5d9e23f93 --- /dev/null +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_dn.html @@ -0,0 +1,83 @@ + + + +Jacobi Elliptic Function dn + + + + + + + + + + + + + + + +
    Boost C++ LibrariesHomeLibrariesPeopleFAQMore
    +
    +
    +PrevUpHomeNext +
    +
    + +
    + + Synopsis +
    +

    +

    +
    #include <boost/math/special_functions/jacobi_elliptic.hpp>
    +
    +

    +

    +
    namespace boost { namespace math {
    +
    + template <class T, class U>
    + calculated-result-type jacobi_dn(T k, U theta);
    +
    + template <class T, class U, class Policy>
    + calculated-result-type jacobi_dn(T k, U theta, const Policy& pol);
    +
    +}} // namespaces
    +
    +
    + + Description +
    +

    + This function returns the Jacobi elliptic function dn. +

    +

    + The final Policy argument is + optional and can be used to control the behaviour of the function: how + it handles errors, what level of precision to use etc. Refer to the policy documentation for more details. +

    +

    + This function is a trivial wrapper around jacobi_elliptic. +

    +

    + +

    +
    + + + +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_ds.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_ds.html new file mode 100644 index 000000000..266cff709 --- /dev/null +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_ds.html @@ -0,0 +1,87 @@ + + + +Jacobi Elliptic Function ds + + + + + + + + + + + + + + + +
    Boost C++ LibrariesHomeLibrariesPeopleFAQMore
    +
    +
    +PrevUpHomeNext +
    +
    + +
    + + Synopsis +
    +

    +

    +
    #include <boost/math/special_functions/jacobi_elliptic.hpp>
    +
    +

    +

    +
    namespace boost { namespace math {
    +
    + template <class T, class U>
    + calculated-result-type jacobi_ds(T k, U theta);
    +
    + template <class T, class U, class Policy>
    + calculated-result-type jacobi_ds(T k, U theta, const Policy& pol);
    +
    +}} // namespaces
    +
    +
    + + Description +
    +

    + This function returns the Jacobi elliptic function ds. +

    +

    + The final Policy argument is + optional and can be used to control the behaviour of the function: how + it handles errors, what level of precision to use etc. Refer to the policy documentation for more details. +

    +

    + This function is a trivial wrapper around jacobi_elliptic, + with: +

    +

    + ds(x, k) = dn(x, k) / sn(x, k) +

    +

    + +

    +
    + + + +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_elliptic.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_elliptic.html new file mode 100644 index 000000000..148a98815 --- /dev/null +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_elliptic.html @@ -0,0 +1,301 @@ + + + +Jacobi Elliptic SN, CN and DN + + + + + + + + + + + + + + + +
    Boost C++ LibrariesHomeLibrariesPeopleFAQMore
    +
    +
    +PrevUpHomeNext +
    +
    + +
    + + Synopsis +
    +

    +

    +
    #include <boost/math/special_functions/jacobi_elliptic.hpp>
    +
    +

    +

    +
    namespace boost { namespace math {
    +
    + template <class T>
    + calculated-result-type jacobi_elliptic(T k, T phi, T* pcn, T* pdn);
    +
    + template <class T, class Policy>
    + calculated-result-type jacobi_elliptic(T k, T phi, T* pcn, T* pdn, const Policy&);
    +
    +}} // namespaces
    +
    +
    + + Description +
    +

    + The function jacobi_elliptic + calculates the three copolar Jacobi elliptic functions sn(φ, k), + cn(φ, k) and dn(φ, k). The returned + value is sn(φ, k), and if provided, *pcn + is set to cn(φ, k), and *pdn is + set to dn(φ, k). +

    +

    + The functions are defined as follows, given: +

    +

    + +

    +

    + The the angle φ is called the amplitude and: +

    +

    + +

    +
    + + + + + +
    [Note]Note
    +

    + φ is called the amplitude. +

    +

    + k is called the modulus. +

    +
    +
    + + + + + +
    [Caution]Caution
    +

    + Rather like other elliptic functions, the Jacobi functions are expressed + in a variety of different ways. In particular, the parameter k + (the modulus) may also be expressed using a modular angle α, or a parameter + m. These are related by: +

    +

    + k = sinα +

    +

    + m = k2 = sin2α +

    +

    + So that the function sn (for example) may be expressed + as either: +

    +

    + sn(φ, k) +

    +

    + sn(φ \ α) +

    +

    + sn(φ| m) +

    +

    + To further complicate matters, some texts refer to the complement + of the parameter m, or 1 - m, where: +

    +

    + 1 - m = 1 - k2 = cos2α +

    +

    + This implementation uses k throughout, and makes + this the first argument to the functions: this is for alignment with + the elliptic integrals which match the requirements of the Technical + Report on C++ Library Extensions. However, you should be extra + careful when using these functions! +

    +
    +

    + The final Policy argument is + optional and can be used to control the behaviour of the function: how + it handles errors, what level of precision to use etc. Refer to the policy documentation for more details. +

    +

    + The following graphs illustrate how these functions change as k + changes: for small k these are sine waves, while as + k tends to 1 they become hyperbolic functions: +

    +

    + +

    +

    + +

    +

    + +

    +
    + + Accuracy +
    +

    + These functions are computed using only basic arithmetic operations, so + there isn't much variation in accuracy over differing platforms. Note that + only results for the widest floating point type on the system are given + as narrower types have effectively zero error. + All values are relative errors in units of epsilon. +

    +
    +

    Table 47. Errors Rates in the Jacobi Elliptic Functions

    +
    ++++++ + + + + + + + + + + + + + + + + + + + + +
    +

    + Significand Size +

    +
    +

    + Platform and Compiler +

    +
    +

    + φ < 1 +

    +
    +

    + Large φ +

    +
    +

    + 53 +

    +
    +

    + Win32 / Visual C++ 8.0 +

    +
    +

    + Peak=2 Mean=0.5 +

    +
    +

    + Peak=44000 Mean=2500 +

    +
    +

    + 64 +

    +
    +

    + Red Hat Linux / G++ 3.4 +

    +
    +

    + Peak=2.6 Mean=1.7 +

    +
    +

    + Peak=2.2 Mean=1.8 +

    +
    +
    +
    + + Testing +
    +

    + The tests use a mixture of spot test values calculated using the online + calculator at functions.wolfram.com, + and random test data generated using MPFR at 1000-bit precision and this + implementation. +

    +
    + + Implementation +
    +

    + For k > 1 we apply the relations: +

    +

    + +

    +

    + Then filter off the special cases: +

    +

    + sn(0, k) = 0 and cn(0, k) = dn(0, k) = 1. +

    +

    + sn(x, 0) = sin(x), cn(x, 0) = cos(x) and dn(x, 0) = 1. +

    +

    + sn(x, 1) = tanh(x), cn(x, 1) = dn(x, 1) = 1 / cosh(x). +

    +

    + And for k4 < ε we have: +

    +

    + +

    +

    + Otherwise the values are calculated using the method of arithmetic + geometric means. +

    +
    + + + +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_nc.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_nc.html new file mode 100644 index 000000000..298eedb86 --- /dev/null +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_nc.html @@ -0,0 +1,87 @@ + + + +Jacobi Elliptic Function nc + + + + + + + + + + + + + + + +
    Boost C++ LibrariesHomeLibrariesPeopleFAQMore
    +
    +
    +PrevUpHomeNext +
    +
    + +
    + + Synopsis +
    +

    +

    +
    #include <boost/math/special_functions/jacobi_elliptic.hpp>
    +
    +

    +

    +
    namespace boost { namespace math {
    +
    + template <class T, class U>
    + calculated-result-type jacobi_nc(T k, U theta);
    +
    + template <class T, class U, class Policy>
    + calculated-result-type jacobi_nc(T k, U theta, const Policy& pol);
    +
    +}} // namespaces
    +
    +
    + + Description +
    +

    + This function returns the Jacobi elliptic function nc. +

    +

    + The final Policy argument is + optional and can be used to control the behaviour of the function: how + it handles errors, what level of precision to use etc. Refer to the policy documentation for more details. +

    +

    + This function is a trivial wrapper around jacobi_elliptic, + with: +

    +

    + nc(x, k) = 1 / cn(x, k) +

    +

    + +

    +
    + + + +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_nd.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_nd.html new file mode 100644 index 000000000..a04fb1141 --- /dev/null +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_nd.html @@ -0,0 +1,87 @@ + + + +Jacobi Elliptic Function nd + + + + + + + + + + + + + + + +
    Boost C++ LibrariesHomeLibrariesPeopleFAQMore
    +
    +
    +PrevUpHomeNext +
    +
    + +
    + + Synopsis +
    +

    +

    +
    #include <boost/math/special_functions/jacobi_elliptic.hpp>
    +
    +

    +

    +
    namespace boost { namespace math {
    +
    + template <class T, class U>
    + calculated-result-type jacobi_nd(T k, U theta);
    +
    + template <class T, class U, class Policy>
    + calculated-result-type jacobi_nd(T k, U theta, const Policy& pol);
    +
    +}} // namespaces
    +
    +
    + + Description +
    +

    + This function returns the Jacobi elliptic function nd. +

    +

    + The final Policy argument is + optional and can be used to control the behaviour of the function: how + it handles errors, what level of precision to use etc. Refer to the policy documentation for more details. +

    +

    + This function is a trivial wrapper around jacobi_elliptic, + with: +

    +

    + nd(x, k) = 1 / dn(x, k) +

    +

    + +

    +
    + + + +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_ns.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_ns.html new file mode 100644 index 000000000..f7e362afd --- /dev/null +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_ns.html @@ -0,0 +1,87 @@ + + + +Jacobi Elliptic Function ns + + + + + + + + + + + + + + + +
    Boost C++ LibrariesHomeLibrariesPeopleFAQMore
    +
    +
    +PrevUpHomeNext +
    +
    + +
    + + Synopsis +
    +

    +

    +
    #include <boost/math/special_functions/jacobi_elliptic.hpp>
    +
    +

    +

    +
    namespace boost { namespace math {
    +
    + template <class T, class U>
    + calculated-result-type jacobi_ns(T k, U theta);
    +
    + template <class T, class U, class Policy>
    + calculated-result-type jacobi_ns(T k, U theta, const Policy& pol);
    +
    +}} // namespaces
    +
    +
    + + Description +
    +

    + This function returns the Jacobi elliptic function ns. +

    +

    + The final Policy argument is + optional and can be used to control the behaviour of the function: how + it handles errors, what level of precision to use etc. Refer to the policy documentation for more details. +

    +

    + This function is a trivial wrapper around jacobi_elliptic, + with: +

    +

    + ns(x, k) = 1 / sn(x, k) +

    +

    + +

    +
    + + + +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sc.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sc.html new file mode 100644 index 000000000..3d044a2d5 --- /dev/null +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sc.html @@ -0,0 +1,87 @@ + + + +Jacobi Elliptic Function sc + + + + + + + + + + + + + + + +
    Boost C++ LibrariesHomeLibrariesPeopleFAQMore
    +
    +
    +PrevUpHomeNext +
    +
    + +
    + + Synopsis +
    +

    +

    +
    #include <boost/math/special_functions/jacobi_elliptic.hpp>
    +
    +

    +

    +
    namespace boost { namespace math {
    +
    + template <class T, class U>
    + calculated-result-type jacobi_sc(T k, U theta);
    +
    + template <class T, class U, class Policy>
    + calculated-result-type jacobi_sc(T k, U theta, const Policy& pol);
    +
    +}} // namespaces
    +
    +
    + + Description +
    +

    + This function returns the Jacobi elliptic function sc. +

    +

    + The final Policy argument is + optional and can be used to control the behaviour of the function: how + it handles errors, what level of precision to use etc. Refer to the policy documentation for more details. +

    +

    + This function is a trivial wrapper around jacobi_elliptic, + with: +

    +

    + sc(x, k) = sn(x, k) / cn(x, k) +

    +

    + +

    +
    + + + +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sd.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sd.html new file mode 100644 index 000000000..d90cc1fc4 --- /dev/null +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sd.html @@ -0,0 +1,87 @@ + + + +Jacobi Elliptic Function sd + + + + + + + + + + + + + + + +
    Boost C++ LibrariesHomeLibrariesPeopleFAQMore
    +
    +
    +PrevUpHomeNext +
    +
    + +
    + + Synopsis +
    +

    +

    +
    #include <boost/math/special_functions/jacobi_elliptic.hpp>
    +
    +

    +

    +
    namespace boost { namespace math {
    +
    + template <class T, class U>
    + calculated-result-type jacobi_sd(T k, U theta);
    +
    + template <class T, class U, class Policy>
    + calculated-result-type jacobi_sd(T k, U theta, const Policy& pol);
    +
    +}} // namespaces
    +
    +
    + + Description +
    +

    + This function returns the Jacobi elliptic function sd. +

    +

    + The final Policy argument is + optional and can be used to control the behaviour of the function: how + it handles errors, what level of precision to use etc. Refer to the policy documentation for more details. +

    +

    + This function is a trivial wrapper around jacobi_elliptic, + with: +

    +

    + sd(x, k) = sn(x, k) / dn(x, k) +

    +

    + +

    +
    + + + +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sn.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sn.html new file mode 100644 index 000000000..a25daf612 --- /dev/null +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sn.html @@ -0,0 +1,83 @@ + + + +Jacobi Elliptic Function sn + + + + + + + + + + + + + + + +
    Boost C++ LibrariesHomeLibrariesPeopleFAQMore
    +
    +
    +PrevUpHomeNext +
    +
    + +
    + + Synopsis +
    +

    +

    +
    #include <boost/math/special_functions/jacobi_elliptic.hpp>
    +
    +

    +

    +
    namespace boost { namespace math {
    +
    + template <class T, class U>
    + calculated-result-type jacobi_sn(T k, U theta);
    +
    + template <class T, class U, class Policy>
    + calculated-result-type jacobi_sn(T k, U theta, const Policy& pol);
    +
    +}} // namespaces
    +
    +
    + + Description +
    +

    + This function returns the Jacobi elliptic function sn. +

    +

    + The final Policy argument is + optional and can be used to control the behaviour of the function: how + it handles errors, what level of precision to use etc. Refer to the policy documentation for more details. +

    +

    + This function is a trivial wrapper around jacobi_elliptic. +

    +

    + +

    +
    + + + +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/sf_and_dist/html/math_toolkit/special/zetas.html b/doc/sf_and_dist/html/math_toolkit/special/zetas.html index f1d766361..b50621460 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/zetas.html +++ b/doc/sf_and_dist/html/math_toolkit/special/zetas.html @@ -6,7 +6,7 @@ - + @@ -20,7 +20,7 @@
    -PrevUpHomeNext +PrevUpHomeNext

    @@ -39,7 +39,7 @@
    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html b/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html index cfd61a2b9..572d5742b 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html +++ b/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html @@ -91,7 +91,7 @@ shown will have effectively zero error.

    -

    Table 47. Errors In the Function zeta(z)

    +

    Table 48. Errors In the Function zeta(z)

    diff --git a/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/intro.html b/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/intro.html index bdf6f01f7..f06505e43 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/intro.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/intro.html @@ -154,7 +154,7 @@ The following string representations are used:

    -

    Table 50. C99 Representation of Infinity and NaN

    +

    Table 51. C99 Representation of Infinity and NaN

    diff --git a/doc/sf_and_dist/jacobi_elliptic.qbk b/doc/sf_and_dist/jacobi_elliptic.qbk new file mode 100644 index 000000000..faf2635e2 --- /dev/null +++ b/doc/sf_and_dist/jacobi_elliptic.qbk @@ -0,0 +1,513 @@ +[/ +Copyright (c) 2012 John Maddock +Use, modification and distribution are subject to the +Boost Software License, Version 1.0. (See accompanying file +LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +] + +[section:jacobi Jacobi Elliptic Functions] + +[section:jacobi_elliptic Jacobi Elliptic SN, CN and DN] + +[heading Synopsis] + +`` + #include +`` + + namespace boost { namespace math { + + template + ``__sf_result`` jacobi_elliptic(T k, T phi, T* pcn, T* pdn); + + template + ``__sf_result`` jacobi_elliptic(T k, T phi, T* pcn, T* pdn, const Policy&); + + }} // namespaces + +[heading Description] + +The function __jacobi_elliptic calculates the three copolar Jacobi elliptic functions +['sn([phi], k)], ['cn([phi], k)] and ['dn([phi], k)]. The returned value is +['sn([phi], k)], and if provided, ['*pcn] is +set to ['cn([phi], k)], and ['*pdn] is set to ['dn([phi], k)]. + +The functions are defined as follows, given: + +[equation jacobi1] + +The the angle [phi] is called the ['amplitude] and: + +[equation jacobi2] + +[note ['[phi]] is called the amplitude. + +['k] is called the modulus. + +] + +[caution Rather like other elliptic functions, the Jacobi functions +are expressed in a variety of different ways. In particular, +the parameter /k/ (the modulus) may also be expressed using a modular +angle [alpha], or a parameter /m/. These are related by: + +k = sin[alpha] + +m = k[super 2] = sin[super 2][alpha] + +So that the function ['sn] (for example) may be expressed as +either: + +sn([phi], k) + +sn([phi] \\ [alpha]) + +sn([phi]| m) + +To further complicate matters, some texts refer to the ['complement +of the parameter m], or 1 - m, where: + +1 - m = 1 - k[super 2] = cos[super 2][alpha] + +This implementation uses /k/ throughout, and makes this the first argument +to the functions: this is for alignment with the elliptic integrals which match the requirements +of the [@http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1836.pdf +Technical Report on C++ Library Extensions]. However, you should +be extra careful when using these functions!] + +[optional_policy] + +The following graphs illustrate how these functions change as /k/ changes: for small /k/ +these are sine waves, while as /k/ tends to 1 they become hyperbolic functions: + +[graph jacobi_sn] + +[graph jacobi_cn] + +[graph jacobi_dn] + +[heading Accuracy] + +These functions are computed using only basic arithmetic operations, so +there isn't much variation in accuracy over differing platforms. +Note that only results for the widest floating point type on the +system are given as narrower types have __zero_error. All values +are relative errors in units of epsilon. + +[table Errors Rates in the Jacobi Elliptic Functions +[[Significand Size] [Platform and Compiler] [[phi] < 1] [Large [phi]] ] +[[53] [Win32 / Visual C++ 8.0] [Peak=2 Mean=0.5] [Peak=44000 Mean=2500] ] +[[64] [Red Hat Linux / G++ 3.4] [Peak=2.6 Mean=1.7] [Peak=2.2 Mean=1.8] ] +] + + +[heading Testing] + +The tests use a mixture of spot test values calculated using the online +calculator at [@http://functions.wolfram.com/ functions.wolfram.com], +and random test data generated using +MPFR at 1000-bit precision and this implementation. + +[heading Implementation] + +For ['k > 1] we apply the relations: + +[equation jacobi3] + +Then filter off the special cases: + +['sn(0, k) = 0] and ['cn(0, k) = dn(0, k) = 1]. + +['sn(x, 0) = sin(x), cn(x, 0) = cos(x) and dn(x, 0) = 1]. + +['sn(x, 1) = tanh(x), cn(x, 1) = dn(x, 1) = 1 / cosh(x)]. + +And for ['k[super 4] < [epsilon]] we have: + +[equation jacobi4] + +Otherwise the values are calculated using the method of [@http://dlmf.nist.gov/22.20#SS2 arithmetic geometric means]. + +[endsect] + +[section:jacobi_cd Jacobi Elliptic Function cd] + +[heading Synopsis] + +`` + #include +`` + + namespace boost { namespace math { + + template + ``__sf_result`` jacobi_cd(T k, U theta); + + template + ``__sf_result`` jacobi_cd(T k, U theta, const Policy& pol); + + }} // namespaces + +[heading Description] + +This function returns the Jacobi elliptic function ['cd]. + +[optional_policy] + +This function is a trivial wrapper around __jacobi_elliptic, with: + +['cd(x, k) = cn(x, k) / dn(x, k)] + +[graph jacobi_cd] + +[endsect] + +[section:jacobi_cn Jacobi Elliptic Function cn] + +[heading Synopsis] + +`` + #include +`` + + namespace boost { namespace math { + + template + ``__sf_result`` jacobi_cn(T k, U theta); + + template + ``__sf_result`` jacobi_cn(T k, U theta, const Policy& pol); + + }} // namespaces + +[heading Description] + +This function returns the Jacobi elliptic function ['cn]. + +[optional_policy] + +This function is a trivial wrapper around __jacobi_elliptic. + +[graph jacobi_cn] + +[endsect] + +[section:jacobi_cs Jacobi Elliptic Function cs] + +[heading Synopsis] + +`` + #include +`` + + namespace boost { namespace math { + + template + ``__sf_result`` jacobi_cs(T k, U theta); + + template + ``__sf_result`` jacobi_cs(T k, U theta, const Policy& pol); + + }} // namespaces + +[heading Description] + +This function returns the Jacobi elliptic function ['cs]. + +[optional_policy] + +This function is a trivial wrapper around __jacobi_elliptic, with: + +['cs(x, k) = cn(x, k) / sn(x, k)] + +[graph jacobi_cs] + +[endsect] + +[section:jacobi_dc Jacobi Elliptic Function dc] + +[heading Synopsis] + +`` + #include +`` + + namespace boost { namespace math { + + template + ``__sf_result`` jacobi_dc(T k, U theta); + + template + ``__sf_result`` jacobi_dc(T k, U theta, const Policy& pol); + + }} // namespaces + +[heading Description] + +This function returns the Jacobi elliptic function ['dc]. + +[optional_policy] + +This function is a trivial wrapper around __jacobi_elliptic, with: + +['dc(x, k) = dn(x, k) / cn(x, k)] + +[graph jacobi_dc] + +[endsect] + +[section:jacobi_dn Jacobi Elliptic Function dn] + +[heading Synopsis] + +`` + #include +`` + + namespace boost { namespace math { + + template + ``__sf_result`` jacobi_dn(T k, U theta); + + template + ``__sf_result`` jacobi_dn(T k, U theta, const Policy& pol); + + }} // namespaces + +[heading Description] + +This function returns the Jacobi elliptic function ['dn]. + +[optional_policy] + +This function is a trivial wrapper around __jacobi_elliptic. + +[graph jacobi_dn] + +[endsect] + +[section:jacobi_ds Jacobi Elliptic Function ds] + +[heading Synopsis] + +`` + #include +`` + + namespace boost { namespace math { + + template + ``__sf_result`` jacobi_ds(T k, U theta); + + template + ``__sf_result`` jacobi_ds(T k, U theta, const Policy& pol); + + }} // namespaces + +[heading Description] + +This function returns the Jacobi elliptic function ['ds]. + +[optional_policy] + +This function is a trivial wrapper around __jacobi_elliptic, with: + +['ds(x, k) = dn(x, k) / sn(x, k)] + +[graph jacobi_ds] + +[endsect] + +[section:jacobi_nc Jacobi Elliptic Function nc] + +[heading Synopsis] + +`` + #include +`` + + namespace boost { namespace math { + + template + ``__sf_result`` jacobi_nc(T k, U theta); + + template + ``__sf_result`` jacobi_nc(T k, U theta, const Policy& pol); + + }} // namespaces + +[heading Description] + +This function returns the Jacobi elliptic function ['nc]. + +[optional_policy] + +This function is a trivial wrapper around __jacobi_elliptic, with: + +['nc(x, k) = 1 / cn(x, k)] + +[graph jacobi_nc] + +[endsect] + +[section:jacobi_nd Jacobi Elliptic Function nd] + +[heading Synopsis] + +`` + #include +`` + + namespace boost { namespace math { + + template + ``__sf_result`` jacobi_nd(T k, U theta); + + template + ``__sf_result`` jacobi_nd(T k, U theta, const Policy& pol); + + }} // namespaces + +[heading Description] + +This function returns the Jacobi elliptic function ['nd]. + +[optional_policy] + +This function is a trivial wrapper around __jacobi_elliptic, with: + +['nd(x, k) = 1 / dn(x, k)] + +[graph jacobi_nd] + +[endsect] + +[section:jacobi_ns Jacobi Elliptic Function ns] + +[heading Synopsis] + +`` + #include +`` + + namespace boost { namespace math { + + template + ``__sf_result`` jacobi_ns(T k, U theta); + + template + ``__sf_result`` jacobi_ns(T k, U theta, const Policy& pol); + + }} // namespaces + +[heading Description] + +This function returns the Jacobi elliptic function ['ns]. + +[optional_policy] + +This function is a trivial wrapper around __jacobi_elliptic, with: + +['ns(x, k) = 1 / sn(x, k)] + +[graph jacobi_ns] + +[endsect] + +[section:jacobi_sc Jacobi Elliptic Function sc] + +[heading Synopsis] + +`` + #include +`` + + namespace boost { namespace math { + + template + ``__sf_result`` jacobi_sc(T k, U theta); + + template + ``__sf_result`` jacobi_sc(T k, U theta, const Policy& pol); + + }} // namespaces + +[heading Description] + +This function returns the Jacobi elliptic function ['sc]. + +[optional_policy] + +This function is a trivial wrapper around __jacobi_elliptic, with: + +['sc(x, k) = sn(x, k) / cn(x, k)] + +[graph jacobi_sc] + +[endsect] + +[section:jacobi_sd Jacobi Elliptic Function sd] + +[heading Synopsis] + +`` + #include +`` + + namespace boost { namespace math { + + template + ``__sf_result`` jacobi_sd(T k, U theta); + + template + ``__sf_result`` jacobi_sd(T k, U theta, const Policy& pol); + + }} // namespaces + +[heading Description] + +This function returns the Jacobi elliptic function ['sd]. + +[optional_policy] + +This function is a trivial wrapper around __jacobi_elliptic, with: + +['sd(x, k) = sn(x, k) / dn(x, k)] + +[graph jacobi_sd] + +[endsect] + +[section:jacobi_sn Jacobi Elliptic Function sn] + +[heading Synopsis] + +`` + #include +`` + + namespace boost { namespace math { + + template + ``__sf_result`` jacobi_sn(T k, U theta); + + template + ``__sf_result`` jacobi_sn(T k, U theta, const Policy& pol); + + }} // namespaces + +[heading Description] + +This function returns the Jacobi elliptic function ['sn]. + +[optional_policy] + +This function is a trivial wrapper around __jacobi_elliptic. + +[graph jacobi_sn] + +[endsect] + + +[endsect] + diff --git a/doc/sf_and_dist/math.qbk b/doc/sf_and_dist/math.qbk index 469fc5f50..c802e2d49 100644 --- a/doc/sf_and_dist/math.qbk +++ b/doc/sf_and_dist/math.qbk @@ -157,6 +157,9 @@ and use the function's name as the link text.] [def __sph_hankel_1 [link math_toolkit.special.hankel.sph_hankel sph_hankel_1]] [def __sph_hankel_2 [link math_toolkit.special.hankel.sph_hankel sph_hankel_2]] +[/Jacobi Elliptic Functions] +[def __jacobi_elliptic [link math_toolkit.special.jacobi.jacobi_elliptic jacobi_elliptic]] + [/sinus cardinals] [def __sinc_pi [link math_toolkit.special.sinc.sinc_pi sinc_pi]] [def __sinhc_pi [link math_toolkit.special.sinc.sinhc_pi sinhc_pi]] @@ -436,6 +439,8 @@ and as a CD ISBN 0-9504833-2-X 978-0-9504833-2-0, Classification 519.2-dc22. [include ellint_legendre.qbk] [endsect] [/section:ellint Elliptic Integrals] +[include jacobi_elliptic.qbk] + [section:zetas Zeta Functions] [include zeta.qbk] [endsect] diff --git a/include/boost/math/special_functions.hpp b/include/boost/math/special_functions.hpp index 00fe866f4..d0deea6f0 100644 --- a/include/boost/math/special_functions.hpp +++ b/include/boost/math/special_functions.hpp @@ -36,6 +36,7 @@ #include #include #include +#include #include #include #include diff --git a/include/boost/math/special_functions/hankel.hpp b/include/boost/math/special_functions/hankel.hpp index bc3fc2d74..a0852ee4a 100644 --- a/include/boost/math/special_functions/hankel.hpp +++ b/include/boost/math/special_functions/hankel.hpp @@ -130,7 +130,7 @@ inline std::complex >: } template -inline std::complex::result_type> sph_hankel_1(T1 v, T2 x, const Policy& pol) +inline std::complex::result_type> sph_hankel_1(T1 v, T2 x, const Policy&) { BOOST_FPU_EXCEPTION_GUARD typedef typename detail::bessel_traits::result_type result_type; @@ -152,7 +152,7 @@ inline std::complex >: } template -inline std::complex::result_type> sph_hankel_2(T1 v, T2 x, const Policy& pol) +inline std::complex::result_type> sph_hankel_2(T1 v, T2 x, const Policy&) { BOOST_FPU_EXCEPTION_GUARD typedef typename detail::bessel_traits::result_type result_type; diff --git a/include/boost/math/special_functions/jacobi_elliptic.hpp b/include/boost/math/special_functions/jacobi_elliptic.hpp new file mode 100644 index 000000000..6d303b722 --- /dev/null +++ b/include/boost/math/special_functions/jacobi_elliptic.hpp @@ -0,0 +1,318 @@ +// Copyright John Maddock 2012. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt +// or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifndef BOOST_MATH_JACOBI_ELLIPTIC_HPP +#define BOOST_MATH_JACOBI_ELLIPTIC_HPP + +#include + +namespace boost{ namespace math{ + +namespace detail{ + +template +T jacobi_recurse(const T& x, const T& k, T anm1, T bnm1, unsigned N, T* pTn, const Policy& pol) +{ + BOOST_MATH_STD_USING + ++N; + T Tn; + T cn = (anm1 - bnm1) / 2; + T an = (anm1 + bnm1) / 2; + if(cn < policies::get_epsilon()) + { + Tn = ldexp(T(1), (int)N) * x * an; + } + else + Tn = jacobi_recurse(x, k, an, sqrt(anm1 * bnm1), N, 0, pol); + if(pTn) + *pTn = Tn; + return (Tn + asin((cn / an) * sin(Tn))) / 2; +} + +template +T jacobi_imp(const T& x, const T& k, T* cn, T* dn, const Policy& pol, const char* function) +{ + BOOST_MATH_STD_USING + if(k < 0) + { + *cn = policies::raise_domain_error(function, "Modulus k must be positive but got %1%.", k, pol); + *dn = *cn; + return *cn; + } + if(k > 1) + { + T xp = x * k; + T kp = 1 / k; + T snp, cnp, dnp; + snp = jacobi_imp(xp, kp, &cnp, &dnp, pol, function); + *cn = dnp; + *dn = cnp; + return snp * kp; + } + // + // Special cases first: + // + if(x == 0) + { + *cn = *dn = 1; + return 0; + } + if(k == 0) + { + *cn = cos(x); + *dn = 1; + return sin(x); + } + if(k == 1) + { + *cn = *dn = 1 / cosh(x); + return tanh(x); + } + // + // Asymptotic forms from A&S 16.13: + // + if(k < tools::forth_root_epsilon()) + { + T su = sin(x); + T cu = cos(x); + T m = k * k; + *dn = 1 - m * su * su / 2; + *cn = cu + m * (x - su * cu) * su / 4; + return su - m * (x - su * cu) * cu / 4; + } + /* Can't get this to work to adequate precision - disabled for now... + // + // Asymptotic forms from A&S 16.15: + // + if(k > 1 - tools::root_epsilon()) + { + T tu = tanh(x); + T su = sinh(x); + T cu = cosh(x); + T sec = 1 / cu; + T kp = 1 - k; + T m1 = 2 * kp - kp * kp; + *dn = sec + m1 * (su * cu + x) * tu * sec / 4; + *cn = sec - m1 * (su * cu - x) * tu * sec / 4; + T sn = tu; + T sn2 = m1 * (x * sec * sec - tu) / 4; + T sn3 = (72 * x * cu + 4 * (8 * x * x - 5) * su - 19 * sinh(3 * x) + sinh(5 * x)) * sec * sec * sec * m1 * m1 / 512; + return sn + sn2 - sn3; + }*/ + T T1; + T kc = 1 - k; + T k_prime = k < 0.5 ? T(sqrt(1 - k * k)) : T(sqrt(2 * kc - kc * kc)); + T T0 = jacobi_recurse(x, k, T(1), k_prime, 0, &T1, pol); + *cn = cos(T0); + *dn = cos(T0) / cos(T1 - T0); + return sin(T0); +} + +} // namespace detail + +template +inline typename tools::promote_args::type jacobi_elliptic(T k, T theta, T* pcn, T* pdn, const Policy&) +{ + BOOST_FPU_EXCEPTION_GUARD + typedef typename tools::promote_args::type result_type; + typedef typename policies::evaluation::type value_type; + typedef typename policies::normalise< + Policy, + policies::promote_float, + policies::promote_double, + policies::discrete_quantile<>, + policies::assert_undefined<> >::type forwarding_policy; + + static const char* function = "boost::math::jacobi_elliptic<%1%>(%1%)"; + + value_type sn, cn, dn; + sn = detail::jacobi_imp(static_cast(theta), static_cast(k), &cn, &dn, forwarding_policy(), function); + if(pcn) + *pcn = policies::checked_narrowing_cast(cn, function); + if(pdn) + *pdn = policies::checked_narrowing_cast(dn, function); + return policies::checked_narrowing_cast(sn, function);; +} + +template +inline typename tools::promote_args::type jacobi_elliptic(T k, T theta, T* pcn = 0, T* pdn = 0) +{ + return jacobi_elliptic(k, theta, pcn, pdn, policies::policy<>()); +} + +template +inline typename tools::promote_args::type jacobi_sn(U k, T theta, const Policy& pol) +{ + typedef typename tools::promote_args::type result_type; + return jacobi_elliptic(static_cast(k), static_cast(theta), static_cast(0), static_cast(0), pol); +} + +template +inline typename tools::promote_args::type jacobi_sn(U k, T theta) +{ + return jacobi_sn(k, theta, policies::policy<>()); +} + +template +inline typename tools::promote_args::type jacobi_cn(T k, U theta, const Policy& pol) +{ + typedef typename tools::promote_args::type result_type; + result_type cn; + jacobi_elliptic(static_cast(k), static_cast(theta), &cn, static_cast(0), pol); + return cn; +} + +template +inline typename tools::promote_args::type jacobi_cn(T k, U theta) +{ + return jacobi_cn(k, theta, policies::policy<>()); +} + +template +inline typename tools::promote_args::type jacobi_dn(T k, U theta, const Policy& pol) +{ + typedef typename tools::promote_args::type result_type; + result_type dn; + jacobi_elliptic(static_cast(k), static_cast(theta), static_cast(0), &dn, pol); + return dn; +} + +template +inline typename tools::promote_args::type jacobi_dn(T k, U theta) +{ + return jacobi_dn(k, theta, policies::policy<>()); +} + +template +inline typename tools::promote_args::type jacobi_cd(T k, U theta, const Policy& pol) +{ + typedef typename tools::promote_args::type result_type; + result_type cn, dn; + jacobi_elliptic(static_cast(k), static_cast(theta), &cn, &dn, pol); + return cn / dn; +} + +template +inline typename tools::promote_args::type jacobi_cd(T k, U theta) +{ + return jacobi_cd(k, theta, policies::policy<>()); +} + +template +inline typename tools::promote_args::type jacobi_dc(T k, U theta, const Policy& pol) +{ + typedef typename tools::promote_args::type result_type; + result_type cn, dn; + jacobi_elliptic(static_cast(k), static_cast(theta), &cn, &dn, pol); + return dn / cn; +} + +template +inline typename tools::promote_args::type jacobi_dc(T k, U theta) +{ + return jacobi_dc(k, theta, policies::policy<>()); +} + +template +inline typename tools::promote_args::type jacobi_ns(T k, U theta, const Policy& pol) +{ + typedef typename tools::promote_args::type result_type; + return 1 / jacobi_elliptic(static_cast(k), static_cast(theta), static_cast(0), static_cast(0), pol); +} + +template +inline typename tools::promote_args::type jacobi_ns(T k, U theta) +{ + return jacobi_ns(k, theta, policies::policy<>()); +} + +template +inline typename tools::promote_args::type jacobi_sd(T k, U theta, const Policy& pol) +{ + typedef typename tools::promote_args::type result_type; + result_type sn, dn; + sn = jacobi_elliptic(static_cast(k), static_cast(theta), static_cast(0), &dn, pol); + return sn / dn; +} + +template +inline typename tools::promote_args::type jacobi_sd(T k, U theta) +{ + return jacobi_sd(k, theta, policies::policy<>()); +} + +template +inline typename tools::promote_args::type jacobi_ds(T k, U theta, const Policy& pol) +{ + typedef typename tools::promote_args::type result_type; + result_type sn, dn; + sn = jacobi_elliptic(static_cast(k), static_cast(theta), static_cast(0), &dn, pol); + return dn / sn; +} + +template +inline typename tools::promote_args::type jacobi_ds(T k, U theta) +{ + return jacobi_ds(k, theta, policies::policy<>()); +} + +template +inline typename tools::promote_args::type jacobi_nc(T k, U theta, const Policy& pol) +{ + return 1 / jacobi_cn(k, theta, pol); +} + +template +inline typename tools::promote_args::type jacobi_nc(T k, U theta) +{ + return jacobi_nc(k, theta, policies::policy<>()); +} + +template +inline typename tools::promote_args::type jacobi_nd(T k, U theta, const Policy& pol) +{ + return 1 / jacobi_dn(k, theta, pol); +} + +template +inline typename tools::promote_args::type jacobi_nd(T k, U theta) +{ + return jacobi_nd(k, theta, policies::policy<>()); +} + +template +inline typename tools::promote_args::type jacobi_sc(T k, U theta, const Policy& pol) +{ + typedef typename tools::promote_args::type result_type; + result_type sn, cn; + sn = jacobi_elliptic(static_cast(k), static_cast(theta), &cn, static_cast(0), pol); + return sn / cn; +} + +template +inline typename tools::promote_args::type jacobi_sc(T k, U theta) +{ + return jacobi_sc(k, theta, policies::policy<>()); +} + +template +inline typename tools::promote_args::type jacobi_cs(T k, U theta, const Policy& pol) +{ + typedef typename tools::promote_args::type result_type; + result_type sn, cn; + sn = jacobi_elliptic(static_cast(k), static_cast(theta), &cn, static_cast(0), pol); + return cn / sn; +} + +template +inline typename tools::promote_args::type jacobi_cs(T k, U theta) +{ + return jacobi_cs(k, theta, policies::policy<>()); +} + +}} // namespaces + +#endif // BOOST_MATH_JACOBI_ELLIPTIC_HPP diff --git a/include/boost/math/special_functions/math_fwd.hpp b/include/boost/math/special_functions/math_fwd.hpp index 982cdf7ca..65c87ff58 100644 --- a/include/boost/math/special_functions/math_fwd.hpp +++ b/include/boost/math/special_functions/math_fwd.hpp @@ -713,6 +713,86 @@ namespace boost template typename tools::promote_args::type owens_t(T1 h, T2 a); + // Jacobi Functions: + template + typename tools::promote_args::type jacobi_elliptic(T k, T theta, T* pcn, T* pdn, const Policy&); + + template + typename tools::promote_args::type jacobi_elliptic(T k, T theta, T* pcn, T* pdn); + + template + typename tools::promote_args::type jacobi_sn(U k, T theta, const Policy& pol); + + template + typename tools::promote_args::type jacobi_sn(U k, T theta); + + template + typename tools::promote_args::type jacobi_cn(T k, U theta, const Policy& pol); + + template + typename tools::promote_args::type jacobi_cn(T k, U theta); + + template + typename tools::promote_args::type jacobi_dn(T k, U theta, const Policy& pol); + + template + typename tools::promote_args::type jacobi_dn(T k, U theta); + + template + typename tools::promote_args::type jacobi_cd(T k, U theta, const Policy& pol); + + template + typename tools::promote_args::type jacobi_cd(T k, U theta); + + template + typename tools::promote_args::type jacobi_dc(T k, U theta, const Policy& pol); + + template + typename tools::promote_args::type jacobi_dc(T k, U theta); + + template + typename tools::promote_args::type jacobi_ns(T k, U theta, const Policy& pol); + + template + typename tools::promote_args::type jacobi_ns(T k, U theta); + + template + typename tools::promote_args::type jacobi_sd(T k, U theta, const Policy& pol); + + template + typename tools::promote_args::type jacobi_sd(T k, U theta); + + template + typename tools::promote_args::type jacobi_ds(T k, U theta, const Policy& pol); + + template + typename tools::promote_args::type jacobi_ds(T k, U theta); + + template + typename tools::promote_args::type jacobi_nc(T k, U theta, const Policy& pol); + + template + typename tools::promote_args::type jacobi_nc(T k, U theta); + + template + typename tools::promote_args::type jacobi_nd(T k, U theta, const Policy& pol); + + template + typename tools::promote_args::type jacobi_nd(T k, U theta); + + template + typename tools::promote_args::type jacobi_sc(T k, U theta, const Policy& pol); + + template + typename tools::promote_args::type jacobi_sc(T k, U theta); + + template + typename tools::promote_args::type jacobi_cs(T k, U theta, const Policy& pol); + + template + typename tools::promote_args::type jacobi_cs(T k, U theta); + + template typename tools::promote_args::type zeta(T s); @@ -1114,6 +1194,60 @@ namespace boost template \ inline std::complex::result_type> sph_hankel_2(T1 v, T2 x)\ { return boost::math::sph_hankel_2(v, x, Policy()); }\ + \ + template \ + inline typename boost::math::tools::promote_args::type jacobi_elliptic(T k, T theta, T* pcn, T* pdn)\ + { return boost::math::jacobi_elliptic(k, theta, pcn, pdn, Policy()); }\ + \ + template \ + inline typename boost::math::tools::promote_args::type jacobi_sn(U k, T theta)\ + { return boost::math::jacobi_sn(k, theta, Policy()); }\ + \ + template \ + inline typename boost::math::tools::promote_args::type jacobi_cn(T k, U theta)\ + { return boost::math::jacobi_cn(k, theta, Policy()); }\ + \ + template \ + inline typename boost::math::tools::promote_args::type jacobi_dn(T k, U theta)\ + { return boost::math::jacobi_dn(k, theta, Policy()); }\ + \ + template \ + inline typename boost::math::tools::promote_args::type jacobi_cd(T k, U theta)\ + { return boost::math::jacobi_cd(k, theta, Policy()); }\ + \ + template \ + inline typename boost::math::tools::promote_args::type jacobi_dc(T k, U theta)\ + { return boost::math::jacobi_dc(k, theta, Policy()); }\ + \ + template \ + inline typename boost::math::tools::promote_args::type jacobi_ns(T k, U theta)\ + { return boost::math::jacobi_ns(k, theta, Policy()); }\ + \ + template \ + inline typename boost::math::tools::promote_args::type jacobi_sd(T k, U theta)\ + { return boost::math::jacobi_sd(k, theta, Policy()); }\ + \ + template \ + inline typename boost::math::tools::promote_args::type jacobi_ds(T k, U theta)\ + { return boost::math::jacobi_ds(k, theta, Policy()); }\ + \ + template \ + inline typename boost::math::tools::promote_args::type jacobi_nc(T k, U theta)\ + { return boost::math::jacobi_nc(k, theta, Policy()); }\ + \ + template \ + inline typename boost::math::tools::promote_args::type jacobi_nd(T k, U theta)\ + { return boost::math::jacobi_nd(k, theta, Policy()); }\ + \ + template \ + inline typename boost::math::tools::promote_args::type jacobi_sc(T k, U theta)\ + { return boost::math::jacobi_sc(k, theta, Policy()); }\ + \ + template \ + inline typename boost::math::tools::promote_args::type jacobi_cs(T k, U theta)\ + { return boost::math::jacobi_cs(k, theta, Policy()); }\ + \ + diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 6e8f795fa..9b57dfd1d 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -445,6 +445,7 @@ run test_inverse_gamma_distribution.cpp ../../test/build//boost_test_exec_monito run test_inverse_gaussian.cpp ../../test/build//boost_test_exec_monitor ; +run test_jacobi.cpp pch_light ../../test/build//boost_test_exec_monitor ; run test_laplace.cpp ../../test/build//boost_unit_test_framework ; run test_inv_hyp.cpp pch ../../test/build//boost_test_exec_monitor ; run test_laguerre.cpp test_instances pch_light ../../test/build//boost_test_exec_monitor ; diff --git a/test/compile_test/instantiate.hpp b/test/compile_test/instantiate.hpp index 4c57732d7..1f815291d 100644 --- a/test/compile_test/instantiate.hpp +++ b/test/compile_test/instantiate.hpp @@ -212,6 +212,19 @@ void instantiate(RealType) boost::math::ellint_rd(v1, v2, v3); boost::math::ellint_rf(v1, v2, v3); boost::math::ellint_rj(v1, v2, v3, v1); + boost::math::jacobi_elliptic(v1, v2, &v1, &v2); + boost::math::jacobi_cd(v1, v2); + boost::math::jacobi_cn(v1, v2); + boost::math::jacobi_cs(v1, v2); + boost::math::jacobi_dc(v1, v2); + boost::math::jacobi_dn(v1, v2); + boost::math::jacobi_ds(v1, v2); + boost::math::jacobi_nc(v1, v2); + boost::math::jacobi_nd(v1, v2); + boost::math::jacobi_ns(v1, v2); + boost::math::jacobi_sc(v1, v2); + boost::math::jacobi_sd(v1, v2); + boost::math::jacobi_sn(v1, v2); boost::math::hypot(v1, v2); boost::math::sinc_pi(v1); boost::math::sinhc_pi(v1); @@ -341,6 +354,19 @@ void instantiate(RealType) boost::math::ellint_rd(v1, v2, v3, pol); boost::math::ellint_rf(v1, v2, v3, pol); boost::math::ellint_rj(v1, v2, v3, v1, pol); + boost::math::jacobi_elliptic(v1, v2, &v1, &v2, pol); + boost::math::jacobi_cd(v1, v2, pol); + boost::math::jacobi_cn(v1, v2, pol); + boost::math::jacobi_cs(v1, v2, pol); + boost::math::jacobi_dc(v1, v2, pol); + boost::math::jacobi_dn(v1, v2, pol); + boost::math::jacobi_ds(v1, v2, pol); + boost::math::jacobi_nc(v1, v2, pol); + boost::math::jacobi_nd(v1, v2, pol); + boost::math::jacobi_ns(v1, v2, pol); + boost::math::jacobi_sc(v1, v2, pol); + boost::math::jacobi_sd(v1, v2, pol); + boost::math::jacobi_sn(v1, v2, pol); boost::math::hypot(v1, v2, pol); boost::math::sinc_pi(v1, pol); boost::math::sinhc_pi(v1, pol); @@ -481,6 +507,19 @@ void instantiate(RealType) test::ellint_rd(v1, v2, v3); test::ellint_rf(v1, v2, v3); test::ellint_rj(v1, v2, v3, v1); + test::jacobi_elliptic(v1, v2, &v1, &v2); + test::jacobi_cd(v1, v2); + test::jacobi_cn(v1, v2); + test::jacobi_cs(v1, v2); + test::jacobi_dc(v1, v2); + test::jacobi_dn(v1, v2); + test::jacobi_ds(v1, v2); + test::jacobi_nc(v1, v2); + test::jacobi_nd(v1, v2); + test::jacobi_ns(v1, v2); + test::jacobi_sc(v1, v2); + test::jacobi_sd(v1, v2); + test::jacobi_sn(v1, v2); test::hypot(v1, v2); test::sinc_pi(v1); test::sinhc_pi(v1); @@ -648,6 +687,18 @@ void instantiate_mixed(RealType) boost::math::ellint_rf(fr, dr, lr); boost::math::ellint_rj(i, i, s, l); boost::math::ellint_rj(i, fr, dr, lr); + boost::math::jacobi_cd(i, fr); + boost::math::jacobi_cn(i, fr); + boost::math::jacobi_cs(i, fr); + boost::math::jacobi_dc(i, fr); + boost::math::jacobi_dn(i, fr); + boost::math::jacobi_ds(i, fr); + boost::math::jacobi_nc(i, fr); + boost::math::jacobi_nd(i, fr); + boost::math::jacobi_ns(i, fr); + boost::math::jacobi_sc(i, fr); + boost::math::jacobi_sd(i, fr); + boost::math::jacobi_sn(i, fr); boost::math::hypot(i, s); boost::math::hypot(fr, lr); boost::math::sinc_pi(i); @@ -761,6 +812,18 @@ void instantiate_mixed(RealType) boost::math::ellint_rf(fr, dr, lr, pol); boost::math::ellint_rj(i, i, s, l, pol); boost::math::ellint_rj(i, fr, dr, lr, pol); + boost::math::jacobi_cd(i, fr, pol); + boost::math::jacobi_cn(i, fr, pol); + boost::math::jacobi_cs(i, fr, pol); + boost::math::jacobi_dc(i, fr, pol); + boost::math::jacobi_dn(i, fr, pol); + boost::math::jacobi_ds(i, fr, pol); + boost::math::jacobi_nc(i, fr, pol); + boost::math::jacobi_nd(i, fr, pol); + boost::math::jacobi_ns(i, fr, pol); + boost::math::jacobi_sc(i, fr, pol); + boost::math::jacobi_sd(i, fr, pol); + boost::math::jacobi_sn(i, fr, pol); boost::math::hypot(i, s, pol); boost::math::hypot(fr, lr, pol); boost::math::sinc_pi(i, pol); diff --git a/test/jacobi_elliptic.ipp b/test/jacobi_elliptic.ipp new file mode 100644 index 000000000..3ec0407cb --- /dev/null +++ b/test/jacobi_elliptic.ipp @@ -0,0 +1,407 @@ +#ifndef SC_ +# define SC_(x) static_cast(BOOST_JOIN(x, L)) +#endif + static const boost::array, 400> jacobi_elliptic = {{ + { SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.7384321813508780300050309993112921610348339609531096226291156957843807163438391463300771570266454611e-02), SC_(9.9524685071841496279438927849850673342525676921414792528840427410727111940782381944976305408868157855e-01), SC_(9.9995488439733316729114394585903874689886199946693440341361736436672692239264636048488084336908171547e-01) }, + { SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7383306026428126815811673852101862643417212675894886262329096942831342806175591481538515201116435095e-02), SC_(9.9524695011206291426731901545274769005867525867705503210833924341584688692109569818882782443312019870e-01), SC_(9.9992353321916073154296514614318371763529995049379965142148455053362169878708374701587696243287582131e-01) }, + { SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(1.3547700643539428710937500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7382963663268679354766311462039914384149178492941126840831062817834448292082576674044335924290112792e-02), SC_(9.9524698361168545268757042933526662768772514619668023376490370653166168736869277815425438301697322693e-01), SC_(9.9991296657753407444565165371686075323189094367991128619066744668429579140503359966446931860569605749e-01) }, + { SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(1.8838196992874145507812500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7380331287488173017819681812505333548000401340832607031998520409371778408842832201970632399407455377e-02), SC_(9.9524724118097360944629737689090579536626111956092105184429209919209960381948277540779135011872980164e-01), SC_(9.9983172185713251267253025953154802657840786163407200767760200375372426265381549093953869220602182213e-01) }, + { 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SC_(9.9524787361843859046684503694959443606213073331077397309037690642929126741546581484860725317608308903e-01), SC_(9.9963222736499384529570421859460465646281312249068720158613197297025393833765853405888603462853042983e-01) }, + { SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(3.0816698074340820312500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7371193424879810007588652514672604171038551577576512840133215162813719206019907024377008226545048940e-02), SC_(9.9524813523614031580155154272347701177066765446592058958809789667054121097494545539509044453284397477e-01), SC_(9.9954970099303609847458849068667534444745484953685258900209171332658289031259888119908884757012452532e-01) }, + { SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), 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SC_(9.9858034179693371185530389839478102909306909444244139828444148460849700760700112751223062617432481898e-01) }, + { SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(6.3235926628112792968750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7324357382337915060878514538001614103127959113855749132567239992517451675127438717163091023277436887e-02), SC_(9.9525271637916917939363212827434662588809382803755724970123962674618546815060076204600270615937503766e-01), SC_(9.9810437384215507531192865121492102169160078954931664380383811419406897938852089977538372535612829971e-01) }, + { SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(8.1472349166870117187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7283832207787332968350504435429144214762136106042661009244142576287985290132328716551768340406726525e-02), SC_(9.9525667844580027212519964525662529454780451004601160492220566958669619783126116364988358493401101876e-01), SC_(9.9685402331179302384119860067365790061187418556554456085008029417476701630546266620873973439295183575e-01) }, + { SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(8.3500838279724121093750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7278693925629101473730435341228310212032309563196883073408404976412708107672325578164629264874000079e-02), SC_(9.9525718068654182996379555937806239819599280949500315783758413223431440712177599882842080674201603958e-01), SC_(9.9669550352317052980773857626559666269204531893591114427801701253901312521428606453243059354958930545e-01) }, + { 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SC_(9.9525923660192864077140433651715283184822491030430309366345862602952814976707227038950564349076111474e-01), SC_(9.9604655229407085613020817827545499990274574505860169796764685614255261186781008745763895029260399934e-01) }, + { SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.5750665664672851562500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7244982770042818904024531685011575954627230233210286803989361976045451794730571449048456332621323951e-02), SC_(9.9526047511495907655064681291117857597207801050777388462844588407020878200858505148516677103386126487e-01), SC_(9.9565557382340077224630623621638890196227919522504229996558938083078176693734660018540050675794907254e-01) }, + { SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.6488833427429199218750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7242804401238330394641034407571773598415791334970660265829118621816630813903078372035638501402854060e-02), SC_(9.9526068795676969770830147652098548970870591187020705631353682973051952503866517509360167878496802699e-01), SC_(9.9558838001891729294499891780505516968777413390971340214047171239353816575095609120301571391073133445e-01) }, + { SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.6769475936889648437500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7241971830040626580775446834986136249520903646682302901559733248423563672355475550286992004247011330e-02), SC_(9.9526076930350549471991585281853568963609976679114746406156151825336912211360294679020458186631077546e-01), SC_(9.9556269875012748079193459899059614648026964684907523159920139031085488131527377860967239854162520648e-01) }, + { SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.6886777877807617187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7241623119621507768675533305231494633519052635102622629454283243024320020666848207623354683904466225e-02), SC_(9.9526080337420175720684817572609318291152213025067248310909549916814881246189911074085103017210067969e-01), SC_(9.9555194254819173899689090341202623861942977239356687223773368135903981199872362824922639858352857970e-01) }, + { SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.9288129806518554687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7234391800827738968992450665433357666742411135127401009733638701177282347102378993477236969678654384e-02), SC_(9.9526150988125885796360273996610273175186092020643789825948701988318876024022145047763437281682892141e-01), SC_(9.9532889129818059354033929751614120883992975273268479379992266644335702830351636902588795874617070406e-01) }, + { SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7233298644478973403186335285900151115960047949746687839215967221911192031090096952634390287961810058e-02), SC_(9.9526161667910893238555566309439694986630762455664353906763841267218133910312675011879044026031301748e-01), SC_(9.9529517329166101513341571318056995313554164948688445541889776316051021077409476762097381272562596493e-01) }, + { 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SC_(9.9194869987030175974065452521412422683585122017884833703172127477318391160839598306916141357487061604e-01), SC_(9.9987068186822403724749028083081518011247091434035237209533262760757214065053721683798188881413986251e-01) }, + { SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.3547700643539428710937500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.2663959243421258905813608345822828017922530244400625498512136982817465216522876223180316746892978949e-01), SC_(9.9194879587007742159475715284033058520863291944391982961636532662432995118718631907184665515795900253e-01), SC_(9.9985281208317985060971531909892334434677570476838685775408615707510438112357380797799157313711172762e-01) }, + { SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), 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SC_(7.5978278283822479211376439731268141642022108080095832555933973987704296865652470937104603229869288191e-01), SC_(6.5017699351992065569746064599627737154536888227390453834366792436726148721533868773119735826598551074e-01), SC_(6.5644473766197150059277953711487155980360915730283952501378037406371103715133686833849501666306310513e-01) }, + { SC_(9.9288129806518554687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.5918336733663972037219871212498362117551081339580453396486836115142190979661014478954656059145811300e-01), SC_(6.5087680459469498453412617782386488677994476550785121126771057160918237120006786151538232665099459464e-01), SC_(6.5399747100900172007298509080282708005245020667670621531355072097410857580673026605001215944240422120e-01) }, + { SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(8.3885482409737487793132986525390252548599016635647076881425605198439856189635291019635684986647676933e-01), SC_(5.4435520029532394631766859531442445028924423939805843855900693679606882689380332392533232650416764803e-01), SC_(9.9664694089105561049436599014171427205430440750206219053630830466477486541729108074262628038967567197e-01) }, + { SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.3836846976079144894023795726943708541833389995672584811366755923228253071174017567635353431121846609e-01), SC_(5.4510394321720780766887536717356250054610572085005960031610835416626521365025255202834856505988398552e-01), SC_(9.9431680058555042048560821892288124889668236747200833373307558342592799237570669113081508646858944123e-01) }, + { SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.3547700643539428710937500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.3820441560966632694840359993609916279790205370061844267576841794174497598281495713485622976344391591e-01), SC_(5.4535617503834845711324861801153301842141480493596794361183694684559717959677144037999716529712971962e-01), SC_(9.9353143444262221939465586259809215783089086048975947684621927841892919843078927555582450058279233656e-01) }, + { SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.8838196992874145507812500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.3694080839939330368414271429214551959961793583075530257748487453202093020709691019075041846416360706e-01), SC_(5.4729341603546632401734901252585114956817351177725909693254699621320094637152673766320203739840879612e-01), SC_(9.8749272761250703526071418423335735642830175784158270003092854064131945258173428320458022832662895698e-01) }, + { SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(2.2103404998779296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.3595219488333541745953223658793448369279376370877659139211318590602107483272687491384205103621224117e-01), SC_(5.4880226664048500692879221583078985251740360874646904338195445074557839493958187702092044696804312843e-01), SC_(9.8278105708386568298282282875597998137429996085178472000521847835028605762176132021719290137727508239e-01) }, + { SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(2.7849817276000976562500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.3382140916514258364057514275189395234076096015656622904743683896148751450562302576019453974647090151e-01), SC_(5.5203429025546581114852096977818457319004303981372761755614161259277270015439079181206829579325032785e-01), SC_(9.7266382772180763980428823267587850291886472907988601665506049159784515142450655743912151433457442980e-01) }, + { SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(3.0816698074340820312500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.3252411677796080099984218005465406247603158092900382879848475335969228461284474294838346745658610338e-01), SC_(5.5398880402321876447537992744785992051147320066434509696867298206540346295080549987859520437777915381e-01), SC_(9.6652925010955620940395542670963601024004192923501024067547444076347996257852171861223080733972851268e-01) }, + { SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(5.4688143730163574218750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.1702126153451325670867681664834862284442900110619845692881310008319720517769069946797733509893494105e-01), SC_(5.7660754261503767522810562864064328455649166811864815390603109965795766966575540449279700563129428370e-01), SC_(8.9462699615741016868034408689337159403352108892081501750962490910797925647981891785415699133208532444e-01) }, + { SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(5.4722046852111816406250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.1699261272360843718094896717933608151745983515066309372984104102996139405622722607210355081833891513e-01), SC_(5.7664813426824850966137934301882037328247242522271394061105905414771445854256739255757146117096354987e-01), SC_(8.9449643518753563454611035039011276118628076201799942256582642209492573307351767556846756787034337047e-01) }, + { SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(6.3235926628112792968750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.0917470232222200804623180098129133036872476212345687946408231027401224355414186080302191412417315445e-01), SC_(5.8756812466448807626035048020623505899237385118588318521559957175811892777170782847243623726402163039e-01), SC_(8.5917067186634159636297999262881680727474209461119658335870527906879501356002165645327808755884914641e-01) }, + { SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.1472349166870117187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.8807119444979816800923969304385287292785209340565035630430040254664427368175755115143127657804319275e-01), SC_(6.1558410674616056493571795007635947841655775384258519636348871522168706473724532307349806008226940840e-01), SC_(7.6665429525726110361447413684552291171054174846338591438308890401356527577849589856356276150225732188e-01) }, + { SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.3500838279724121093750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.8533974060861189062248546305583049909685081062975650698710874051826667020351572955065423608667621888e-01), SC_(6.1906501421159166628343674250361648671913040974698965825105617076167069374238270072189557585460007272e-01), SC_(7.5496484350046113300800020039074081961933680785286101512645919124096025389484980045855949751906931482e-01) }, + { SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.0579175949096679687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.7518052347000925314010007943527768455040920946345973339627012081381376695222757183254277030896944957e-01), SC_(6.3173978506404235602086192410695037495356623570300207001965408561482576560706910009779017218552967902e-01), SC_(7.1202695591348996943901212719172676293237917080282599202090818283760895203386224684127468737115722039e-01) }, + { SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.1337585449218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.7403326959640178723563496098403563126044877288657909026716436291016997542128873110698916026557616324e-01), SC_(6.3314492618823376986676740088221455887438346847232176226658849048417517890369368618344349029048271542e-01), SC_(7.0723024179015572507350410631921738029759560477969903360400060435126461530726016656465837852310688792e-01) }, + { SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.5750665664672851562500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.6712800823285619471798123561258913583803638220534736201364708009370629428320353958750416444955694982e-01), SC_(6.4149405218185064504992339458407016741795699167416304441730489787216690117110750201301703730190120252e-01), SC_(6.7857602589593721337697403304549699145452424462317392210364305668406670401778150852638680470506706518e-01) }, + { SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.6488833427429199218750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.6593441813020686107904272195284976164911143038148978940760933715399917785398101606027733051459971132e-01), SC_(6.4291870957652293482277601636810697919275457997668849096935959115861162055784408260876292546568984644e-01), SC_(6.7366024601538257589655742562219072544530334312218911862590121331700593411003613779831508617892420325e-01) }, + { SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.6769475936889648437500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.6547770865632652104311857431350648982519639693036504351701283181609474922881977308885338563907679349e-01), SC_(6.4346241347126103408603307544875846579869659656475523368458255827578551435308991733382243465986469958e-01), SC_(6.7178215521760534606784911003038819524570089099102635584446923804691272196126068898352982615576142014e-01) }, + { SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.6886777877807617187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.6528633729797841460176785222203390514942625072618331938529597075420681577693034777030027274670865291e-01), SC_(6.4369000454026378494764961458275300252507916799112249356864558832261907901572939091058344628185994802e-01), SC_(6.7099566282750678306967995163385198199449520575839393027024329721293501791261343629006364525136879702e-01) }, + { SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.9288129806518554687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.6130656170513378346158650596006841065509926127276492299715158864622868192915634720105938405478654273e-01), SC_(6.4839210290125166440291833468322114687478245067783826919074500661090573579759551799996853065323027448e-01), SC_(6.5470204815482800802602415811048971704607358039770120289884409108362609917793951796905679822441221683e-01) }, + { SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.6070308834386404159049681239553434730978977615881969147142722819631969635063229458010769940901615571e-01), SC_(6.4910000106617422443762696869434170692368988825415526998433303308325407487195203453870690819261137407e-01), SC_(6.5224167903128336698276201258993391810194122946207851950380395682119994293224476046299862066823494348e-01) } + }}; +//#undef SC_ + diff --git a/test/jacobi_elliptic_small.ipp b/test/jacobi_elliptic_small.ipp new file mode 100644 index 000000000..845aca2c8 --- /dev/null +++ b/test/jacobi_elliptic_small.ipp @@ -0,0 +1,1688 @@ +#ifndef SC_ +# define SC_(x) static_cast(BOOST_JOIN(x, L)) +#endif + static const boost::array, 1681> jacobi_elliptic_small = {{ + { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.6504814008555523940913182524024344909690304914367592725655712600281923768045401283620998764707764693e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973696151635920379696565170086974190992e-01), SC_(9.9999999999999999999999999999999999999999999999628966995620346223342181461431515637620350243665215080e-01) }, + { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(2.0654207510961697380480472929775714874267578125000000000000000000000000000000000000000000000000000000e-12), SC_(1.6504814008555523940913182524024344909690304914356038800613310054830865914687618301634103078917338168e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973696151826615763590211178195021758793e-01), SC_(9.9999999999999999999999999999999999999999999999418956903357324218784742231100976423667721244640328945e-01) }, + { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(6.9332300317581641024844429921358823776245117187500000000000000000000000000000000000000000000000000000e-12), SC_(1.6504814008555523940913182524024344909690304914027798723391089616386590188266692256822553895004737691e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973696157244157188296862020758148130289e-01), SC_(9.9999999999999999999999999999999999999999999993452696204168490870911613561919090434443527881778962629e-01) }, + { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.3351444949627477853937307372689247131347656250000000000000000000000000000000000000000000000000000000e-11), SC_(1.6504814008555523940913182524024344909690304913052218556582079673621348947108779104417637686162896722e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973696173345926391915144123663683144195e-01), SC_(9.9999999999999999999999999999999999999999999975720048632921041975214334983463922773663246301371558079e-01) }, + { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.6399812063916385795891983434557914733886718750000000000000000000000000000000000000000000000000000000e-11), SC_(1.6504814008555523940913182524024344909690304912372618758507282714946015960583626600059283156291032012e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973696184562594659391558357034445701976e-01), SC_(9.9999999999999999999999999999999999999999999963367292684459290855251530901083881607676209352596350232e-01) }, + { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(5.7301594025283009159466018900275230407714843750000000000000000000000000000000000000000000000000000000e-11), SC_(1.6504814008555523940913182524024344909690304889783532888043627371778016267672955616082803704829236507e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973696557391255574683748524224459833699e-01), SC_(9.9999999999999999999999999999999999999999999552776433700754495454636367587944076648284400103707184302e-01) }, + { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.1137313293829720350913703441619873046875000000000000000000000000000000000000000000000000000000000000e-10), SC_(1.6504814008555523940913182524024344909690304821439689287767962044790479566381944530155678406625631702e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973697685393682827041343608589118700995e-01), SC_(9.9999999999999999999999999999999999999999998310523532852882161708648652005740665368880880910156584491e-01) }, + { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.4214707189097453010617755353450775146484375000000000000000000000000000000000000000000000000000000000e-10), SC_(1.6504814008555523940913182524024344909690304762977332560523723670737117904598123506030905571007525820e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973698650304007112032323166148527367075e-01), SC_(9.9999999999999999999999999999999999999999997247881626734957219094542687145216261006406307420236809325e-01) }, + { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(3.8006320313144215106149204075336456298828125000000000000000000000000000000000000000000000000000000000e-10), SC_(1.6504814008555523940913182524024344909690303831976744007277642905699914309078508034857277902993981434e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973714016295563039085806793646480974079e-01), SC_(9.9999999999999999999999999999999999999999980325535429971135087765023210979692154823009643251966522036e-01) }, + { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(6.0916272026645401638234034180641174316406250000000000000000000000000000000000000000000000000000000000e-10), SC_(1.6504814008555523940913182524024344909690302133731854710685114641012066105734375850645869948919458138e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973742045511601859311127502555051080985e-01), SC_(9.9999999999999999999999999999999999999999949457361664130189602800079536313829981986427076949318817789e-01) }, + { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.0221641311147777742007747292518615722656250000000000000000000000000000000000000000000000000000000000e-09), SC_(1.6504814008555523940913182524024344909690297085106157246959147019549187034633366860135865373130072792e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973825372139737312017993425357327472681e-01), SC_(9.9999999999999999999999999999999999999999857690940760870814533399831245189911999724717703220387897201e-01) }, + { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(2.8819222563924995483830571174621582031250000000000000000000000000000000000000000000000000000000000000e-09), 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SC_(9.9649068766424200577985721184356752955601723188930074293915835068113130632428255591007970917819025182e-01), SC_(-8.3703700028410244770061826214701529976799484885620218724844567694731485856500558608813841851268272143e-02), SC_(9.9869544539219827767678663556107790796001205357457841120474538750514167458555525624218345986227679244e-01) }, + { SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.1201295256614685058593750000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.9684313604934398930539235390129770939609825850290918420113575774717084081891501166979587762444196098e-01), SC_(-7.9396234868594807401272204725688142828934281134460946403103848657930854463427457876250364818746217174e-02), SC_(9.9374654270592187744997687020550454797638290050151265651320047733411371840069209832488090292039717367e-01) }, + { SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(2.3480379581451416015625000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.9814934866490320978806688580871390672680066453416779059422743215014552518552147816785137038565167474e-01), SC_(-6.0810178094045119247364122651955570809342076623943187762098707626057061856818089052462136539473338148e-02), SC_(9.7214764923305873458032862854350162073206678556449933567459172269681798829001261625830288160524321418e-01) }, + { SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(4.8987305164337158203125000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.9976967292952005755481095245256024937692734652402590999991494952154282866789560889911025306718779168e-01), SC_(2.1461619006973565646536174052546379410807514047370718515791347175325100002601713407336650423975813432e-02), SC_(8.7185717081396898541065289390703478456116878515433892820948672390341209634334005744800539221410270970e-01) }, + { SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(7.5183129310607910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.8539034324839560936682949899637621959818856082648192169501428326661400191997487509531927187367953439e-01), SC_(1.7031110190709553832350904690514019306839852576492774590778059270526592192267334810770243087477878657e-01), SC_(6.7167349511579774208520897966660216379314520347464078477957664271219777907511857160535742769433089892e-01) }, + { SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(4.0815375315288640577475196367102453532926947422123146010409415723479279392954356853433706994064428463e-01), SC_(9.1291320167210457006284950226993895289063450955873095160130726593569036267152905012436288527918734100e-01), SC_(-7.3708797978087103688004545584461400336979146221355035197387826317949437602283858594803646637152865976e-01) } + }}; +//#undef SC_ + diff --git a/test/jacobi_large_phi.ipp b/test/jacobi_large_phi.ipp new file mode 100644 index 000000000..1c509eaa5 --- /dev/null +++ b/test/jacobi_large_phi.ipp @@ -0,0 +1,307 @@ +#ifndef SC_ +# define SC_(x) static_cast(BOOST_JOIN(x, L)) +#endif + static const boost::array, 300> jacobi_large_phi = {{ + { SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.1058797357690320086682997888107252211628291495151688601393407863373061954395848396257429511756176811e-01), SC_(-9.9386633915238026812869743952282655015178929533806734450981604274006648191113417152643248132020074274e-01), SC_(9.9990138922139577345821742312959843927086669798900631576940452344894647029651168866543336495621319962e-01) }, + { SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(1.3547700643539428710937500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.9796027195728077189442848498661232305049387865637023002287165495702857395230146075769449539819678763e-02), SC_(-9.9980403945336507845151345500450800737097833473134761034812701539547907788852267602747381881654129683e-01), SC_(9.9999640368228571150326548705630160155372276544820513372782759452847671460675392468118278515564642670e-01) }, + { SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(2.2103404998779296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-9.4524463054363015830543554229266024611315133648646726829860103132985305860006657410579310878453671719e-01), SC_(-3.2636266396209619739852328880763978392918068940083223909131243802010656037702645968281828914985898722e-01), SC_(9.7793033147839850499560648584765033296353170435094191917820984988398156187728059208365609303718763468e-01) }, + { SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(3.0816698074340820312500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(3.8467092829206275416395221453254971947309775360749050985209931262282264520459122402381792953068010283e-02), SC_(9.9925986748656589242807594841179280186636858779886436718703277243900358292074844422479042190466225049e-01), SC_(9.9992973546117087872258976240789404601766963067622683679015332787486976781350082685530756477017893531e-01) }, + { SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(6.3235926628112792968750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.1828487869642382837142082205368890409594444563859603885036504087100530651689815737374300479572152806e-01), SC_(-5.7481288894454945115324043802657481607935129579981996144467071525751961910351319915758240211691782206e-01), SC_(8.5571342814553735162229894739444873282853333740663537333659164564589208017713251914590680386027272809e-01) }, + { SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(8.1472349166870117187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.0342555778181684908553725700040860110642531214149151205515131896190048290879021057059409802362096946e-01), SC_(5.9540521756445540531188114127706021212880690887199697020660799772318324844598317460087416642725615927e-01), SC_(7.5600167963587697285196939810169457229824831904454088987922148028116675585554507425145383067593756070e-01) }, + { SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(8.3500838279724121093750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-5.2923808769191278344096906576129452977508979277324972114028585485897292732749175191104387817153243622e-01), SC_(-8.4847336230208620189522999730668948980498026956351676759653713074643763505826560196595716137493813219e-01), SC_(8.9705533240946393665356057247371866574922627996248245980741140274917656623741748929349898927165638735e-01) }, + { SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.0579175949096679687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-4.3588329433998778344118299461470119260462800471832395414994779852496041561445544177910644873466410470e-01), SC_(-9.0000319650283441310099684480078605946721143546738341042331933310537915309970277408204072796535470377e-01), SC_(9.1875870906845118047635806822648200063819834288643294354356983053626866318919800547192402870664676236e-01) }, + { SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.1337585449218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-9.5600856122085672092800268968580894468432579079804656774052584258946328842723868281852714693291460848e-01), SC_(2.9333876469438444648579701071867907567539764964724421796135027276816072964646665290023055039395020032e-01), SC_(4.8737075577081420166881282500675564846609614724320216534645035828942396447404446035830276248915799790e-01) }, + { SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.6886777877807617187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-9.7736452897241769061181430418007365494795330898556587924749704567000625360724157676092701517939511727e-01), SC_(-2.1156223081288422793211063644770138572453563413600394268502697586678182945457777132434950354231163677e-01), SC_(3.2141922402480394843964588019150294350276272721151544568588531146246464930473505445135251473893910091e-01) }, + { SC_(-1.5605529785156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.9634594511488441239446124536812458462568892642529680265004423990558267843732051305555937342925952892e-01), SC_(-8.5409353428812105256571523319257903922757730296962059795625764794071278796936359904999417711418506963e-02), SC_(9.9196370140536661517806007451248913316445364776565729227577579281057604045077901201671022992954940866e-01) }, + { SC_(-1.5605529785156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(1.3547700643539428710937500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.8507961426602883228803019073961981958060099984011753039084360078720386446123667023988475150255949526e-01), SC_(-1.7209925495914224056702706138188187847064943449563917074969927279924070607243598857996086522477531487e-01), SC_(9.9105478803571702730047795909209167869766318761675764394396722003662904738763622827899377822295432355e-01) }, + { SC_(-1.5605529785156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(2.2103404998779296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.8248612785073414182685509102670101867866606445715181205154091509183064961414026941361152523421096695e-01), SC_(-9.8320842812805745037945796017375413735001762909773273395230181538881053153180460745843274908711290409e-01), SC_(9.9918618660790569357913493985971747365339871345709645144590218630847755475249250020453080799416154091e-01) }, + { SC_(-1.5605529785156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(3.0816698074340820312500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-9.9158838874949604426827150019504117982370531426684233581077142421174586823163566938385360504094435130e-01), SC_(1.2943132270504812677590848413999258821957368076167066407580166536160746634327211207828164566323979708e-01), SC_(9.5216807427332399209612601388142889559348170701718081235058316586516533919961845371369694752105796844e-01) }, + { SC_(-1.5605529785156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(6.3235926628112792968750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(3.4850849856189024097670989535486539667872022677162829380888596814546374460520548474036175153271561409e-01), SC_(9.3730562061162150476751438595734314944960838837159437927593351031354238223322792887550880643854386618e-01), SC_(9.7541351185979966500632289702714211007616769474888190781321539444569874004850576581698447098984473774e-01) }, + { SC_(-1.5605529785156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(8.1472349166870117187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-9.9768647828943160251387270175978040354991051978569998213156792178899072069031856957855604912863677927e-01), SC_(-6.7983020221460620602477920740337096785069318374339062937396833159665852445264612438240658448058446372e-02), SC_(5.8248896313210669614394305122189656389869009767463887294045928688078276659240087367291744920068430718e-01) }, + { SC_(-1.5605529785156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(8.3500838279724121093750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.1666788045635083193371938920056375449022051643456650047952514782286715843857567412246372159950161759e-01), SC_(3.9964984291209386199380881912105158376718408574530690430179110562688471984148465105325478026822099931e-01), SC_(6.4352467823650631744048456295799149574644278344437481712696368654316089787975896784931564053208489969e-01) }, + { SC_(-1.5605529785156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.0579175949096679687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(6.6177046252416079555508635934682224965776227840898130220764534668450302789945037304177484207002111431e-01), SC_(7.4970651253044233646081247800563589896058506359539248199555934055757606449113476755285508234546147573e-01), SC_(8.0043000495681302502202318394250860224011843001834972620558908558545445241188040905957841914651309679e-01) }, + { SC_(-1.5605529785156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.1337585449218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.1162702067722820974181218645132596905845071555268450086333168727109070541904086340801164800949228836e-01), SC_(-4.1101846086418129416964169549534333473677856285816052126950157698922759495871524825487291772477361094e-01), SC_(5.5378739019092779516643345615954795852701624863384590572209755287128537152072227700404247969883944714e-01) }, + { SC_(-1.5605529785156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.6886777877807617187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.7847669401956797520765296060791765953322345138944187516386700694418973456687058302575886514423462073e-01), SC_(4.7778520075913856591407588537681940529299391433582939902608346698041301213222272262365837200005720441e-01), SC_(5.2495859897413680745296958425083017259125722923178059389226618992244314329629094407200132362457267991e-01) }, + { SC_(-1.4920532226562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.1215063872819339944338796668283511740964381708479698144676263852216765632126590041646227209364115669e-01), SC_(-5.8344780401796653568237512173126783312676925509867411666724236685734614984177049850333919234571133200e-01), SC_(9.9466763573814396963023807556320926109310668693939583577827334971414158421302798841901269607361008156e-01) }, + { SC_(-1.4920532226562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(1.3547700643539428710937500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.6054976086331288037125322608257848444816810017465420845629110898722376190810025438323697643864861936e-01), SC_(-6.4927964795668560314267237713980719915991455923114876289126085678131101947480980783506908969590434871e-01), SC_(9.9467752343771017769896939755587427956446894137686630938344801931680613896887371931817915877777484193e-01) }, + { SC_(-1.4920532226562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(2.2103404998779296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-2.9941013393828249562468043933256085053746533499014814474287338856196084573838173370275474866710041035e-01), SC_(-9.5412450534249445851367611999737097642434633331272683048477783407499681353395158460974738323907141592e-01), SC_(9.9780771168797610663602334889053920347639015008566581212273270194963843366318308150733275553306657420e-01) }, + { SC_(-1.4920532226562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(3.0816698074340820312500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-8.6719864943440637930669039110209116098037189939204590982866000932993993709050680857205265739773125776e-01), SC_(4.9796235040326246366335080891937548199238428693661611992997463196657958427036916819693071051983811639e-01), SC_(9.6362945111052285103631254630096889819955734117210904878248366677107871195046059356266384495429961450e-01) }, + { SC_(-1.4920532226562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(6.3235926628112792968750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.8985504234083673157036235273870644307270460421766787483340617817060806864573895864468342499948286678e-02), SC_(9.9508887540336024159212127845081277863814763122092623489898100955575317932908067435902261605351808347e-01), SC_(9.9803904782565583185366933461079009403715133227249391487654897071038775707482277358544512478341156519e-01) }, + { SC_(-1.4920532226562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(8.1472349166870117187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-5.8814963080461870021198721661557643907886147207612907823072290890103839379488530932608574741256306236e-01), SC_(-8.0875213247594637653736743898670824540865692134900148467304845506829461075322553449605233010395774104e-01), SC_(8.7771702643062584130996897525584161842225801509545905752278792498355736903130315249715375102515055593e-01) }, + { SC_(-1.4920532226562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(8.3500838279724121093750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-7.0647797165225437502393133050150854956535918064874835574837305117427828927548166159140884257318526734e-02), SC_(9.9750132268368504887528599916517127108470497653756483100770737141575727579830791991377153519171149627e-01), SC_(9.9825848485771567319253605085194118133530665792125170554932334683733494030883559231514998309242203181e-01) }, + { SC_(-1.4920532226562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.0579175949096679687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), 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SC_(8.3500838279724121093750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-2.5661560264047896550977697577574285271994983541443544067356972715404806414952219948705677776708497000e-01), SC_(9.6651354490325887257750254185816231220218423716636053686841904330333698328423906111679391851744157820e-01), SC_(9.7677311539491902219065627087092296908401907255979252384756489646051968319678552175412452558572875080e-01) }, + { SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.0579175949096679687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-2.3043688031022365976100265167863985776533246242764453911544714145699594137367180026912374835735577553e-01), SC_(-9.7308727470504497158374043000785726585723147362213332885195842776034698222933783780401814107209214425e-01), SC_(9.7797376965032175821022437157898388837314600109117623736975241337618528076029566654878957935590182792e-01) }, + { SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.1337585449218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7024515945744297738657357466434755079331657796883714801833862664891641843430559561966177382852691399e-01), SC_(2.4212461780950951071551165255952297503000013061390990430320407464582844014750946659296356182356525586e-01), SC_(4.6330574762904332411829744686422163790342838342235753322328220006082956185458756739898418452935999869e-01) }, + { SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.6886777877807617187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-9.6271921666412527706611162998623278828344436746037642935689292731054871089839252562699168099269047894e-01), SC_(-2.7050269844423550857864806232371501929916695397580524032916105445727409203649388936347088607548210605e-01), SC_(3.6052997174588038100329734639411992177585754440288098151836194079410246809516008674605501002506176314e-01) } + }}; +//#undef SC_ + diff --git a/test/jacobi_near_1.ipp b/test/jacobi_near_1.ipp new file mode 100644 index 000000000..d03f013d1 --- /dev/null +++ b/test/jacobi_near_1.ipp @@ -0,0 +1,347 @@ +#ifndef SC_ +# define SC_(x) static_cast(BOOST_JOIN(x, L)) +#endif + static const boost::array, 340> jacobi_near_1 = {{ + { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000004768371582031250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9936124862178929657881621645181864085183918423681860187396785862520605717123413406685399380582107113e-01), SC_(3.5736462515171262671173658796361885282655550407797367368767246967565775142270960241294075546367351927e-02), SC_(3.5723133911895480121899640922445600550831965573961005650871698226561870552026541364948342613336582806e-02) }, + { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000014305114746093750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9936077436182305740265762942505880070947367818181132794898773596144577761932318153752214737153329561e-01), SC_(3.5749722613432715628553169307272741195011102329188833383668050964850356815583084732679478209132508739e-02), SC_(3.5709736745792682671599404581373263526701044801333523535341814550620045496488948203712498732057017070e-02) }, + { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000033378601074218750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9935982531025601614500364655259025282505814635665229090640399025716517540590131557526316221367105587e-01), SC_(3.5776242897411389640336798137070232128793830106896650516594399176561812055650730083125160534386857905e-02), SC_(3.5682942269816429157188838670831408020383121223997457406594651516016868258020580067207389880661065297e-02) }, + { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000042915344238281250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9935935051865263915735047486113654526010249743927673270177761276038424843029985650910155418309910845e-01), SC_(3.5789503083121607415749831967541532808130587365952231223694356024503294702063563047398592898634045898e-02), SC_(3.5669544959949864105435637819287301450816005044070102625046909813700756220300841914735887869992226382e-02) }, + { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000147819519042968750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9935411611454537922604681816673279309149514529840821022380007801210707169443456723123140131191273797e-01), SC_(3.5935367048574188596130658870586603259325678077312780894068903977052012489188410600116295423084873594e-02), SC_(3.5522171389827658240024209410574445295562666383769236088207845918964017440183503252721885546279178521e-02) }, + { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000290870666503906250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9934694373075237465634151921066970602357861542329676509188178432941256915556744220631478917655855971e-01), SC_(3.6134278130390913627609094654640317241259878826206151457813687944589213129451776496300461550369058584e-02), SC_(3.5321198095556949417067313300717675686827259252339991668193302765590470280891859038544561861120273525e-02) }, + { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000371932983398437500000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9934286167753124814131392571342776632513909244848527380521892160554807524960808842808040249611793657e-01), SC_(3.6246997312365705419622654899909043653736234860893527625677781635672768579458759093245682453664911900e-02), SC_(3.5207308451560232414054205505237899944531489182512040097012760453521655141311995420890008689715696573e-02) }, + { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000996589660644531250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9931097620864165027219465310031542946941250827291810334804095750671116621959312074419161413137564784e-01), SC_(3.7115668240402753402689250059917062222914595826608378093934126249222135687424925800143195563100714367e-02), SC_(3.4329572580251660446610503280495506358429580145905143796049996103343889948196804594921179632733199316e-02) }, + { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0001597404479980468750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9927958990572377979840922995352718001556928368962504869163503233477958808920244802834130239693182256e-01), SC_(3.7951300344632531849121062722660432211073826380488963469452361292471727250417761710007993570196150397e-02), SC_(3.3485145517244791669270158219919377826756232555597493366342767643308973856626129103762653029721538067e-02) }, + { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0002679824829101562500000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9922126738572525883615985096934737542379246872162570557721278008482614426793068921887463636739257892e-01), SC_(3.9457050118640992430999735288370836965982117887075206057330612359482953959031548073429030863323308119e-02), SC_(3.1963362733204485362415093423863407199447848854193799452188513745779920844752052440282754193164327043e-02) }, + { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0007553100585937500000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9893032851875707688561830988272894258600328658118144172720086651889951652362299650709125447015552495e-01), SC_(4.6240661385928097466067420828933763850527867003804137146601696125664302459519863236590458981093024575e-02), SC_(2.5104568923475994083987155204747891917416311244009618734097942128126480441578326069647043926175848547e-02) }, + { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0012483596801757812500000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9858861863794450821691883948411704365274249753358965103850267796074469645752772267528127337525272991e-01), SC_(5.3110928505928287442257797909322905597834515794113431687558113958412726965037911230281021368296317952e-02), SC_(1.8153237543155462803067836701096459698569047964241988599087152572358359059054049298308131438716438194e-02) }, + { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0023207664489746093750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9768013419211395389844759575957044763860216650562470815234213356993397846622838414826864478393798484e-01), SC_(6.8076059216184755781840577950311038573406706672675088844600265894103208744445519993559300403103933746e-02), SC_(2.9943999715622324848586115105215220299985513048294403527193588267688062368550605670306861278056228327e-03) }, + { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0060424804687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9275223561439943369665678089317248964119678445427980155471655857570286843157774469401717822210675502e-01), SC_(1.2017902763216197969677315152451453633920175705926357660874751861325404020389385327834653677322322067e-01), SC_(-4.9965954272454113037709486732652160303751311444701747699562340013704865808780400007504197732543057380e-02) }, + { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0155692100524902343750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.6735637154027865337130077405912181415705275746255993415024144757583603881348060995488920488911672649e-01), SC_(2.5341990932132061632299610199618871011222636428088359622618311788654236921637295363303486915660247366e-01), SC_(-1.8669803992671241292637737591564312105410623529773567523326462874859967205170061052766876529350597205e-01) }, + { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0305857658386230468750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-8.9037307644999185961891548066152364082934652825389480690284822126953747572423134779233931568896247709e-01), SC_(4.5523157264515051576165746439917285541212023356220966397336337241653186704837219828020641191437049015e-01), SC_(-3.9749158628350816926566949245343979471653384960565298443009459540951029451206974073879850780006389752e-01) }, + { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0623893737792968750000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-6.0719134559454416707104305589573667628292047048469766163025850056085681130949692218928367444627674035e-01), SC_(7.9455564300751576105470945564292159344239444001338371721114375059096583894484473548719583963149859832e-01), SC_(-7.6412041425334888578087126653697299732010050441086783313382612821550919553001092840088361833581189685e-01) }, + { SC_(-3.7301321029663085937500000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000004768371582031250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9884941771767374068845949560764111778511322805191229385025226734820765467112509736638548364923940404e-01), SC_(4.7956654648381339311038559193943126801582338467442869043122959184810391359715831466879439189897340727e-02), SC_(4.7946733400930347798831724061773506453356261521274285436701505289849800332902629782014328403231797354e-02) }, + { SC_(-3.7301321029663085937500000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000014305114746093750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9884894542085558748198261281226665105707563473967662902233717417789919585586365668107117785676748824e-01), SC_(4.7966490716380906776917513236059635732930235137306330473936925478681743604444507244368925503697776871e-02), SC_(4.7936726935099251332962549955311982568754220652884694250178964216891229721756133703724300833417873220e-02) }, + { SC_(-3.7301321029663085937500000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000033378601074218750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9884800053322777518286027010639325944449428672631354491199619955982388715763941232935413635713386273e-01), SC_(4.7986162909457619436784171981217094349436045665061053131020958274641500350267899222178077906620064086e-02), SC_(4.7916713904809832240694854347114515405949031305739202442950366657403369649264440385034724801113437354e-02) }, + { SC_(-3.7301321029663085937500000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000042915344238281250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9884752794241685177281814388034819622266182061836822776376735766050551822913199661813487761171553118e-01), SC_(4.7995999034531894188181061791780007699592547063320373697384757078514183641285191596718326417467373772e-02), SC_(4.7906707340354307698066856396015402719730742594732622218887608495079435724059545842872281711027901343e-02) }, + { SC_(-3.7301321029663085937500000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000147819519042968750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9884232297543326038608770002890771616117881226724123750877069057326172687020106828624715574982686243e-01), SC_(4.8104197665487255566450445334046446860024366559464112650876503175575173522280411224172226191479757093e-02), SC_(4.7796632962098612434876534391677461366778071717138792900598918391188478278146891016197818628413892516e-02) }, + { SC_(-3.7301321029663085937500000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000290870666503906250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9883520618188656094442545723741889112072524137858741950795911346620393446252964875214651661121158311e-01), SC_(4.8251744958997729782856355993831530775258031132830738841168426330430358644767129149212735614987033393e-02), SC_(4.7646525130527562772454137301364959335446518913076001744796272588168522535454015225744735632981096234e-02) }, + { SC_(-3.7301321029663085937500000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000371932983398437500000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9883116354307066375357648023573603071848031304015961899178849367381945566316461842889014769257016251e-01), SC_(4.8335356988395413823116124116965570034960397598529377901503533920747148842234337683758463899757491677e-02), SC_(4.7561460746209608329387379461055246799942952449896525646960067576756892567585755712817712026688217943e-02) }, + { SC_(-3.7301321029663085937500000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000996589660644531250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9879977386187957378421584308268955720754710834656872025770372117930851502380130941673515536407903258e-01), SC_(4.8979707363950480825462856407705054171535100231494828482031076682070644607992828836462101165987634001e-02), SC_(4.6905885124410934801365709020446864739215036952801770179504371287944255612531666050428145953083479929e-02) }, + { SC_(-3.7301321029663085937500000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0001597404479980468750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9876918533209429301847668105942393964506072473372678163817667069368803591028328738127139425992104707e-01), SC_(4.9599540633605490351595738331650863461228130910801032634454858207552088074852228196398880355656626972e-02), SC_(4.6275198977371426876988957737001427834950148778468835405976221025560682864073752302857007809789671278e-02) }, + { SC_(-3.7301321029663085937500000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0002679824829101562500000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9871309469784108153217075732685412542923014074289296889075241954178785619479870059717722817000268388e-01), SC_(5.0716412324425238255863353821098353785851543326334904112739303539383628170392015657141530299160026178e-02), SC_(4.5138636089666923850886980782504691325294057987373770645625196731894179709070622317602006304584277816e-02) }, + { SC_(-3.7301321029663085937500000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0007553100585937500000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9844488576463040849667006713557075070979541720020951503058388950804407348075464568603069085585652741e-01), SC_(5.5747736191294206286918350505202186358057536911360398778472260156311743588118293052930563147292452169e-02), SC_(4.0016446286618777391516143355010334736500463418001764201909725908665568010714905993948947357429081489e-02) }, + { SC_(-3.7301321029663085937500000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0012483596801757812500000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9814735532827967677710397737101870105197240105729104487104473579791998615872184246731575441258339540e-01), SC_(6.0842888254593837465209677375391817316105531458115344815449663418792266587914446692533472501724137846e-02), SC_(3.4825673806378223854416743345768709046750138031888498314419767132398576036290680446789151555269210869e-02) }, + { SC_(-3.7301321029663085937500000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0023207664489746093750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), 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SC_(9.9915879545421819350530688005623615186240544270827593274622412564050735515128475466608299752025526140e-01), SC_(4.1008553576976706311793253202245137451698422113077721150856829330199964424353347050839790650622532029e-02), SC_(-1.3154931678629558158982660699935247723551027344608329867102808264119755379967383078768146573341990972e-02) }, + { SC_(4.9646129608154296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0012483596801757812500000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(9.9827648539531403745215917352563214138968446312144447102479978693505240691548978979441840473622948646e-01), SC_(5.8686103182775385959094432164210470495146664187835729337215293512993909532328740626483958923893141231e-02), SC_(-3.0893124798500284820335880409303644182778189826173654652430374404846006649343381743921738919251947699e-02) }, + { SC_(4.9646129608154296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0023207664489746093750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(9.9526992589997827420306117917427182178979741082729092965897483434868497193943333068777040666157481100e-01), SC_(9.7148209448510965618814190119451117927847310257093339481999337817751394945307795550093447421264799168e-02), SC_(-6.9532095588469802480589239010157975152091841708321990467488846359840797625840328044562828776517609113e-02) }, + { SC_(4.9646129608154296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0060424804687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(9.7327357090730138720367359153239323902247504897821653720406237386695349159240208217001492967466592893e-01), SC_(2.2964876697546228888931649787788742930944361620108470728002449961617243383843764035729632038084809597e-01), SC_(-2.0311659859397708228829612914540972881961033272228812487026550233039579579564016302202736438925829861e-01) }, + { SC_(4.9646129608154296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0155692100524902343750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(8.4069051112564740388498305703743050846741943876819566564676351892344788777074732833738047977587592836e-01), SC_(5.4151589496828042658602571182616923878595213758699386834940240440502083614232854508648303249637786229e-01), SC_(-5.2063493838617445779646407770009371209785483807741597530330738738065076402146210854614754006055477215e-01) }, + { SC_(4.9646129608154296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0305857658386230468750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(4.8671357579638665629126370168770921319757407213502466576345439294626879685237098285286502834996393092e-01), SC_(8.7356161496227327149253838986791328231133879539230423927448398220130445285498224963240552394450600870e-01), SC_(-8.6509962228485538958789361261824061503929655387763193064181839580439422746694246738587153880942281811e-01) }, + { SC_(4.9646129608154296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0623893737792968750000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-2.2293187234404279005404405123453640992362355261738577610576210777344443465871289033909805344032394449e-01), SC_(9.7483402704931233304677248889105249284034868811789307005518001217555908178599047906139783223849231970e-01), SC_(-9.7154855780636670580019454689623684007923466283994781397066875280116362115119765459157832338091463773e-01) } + }}; +//#undef SC_ + diff --git a/test/test_instances.hpp b/test/test_instances.hpp index 3214a7c07..cb07620b1 100644 --- a/test/test_instances.hpp +++ b/test/test_instances.hpp @@ -365,4 +365,32 @@ namespace boost{ namespace math{ template tools::promote_args::type zeta(BOOST_MATH_TEST_TYPE s); + // Jacobi Functions: + template tools::promote_args::type jacobi_elliptic(BOOST_MATH_TEST_TYPE k, BOOST_MATH_TEST_TYPE theta, BOOST_MATH_TEST_TYPE* pcn, BOOST_MATH_TEST_TYPE* pdn, const policies::policy<>&); + template tools::promote_args::type jacobi_elliptic(BOOST_MATH_TEST_TYPE k, BOOST_MATH_TEST_TYPE theta, BOOST_MATH_TEST_TYPE* pcn, BOOST_MATH_TEST_TYPE* pdn); + template tools::promote_args::type jacobi_sn(BOOST_MATH_TEST_TYPE k, BOOST_MATH_TEST_TYPE theta, const policies::policy<>& pol); + template tools::promote_args::type jacobi_sn(BOOST_MATH_TEST_TYPE k, BOOST_MATH_TEST_TYPE theta); + template tools::promote_args::type jacobi_cn(BOOST_MATH_TEST_TYPE k, BOOST_MATH_TEST_TYPE theta, const policies::policy<>& pol); + template tools::promote_args::type jacobi_cn(BOOST_MATH_TEST_TYPE k, BOOST_MATH_TEST_TYPE theta); + template tools::promote_args::type jacobi_dn(BOOST_MATH_TEST_TYPE k, BOOST_MATH_TEST_TYPE theta, const policies::policy<>& pol); + template tools::promote_args::type jacobi_dn(BOOST_MATH_TEST_TYPE k, BOOST_MATH_TEST_TYPE theta); + template tools::promote_args::type jacobi_cd(BOOST_MATH_TEST_TYPE k, BOOST_MATH_TEST_TYPE theta, const policies::policy<>& pol); + template tools::promote_args::type jacobi_cd(BOOST_MATH_TEST_TYPE k, BOOST_MATH_TEST_TYPE theta); + template tools::promote_args::type jacobi_dc(BOOST_MATH_TEST_TYPE k, BOOST_MATH_TEST_TYPE theta, const policies::policy<>& pol); + template tools::promote_args::type jacobi_dc(BOOST_MATH_TEST_TYPE k, BOOST_MATH_TEST_TYPE theta); + template tools::promote_args::type jacobi_ns(BOOST_MATH_TEST_TYPE k, BOOST_MATH_TEST_TYPE theta, const policies::policy<>& pol); + template tools::promote_args::type jacobi_ns(BOOST_MATH_TEST_TYPE k, BOOST_MATH_TEST_TYPE theta); + template tools::promote_args::type jacobi_sd(BOOST_MATH_TEST_TYPE k, BOOST_MATH_TEST_TYPE theta, const policies::policy<>& pol); + template tools::promote_args::type jacobi_sd(BOOST_MATH_TEST_TYPE k, BOOST_MATH_TEST_TYPE theta); + template tools::promote_args::type jacobi_ds(BOOST_MATH_TEST_TYPE k, BOOST_MATH_TEST_TYPE theta, const policies::policy<>& pol); + template tools::promote_args::type jacobi_ds(BOOST_MATH_TEST_TYPE k, BOOST_MATH_TEST_TYPE theta); + template tools::promote_args::type jacobi_nc(BOOST_MATH_TEST_TYPE k, BOOST_MATH_TEST_TYPE theta, const policies::policy<>& pol); + template tools::promote_args::type jacobi_nc(BOOST_MATH_TEST_TYPE k, BOOST_MATH_TEST_TYPE theta); + template tools::promote_args::type jacobi_nd(BOOST_MATH_TEST_TYPE k, BOOST_MATH_TEST_TYPE theta, const policies::policy<>& pol); + template tools::promote_args::type jacobi_nd(BOOST_MATH_TEST_TYPE k, BOOST_MATH_TEST_TYPE theta); + template tools::promote_args::type jacobi_sc(BOOST_MATH_TEST_TYPE k, BOOST_MATH_TEST_TYPE theta, const policies::policy<>& pol); + template tools::promote_args::type jacobi_sc(BOOST_MATH_TEST_TYPE k, BOOST_MATH_TEST_TYPE theta); + template tools::promote_args::type jacobi_cs(BOOST_MATH_TEST_TYPE k, BOOST_MATH_TEST_TYPE theta, const policies::policy<>& pol); + template tools::promote_args::type jacobi_cs(BOOST_MATH_TEST_TYPE k, BOOST_MATH_TEST_TYPE theta); + }} // namespaces diff --git a/test/test_jacobi.cpp b/test/test_jacobi.cpp new file mode 100644 index 000000000..e31b3ccce --- /dev/null +++ b/test/test_jacobi.cpp @@ -0,0 +1,114 @@ +// Copyright John Maddock 2012 + +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include +#include + +// +// DESCRIPTION: +// ~~~~~~~~~~~~ +// +// This file tests the Jacobi Elliptic Functions. +// There are two sets of tests, spot +// tests which compare our results with selected values computed +// using the online special function calculator at +// functions.wolfram.com, while the bulk of the accuracy tests +// use values generated with NTL::RR at 1000-bit precision +// and our generic versions of these functions. +// +// Note that when this file is first run on a new platform many of +// these tests will fail: the default accuracy is 1 epsilon which +// is too tight for most platforms. In this situation you will +// need to cast a human eye over the error rates reported and make +// a judgement as to whether they are acceptable. Either way please +// report the results to the Boost mailing list. Acceptable rates of +// error are marked up below as a series of regular expressions that +// identify the compiler/stdlib/platform/data-type/test-data/test-function +// along with the maximum expected peek and RMS mean errors for that +// test. +// + +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + const char* largest_type; +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + if(boost::math::policies::digits >() == boost::math::policies::digits >()) + { + largest_type = "(long\\s+)?double|real_concept"; + } + else + { + largest_type = "long double|real_concept"; + } +#else + largest_type = "(long\\s+)?double"; +#endif + + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + largest_type, // test type(s) + ".*Mathworld.*", // test data group + ".*", 500, 250); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + largest_type, // test type(s) + ".*Large Phi.*", // test data group + ".*", 50000, 5000); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + largest_type, // test type(s) + ".*near 1.*", // test data group + ".*", 7000, 500); // test function + // + // Catch all cases come last: + // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + largest_type, // test type(s) + ".*", // test data group + ".*", 50, 20); // test function + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + + +int test_main(int, char* []) +{ + expected_results(); + BOOST_MATH_CONTROL_FP; + + test_spots(0.0F, "float"); + test_spots(0.0, "double"); +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + test_spots(0.0L, "long double"); +#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS + test_spots(boost::math::concepts::real_concept(0), "real_concept"); +#endif +#else + std::cout << "The long double tests have been disabled on this platform " + "either because the long double overloads of the usual math functions are " + "not available at all, or because they are too inaccurate for these tests " + "to pass." << std::cout; +#endif + + return 0; +} diff --git a/test/test_jacobi.hpp b/test/test_jacobi.hpp new file mode 100644 index 000000000..08567f539 --- /dev/null +++ b/test/test_jacobi.hpp @@ -0,0 +1,182 @@ +// Copyright John Maddock 2006. +// Copyright Paul A. Bristow 2007, 2009 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning(disable : 4756) // overflow in constant arithmetic +// Constants are too big for float case, but this doesn't matter for test. +#endif + +#include +#include +#include +#include +#include +#include "functor.hpp" + +#include "handle_test_result.hpp" +#include "table_type.hpp" + +#include + +#ifndef SC_ +#define SC_(x) static_cast::type>(BOOST_JOIN(x, L)) +#endif + +template +void do_test_sn(T& data, const char* type_name, const char* test) +{ + typedef typename T::value_type row_type; + typedef Real value_type; + + std::cout << "Testing: " << test << std::endl; + +#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) + value_type (*fp2)(value_type, value_type) = boost::math::jacobi_sn; +#else + value_type (*fp2)(value_type, value_type) = boost::math::jacobi_sn; +#endif + boost::math::tools::test_result result; + + result = boost::math::tools::test_hetero( + data, + bind_func(fp2, 1, 0), + extract_result(2)); + handle_test_result(result, data[result.worst()], result.worst(), + type_name, "boost::math::jacobi_sn", test); + +#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) + fp2 = boost::math::jacobi_cn; +#else + fp2 = boost::math::jacobi_cn; +#endif + result = boost::math::tools::test_hetero( + data, + bind_func(fp2, 1, 0), + extract_result(3)); + handle_test_result(result, data[result.worst()], result.worst(), + type_name, "boost::math::jacobi_cn", test); + +#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) + fp2 = boost::math::jacobi_dn; +#else + fp2 = boost::math::jacobi_dn; +#endif + result = boost::math::tools::test_hetero( + data, + bind_func(fp2, 1, 0), + extract_result(4)); + handle_test_result(result, data[result.worst()], result.worst(), + type_name, "boost::math::jacobi_dn", test); + + std::cout << std::endl; + +} + +template +void test_spots(T, const char* type_name) +{ + // Function values calculated on http://functions.wolfram.com/ + // Note that Mathematica's Sn/Cn/Dn accepts k^2 as the second parameter. + // Arguments here are theta, k, sn, cn, dn + static const boost::array, 36> data1 = {{ + {{ SC_(0), SC_(0), SC_(0), SC_(1), SC_(1) }}, + {{ ldexp(T(1), -25), ldexp(T(1), -25), SC_(2.98023223876953080883700663838486782870427050521881839342311e-8), SC_(0.99999999999999955591079014993741669975171697261290223678373), SC_(0.99999999999999999999999999999960556954738949421406900774443) }}, + {{ -ldexp(T(1), -25), ldexp(T(1), -25), SC_(-2.98023223876953080883700663838486782870427050521881839342311e-8), SC_(0.99999999999999955591079014993741669975171697261290223678373), SC_(0.99999999999999999999999999999960556954738949421406900774443) }}, + {{ SC_(0.25), ldexp(T(1), -25), SC_(0.247403959254522927383635623557663763268693729825996390997241), SC_(0.968912421710644784709721529742747886950140086772629513814665), SC_(0.99999999999999997281786831901333837240938011109848356555885) }}, + {{ SC_(-0.25), ldexp(T(1), -25), SC_(-0.247403959254522927383635623557663763268693729825996390997241), SC_(0.968912421710644784709721529742747886950140086772629513814665), SC_(0.99999999999999997281786831901333837240938011109848356555885) }}, + {{ SC_(1.25), ldexp(T(1), -25), SC_(0.948984619355586147780156037971989352776684194861616269831136), SC_(0.315322362395268865789580233344649598639316847638615703458263), SC_(0.99999999999999960006577747263860127231780811081154547949983) }}, + {{ SC_(-1.25), ldexp(T(1), -25), SC_(-0.948984619355586147780156037971989352776684194861616269831136), SC_(0.315322362395268865789580233344649598639316847638615703458263), SC_(0.99999999999999960006577747263860127231780811081154547949983) }}, + {{ SC_(25), ldexp(T(1), -25), SC_(-0.132351750097778560056127137329035522219365438979106560464704), SC_(0.991202811863472859528158119981178957382802975691690722810123), SC_(0.99999999999999999222089563757583834413059580275315226870704) }}, + {{ SC_(-25), ldexp(T(1), -25), SC_(0.132351750097778560056127137329035522219365438979106560464704), SC_(0.991202811863472859528158119981178957382802975691690722810123), SC_(0.99999999999999999222089563757583834413059580275315226870704) }}, + {{ ldexp(T(1), -25), SC_(0.5), SC_(2.98023223876953058825550995757802173334628440851964836958219e-8), SC_(0.99999999999999955591079014993744956895610118130967536624417), SC_(0.99999999999999988897769753748438088116649141278818704012037) }}, + {{ -ldexp(T(1), -25), SC_(0.5), SC_(-2.98023223876953058825550995757802173334628440851964836958219e-8), SC_(0.99999999999999955591079014993744956895610118130967536624417), SC_(0.99999999999999988897769753748438088116649141278818704012037) }}, + {{ SC_(0.25), SC_(0.5), SC_(0.246781405136141600483623741101255389743847413013817188632739), SC_(0.969071172865559727608777289021929824625726812182428398055476), SC_(0.992358168465276394946615469032829292963938826683866720698130) }}, + {{ SC_(-0.25), SC_(0.5), SC_(-0.246781405136141600483623741101255389743847413013817188632739), SC_(0.969071172865559727608777289021929824625726812182428398055476), SC_(0.992358168465276394946615469032829292963938826683866720698130) }}, + {{ SC_(1.25), SC_(0.5), SC_(0.928561236426319775700204388269999130782711902203415239399579), SC_(0.371179242693370810357222594552131893184749696381729988511999), SC_(0.885688154799196841458565445994481097477880319663264816077719) }}, + {{ SC_(-1.25), SC_(0.5), SC_(-0.928561236426319775700204388269999130782711902203415239399579), SC_(0.371179242693370810357222594552131893184749696381729988511999), SC_(0.885688154799196841458565445994481097477880319663264816077719) }}, + {{ SC_(25), SC_(0.5), SC_(-0.969223071486651608400225080456020493867827336842041561445359), SC_(-0.246184154035106463351874891855925292474628176040625311168501), SC_(0.874729477852721764836147376110255133761608728373832418508248) }}, + {{ SC_(-25), SC_(0.5), SC_(0.969223071486651608400225080456020493867827336842041561445359), SC_(-0.246184154035106463351874891855925292474628176040625311168501), SC_(0.874729477852721764836147376110255133761608728373832418508248) }}, + {{ ldexp(T(1), -25), 1 - ldexp(T(1), -9), SC_(2.98023223876953036939562331632512854347569015560128614888589e-8), SC_(0.99999999999999955591079014993754766348947956082687878223721), SC_(0.99999999999999955764381956001984590118394542979655101564079) }}, + {{ -ldexp(T(1), -25), 1 - ldexp(T(1), -9), SC_(-2.98023223876953036939562331632512854347569015560128614888589e-8), SC_(0.99999999999999955591079014993754766348947956082687878223721), SC_(0.99999999999999955764381956001984590118394542979655101564079) }}, + {{ SC_(0.25), 1 - ldexp(T(1), -9), SC_(0.244928335616519632082236089277654937383208524525331032303082), SC_(0.969541185516180906431546524888118346090913555188425579774305), SC_(0.969661908643964623248878987955178702010392829596222190545649) }}, + {{ SC_(-0.25), 1 - ldexp(T(1), -9), SC_(-0.244928335616519632082236089277654937383208524525331032303082), SC_(0.969541185516180906431546524888118346090913555188425579774305), SC_(0.969661908643964623248878987955178702010392829596222190545649) }}, + {{ SC_(1.25), 1 - ldexp(T(1), -9), SC_(0.848768940045053312079390719205939167551169094157365783446523), SC_(0.528763923140371497228677918580246099580380684604621321430057), SC_(0.531415689278260818860813380561526095359692710060403584603095) }}, + {{ SC_(-1.25), 1 - ldexp(T(1), -9), SC_(-0.848768940045053312079390719205939167551169094157365783446523), SC_(0.528763923140371497228677918580246099580380684604621321430057), SC_(0.531415689278260818860813380561526095359692710060403584603095) }}, + {{ SC_(25), 1 - ldexp(T(1), -9), SC_(-0.0252326124525503880903568715488227138184083895871544015366337), SC_(-0.999681606947341709011836635135181960590782564534371631099332), SC_(0.999682849652724146508471774051629114156076052044812654903417) }}, + {{ SC_(-25), 1 - ldexp(T(1), -9), SC_(0.0252326124525503880903568715488227138184083895871544015366337), SC_(-0.999681606947341709011836635135181960590782564534371631099332), SC_(0.999682849652724146508471774051629114156076052044812654903417) }}, + + // Try modulus > 1 + {{ ldexp(T(1), -25), SC_(1.5), SC_(2.98023223876952981622027157475276613133414644789222481971590e-8), SC_(0.999999999999999555910790149937712522591174851747994454928040), SC_(0.999999999999999000799277837359575841918151654603571877092161) }}, + {{ -ldexp(T(1), -25), SC_(1.5), SC_(-2.98023223876952981622027157475276613133414644789222481971590e-8), SC_(0.999999999999999555910790149937712522591174851747994454928040), SC_(0.999999999999999000799277837359575841918151654603571877092161) }}, + {{ SC_(0.25), SC_(1.5), SC_(0.241830488135945315134822478837394038661484435596992059686086), SC_(0.970318512143270619246031961334217540099946232418710982266812), SC_(0.931888155181641649031244632258710371461078255228024421800363) }}, + {{ SC_(-0.25), SC_(1.5), SC_(-0.241830488135945315134822478837394038661484435596992059686086), SC_(0.970318512143270619246031961334217540099946232418710982266812), SC_(0.931888155181641649031244632258710371461078255228024421800363) }}, + {{ SC_(1.25), SC_(1.5), SC_(0.665875890711922169121186264316618499018039094009893317545462), SC_(0.746062529663971452521312655373498959968622875614588791642250), SC_(-0.0486921028438866868299166778939466685768843580182675008164949) }}, + {{ SC_(-1.25), SC_(1.5), SC_(-0.665875890711922169121186264316618499018039094009893317545462), SC_(0.746062529663971452521312655373498959968622875614588791642250), SC_(-0.0486921028438866868299166778939466685768843580182675008164949) }}, + {{ SC_(25), SC_(1.5), SC_(0.618665338981368217712277210270169521641154921220796362724248), SC_(0.785654630447163313102421517325310755764805805534154371583941), SC_(0.372585153048138377269609818284480926623056458773704266654150) }}, + {{ SC_(-25), SC_(1.5), SC_(-0.618665338981368217712277210270169521641154921220796362724248), SC_(0.785654630447163313102421517325310755764805805534154371583941), SC_(0.372585153048138377269609818284480926623056458773704266654150) }}, + + // Special Values: + {{ SC_(0), SC_(0.5), SC_(0), SC_(1), SC_(1) }}, + {{ SC_(5), SC_(0), SC_(-0.958924274663138468893154406155993973352461543964601778131672), SC_(0.283662185463226264466639171513557308334422592252215944930359), SC_(1) }}, + {{ SC_(5), SC_(1), SC_(0.999909204262595131210990447534473021089812615990547862736429), SC_(0.0134752822213045573055191382448821552908373539417006868332819), SC_(0.0134752822213045573055191382448821552908373539417006868332819) }}, + }}; + do_test_sn(data1, type_name, "Jacobi Elliptic: Mathworld Data"); + +#include "jacobi_elliptic.ipp" + do_test_sn(jacobi_elliptic, type_name, "Jacobi Elliptic: Random Data"); +#include "jacobi_elliptic_small.ipp" + do_test_sn(jacobi_elliptic_small, type_name, "Jacobi Elliptic: Random Small Values"); +#include "jacobi_near_1.ipp" + do_test_sn(jacobi_near_1, type_name, "Jacobi Elliptic: Modulus near 1"); +#include "jacobi_large_phi.ipp" + do_test_sn(jacobi_large_phi, type_name, "Jacobi Elliptic: Large Phi"); + + // + // Sanity checks for all the various derived functions - these are all + // trivial wrappers around the main three that are tested above - so just + // use a simple sanity check for each one. + // Test values are from functions.wolfram.com: + // + T tol = boost::math::tools::epsilon() * 100; + boost::math::policies::policy<> pol; + BOOST_CHECK_CLOSE_FRACTION(boost::math::jacobi_cd(T(0.5), T(0.5)), static_cast(0.905869360370352996327275878479104183407762212476128499788493L), tol); + BOOST_CHECK_CLOSE_FRACTION(boost::math::jacobi_cd(T(0.5), T(0.5), pol), static_cast(0.905869360370352996327275878479104183407762212476128499788493L), tol); + + BOOST_CHECK_CLOSE_FRACTION(boost::math::jacobi_cn(T(0.5), T(0.5)), static_cast(0.879941022963758342138211939938800035594045353539382810624647L), tol); + BOOST_CHECK_CLOSE_FRACTION(boost::math::jacobi_cn(T(0.5), T(0.5), pol), static_cast(0.879941022963758342138211939938800035594045353539382810624647L), tol); + + BOOST_CHECK_CLOSE_FRACTION(boost::math::jacobi_cs(T(0.5), T(0.5)), static_cast(1.85218402142505803268146025319200184620073865036147924150565L), tol); + BOOST_CHECK_CLOSE_FRACTION(boost::math::jacobi_cs(T(0.5), T(0.5), pol), static_cast(1.85218402142505803268146025319200184620073865036147924150565L), tol); + + BOOST_CHECK_CLOSE_FRACTION(boost::math::jacobi_dc(T(0.5), T(0.5)), static_cast(1.10391193669599654696698383614539220889596741980833071370343L), tol); + BOOST_CHECK_CLOSE_FRACTION(boost::math::jacobi_dc(T(0.5), T(0.5), pol), static_cast(1.10391193669599654696698383614539220889596741980833071370343L), tol); + + BOOST_CHECK_CLOSE_FRACTION(boost::math::jacobi_dn(T(0.5), T(0.5)), static_cast(0.971377398838178842823315157470233933307542433588855341182382L), tol); + BOOST_CHECK_CLOSE_FRACTION(boost::math::jacobi_dn(T(0.5), T(0.5), pol), static_cast(0.971377398838178842823315157470233933307542433588855341182382L), tol); + + BOOST_CHECK_CLOSE_FRACTION(boost::math::jacobi_ds(T(0.5), T(0.5)), static_cast(2.04464805020871497502900445828888632133468724223115900866414L), tol); + BOOST_CHECK_CLOSE_FRACTION(boost::math::jacobi_ds(T(0.5), T(0.5), pol), static_cast(2.04464805020871497502900445828888632133468724223115900866414L), tol); + + BOOST_CHECK_CLOSE_FRACTION(boost::math::jacobi_nc(T(0.5), T(0.5)), static_cast(1.13643979983097851593855424992691981204889859711476187519109L), tol); + BOOST_CHECK_CLOSE_FRACTION(boost::math::jacobi_nc(T(0.5), T(0.5), pol), static_cast(1.13643979983097851593855424992691981204889859711476187519109L), tol); + + BOOST_CHECK_CLOSE_FRACTION(boost::math::jacobi_nd(T(0.5), T(0.5)), static_cast(1.02946599457230050141998045852435702297405263760707971258676L), tol); + BOOST_CHECK_CLOSE_FRACTION(boost::math::jacobi_nd(T(0.5), T(0.5), pol), static_cast(1.02946599457230050141998045852435702297405263760707971258676L), tol); + + BOOST_CHECK_CLOSE_FRACTION(boost::math::jacobi_ns(T(0.5), T(0.5)), static_cast(2.10489563855842977359275221390569031239706339764770047142101L), tol); + BOOST_CHECK_CLOSE_FRACTION(boost::math::jacobi_ns(T(0.5), T(0.5), pol), static_cast(2.10489563855842977359275221390569031239706339764770047142101L), tol); + + BOOST_CHECK_CLOSE_FRACTION(boost::math::jacobi_sc(T(0.5), T(0.5)), static_cast(0.539903156723383602910722041849329275299051877814755451255071L), tol); + BOOST_CHECK_CLOSE_FRACTION(boost::math::jacobi_sc(T(0.5), T(0.5), pol), static_cast(0.539903156723383602910722041849329275299051877814755451255071L), tol); + + BOOST_CHECK_CLOSE_FRACTION(boost::math::jacobi_sd(T(0.5), T(0.5)), static_cast(0.489081727242945953222289853693492188561192086497066116267160L), tol); + BOOST_CHECK_CLOSE_FRACTION(boost::math::jacobi_sd(T(0.5), T(0.5), pol), static_cast(0.489081727242945953222289853693492188561192086497066116267160L), tol); + + BOOST_CHECK_CLOSE_FRACTION(boost::math::jacobi_sn(T(0.5), T(0.5)), static_cast(0.475082936028536510082218324703870258745078171807428948028252L), tol); + BOOST_CHECK_CLOSE_FRACTION(boost::math::jacobi_sn(T(0.5), T(0.5), pol), static_cast(0.475082936028536510082218324703870258745078171807428948028252L), tol); + +} + From 7e2f70a685cb85ab6b2304b73d7927f688aa5e93 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 17 May 2012 10:13:27 +0000 Subject: [PATCH 003/115] Fix some gcc-linux test errors and warnings. Update docs to match. [SVN r78493] --- doc/sf_and_dist/html/index.html | 2 +- doc/sf_and_dist/html/index/s13.html | 4 +- doc/sf_and_dist/html/index/s14.html | 4 +- doc/sf_and_dist/html/index/s15.html | 4 +- doc/sf_and_dist/html/index/s16.html | 4 +- doc/sf_and_dist/html/index/s17.html | 4 +- .../main_overview/conventions.html | 2 +- .../main_overview/navigation.html | 2 +- .../special/jacobi/jacobi_elliptic.html | 18 +- doc/sf_and_dist/jacobi_elliptic.qbk | 6 +- test/jacobi_elliptic.ipp | 800 ++-- test/jacobi_elliptic_small.ipp | 3362 ++++++++--------- test/jacobi_large_phi.ipp | 600 +-- test/jacobi_near_1.ipp | 680 ++-- test/test_jacobi.cpp | 21 + 15 files changed, 2769 insertions(+), 2744 deletions(-) diff --git a/doc/sf_and_dist/html/index.html b/doc/sf_and_dist/html/index.html index 85dacbe28..7aade3401 100644 --- a/doc/sf_and_dist/html/index.html +++ b/doc/sf_and_dist/html/index.html @@ -570,7 +570,7 @@

    - +

    Last revised: May 16, 2012 at 16:09:40 GMT

    Last revised: May 17, 2012 at 10:07:59 GMT


    diff --git a/doc/sf_and_dist/html/index/s13.html b/doc/sf_and_dist/html/index/s13.html index 9e64e628d..f5454540a 100644 --- a/doc/sf_and_dist/html/index/s13.html +++ b/doc/sf_and_dist/html/index/s13.html @@ -22,9 +22,9 @@
    PrevUpHomeNext
    -
    +

    -Function Index

    +Function Index

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    diff --git a/doc/sf_and_dist/html/index/s14.html b/doc/sf_and_dist/html/index/s14.html index f39426b2c..6902d2e2b 100644 --- a/doc/sf_and_dist/html/index/s14.html +++ b/doc/sf_and_dist/html/index/s14.html @@ -22,9 +22,9 @@
    PrevUpHomeNext
    -
    +

    -Class Index

    +Class Index

    B C D E F G H I L M N P R S T U W

    diff --git a/doc/sf_and_dist/html/index/s15.html b/doc/sf_and_dist/html/index/s15.html index d00091a6d..18073d047 100644 --- a/doc/sf_and_dist/html/index/s15.html +++ b/doc/sf_and_dist/html/index/s15.html @@ -22,9 +22,9 @@
    PrevUpHomeNext
    -
    +

    -Typedef Index

    +Typedef Index

    A B C D E F G H I L N O P R S T U V W

    diff --git a/doc/sf_and_dist/html/index/s16.html b/doc/sf_and_dist/html/index/s16.html index 49c699e23..7e48607e9 100644 --- a/doc/sf_and_dist/html/index/s16.html +++ b/doc/sf_and_dist/html/index/s16.html @@ -22,9 +22,9 @@
    PrevUpHomeNext
    -
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    -Macro Index

    +Macro Index

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    diff --git a/doc/sf_and_dist/html/index/s17.html b/doc/sf_and_dist/html/index/s17.html index eadce3121..2cc4aaef7 100644 --- a/doc/sf_and_dist/html/index/s17.html +++ b/doc/sf_and_dist/html/index/s17.html @@ -21,9 +21,9 @@
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    diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html b/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html index d573de825..2425d341c 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html @@ -27,7 +27,7 @@ Document Conventions

    - +

    This documentation aims to use of the following naming and formatting conventions. diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html index 32cfa7acb..853c7b232 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html @@ -27,7 +27,7 @@ Navigation

- +

Boost.Math documentation is provided in both HTML and PDF formats. diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_elliptic.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_elliptic.html index 148a98815..42584a0f1 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_elliptic.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_elliptic.html @@ -156,11 +156,13 @@ Accuracy

- These functions are computed using only basic arithmetic operations, so - there isn't much variation in accuracy over differing platforms. Note that - only results for the widest floating point type on the system are given - as narrower types have effectively zero error. - All values are relative errors in units of epsilon. + These functions are computed using only basic arithmetic operations and + trigomometric functions, so there isn't much variation in accuracy over + differing platforms. Typically errors are trivially small for small angles, + and as is typical for cyclic functions, grow as the angle increases. Note + that only results for the widest floating point type on the system are + given as narrower types have effectively zero + error. All values are relative errors in units of epsilon.

Table 47. Errors Rates in the Jacobi Elliptic Functions

@@ -224,17 +226,17 @@

- Red Hat Linux / G++ 3.4 + Ubuntu Linux / G++ 4.7

- Peak=2.6 Mean=1.7 + Peak=2.0 Mean=0.5

- Peak=2.2 Mean=1.8 + Peak=25000 Mean=1500

diff --git a/doc/sf_and_dist/jacobi_elliptic.qbk b/doc/sf_and_dist/jacobi_elliptic.qbk index faf2635e2..3c6413a67 100644 --- a/doc/sf_and_dist/jacobi_elliptic.qbk +++ b/doc/sf_and_dist/jacobi_elliptic.qbk @@ -88,8 +88,10 @@ these are sine waves, while as /k/ tends to 1 they become hyperbolic functions: [heading Accuracy] -These functions are computed using only basic arithmetic operations, so +These functions are computed using only basic arithmetic operations and trigomometric functions, so there isn't much variation in accuracy over differing platforms. +Typically errors are trivially small for small angles, and as is typical for cyclic +functions, grow as the angle increases. Note that only results for the widest floating point type on the system are given as narrower types have __zero_error. All values are relative errors in units of epsilon. @@ -97,7 +99,7 @@ are relative errors in units of epsilon. [table Errors Rates in the Jacobi Elliptic Functions [[Significand Size] [Platform and Compiler] [[phi] < 1] [Large [phi]] ] [[53] [Win32 / Visual C++ 8.0] [Peak=2 Mean=0.5] [Peak=44000 Mean=2500] ] -[[64] [Red Hat Linux / G++ 3.4] [Peak=2.6 Mean=1.7] [Peak=2.2 Mean=1.8] ] +[[64] [Ubuntu Linux / G++ 4.7] [Peak=2.0 Mean=0.5] [Peak=25000 Mean=1500] ] ] diff --git a/test/jacobi_elliptic.ipp b/test/jacobi_elliptic.ipp index 3ec0407cb..dcaae4f5b 100644 --- a/test/jacobi_elliptic.ipp +++ b/test/jacobi_elliptic.ipp @@ -2,406 +2,406 @@ # define SC_(x) static_cast(BOOST_JOIN(x, L)) #endif static const boost::array, 400> jacobi_elliptic = {{ - { SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.7384321813508780300050309993112921610348339609531096226291156957843807163438391463300771570266454611e-02), SC_(9.9524685071841496279438927849850673342525676921414792528840427410727111940782381944976305408868157855e-01), SC_(9.9995488439733316729114394585903874689886199946693440341361736436672692239264636048488084336908171547e-01) }, - { SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7383306026428126815811673852101862643417212675894886262329096942831342806175591481538515201116435095e-02), SC_(9.9524695011206291426731901545274769005867525867705503210833924341584688692109569818882782443312019870e-01), SC_(9.9992353321916073154296514614318371763529995049379965142148455053362169878708374701587696243287582131e-01) }, - { SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(1.3547700643539428710937500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7382963663268679354766311462039914384149178492941126840831062817834448292082576674044335924290112792e-02), SC_(9.9524698361168545268757042933526662768772514619668023376490370653166168736869277815425438301697322693e-01), SC_(9.9991296657753407444565165371686075323189094367991128619066744668429579140503359966446931860569605749e-01) }, - { SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(1.8838196992874145507812500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7380331287488173017819681812505333548000401340832607031998520409371778408842832201970632399407455377e-02), SC_(9.9524724118097360944629737689090579536626111956092105184429209919209960381948277540779135011872980164e-01), SC_(9.9983172185713251267253025953154802657840786163407200767760200375372426265381549093953869220602182213e-01) }, - { SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(2.2103404998779296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7378277454797060918439287025630752988524259325176347053163180340804501139998370882347991305783292950e-02), SC_(9.9524744213684697238369251137951559191374873239697065458847170083807556278595809556474002748294261664e-01), SC_(9.9976833370589598055738289274893465677056797771478451409770833086130339040015264801585644093126658918e-01) }, - { SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(2.7849817276000976562500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7373867428466078827183319249605829662038878958674322241785141561706308176062148140500575389736858636e-02), SC_(9.9524787361843859046684503694959443606213073331077397309037690642929126741546581484860725317608308903e-01), SC_(9.9963222736499384529570421859460465646281312249068720158613197297025393833765853405888603462853042983e-01) }, - { SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(3.0816698074340820312500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7371193424879810007588652514672604171038551577576512840133215162813719206019907024377008226545048940e-02), SC_(9.9524813523614031580155154272347701177066765446592058958809789667054121097494545539509044453284397477e-01), SC_(9.9954970099303609847458849068667534444745484953685258900209171332658289031259888119908884757012452532e-01) }, - { 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SC_(9.5750665664672851562500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.6712800823285619471798123561258913583803638220534736201364708009370629428320353958750416444955694982e-01), SC_(6.4149405218185064504992339458407016741795699167416304441730489787216690117110750201301703730190120252e-01), SC_(6.7857602589593721337697403304549699145452424462317392210364305668406670401778150852638680470506706518e-01) }}, + {{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.6488833427429199218750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.6593441813020686107904272195284976164911143038148978940760933715399917785398101606027733051459971132e-01), SC_(6.4291870957652293482277601636810697919275457997668849096935959115861162055784408260876292546568984644e-01), SC_(6.7366024601538257589655742562219072544530334312218911862590121331700593411003613779831508617892420325e-01) }}, + {{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.6769475936889648437500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.6547770865632652104311857431350648982519639693036504351701283181609474922881977308885338563907679349e-01), SC_(6.4346241347126103408603307544875846579869659656475523368458255827578551435308991733382243465986469958e-01), SC_(6.7178215521760534606784911003038819524570089099102635584446923804691272196126068898352982615576142014e-01) }}, + {{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.6886777877807617187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.6528633729797841460176785222203390514942625072618331938529597075420681577693034777030027274670865291e-01), SC_(6.4369000454026378494764961458275300252507916799112249356864558832261907901572939091058344628185994802e-01), SC_(6.7099566282750678306967995163385198199449520575839393027024329721293501791261343629006364525136879702e-01) }}, + {{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.9288129806518554687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.6130656170513378346158650596006841065509926127276492299715158864622868192915634720105938405478654273e-01), SC_(6.4839210290125166440291833468322114687478245067783826919074500661090573579759551799996853065323027448e-01), SC_(6.5470204815482800802602415811048971704607358039770120289884409108362609917793951796905679822441221683e-01) }}, + {{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.6070308834386404159049681239553434730978977615881969147142722819631969635063229458010769940901615571e-01), SC_(6.4910000106617422443762696869434170692368988825415526998433303308325407487195203453870690819261137407e-01), SC_(6.5224167903128336698276201258993391810194122946207851950380395682119994293224476046299862066823494348e-01) }} }}; //#undef SC_ diff --git a/test/jacobi_elliptic_small.ipp b/test/jacobi_elliptic_small.ipp index 845aca2c8..13549a684 100644 --- a/test/jacobi_elliptic_small.ipp +++ b/test/jacobi_elliptic_small.ipp @@ -2,1687 +2,1687 @@ # define SC_(x) static_cast(BOOST_JOIN(x, L)) #endif static const boost::array, 1681> jacobi_elliptic_small = {{ - { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.6504814008555523940913182524024344909690304914367592725655712600281923768045401283620998764707764693e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973696151635920379696565170086974190992e-01), SC_(9.9999999999999999999999999999999999999999999999628966995620346223342181461431515637620350243665215080e-01) }, - { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(2.0654207510961697380480472929775714874267578125000000000000000000000000000000000000000000000000000000e-12), SC_(1.6504814008555523940913182524024344909690304914356038800613310054830865914687618301634103078917338168e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973696151826615763590211178195021758793e-01), SC_(9.9999999999999999999999999999999999999999999999418956903357324218784742231100976423667721244640328945e-01) }, - { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(6.9332300317581641024844429921358823776245117187500000000000000000000000000000000000000000000000000000e-12), SC_(1.6504814008555523940913182524024344909690304914027798723391089616386590188266692256822553895004737691e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973696157244157188296862020758148130289e-01), SC_(9.9999999999999999999999999999999999999999999993452696204168490870911613561919090434443527881778962629e-01) }, - { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.3351444949627477853937307372689247131347656250000000000000000000000000000000000000000000000000000000e-11), SC_(1.6504814008555523940913182524024344909690304913052218556582079673621348947108779104417637686162896722e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973696173345926391915144123663683144195e-01), SC_(9.9999999999999999999999999999999999999999999975720048632921041975214334983463922773663246301371558079e-01) }, - { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.6399812063916385795891983434557914733886718750000000000000000000000000000000000000000000000000000000e-11), SC_(1.6504814008555523940913182524024344909690304912372618758507282714946015960583626600059283156291032012e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973696184562594659391558357034445701976e-01), SC_(9.9999999999999999999999999999999999999999999963367292684459290855251530901083881607676209352596350232e-01) }, - { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(5.7301594025283009159466018900275230407714843750000000000000000000000000000000000000000000000000000000e-11), SC_(1.6504814008555523940913182524024344909690304889783532888043627371778016267672955616082803704829236507e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973696557391255574683748524224459833699e-01), SC_(9.9999999999999999999999999999999999999999999552776433700754495454636367587944076648284400103707184302e-01) }, - { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.1137313293829720350913703441619873046875000000000000000000000000000000000000000000000000000000000000e-10), SC_(1.6504814008555523940913182524024344909690304821439689287767962044790479566381944530155678406625631702e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973697685393682827041343608589118700995e-01), SC_(9.9999999999999999999999999999999999999999998310523532852882161708648652005740665368880880910156584491e-01) }, - { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.4214707189097453010617755353450775146484375000000000000000000000000000000000000000000000000000000000e-10), SC_(1.6504814008555523940913182524024344909690304762977332560523723670737117904598123506030905571007525820e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973698650304007112032323166148527367075e-01), SC_(9.9999999999999999999999999999999999999999997247881626734957219094542687145216261006406307420236809325e-01) }, - { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(3.8006320313144215106149204075336456298828125000000000000000000000000000000000000000000000000000000000e-10), SC_(1.6504814008555523940913182524024344909690303831976744007277642905699914309078508034857277902993981434e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973714016295563039085806793646480974079e-01), SC_(9.9999999999999999999999999999999999999999980325535429971135087765023210979692154823009643251966522036e-01) }, - { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(6.0916272026645401638234034180641174316406250000000000000000000000000000000000000000000000000000000000e-10), SC_(1.6504814008555523940913182524024344909690302133731854710685114641012066105734375850645869948919458138e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973742045511601859311127502555051080985e-01), SC_(9.9999999999999999999999999999999999999999949457361664130189602800079536313829981986427076949318817789e-01) }, - { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.0221641311147777742007747292518615722656250000000000000000000000000000000000000000000000000000000000e-09), SC_(1.6504814008555523940913182524024344909690297085106157246959147019549187034633366860135865373130072792e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973825372139737312017993425357327472681e-01), SC_(9.9999999999999999999999999999999999999999857690940760870814533399831245189911999724717703220387897201e-01) }, - { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(2.8819222563924995483830571174621582031250000000000000000000000000000000000000000000000000000000000000e-09), SC_(1.6504814008555523940913182524024344909690242677885948711088664385488861032724509329344622403207481410e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133974723353190001720047690056131101093059e-01), SC_(9.9999999999999999999999999999999999999998868757284550027385876551628249984105649518984138605236580531e-01) }, - { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(4.7627768395841485471464693546295166015625000000000000000000000000000000000000000000000000000000000000e-09), SC_(1.6504814008555523940913182524024344909690134933098417362621376030351507143097515536131758800073666674e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133976501660868597958778702500430601729980e-01), SC_(9.9999999999999999999999999999999999999996910332533889451002177040231472679603830330500099612602677035e-01) }, - { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(8.8541334264391480246558785438537597656250000000000000000000000000000000000000000000000000000000000000e-09), SC_(1.6504814008555523940913182524024344909689717461858586327957602950267806604551468156898254148882224748e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133983391946035930262518846860865434979203e-01), SC_(9.9999999999999999999999999999999999999989322160265823321349052149682027615133455037665915804501555188e-01) }, - { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(2.3050326092288742074742913246154785156250000000000000000000000000000000000000000000000000000000000000e-08), SC_(1.6504814008555523940913182524024344909686323523656956557466573268843129097061735969718419269903756412e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244134039408264810361040874003831061763988570e-01), SC_(9.9999999999999999999999999999999999999927632191511183545177421364285740672490570631107123629541620207e-01) }, - { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(5.9392490925347374286502599716186523437500000000000000000000000000000000000000000000000000000000000000e-08), SC_(1.6504814008555523940913182524024344909663872080081406338583759571333756176566943414887198590991250826e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244134409965165248396214212813572057652287157e-01), SC_(9.9999999999999999999999999999999999999519543189770621643635884806523323694404582563651057704462697028e-01) }, - { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.1667648891489079687744379043579101562500000000000000000000000000000000000000000000000000000000000000e-07), SC_(1.6504814008555523940913182524024344909588293831710191198186747356949388380517396812042654193369934302e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244135657370097707716573801601901386768273769e-01), SC_(9.9999999999999999999999999999999999998145794021824142620974495770659414222168637044587970657748003597e-01) }, - { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(2.3799674409019644372165203094482421875000000000000000000000000000000000000000000000000000000000000000e-07), SC_(1.6504814008555523940913182524024344909265858679866731016390766452234122292419645132917080994605064614e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244140979102308704385651739160793286510212057e-01), SC_(9.9999999999999999999999999999999999992285046636067702713907942013032905297195860994461375719475855459e-01) }, - { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(4.6846594159433152526617050170898437500000000000000000000000000000000000000000000000000000000000000000e-07), SC_(1.6504814008555523940913182524024344908045794234673931872034147213497000375265822385091582975735928436e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244161116039055063020239008290949554874460617e-01), SC_(9.9999999999999999999999999999999999970108526902606423004774330258537078837146430522090471722713952519e-01) }, - { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(9.3826997726864647120237350463867187500000000000000000000000000000000000000000000000000000000000000000e-07), SC_(1.6504814008555523940913182524024344903093459707187946270419675021577786501184313307591933565375527000e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244242853399339366916813650688688000362016475e-01), SC_(9.9999999999999999999999999999999999880092343898322941123574529398516994582299038041465074714265274086e-01) }, - { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.1039855962735600769519805908203125000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(1.6504814008555523940913182524024344900557430873575286480834184767300136835270193965664311004583807788e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244284710083558477870086857644172480108004954e-01), SC_(9.9999999999999999999999999999999999833996177671340856797365910449015966708782329210939364313955500541e-01) }, - { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(3.2917760108830407261848449707031250000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(1.6504814008555523940913182524024344828493076459684986213773022347093484446159289129769394585309247486e-12), SC_(9.9999999999999999999999863795557271494668646082344582907245474118849806364601873345118093854029707223e-01), SC_(9.9999999999999999999999999999999998524117356076599440004095602362538092572757468874215804799068642818e-01) }, - { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(7.5172138167545199394226074218750000000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(1.6504814008555523940913182524024344486247790091707702262795314936221015531815002316170628477073465482e-12), SC_(9.9999999999999999999999863795557271494668646082344582907251122813646614652970895342707489706828991315e-01), SC_(9.9999999999999999999999999999999992303290762261561334779801430374930423054200867021151405157838736656e-01) }, - { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.5114666894078254699707031250000000000000000000000000000000000000000000000000000000000000000000000000e-05), SC_(1.6504814008555523940913182524024343197792581537814943695196301355019723927496347050918189746703855313e-12), SC_(9.9999999999999999999999863795557271494668646082344582907272388527222151271310577616873634865441592576e-01), SC_(9.9999999999999999999999999999999968883665290214396116379872831911234710973570091992907537181511730001e-01) }, - { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(2.9863993404433131217956542968750000000000000000000000000000000000000000000000000000000000000000000000e-05), SC_(1.6504814008555523940913182524024338226614063923213889688236305211576366686595773701290696153140447922e-12), SC_(9.9999999999999999999999863795557271494668646082344582907354436904058707022213171582426154214436188544e-01), SC_(9.9999999999999999999999999999999878524964216011785539130673086897560712513367984413617815284173143395e-01) }, - { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(3.3870281185954809188842773437500000000000000000000000000000000000000000000000000000000000000000000000e-05), SC_(1.6504814008555523940913182524024336313257796690717232582958808272013242449790984161961450928911993045e-12), SC_(9.9999999999999999999999863795557271494668646082344582907386016493381483439646119915145634254466691917e-01), SC_(9.9999999999999999999999999999999843746815254611571572970309361929540121712190245822855953446615016498e-01) }, - { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(9.0660119894891977310180664062500000000000000000000000000000000000000000000000000000000000000000000000e-05), SC_(1.6504814008555523940913182524024283319260934630243189760434925456680697497307076585496917868114187467e-12), SC_(9.9999999999999999999999863795557271494668646082344582908260672555159766629352771353376223276775491667e-01), SC_(9.9999999999999999999999999999998880500634450812967602838998059802892239606075824273672160120376317752e-01) }, - { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), 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SC_(9.0660119894891977310180664062500000000000000000000000000000000000000000000000000000000000000000000000e-05), SC_(9.9639439263328541366719031725241577314079198743209947847909476415592779981710088614620793535022214474e-01), SC_(-8.4842290922312241463028290901886236468697679576893295365022598381737118235652753487965129582714048961e-02), SC_(9.9999999591995330997524068647525151887288634403876011421441510310561160493295521892857438617062912841e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(2.1949532674625515937805175781250000000000000000000000000000000000000000000000000000000000000000000000e-04), SC_(9.9639439410826067431307822604787492127597668642195114647761391647693455985378034591691491702705577906e-01), SC_(-8.4842273600087509888806940837110422629864742105524848164093163940289071489404486929406333024041952399e-02), SC_(9.9999997608429891075272698981098375011760545789757386788033103243299232149774232751941797398008621709e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(4.3952150736004114151000976562500000000000000000000000000000000000000000000000000000000000000000000000e-04), SC_(9.9639439946057283654855935236752624035880191284049054750658244297828725656065644035418378639820004094e-01), SC_(-8.4842210742085271589035996870541465107472441820952998743617829037111050036348887366217833042583183538e-02), SC_(9.9999990410568885432730450661406780382747893720931957290008095471902273911676718477882188550504429360e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(6.3331518322229385375976562500000000000000000000000000000000000000000000000000000000000000000000000000e-04), SC_(9.9639440713495471434923143724675451317717484796503726041028796498492176802332554253832509916871965935e-01), SC_(-8.4842120613419993829653470484176332143015609165075405322937128639532532687627013454703366335136057687e-02), SC_(9.9999980089947286502621224734144392936772145074199619421807467791812848947570762271107897628498946539e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.1151232756674289703369140625000000000000000000000000000000000000000000000000000000000000000000000000e-03), SC_(9.9639443823016524654104629623362614491579693467989253808727772715845343535280963682357379812867245026e-01), SC_(-8.4841755427344930663007460100028833354954911466256337396719760700291713295727386906732582556927571057e-02), SC_(9.9999938272528249391312307608807398374816383372852435374472406644589615977465186408873728224171642189e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.9624670967459678649902343750000000000000000000000000000000000000000000000000000000000000000000000000e-03), SC_(9.9639453448794504753671533455904797532119598152365059838083231543209853813817276459987896643847885629e-01), SC_(-8.4840624953799622786068044598030741055063642230082296390150800205369862431346329264619378174286838014e-02), SC_(9.9999808822023431586330507223399599331299259546946802809286583619824066393501989056548364182611503082e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(5.5537540465593338012695312500000000000000000000000000000000000000000000000000000000000000000000000000e-03), SC_(9.9639553077217003511353530043413808033920247930882092573188708783469515876938649937674371540560702420e-01), SC_(-8.4828923470981032069634272050225777540758810269842969047296062581637761984301166734820582381456553004e-02), SC_(9.9998468876732348097939012173864087757227234405891503826150435694363062945422284532826470182539791518e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(8.6911283433437347412109375000000000000000000000000000000000000000000000000000000000000000000000000000e-03), SC_(9.9639718000461594989260420944042571499940208837940453162707360749418854616064045702840166901838974039e-01), SC_(-8.4809549455523940355185466702194582862099119856342307034787941990006897379697771484768623427437519652e-02), SC_(9.9996250309238530117640656410289279207641184807525627009919430951232501378233250614276839898342947194e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(2.9933363199234008789062500000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.9642739273361037624425236003709998424423669985681772457419514437854858892669295864838396904074334791e-01), SC_(-8.4453839522542653735176696295242418341771308961936320935099661751459635173562095780038126996050284763e-02), SC_(9.9955509327307226870482882280431162855249849172060889261100838598526189994716425561466757382237089590e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(5.1242604851722717285156250000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.9649068766424200577985721184356752955601723188930074293915835068113130632428255591007970917819025182e-01), SC_(-8.3703700028410244770061826214701529976799484885620218724844567694731485856500558608813841851268272143e-02), SC_(9.9869544539219827767678663556107790796001205357457841120474538750514167458555525624218345986227679244e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.1201295256614685058593750000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.9684313604934398930539235390129770939609825850290918420113575774717084081891501166979587762444196098e-01), SC_(-7.9396234868594807401272204725688142828934281134460946403103848657930854463427457876250364818746217174e-02), SC_(9.9374654270592187744997687020550454797638290050151265651320047733411371840069209832488090292039717367e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(2.3480379581451416015625000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.9814934866490320978806688580871390672680066453416779059422743215014552518552147816785137038565167474e-01), SC_(-6.0810178094045119247364122651955570809342076623943187762098707626057061856818089052462136539473338148e-02), SC_(9.7214764923305873458032862854350162073206678556449933567459172269681798829001261625830288160524321418e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(4.8987305164337158203125000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.9976967292952005755481095245256024937692734652402590999991494952154282866789560889911025306718779168e-01), SC_(2.1461619006973565646536174052546379410807514047370718515791347175325100002601713407336650423975813432e-02), SC_(8.7185717081396898541065289390703478456116878515433892820948672390341209634334005744800539221410270970e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(7.5183129310607910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.8539034324839560936682949899637621959818856082648192169501428326661400191997487509531927187367953439e-01), SC_(1.7031110190709553832350904690514019306839852576492774590778059270526592192267334810770243087477878657e-01), SC_(6.7167349511579774208520897966660216379314520347464078477957664271219777907511857160535742769433089892e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(4.0815375315288640577475196367102453532926947422123146010409415723479279392954356853433706994064428463e-01), SC_(9.1291320167210457006284950226993895289063450955873095160130726593569036267152905012436288527918734100e-01), SC_(-7.3708797978087103688004545584461400336979146221355035197387826317949437602283858594803646637152865976e-01) }} }}; //#undef SC_ diff --git a/test/jacobi_large_phi.ipp b/test/jacobi_large_phi.ipp index 1c509eaa5..a2fc15964 100644 --- a/test/jacobi_large_phi.ipp +++ b/test/jacobi_large_phi.ipp @@ -2,306 +2,306 @@ # define SC_(x) static_cast(BOOST_JOIN(x, L)) #endif static const boost::array, 300> jacobi_large_phi = {{ - { SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.1058797357690320086682997888107252211628291495151688601393407863373061954395848396257429511756176811e-01), SC_(-9.9386633915238026812869743952282655015178929533806734450981604274006648191113417152643248132020074274e-01), SC_(9.9990138922139577345821742312959843927086669798900631576940452344894647029651168866543336495621319962e-01) }, - { SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(1.3547700643539428710937500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.9796027195728077189442848498661232305049387865637023002287165495702857395230146075769449539819678763e-02), SC_(-9.9980403945336507845151345500450800737097833473134761034812701539547907788852267602747381881654129683e-01), SC_(9.9999640368228571150326548705630160155372276544820513372782759452847671460675392468118278515564642670e-01) }, - { SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(2.2103404998779296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-9.4524463054363015830543554229266024611315133648646726829860103132985305860006657410579310878453671719e-01), SC_(-3.2636266396209619739852328880763978392918068940083223909131243802010656037702645968281828914985898722e-01), SC_(9.7793033147839850499560648584765033296353170435094191917820984988398156187728059208365609303718763468e-01) }, - { SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(3.0816698074340820312500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(3.8467092829206275416395221453254971947309775360749050985209931262282264520459122402381792953068010283e-02), SC_(9.9925986748656589242807594841179280186636858779886436718703277243900358292074844422479042190466225049e-01), SC_(9.9992973546117087872258976240789404601766963067622683679015332787486976781350082685530756477017893531e-01) }, - { SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(6.3235926628112792968750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.1828487869642382837142082205368890409594444563859603885036504087100530651689815737374300479572152806e-01), SC_(-5.7481288894454945115324043802657481607935129579981996144467071525751961910351319915758240211691782206e-01), SC_(8.5571342814553735162229894739444873282853333740663537333659164564589208017713251914590680386027272809e-01) }, - { SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(8.1472349166870117187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.0342555778181684908553725700040860110642531214149151205515131896190048290879021057059409802362096946e-01), SC_(5.9540521756445540531188114127706021212880690887199697020660799772318324844598317460087416642725615927e-01), SC_(7.5600167963587697285196939810169457229824831904454088987922148028116675585554507425145383067593756070e-01) }, - { SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(8.3500838279724121093750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-5.2923808769191278344096906576129452977508979277324972114028585485897292732749175191104387817153243622e-01), SC_(-8.4847336230208620189522999730668948980498026956351676759653713074643763505826560196595716137493813219e-01), SC_(8.9705533240946393665356057247371866574922627996248245980741140274917656623741748929349898927165638735e-01) }, - { SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.0579175949096679687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-4.3588329433998778344118299461470119260462800471832395414994779852496041561445544177910644873466410470e-01), SC_(-9.0000319650283441310099684480078605946721143546738341042331933310537915309970277408204072796535470377e-01), SC_(9.1875870906845118047635806822648200063819834288643294354356983053626866318919800547192402870664676236e-01) }, - { SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.1337585449218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-9.5600856122085672092800268968580894468432579079804656774052584258946328842723868281852714693291460848e-01), SC_(2.9333876469438444648579701071867907567539764964724421796135027276816072964646665290023055039395020032e-01), SC_(4.8737075577081420166881282500675564846609614724320216534645035828942396447404446035830276248915799790e-01) }, - { SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.6886777877807617187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-9.7736452897241769061181430418007365494795330898556587924749704567000625360724157676092701517939511727e-01), SC_(-2.1156223081288422793211063644770138572453563413600394268502697586678182945457777132434950354231163677e-01), SC_(3.2141922402480394843964588019150294350276272721151544568588531146246464930473505445135251473893910091e-01) }, - { SC_(-1.5605529785156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.9634594511488441239446124536812458462568892642529680265004423990558267843732051305555937342925952892e-01), SC_(-8.5409353428812105256571523319257903922757730296962059795625764794071278796936359904999417711418506963e-02), SC_(9.9196370140536661517806007451248913316445364776565729227577579281057604045077901201671022992954940866e-01) }, - { SC_(-1.5605529785156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(1.3547700643539428710937500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.8507961426602883228803019073961981958060099984011753039084360078720386446123667023988475150255949526e-01), SC_(-1.7209925495914224056702706138188187847064943449563917074969927279924070607243598857996086522477531487e-01), SC_(9.9105478803571702730047795909209167869766318761675764394396722003662904738763622827899377822295432355e-01) }, - { SC_(-1.5605529785156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(2.2103404998779296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.8248612785073414182685509102670101867866606445715181205154091509183064961414026941361152523421096695e-01), SC_(-9.8320842812805745037945796017375413735001762909773273395230181538881053153180460745843274908711290409e-01), SC_(9.9918618660790569357913493985971747365339871345709645144590218630847755475249250020453080799416154091e-01) }, - { SC_(-1.5605529785156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(3.0816698074340820312500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-9.9158838874949604426827150019504117982370531426684233581077142421174586823163566938385360504094435130e-01), SC_(1.2943132270504812677590848413999258821957368076167066407580166536160746634327211207828164566323979708e-01), SC_(9.5216807427332399209612601388142889559348170701718081235058316586516533919961845371369694752105796844e-01) }, - { SC_(-1.5605529785156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(6.3235926628112792968750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(3.4850849856189024097670989535486539667872022677162829380888596814546374460520548474036175153271561409e-01), SC_(9.3730562061162150476751438595734314944960838837159437927593351031354238223322792887550880643854386618e-01), SC_(9.7541351185979966500632289702714211007616769474888190781321539444569874004850576581698447098984473774e-01) }, - { SC_(-1.5605529785156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(8.1472349166870117187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-9.9768647828943160251387270175978040354991051978569998213156792178899072069031856957855604912863677927e-01), SC_(-6.7983020221460620602477920740337096785069318374339062937396833159665852445264612438240658448058446372e-02), SC_(5.8248896313210669614394305122189656389869009767463887294045928688078276659240087367291744920068430718e-01) }, - { SC_(-1.5605529785156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(8.3500838279724121093750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.1666788045635083193371938920056375449022051643456650047952514782286715843857567412246372159950161759e-01), SC_(3.9964984291209386199380881912105158376718408574530690430179110562688471984148465105325478026822099931e-01), SC_(6.4352467823650631744048456295799149574644278344437481712696368654316089787975896784931564053208489969e-01) }, - { SC_(-1.5605529785156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.0579175949096679687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(6.6177046252416079555508635934682224965776227840898130220764534668450302789945037304177484207002111431e-01), SC_(7.4970651253044233646081247800563589896058506359539248199555934055757606449113476755285508234546147573e-01), SC_(8.0043000495681302502202318394250860224011843001834972620558908558545445241188040905957841914651309679e-01) }, - { SC_(-1.5605529785156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.1337585449218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), 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SC_(-9.7776321201636010382337424408562096668543234507605495641318225337144791625772419859562530121151790673e-01), SC_(2.0971194822291466346030421849595858014680805590559492690127261632363629066019576649612096090094549878e-01), SC_(5.7742960193439094700348356947016724682361321289632632659151235741183259429995820997477679950807256189e-01) }}, + {{ SC_(1.9715252685546875000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.0579175949096679687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.5335552637509468619177212910424271793500604536736315130170091868994872898355573407901286288639274304e-01), SC_(-5.2132940220659440319333211591248886524580006933686352224178661371782672213885596221974167956318085725e-01), SC_(6.3445182831800375269300932933670770833130898600306348885566817247186267453097547880914732346671069865e-01) }}, + {{ SC_(1.9715252685546875000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.1337585449218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(3.2552432416186685026934526193128921379766826802420069334155189741447969109871574924231483351424206599e-01), SC_(9.4553366644396106872879025738016398857917167142462917144519103981246913164050418116860896385695109638e-01), SC_(9.5477600273005629053462961893870689852992588659840987337775533495567475431257098929765560217201525781e-01) }}, + {{ SC_(1.9715252685546875000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.6886777877807617187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-3.9412307228568629478091636297546153976117178431143042104414325984436672903094560979335786919432390159e-01), SC_(-9.1905767168991723490423535241594951632963991958559280799910799985557761425472976757206816773545655546e-01), SC_(9.2422301160881704148508838860716761915357124551323944774087944758929470657071593948190980722116431319e-01) }}, + {{ SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.4054705213152072851451664130651061216499217259757217431721599006205998223273563720851776196554659711e-01), SC_(-9.9007400033388392914671454535086242072251869165129442669867317682364702240378428827847175171458794744e-01), SC_(9.9984071853366842614471458726841084906264079357521344888761890568442619129819452826610841761945249390e-01) }}, + {{ SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(1.3547700643539428710937500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(2.5070640492058129942565255217740163494695763216559037381456171424195061110398681756028914124819463101e-01), SC_(-9.6806316866813889172199931228900862951312842168003652810485498962347027876607999917857526043808893858e-01), SC_(9.9942302452559713852269084116030636732630369591763149069010267256421389522467628458268739532812633610e-01) }}, + {{ SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(2.2103404998779296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7460959847396629023213294151850600468186754526453359707119955774767291431614264354511495305616871082e-01), SC_(2.2391098803411637082502445867797619686052486034294717623183478584718412642662476193997851593899862294e-01), SC_(9.7652107100176220018304071389988193041833109679443427832086050938061220329457600374867819614433504174e-01) }}, + {{ SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(3.0816698074340820312500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-8.7591137819560965793227178075846254493991687812511266984816459225474516690755277726181572540400781692e-01), SC_(4.8247202773577212421607049007306835524095045191215664111886203507494519542708812099117851390243407605e-01), SC_(9.6288079930202121551356736451843753542939778244370285463921850847493493915725115345472885123365413983e-01) }}, + {{ SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(6.3235926628112792968750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-4.6250242396649649980482066020190351615612321919279456557494609907194412689120822625415608757186732226e-01), SC_(8.8661801686245645800217768700725799498166537819118235942894900353237994345457404176820430584219016246e-01), SC_(9.5627540398922768507958728734673192109735702301637317713655951281056100713965361590625156345008848052e-01) }}, + {{ SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(8.1472349166870117187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-1.1735531008826291520919245508896005477690524195845718339880048475212741686661323687535843820697763115e-01), SC_(-9.9308999148822744363057759901009520225182513004952136286524553869898571573704761432739426689545184600e-01), SC_(9.9541866617977664359846799474228301142404409511589411389238630589212796142638172458066619231854538725e-01) }}, + {{ SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(8.3500838279724121093750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-2.5661560264047896550977697577574285271994983541443544067356972715404806414952219948705677776708497000e-01), SC_(9.6651354490325887257750254185816231220218423716636053686841904330333698328423906111679391851744157820e-01), SC_(9.7677311539491902219065627087092296908401907255979252384756489646051968319678552175412452558572875080e-01) }}, + {{ SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.0579175949096679687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-2.3043688031022365976100265167863985776533246242764453911544714145699594137367180026912374835735577553e-01), SC_(-9.7308727470504497158374043000785726585723147362213332885195842776034698222933783780401814107209214425e-01), SC_(9.7797376965032175821022437157898388837314600109117623736975241337618528076029566654878957935590182792e-01) }}, + {{ SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.1337585449218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7024515945744297738657357466434755079331657796883714801833862664891641843430559561966177382852691399e-01), SC_(2.4212461780950951071551165255952297503000013061390990430320407464582844014750946659296356182356525586e-01), SC_(4.6330574762904332411829744686422163790342838342235753322328220006082956185458756739898418452935999869e-01) }}, + {{ SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.6886777877807617187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-9.6271921666412527706611162998623278828344436746037642935689292731054871089839252562699168099269047894e-01), SC_(-2.7050269844423550857864806232371501929916695397580524032916105445727409203649388936347088607548210605e-01), SC_(3.6052997174588038100329734639411992177585754440288098151836194079410246809516008674605501002506176314e-01) }} }}; //#undef SC_ diff --git a/test/jacobi_near_1.ipp b/test/jacobi_near_1.ipp index d03f013d1..9b1eea7a4 100644 --- a/test/jacobi_near_1.ipp +++ b/test/jacobi_near_1.ipp @@ -2,346 +2,346 @@ # define SC_(x) static_cast(BOOST_JOIN(x, L)) #endif static const boost::array, 340> jacobi_near_1 = {{ - { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000004768371582031250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9936124862178929657881621645181864085183918423681860187396785862520605717123413406685399380582107113e-01), SC_(3.5736462515171262671173658796361885282655550407797367368767246967565775142270960241294075546367351927e-02), SC_(3.5723133911895480121899640922445600550831965573961005650871698226561870552026541364948342613336582806e-02) }, - { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000014305114746093750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9936077436182305740265762942505880070947367818181132794898773596144577761932318153752214737153329561e-01), SC_(3.5749722613432715628553169307272741195011102329188833383668050964850356815583084732679478209132508739e-02), SC_(3.5709736745792682671599404581373263526701044801333523535341814550620045496488948203712498732057017070e-02) }, - { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000033378601074218750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9935982531025601614500364655259025282505814635665229090640399025716517540590131557526316221367105587e-01), SC_(3.5776242897411389640336798137070232128793830106896650516594399176561812055650730083125160534386857905e-02), SC_(3.5682942269816429157188838670831408020383121223997457406594651516016868258020580067207389880661065297e-02) }, - { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000042915344238281250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9935935051865263915735047486113654526010249743927673270177761276038424843029985650910155418309910845e-01), SC_(3.5789503083121607415749831967541532808130587365952231223694356024503294702063563047398592898634045898e-02), SC_(3.5669544959949864105435637819287301450816005044070102625046909813700756220300841914735887869992226382e-02) }, - { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000147819519042968750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9935411611454537922604681816673279309149514529840821022380007801210707169443456723123140131191273797e-01), SC_(3.5935367048574188596130658870586603259325678077312780894068903977052012489188410600116295423084873594e-02), SC_(3.5522171389827658240024209410574445295562666383769236088207845918964017440183503252721885546279178521e-02) }, - { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000290870666503906250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9934694373075237465634151921066970602357861542329676509188178432941256915556744220631478917655855971e-01), SC_(3.6134278130390913627609094654640317241259878826206151457813687944589213129451776496300461550369058584e-02), SC_(3.5321198095556949417067313300717675686827259252339991668193302765590470280891859038544561861120273525e-02) }, - { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000371932983398437500000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9934286167753124814131392571342776632513909244848527380521892160554807524960808842808040249611793657e-01), SC_(3.6246997312365705419622654899909043653736234860893527625677781635672768579458759093245682453664911900e-02), SC_(3.5207308451560232414054205505237899944531489182512040097012760453521655141311995420890008689715696573e-02) }, - { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000996589660644531250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9931097620864165027219465310031542946941250827291810334804095750671116621959312074419161413137564784e-01), SC_(3.7115668240402753402689250059917062222914595826608378093934126249222135687424925800143195563100714367e-02), SC_(3.4329572580251660446610503280495506358429580145905143796049996103343889948196804594921179632733199316e-02) }, - { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0001597404479980468750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9927958990572377979840922995352718001556928368962504869163503233477958808920244802834130239693182256e-01), SC_(3.7951300344632531849121062722660432211073826380488963469452361292471727250417761710007993570196150397e-02), SC_(3.3485145517244791669270158219919377826756232555597493366342767643308973856626129103762653029721538067e-02) }, - { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0002679824829101562500000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9922126738572525883615985096934737542379246872162570557721278008482614426793068921887463636739257892e-01), SC_(3.9457050118640992430999735288370836965982117887075206057330612359482953959031548073429030863323308119e-02), SC_(3.1963362733204485362415093423863407199447848854193799452188513745779920844752052440282754193164327043e-02) }, - { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0007553100585937500000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9893032851875707688561830988272894258600328658118144172720086651889951652362299650709125447015552495e-01), SC_(4.6240661385928097466067420828933763850527867003804137146601696125664302459519863236590458981093024575e-02), SC_(2.5104568923475994083987155204747891917416311244009618734097942128126480441578326069647043926175848547e-02) }, - { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0012483596801757812500000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9858861863794450821691883948411704365274249753358965103850267796074469645752772267528127337525272991e-01), SC_(5.3110928505928287442257797909322905597834515794113431687558113958412726965037911230281021368296317952e-02), SC_(1.8153237543155462803067836701096459698569047964241988599087152572358359059054049298308131438716438194e-02) }, - { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0023207664489746093750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9768013419211395389844759575957044763860216650562470815234213356993397846622838414826864478393798484e-01), SC_(6.8076059216184755781840577950311038573406706672675088844600265894103208744445519993559300403103933746e-02), SC_(2.9943999715622324848586115105215220299985513048294403527193588267688062368550605670306861278056228327e-03) }, - { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0060424804687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9275223561439943369665678089317248964119678445427980155471655857570286843157774469401717822210675502e-01), SC_(1.2017902763216197969677315152451453633920175705926357660874751861325404020389385327834653677322322067e-01), SC_(-4.9965954272454113037709486732652160303751311444701747699562340013704865808780400007504197732543057380e-02) }, - { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0155692100524902343750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.6735637154027865337130077405912181415705275746255993415024144757583603881348060995488920488911672649e-01), SC_(2.5341990932132061632299610199618871011222636428088359622618311788654236921637295363303486915660247366e-01), SC_(-1.8669803992671241292637737591564312105410623529773567523326462874859967205170061052766876529350597205e-01) }, - { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0305857658386230468750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-8.9037307644999185961891548066152364082934652825389480690284822126953747572423134779233931568896247709e-01), SC_(4.5523157264515051576165746439917285541212023356220966397336337241653186704837219828020641191437049015e-01), SC_(-3.9749158628350816926566949245343979471653384960565298443009459540951029451206974073879850780006389752e-01) }, - { SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0623893737792968750000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-6.0719134559454416707104305589573667628292047048469766163025850056085681130949692218928367444627674035e-01), SC_(7.9455564300751576105470945564292159344239444001338371721114375059096583894484473548719583963149859832e-01), SC_(-7.6412041425334888578087126653697299732010050441086783313382612821550919553001092840088361833581189685e-01) }, - { SC_(-3.7301321029663085937500000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000004768371582031250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9884941771767374068845949560764111778511322805191229385025226734820765467112509736638548364923940404e-01), SC_(4.7956654648381339311038559193943126801582338467442869043122959184810391359715831466879439189897340727e-02), SC_(4.7946733400930347798831724061773506453356261521274285436701505289849800332902629782014328403231797354e-02) }, - { SC_(-3.7301321029663085937500000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000014305114746093750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9884894542085558748198261281226665105707563473967662902233717417789919585586365668107117785676748824e-01), SC_(4.7966490716380906776917513236059635732930235137306330473936925478681743604444507244368925503697776871e-02), SC_(4.7936726935099251332962549955311982568754220652884694250178964216891229721756133703724300833417873220e-02) }, - { SC_(-3.7301321029663085937500000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000033378601074218750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9884800053322777518286027010639325944449428672631354491199619955982388715763941232935413635713386273e-01), 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SC_(9.7148209448510965618814190119451117927847310257093339481999337817751394945307795550093447421264799168e-02), SC_(-6.9532095588469802480589239010157975152091841708321990467488846359840797625840328044562828776517609113e-02) }}, + {{ SC_(4.9646129608154296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0060424804687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(9.7327357090730138720367359153239323902247504897821653720406237386695349159240208217001492967466592893e-01), SC_(2.2964876697546228888931649787788742930944361620108470728002449961617243383843764035729632038084809597e-01), SC_(-2.0311659859397708228829612914540972881961033272228812487026550233039579579564016302202736438925829861e-01) }}, + {{ SC_(4.9646129608154296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0155692100524902343750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(8.4069051112564740388498305703743050846741943876819566564676351892344788777074732833738047977587592836e-01), SC_(5.4151589496828042658602571182616923878595213758699386834940240440502083614232854508648303249637786229e-01), SC_(-5.2063493838617445779646407770009371209785483807741597530330738738065076402146210854614754006055477215e-01) }}, + {{ SC_(4.9646129608154296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0305857658386230468750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(4.8671357579638665629126370168770921319757407213502466576345439294626879685237098285286502834996393092e-01), SC_(8.7356161496227327149253838986791328231133879539230423927448398220130445285498224963240552394450600870e-01), SC_(-8.6509962228485538958789361261824061503929655387763193064181839580439422746694246738587153880942281811e-01) }}, + {{ SC_(4.9646129608154296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0623893737792968750000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-2.2293187234404279005404405123453640992362355261738577610576210777344443465871289033909805344032394449e-01), SC_(9.7483402704931233304677248889105249284034868811789307005518001217555908178599047906139783223849231970e-01), SC_(-9.7154855780636670580019454689623684007923466283994781397066875280116362115119765459157832338091463773e-01) }} }}; //#undef SC_ diff --git a/test/test_jacobi.cpp b/test/test_jacobi.cpp index e31b3ccce..31339bc66 100644 --- a/test/test_jacobi.cpp +++ b/test/test_jacobi.cpp @@ -72,6 +72,27 @@ void expected_results() largest_type, // test type(s) ".*near 1.*", // test data group ".*", 7000, 500); // test function + + if(std::numeric_limits::digits == 64) + { + // + // Some errors spill over into double precision: + // + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + "double", // test type(s) + ".*Large Phi.*", // test data group + ".*", 500, 50); // test function + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + "double", // test type(s) + ".*near 1.*", // test data group + ".*", 10, 5); // test function + } // // Catch all cases come last: // From 382d525d1553c9f825fe8d3e9459bc2f9b1b6353 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 21 May 2012 09:45:48 +0000 Subject: [PATCH 004/115] Add basic versions of the Airy functions. Add some extra jacobi, hankel and owens_t tests and fix resulting errors. Allow remez code to work with expression template types. Regenerate docs. [SVN r78527] --- doc/sf_and_dist/airy.qbk | 219 ++++++++++++++++ doc/sf_and_dist/equations/airy.mml | 76 ++++++ doc/sf_and_dist/equations/airy.png | Bin 0 -> 5256 bytes doc/sf_and_dist/equations/airy.svg | 2 + doc/sf_and_dist/equations/airy_ai.mml | 187 +++++++++++++ doc/sf_and_dist/equations/airy_ai.png | Bin 0 -> 10567 bytes doc/sf_and_dist/equations/airy_ai.svg | 2 + doc/sf_and_dist/equations/airy_aip.mml | 179 +++++++++++++ doc/sf_and_dist/equations/airy_aip.png | Bin 0 -> 9732 bytes doc/sf_and_dist/equations/airy_aip.svg | 2 + doc/sf_and_dist/equations/airy_bi.mml | 195 ++++++++++++++ doc/sf_and_dist/equations/airy_bi.png | Bin 0 -> 11036 bytes doc/sf_and_dist/equations/airy_bi.svg | 2 + doc/sf_and_dist/equations/airy_bip.mml | 195 ++++++++++++++ doc/sf_and_dist/equations/airy_bip.png | Bin 0 -> 10991 bytes doc/sf_and_dist/equations/airy_bip.svg | 2 + doc/sf_and_dist/graphs/airy_ai.png | Bin 0 -> 33690 bytes doc/sf_and_dist/graphs/airy_ai.svg | 65 +++++ doc/sf_and_dist/graphs/airy_aip.png | Bin 0 -> 33021 bytes doc/sf_and_dist/graphs/airy_aip.svg | 60 +++++ doc/sf_and_dist/graphs/airy_bi.png | Bin 0 -> 18018 bytes doc/sf_and_dist/graphs/airy_bi.svg | 58 +++++ doc/sf_and_dist/graphs/airy_bip.png | Bin 0 -> 22406 bytes doc/sf_and_dist/graphs/airy_bip.svg | 60 +++++ doc/sf_and_dist/graphs/sf_graphs.cpp | 23 +- doc/sf_and_dist/html/index.html | 9 +- doc/sf_and_dist/html/index/s13.html | 20 +- doc/sf_and_dist/html/index/s14.html | 4 +- doc/sf_and_dist/html/index/s15.html | 4 +- doc/sf_and_dist/html/index/s16.html | 4 +- doc/sf_and_dist/html/index/s17.html | 36 ++- .../main_overview/conventions.html | 2 +- .../main_overview/navigation.html | 2 +- .../html/math_toolkit/special.html | 7 + .../html/math_toolkit/special/airy.html | 50 ++++ .../html/math_toolkit/special/airy/ai.html | 123 +++++++++ .../html/math_toolkit/special/airy/aip.html | 123 +++++++++ .../html/math_toolkit/special/airy/bi.html | 123 +++++++++ .../html/math_toolkit/special/airy/bip.html | 123 +++++++++ .../html/math_toolkit/special/ellint.html | 6 +- .../special/hankel/sph_hankel.html | 6 +- doc/sf_and_dist/math.qbk | 9 + include/boost/math/special_functions.hpp | 1 + include/boost/math/special_functions/airy.hpp | 246 ++++++++++++++++++ .../special_functions/jacobi_elliptic.hpp | 2 + .../boost/math/special_functions/math_fwd.hpp | 41 +++ include/boost/math/tools/remez.hpp | 6 +- test/Jamfile.v2 | 5 + test/compile_test/instantiate.hpp | 16 ++ test/compile_test/sf_airy_incl_test.cpp | 42 +++ test/compile_test/sf_hankel_incl_test.cpp | 46 ++++ test/compile_test/sf_jacobi_incl_test.cpp | 96 +++++++ test/compile_test/sf_owens_t_incl_test.cpp | 24 ++ test/test_airy.cpp | 85 ++++++ test/test_instances.hpp | 11 + 55 files changed, 2576 insertions(+), 23 deletions(-) create mode 100644 doc/sf_and_dist/airy.qbk create mode 100644 doc/sf_and_dist/equations/airy.mml create mode 100644 doc/sf_and_dist/equations/airy.png create mode 100644 doc/sf_and_dist/equations/airy.svg create mode 100644 doc/sf_and_dist/equations/airy_ai.mml create mode 100644 doc/sf_and_dist/equations/airy_ai.png create mode 100644 doc/sf_and_dist/equations/airy_ai.svg create mode 100644 doc/sf_and_dist/equations/airy_aip.mml create mode 100644 doc/sf_and_dist/equations/airy_aip.png create mode 100644 doc/sf_and_dist/equations/airy_aip.svg create mode 100644 doc/sf_and_dist/equations/airy_bi.mml create mode 100644 doc/sf_and_dist/equations/airy_bi.png create mode 100644 doc/sf_and_dist/equations/airy_bi.svg create mode 100644 doc/sf_and_dist/equations/airy_bip.mml create mode 100644 doc/sf_and_dist/equations/airy_bip.png create mode 100644 doc/sf_and_dist/equations/airy_bip.svg create mode 100644 doc/sf_and_dist/graphs/airy_ai.png create mode 100644 doc/sf_and_dist/graphs/airy_ai.svg create mode 100644 doc/sf_and_dist/graphs/airy_aip.png create mode 100644 doc/sf_and_dist/graphs/airy_aip.svg create mode 100644 doc/sf_and_dist/graphs/airy_bi.png create mode 100644 doc/sf_and_dist/graphs/airy_bi.svg create mode 100644 doc/sf_and_dist/graphs/airy_bip.png create mode 100644 doc/sf_and_dist/graphs/airy_bip.svg create mode 100644 doc/sf_and_dist/html/math_toolkit/special/airy.html create mode 100644 doc/sf_and_dist/html/math_toolkit/special/airy/ai.html create mode 100644 doc/sf_and_dist/html/math_toolkit/special/airy/aip.html create mode 100644 doc/sf_and_dist/html/math_toolkit/special/airy/bi.html create mode 100644 doc/sf_and_dist/html/math_toolkit/special/airy/bip.html create mode 100644 include/boost/math/special_functions/airy.hpp create mode 100644 test/compile_test/sf_airy_incl_test.cpp create mode 100644 test/compile_test/sf_hankel_incl_test.cpp create mode 100644 test/compile_test/sf_jacobi_incl_test.cpp create mode 100644 test/compile_test/sf_owens_t_incl_test.cpp create mode 100644 test/test_airy.cpp diff --git a/doc/sf_and_dist/airy.qbk b/doc/sf_and_dist/airy.qbk new file mode 100644 index 000000000..d2ff3e0fa --- /dev/null +++ b/doc/sf_and_dist/airy.qbk @@ -0,0 +1,219 @@ +[/ +Copyright (c) 2012 John Maddock +Use, modification and distribution are subject to the +Boost Software License, Version 1.0. (See accompanying file +LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +] + +[section:airy Airy Functions] + +[section:ai Airy Ai Function] + +[heading Synopsis] + +`` + #include +`` + + namespace boost { namespace math { + + template + ``__sf_result`` airy_ai(T x); + + template + ``__sf_result`` airy_ai(T x, const Policy&); + + }} // namespaces + +[heading Description] + +The function __airy_ai calculates the Airy function Ai which is the first solution to the differential equation: + +[equation airy] + +[optional_policy] + +The following graph illustrates how this function changes as /x/ changes: for negative /x/ +the function is cyclic, while for positive /x/ the value tends to zero: + +[graph airy_ai] + +[heading Accuracy] + +This function is implemented entirely in terms of the Bessel functions +__cyl_bessel_j and __cyl_bessel_k - refer to those functions for detailed accuracy information. + +In general though, the relative error is low (less than 100 [epsilon]) for /x > 0/ while +only the absolute error is low for /x < 0/. + +[heading Testing] + +Since this function is implemented in terms of other special functions, there are only a few +basic sanity checks, using test values from [@http:functions.wolfram.com functions.wolfram.com]. + +[heading Implementation] + +This function is implemented in terms of the Bessel functions using the relations: + +[equation airy_ai] + +[endsect] + +[section:bi Airy Bi Function] + +[heading Synopsis] + +`` + #include +`` + + namespace boost { namespace math { + + template + ``__sf_result`` airy_bi(T x); + + template + ``__sf_result`` airy_bi(T x, const Policy&); + + }} // namespaces + +[heading Description] + +The function __airy_bi calculates the Airy function Bi which is the second solution to the differential equation: + +[equation airy] + +[optional_policy] + +The following graph illustrates how this function changes as /x/ changes: for negative /x/ +the function is cyclic, while for positive /x/ the value tends to infinity: + +[graph airy_bi] + +[heading Accuracy] + +This function is implemented entirely in terms of the Bessel functions +__cyl_bessel_i and __cyl_bessel_j - refer to those functions for detailed accuracy information. + +In general though, the relative error is low (less than 100 [epsilon]) for /x > 0/ while +only the absolute error is low for /x < 0/. + +[heading Testing] + +Since this function is implemented in terms of other special functions, there are only a few +basic sanity checks, using test values from [@http:functions.wolfram.com functions.wolfram.com]. + +[heading Implementation] + +This function is implemented in terms of the Bessel functions using the relations: + +[equation airy_bi] + +[endsect] + +[section:aip Airy Ai' Function] + +[heading Synopsis] + +`` + #include +`` + + namespace boost { namespace math { + + template + ``__sf_result`` airy_ai_prime(T x); + + template + ``__sf_result`` airy_ai_prime(T x, const Policy&); + + }} // namespaces + +[heading Description] + +The function __airy_ai_prime calculates the Airy function Ai' which is the derivative of the first solution to the differential equation: + +[equation airy] + +[optional_policy] + +The following graph illustrates how this function changes as /x/ changes: for negative /x/ +the function is cyclic, while for positive /x/ the value tends to zero: + +[graph airy_aip] + +[heading Accuracy] + +This function is implemented entirely in terms of the Bessel functions +__cyl_bessel_j and __cyl_bessel_k - refer to those functions for detailed accuracy information. + +In general though, the relative error is low (less than 100 [epsilon]) for /x > 0/ while +only the absolute error is low for /x < 0/. + +[heading Testing] + +Since this function is implemented in terms of other special functions, there are only a few +basic sanity checks, using test values from [@http:functions.wolfram.com functions.wolfram.com]. + +[heading Implementation] + +This function is implemented in terms of the Bessel functions using the relations: + +[equation airy_aip] + +[endsect] + +[section:bip Airy Bi' Function] + +[heading Synopsis] + +`` + #include +`` + + namespace boost { namespace math { + + template + ``__sf_result`` airy_bi_prime(T x); + + template + ``__sf_result`` airy_bi_prime(T x, const Policy&); + + }} // namespaces + +[heading Description] + +The function __airy_bi_prime calculates the Airy function Bi' which is the derivative of the second solution to the differential equation: + +[equation airy] + +[optional_policy] + +The following graph illustrates how this function changes as /x/ changes: for negative /x/ +the function is cyclic, while for positive /x/ the value tends to infinity: + +[graph airy_bi] + +[heading Accuracy] + +This function is implemented entirely in terms of the Bessel functions +__cyl_bessel_i and __cyl_bessel_j - refer to those functions for detailed accuracy information. + +In general though, the relative error is low (less than 100 [epsilon]) for /x > 0/ while +only the absolute error is low for /x < 0/. + +[heading Testing] + +Since this function is implemented in terms of other special functions, there are only a few +basic sanity checks, using test values from [@http:functions.wolfram.com functions.wolfram.com]. + +[heading Implementation] + +This function is implemented in terms of the Bessel functions using the relations: + +[equation airy_bip] + +[endsect] + +[endsect] + diff --git a/doc/sf_and_dist/equations/airy.mml b/doc/sf_and_dist/equations/airy.mml new file mode 100644 index 000000000..0b1550e81 --- /dev/null +++ b/doc/sf_and_dist/equations/airy.mml @@ -0,0 +1,76 @@ + +]> + +airy + + + + + + + + + + 2 + + w + + + + + z + 2 + + + + = + z + w + + ; + + w + = + A + i + + + z + + + , + B + i + + + z + + + , + A + i + + + z + + + + ± + + + 2 + π + + + 3 + + + + + + + + + diff --git a/doc/sf_and_dist/equations/airy.png b/doc/sf_and_dist/equations/airy.png new file mode 100644 index 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@@ -248,7 +248,7 @@ int main() double (*f2i)(int, double); double (*f3)(double, double, double); double (*f4)(double, double, double, double); - +#if 0 f = boost::math::zeta; plot.add(f, 1 + find_end_point(f, 0.1, 40.0, false, 1.0), 10, ""); plot.add(f, -20, 1 + find_end_point(f, -0.1, -40.0, false, 1.0), ""); @@ -675,6 +675,27 @@ int main() plot.add(boost::bind(f2, 0.95, _1), -2.5, 2.5, "k=0.95"); plot.add(boost::bind(f2, 1, _1), -2.5, 2.5, "k=1"); plot.plot("Jacobi Elliptic sd", "jacobi_sd.svg", "k", "jacobi_sd(k, phi)"); +#endif + + f = boost::math::airy_ai; + plot.clear(); + plot.add(f, -20, 20, ""); + plot.plot("Ai", "airy_ai.svg", "z", "airy_ai(z)"); + + f = boost::math::airy_bi; + plot.clear(); + plot.add(f, -20, 3, ""); + plot.plot("Bi", "airy_bi.svg", "z", "airy_bi(z)"); + + f = boost::math::airy_ai_prime; + plot.clear(); + plot.add(f, -20, 20, ""); + plot.plot("Ai'", "airy_aip.svg", "z", "airy_ai_prime(z)"); + + f = boost::math::airy_bi_prime; + plot.clear(); + plot.add(f, -20, 3, ""); + plot.plot("Bi'", "airy_bip.svg", "z", "airy_bi_prime(z)"); return 0; } diff --git a/doc/sf_and_dist/html/index.html b/doc/sf_and_dist/html/index.html index 7aade3401..059a8018c 100644 --- a/doc/sf_and_dist/html/index.html +++ b/doc/sf_and_dist/html/index.html @@ -294,6 +294,13 @@

Spherical Hankel Functions
+
Airy Functions
+
+
Airy Ai Function
+
Airy Bi Function
+
Airy Ai' Function
+
Airy Bi' Function
+
Elliptic Integrals
Elliptic @@ -570,7 +577,7 @@

- +

Last revised: May 17, 2012 at 10:07:59 GMT

Last revised: May 20, 2012 at 15:54:08 GMT


diff --git a/doc/sf_and_dist/html/index/s13.html b/doc/sf_and_dist/html/index/s13.html index f5454540a..06437df6b 100644 --- a/doc/sf_and_dist/html/index/s13.html +++ b/doc/sf_and_dist/html/index/s13.html @@ -22,9 +22,9 @@
-
+

-Function Index

+Function Index

A B C D E F G H I J K L M N O P Q R S T U V W Z

@@ -57,6 +57,22 @@
  • +

    airy_ai

    + +
  • +
  • +

    airy_ai_prime

    + +
  • +
  • +

    airy_bi

    + +
  • +
  • +

    airy_bi_prime

    + +
  • +
  • asinh

    • asinh

    • diff --git a/doc/sf_and_dist/html/index/s14.html b/doc/sf_and_dist/html/index/s14.html index 6902d2e2b..daa7f7518 100644 --- a/doc/sf_and_dist/html/index/s14.html +++ b/doc/sf_and_dist/html/index/s14.html @@ -22,9 +22,9 @@
      PrevUpHomeNext
      -
      +

      -Class Index

      +Class Index

    B C D E F G H I L M N P R S T U W

    diff --git a/doc/sf_and_dist/html/index/s15.html b/doc/sf_and_dist/html/index/s15.html index 18073d047..5fb692ac7 100644 --- a/doc/sf_and_dist/html/index/s15.html +++ b/doc/sf_and_dist/html/index/s15.html @@ -22,9 +22,9 @@
    PrevUpHomeNext
    -
    +

    -Typedef Index

    +Typedef Index

    A B C D E F G H I L N O P R S T U V W

    diff --git a/doc/sf_and_dist/html/index/s16.html b/doc/sf_and_dist/html/index/s16.html index 7e48607e9..1cc30f06d 100644 --- a/doc/sf_and_dist/html/index/s16.html +++ b/doc/sf_and_dist/html/index/s16.html @@ -22,9 +22,9 @@
    PrevUpHomeNext
    -
    +

    -Macro Index

    +Macro Index

    B F

    diff --git a/doc/sf_and_dist/html/index/s17.html b/doc/sf_and_dist/html/index/s17.html index 2cc4aaef7..ddfbf0932 100644 --- a/doc/sf_and_dist/html/index/s17.html +++ b/doc/sf_and_dist/html/index/s17.html @@ -21,9 +21,9 @@
    PrevUpHome
    -
    +

    -Index

    +Index

    A B C D E F G H I J K L M N O P Q R S T U V W Z

    @@ -63,6 +63,38 @@
  • +

    Airy Ai Function

    + +
  • +
  • +

    Airy Ai' Function

    + +
  • +
  • +

    Airy Bi Function

    + +
  • +
  • +

    Airy Bi' Function

    + +
  • +
  • +

    airy_ai

    + +
  • +
  • +

    airy_ai_prime

    + +
  • +
  • +

    airy_bi

    + +
  • +
  • +

    airy_bi_prime

    + +
  • +
  • asinh

    • asinh

    • diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html b/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html index 2425d341c..757299775 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html @@ -27,7 +27,7 @@ Document Conventions

    - +

    This documentation aims to use of the following naming and formatting conventions. diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html index 853c7b232..d819395ee 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html @@ -27,7 +27,7 @@ Navigation

    - +

    Boost.Math documentation is provided in both HTML and PDF formats. diff --git a/doc/sf_and_dist/html/math_toolkit/special.html b/doc/sf_and_dist/html/math_toolkit/special.html index 41e84c7d6..f7725eedb 100644 --- a/doc/sf_and_dist/html/math_toolkit/special.html +++ b/doc/sf_and_dist/html/math_toolkit/special.html @@ -97,6 +97,13 @@

    Spherical Hankel Functions
  • +
    Airy Functions
    +
    +
    Airy Ai Function
    +
    Airy Bi Function
    +
    Airy Ai' Function
    +
    Airy Bi' Function
    +
    Elliptic Integrals
    Elliptic diff --git a/doc/sf_and_dist/html/math_toolkit/special/airy.html b/doc/sf_and_dist/html/math_toolkit/special/airy.html new file mode 100644 index 000000000..9b8a2cb4b --- /dev/null +++ b/doc/sf_and_dist/html/math_toolkit/special/airy.html @@ -0,0 +1,50 @@ + + + +Airy Functions + + + + + + + + + + + + + + + +
    Boost C++ LibrariesHomeLibrariesPeopleFAQMore
    +
    +
    +PrevUpHomeNext +
    + + + + +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/sf_and_dist/html/math_toolkit/special/airy/ai.html b/doc/sf_and_dist/html/math_toolkit/special/airy/ai.html new file mode 100644 index 000000000..8e3d83055 --- /dev/null +++ b/doc/sf_and_dist/html/math_toolkit/special/airy/ai.html @@ -0,0 +1,123 @@ + + + +Airy Ai Function + + + + + + + + + + + + + + + +
    Boost C++ LibrariesHomeLibrariesPeopleFAQMore
    +
    +
    +PrevUpHomeNext +
    +
    + +
    + + Synopsis +
    +

    +

    +
    #include <boost/math/special_functions/airy.hpp>
    +
    +

    +

    +
    namespace boost { namespace math {
    +
    + template <class T>
    + calculated-result-type airy_ai(T x);
    +
    + template <class T, class Policy>
    + calculated-result-type airy_ai(T x, const Policy&);
    +
    +}} // namespaces
    +
    +
    + + Description +
    +

    + The function airy_ai + calculates the Airy function Ai which is the first solution to the differential + equation: +

    +

    + +

    +

    + The final Policy argument is + optional and can be used to control the behaviour of the function: how + it handles errors, what level of precision to use etc. Refer to the policy documentation for more details. +

    +

    + The following graph illustrates how this function changes as x + changes: for negative x the function is cyclic, while + for positive x the value tends to zero: +

    +

    + +

    +
    + + Accuracy +
    +

    + This function is implemented entirely in terms of the Bessel functions + cyl_bessel_j + and cyl_bessel_k + - refer to those functions for detailed accuracy information. +

    +

    + In general though, the relative error is low (less than 100 ε) for x + > 0 while only the absolute error is low for x + < 0. +

    +
    + + Testing +
    +

    + Since this function is implemented in terms of other special functions, + there are only a few basic sanity checks, using test values from functions.wolfram.com. +

    +
    + + Implementation +
    +

    + This function is implemented in terms of the Bessel functions using the + relations: +

    +

    + +

    +
    + + + +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/sf_and_dist/html/math_toolkit/special/airy/aip.html b/doc/sf_and_dist/html/math_toolkit/special/airy/aip.html new file mode 100644 index 000000000..a0180d0e3 --- /dev/null +++ b/doc/sf_and_dist/html/math_toolkit/special/airy/aip.html @@ -0,0 +1,123 @@ + + + +Airy Ai' Function + + + + + + + + + + + + + + + +
    Boost C++ LibrariesHomeLibrariesPeopleFAQMore
    +
    +
    +PrevUpHomeNext +
    +
    + +
    + + Synopsis +
    +

    +

    +
    #include <boost/math/special_functions/airy.hpp>
    +
    +

    +

    +
    namespace boost { namespace math {
    +
    + template <class T>
    + calculated-result-type airy_ai_prime(T x);
    +
    + template <class T, class Policy>
    + calculated-result-type airy_ai_prime(T x, const Policy&);
    +
    +}} // namespaces
    +
    +
    + + Description +
    +

    + The function airy_ai_prime + calculates the Airy function Ai' which is the derivative of the first solution + to the differential equation: +

    +

    + +

    +

    + The final Policy argument is + optional and can be used to control the behaviour of the function: how + it handles errors, what level of precision to use etc. Refer to the policy documentation for more details. +

    +

    + The following graph illustrates how this function changes as x + changes: for negative x the function is cyclic, while + for positive x the value tends to zero: +

    +

    + +

    +
    + + Accuracy +
    +

    + This function is implemented entirely in terms of the Bessel functions + cyl_bessel_j + and cyl_bessel_k + - refer to those functions for detailed accuracy information. +

    +

    + In general though, the relative error is low (less than 100 ε) for x + > 0 while only the absolute error is low for x + < 0. +

    +
    + + Testing +
    +

    + Since this function is implemented in terms of other special functions, + there are only a few basic sanity checks, using test values from functions.wolfram.com. +

    +
    + + Implementation +
    +

    + This function is implemented in terms of the Bessel functions using the + relations: +

    +

    + +

    +
    + + + +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/sf_and_dist/html/math_toolkit/special/airy/bi.html b/doc/sf_and_dist/html/math_toolkit/special/airy/bi.html new file mode 100644 index 000000000..aef1cfde6 --- /dev/null +++ b/doc/sf_and_dist/html/math_toolkit/special/airy/bi.html @@ -0,0 +1,123 @@ + + + +Airy Bi Function + + + + + + + + + + + + + + + +
    Boost C++ LibrariesHomeLibrariesPeopleFAQMore
    +
    +
    +PrevUpHomeNext +
    +
    + +
    + + Synopsis +
    +

    +

    +
    #include <boost/math/special_functions/airy.hpp>
    +
    +

    +

    +
    namespace boost { namespace math {
    +
    + template <class T>
    + calculated-result-type airy_bi(T x);
    +
    + template <class T, class Policy>
    + calculated-result-type airy_bi(T x, const Policy&);
    +
    +}} // namespaces
    +
    +
    + + Description +
    +

    + The function airy_bi + calculates the Airy function Bi which is the second solution to the differential + equation: +

    +

    + +

    +

    + The final Policy argument is + optional and can be used to control the behaviour of the function: how + it handles errors, what level of precision to use etc. Refer to the policy documentation for more details. +

    +

    + The following graph illustrates how this function changes as x + changes: for negative x the function is cyclic, while + for positive x the value tends to infinity: +

    +

    + +

    +
    + + Accuracy +
    +

    + This function is implemented entirely in terms of the Bessel functions + cyl_bessel_i + and cyl_bessel_j + - refer to those functions for detailed accuracy information. +

    +

    + In general though, the relative error is low (less than 100 ε) for x + > 0 while only the absolute error is low for x + < 0. +

    +
    + + Testing +
    +

    + Since this function is implemented in terms of other special functions, + there are only a few basic sanity checks, using test values from functions.wolfram.com. +

    +
    + + Implementation +
    +

    + This function is implemented in terms of the Bessel functions using the + relations: +

    +

    + +

    +
    + + + +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/sf_and_dist/html/math_toolkit/special/airy/bip.html b/doc/sf_and_dist/html/math_toolkit/special/airy/bip.html new file mode 100644 index 000000000..50143b930 --- /dev/null +++ b/doc/sf_and_dist/html/math_toolkit/special/airy/bip.html @@ -0,0 +1,123 @@ + + + +Airy Bi' Function + + + + + + + + + + + + + + + +
    Boost C++ LibrariesHomeLibrariesPeopleFAQMore
    +
    +
    +PrevUpHomeNext +
    +
    + +
    + + Synopsis +
    +

    +

    +
    #include <boost/math/special_functions/airy.hpp>
    +
    +

    +

    +
    namespace boost { namespace math {
    +
    + template <class T>
    + calculated-result-type airy_bi_prime(T x);
    +
    + template <class T, class Policy>
    + calculated-result-type airy_bi_prime(T x, const Policy&);
    +
    +}} // namespaces
    +
    +
    + + Description +
    +

    + The function airy_bi_prime + calculates the Airy function Bi' which is the derivative of the second + solution to the differential equation: +

    +

    + +

    +

    + The final Policy argument is + optional and can be used to control the behaviour of the function: how + it handles errors, what level of precision to use etc. Refer to the policy documentation for more details. +

    +

    + The following graph illustrates how this function changes as x + changes: for negative x the function is cyclic, while + for positive x the value tends to infinity: +

    +

    + +

    +
    + + Accuracy +
    +

    + This function is implemented entirely in terms of the Bessel functions + cyl_bessel_i + and cyl_bessel_j + - refer to those functions for detailed accuracy information. +

    +

    + In general though, the relative error is low (less than 100 ε) for x + > 0 while only the absolute error is low for x + < 0. +

    +
    + + Testing +
    +

    + Since this function is implemented in terms of other special functions, + there are only a few basic sanity checks, using test values from functions.wolfram.com. +

    +
    + + Implementation +
    +

    + This function is implemented in terms of the Bessel functions using the + relations: +

    +

    + +

    +
    + + + +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint.html b/doc/sf_and_dist/html/math_toolkit/special/ellint.html index f4760ebf6..f27885254 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/ellint.html +++ b/doc/sf_and_dist/html/math_toolkit/special/ellint.html @@ -6,7 +6,7 @@ - + @@ -20,7 +20,7 @@
    -PrevUpHomeNext +PrevUpHomeNext

    @@ -50,7 +50,7 @@
    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/sf_and_dist/html/math_toolkit/special/hankel/sph_hankel.html b/doc/sf_and_dist/html/math_toolkit/special/hankel/sph_hankel.html index b7779eddf..7c0d69afa 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/hankel/sph_hankel.html +++ b/doc/sf_and_dist/html/math_toolkit/special/hankel/sph_hankel.html @@ -7,7 +7,7 @@ - + @@ -20,7 +20,7 @@

    -PrevUpHomeNext +PrevUpHomeNext

    @@ -116,7 +116,7 @@
    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/sf_and_dist/math.qbk b/doc/sf_and_dist/math.qbk index c802e2d49..5e981bfce 100644 --- a/doc/sf_and_dist/math.qbk +++ b/doc/sf_and_dist/math.qbk @@ -157,6 +157,12 @@ and use the function's name as the link text.] [def __sph_hankel_1 [link math_toolkit.special.hankel.sph_hankel sph_hankel_1]] [def __sph_hankel_2 [link math_toolkit.special.hankel.sph_hankel sph_hankel_2]] +[/Airy Functions] +[def __airy_ai [link math_toolkit.special.airy.ai airy_ai]] +[def __airy_bi [link math_toolkit.special.airy.bi airy_bi]] +[def __airy_bi_prime [link math_toolkit.special.airy.bip airy_bi_prime]] +[def __airy_ai_prime [link math_toolkit.special.airy.aip airy_ai_prime]] + [/Jacobi Elliptic Functions] [def __jacobi_elliptic [link math_toolkit.special.jacobi.jacobi_elliptic jacobi_elliptic]] @@ -433,6 +439,9 @@ and as a CD ISBN 0-9504833-2-X 978-0-9504833-2-0, Classification 519.2-dc22. [/Hankel functions] [include hankel.qbk] +[/Airy Functions] +[include airy.qbk] + [section:ellint Elliptic Integrals] [include ellint_introduction.qbk] [include ellint_carlson.qbk] diff --git a/include/boost/math/special_functions.hpp b/include/boost/math/special_functions.hpp index d0deea6f0..3723bd2d2 100644 --- a/include/boost/math/special_functions.hpp +++ b/include/boost/math/special_functions.hpp @@ -12,6 +12,7 @@ #ifndef BOOST_MATH_SPECIAL_FUNCTIONS_HPP #define BOOST_MATH_SPECIAL_FUNCTIONS_HPP +#include #include #include #include diff --git a/include/boost/math/special_functions/airy.hpp b/include/boost/math/special_functions/airy.hpp new file mode 100644 index 000000000..408cf6758 --- /dev/null +++ b/include/boost/math/special_functions/airy.hpp @@ -0,0 +1,246 @@ +// Copyright John Maddock 2012. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt +// or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifndef BOOST_MATH_AIRY_HPP +#define BOOST_MATH_AIRY_HPP + +#include +#include + +namespace boost{ namespace math{ + +namespace detail{ + +template +T airy_ai_imp(T x, const Policy& pol) +{ + BOOST_MATH_STD_USING + + if(x < 0) + { + T p = -x * sqrt(-x) * 2 / 3; + T v = T(1) / 3; + T j1 = boost::math::cyl_bessel_j(v, p, pol); + T j2 = boost::math::cyl_bessel_j(-v, p, pol); + T ai = sqrt(-x) * (j1 + j2) / 3; + //T bi = sqrt(-x / 3) * (j2 - j1); + return ai; + } + else if(fabs(x * x * x) / 6 < tools::epsilon()) + { + T tg = boost::math::tgamma(constants::twothirds(), pol); + T ai = 1 / (pow(T(3), constants::twothirds()) * tg); + //T bi = 1 / (sqrt(boost::math::cbrt(T(3))) * tg); + return ai; + } + else + { + T p = 2 * x * sqrt(x) / 3; + T v = T(1) / 3; + //T j1 = boost::math::cyl_bessel_i(-v, p, pol); + //T j2 = boost::math::cyl_bessel_i(v, p, pol); + // + // Note that although we can calculate ai from j1 and j2, the accuracy is horrible + // as we're subtracting two very large values, so use the Bessel K relation instead: + // + T ai = cyl_bessel_k(v, p, pol) * sqrt(x / 3) / boost::math::constants::pi(); //sqrt(x) * (j1 - j2) / 3; + //T bi = sqrt(x / 3) * (j1 + j2); + return ai; + } +} + +template +T airy_bi_imp(T x, const Policy& pol) +{ + BOOST_MATH_STD_USING + + if(x < 0) + { + T p = -x * sqrt(-x) * 2 / 3; + T v = T(1) / 3; + T j1 = boost::math::cyl_bessel_j(v, p, pol); + T j2 = boost::math::cyl_bessel_j(-v, p, pol); + //T ai = sqrt(-x) * (j1 + j2) / 3; + T bi = sqrt(-x / 3) * (j2 - j1); + return bi; + } + else if(fabs(x * x * x) / 6 < tools::epsilon()) + { + T tg = boost::math::tgamma(constants::twothirds(), pol); + //T ai = 1 / (pow(T(3), constants::twothirds()) * tg); + T bi = 1 / (sqrt(boost::math::cbrt(T(3))) * tg); + return bi; + } + else + { + T p = 2 * x * sqrt(x) / 3; + T v = T(1) / 3; + T j1 = boost::math::cyl_bessel_i(-v, p, pol); + T j2 = boost::math::cyl_bessel_i(v, p, pol); + T bi = sqrt(x / 3) * (j1 + j2); + return bi; + } +} + +template +T airy_ai_prime_imp(T x, const Policy& pol) +{ + BOOST_MATH_STD_USING + + if(x < 0) + { + T p = -x * sqrt(-x) * 2 / 3; + T v = T(2) / 3; + T j1 = boost::math::cyl_bessel_j(v, p, pol); + T j2 = boost::math::cyl_bessel_j(-v, p, pol); + T aip = -x * (j1 - j2) / 3; + return aip; + } + else if(fabs(x * x) / 2 < tools::epsilon()) + { + T tg = boost::math::tgamma(constants::third(), pol); + T aip = 1 / (boost::math::cbrt(T(3)) * tg); + return -aip; + } + else + { + T p = 2 * x * sqrt(x) / 3; + T v = T(2) / 3; + //T j1 = boost::math::cyl_bessel_i(-v, p, pol); + //T j2 = boost::math::cyl_bessel_i(v, p, pol); + // + // Note that although we can calculate ai from j1 and j2, the accuracy is horrible + // as we're subtracting two very large values, so use the Bessel K relation instead: + // + T aip = -cyl_bessel_k(v, p, pol) * x / (boost::math::constants::root_three() * boost::math::constants::pi()); + return aip; + } +} + +template +T airy_bi_prime_imp(T x, const Policy& pol) +{ + BOOST_MATH_STD_USING + + if(x < 0) + { + T p = -x * sqrt(-x) * 2 / 3; + T v = T(2) / 3; + T j1 = boost::math::cyl_bessel_j(v, p, pol); + T j2 = boost::math::cyl_bessel_j(-v, p, pol); + T aip = -x * (j1 + j2) / constants::root_three(); + return aip; + } + else if(fabs(x * x) / 2 < tools::epsilon()) + { + T tg = boost::math::tgamma(constants::third(), pol); + T bip = sqrt(boost::math::cbrt(T(3))) / tg; + return bip; + } + else + { + T p = 2 * x * sqrt(x) / 3; + T v = T(2) / 3; + T j1 = boost::math::cyl_bessel_i(-v, p, pol); + T j2 = boost::math::cyl_bessel_i(v, p, pol); + T aip = x * (j1 + j2) / boost::math::constants::root_three(); + return aip; + } +} + +} // namespace detail + +template +inline typename tools::promote_args::type airy_ai(T x, const Policy&) +{ + BOOST_FPU_EXCEPTION_GUARD + typedef typename tools::promote_args::type result_type; + typedef typename policies::evaluation::type value_type; + typedef typename policies::normalise< + Policy, + policies::promote_float, + policies::promote_double, + policies::discrete_quantile<>, + policies::assert_undefined<> >::type forwarding_policy; + + return policies::checked_narrowing_cast(detail::airy_ai_imp(static_cast(x), forwarding_policy()), "boost::math::airy<%1%>(%1%)"); +} + +template +inline typename tools::promote_args::type airy_ai(T x) +{ + return airy_ai(x, policies::policy<>()); +} + +template +inline typename tools::promote_args::type airy_bi(T x, const Policy&) +{ + BOOST_FPU_EXCEPTION_GUARD + typedef typename tools::promote_args::type result_type; + typedef typename policies::evaluation::type value_type; + typedef typename policies::normalise< + Policy, + policies::promote_float, + policies::promote_double, + policies::discrete_quantile<>, + policies::assert_undefined<> >::type forwarding_policy; + + return policies::checked_narrowing_cast(detail::airy_bi_imp(static_cast(x), forwarding_policy()), "boost::math::airy<%1%>(%1%)"); +} + +template +inline typename tools::promote_args::type airy_bi(T x) +{ + return airy_bi(x, policies::policy<>()); +} + +template +inline typename tools::promote_args::type airy_ai_prime(T x, const Policy&) +{ + BOOST_FPU_EXCEPTION_GUARD + typedef typename tools::promote_args::type result_type; + typedef typename policies::evaluation::type value_type; + typedef typename policies::normalise< + Policy, + policies::promote_float, + policies::promote_double, + policies::discrete_quantile<>, + policies::assert_undefined<> >::type forwarding_policy; + + return policies::checked_narrowing_cast(detail::airy_ai_prime_imp(static_cast(x), forwarding_policy()), "boost::math::airy<%1%>(%1%)"); +} + +template +inline typename tools::promote_args::type airy_ai_prime(T x) +{ + return airy_ai_prime(x, policies::policy<>()); +} + +template +inline typename tools::promote_args::type airy_bi_prime(T x, const Policy&) +{ + BOOST_FPU_EXCEPTION_GUARD + typedef typename tools::promote_args::type result_type; + typedef typename policies::evaluation::type value_type; + typedef typename policies::normalise< + Policy, + policies::promote_float, + policies::promote_double, + policies::discrete_quantile<>, + policies::assert_undefined<> >::type forwarding_policy; + + return policies::checked_narrowing_cast(detail::airy_bi_prime_imp(static_cast(x), forwarding_policy()), "boost::math::airy<%1%>(%1%)"); +} + +template +inline typename tools::promote_args::type airy_bi_prime(T x) +{ + return airy_bi_prime(x, policies::policy<>()); +} + +}} // namespaces + +#endif // BOOST_MATH_AIRY_HPP diff --git a/include/boost/math/special_functions/jacobi_elliptic.hpp b/include/boost/math/special_functions/jacobi_elliptic.hpp index 6d303b722..f8a75cc89 100644 --- a/include/boost/math/special_functions/jacobi_elliptic.hpp +++ b/include/boost/math/special_functions/jacobi_elliptic.hpp @@ -8,6 +8,8 @@ #define BOOST_MATH_JACOBI_ELLIPTIC_HPP #include +#include +#include namespace boost{ namespace math{ diff --git a/include/boost/math/special_functions/math_fwd.hpp b/include/boost/math/special_functions/math_fwd.hpp index 65c87ff58..8f6ce5355 100644 --- a/include/boost/math/special_functions/math_fwd.hpp +++ b/include/boost/math/special_functions/math_fwd.hpp @@ -639,6 +639,30 @@ namespace boost template std::complex >::result_type> sph_hankel_2(T1 v, T2 x); + template + typename tools::promote_args::type airy_ai(T x, const Policy&); + + template + typename tools::promote_args::type airy_ai(T x); + + template + typename tools::promote_args::type airy_bi(T x, const Policy&); + + template + typename tools::promote_args::type airy_bi(T x); + + template + typename tools::promote_args::type airy_ai_prime(T x, const Policy&); + + template + typename tools::promote_args::type airy_ai_prime(T x); + + template + typename tools::promote_args::type airy_bi_prime(T x, const Policy&); + + template + typename tools::promote_args::type airy_bi_prime(T x); + template typename tools::promote_args::type sin_pi(T x, const Policy&); @@ -1247,6 +1271,23 @@ namespace boost inline typename boost::math::tools::promote_args::type jacobi_cs(T k, U theta)\ { return boost::math::jacobi_cs(k, theta, Policy()); }\ \ + template \ + inline typename boost::math::tools::promote_args::type airy_ai(T x)\ + { return boost::math::airy_ai(x, Policy()); }\ + \ + template \ + inline typename boost::math::tools::promote_args::type airy_bi(T x)\ + { return boost::math::airy_bi(x, Policy()); }\ + \ + template \ + inline typename boost::math::tools::promote_args::type airy_ai_prime(T x)\ + { return boost::math::airy_ai_prime(x, Policy()); }\ + \ + template \ + inline typename boost::math::tools::promote_args::type airy_bi_prime(T x)\ + { return boost::math::airy_bi_prime(x, Policy()); }\ + \ + diff --git a/include/boost/math/tools/remez.hpp b/include/boost/math/tools/remez.hpp index afcbe25af..5c65afc42 100644 --- a/include/boost/math/tools/remez.hpp +++ b/include/boost/math/tools/remez.hpp @@ -449,14 +449,14 @@ T remez_minimax::iterate() A(i, j + offsetN) = x; if(j < orderD) { - T mult = rel_error ? (b[i] - sign * fabs(b[i]) * Elast): (b[i] - sign * Elast); + T mult = rel_error ? T(b[i] - sign * fabs(b[i]) * Elast): T(b[i] - sign * Elast); A(i, j + offsetD) = -x * mult; } x *= x0; } // The last variable to be solved for is the error term, // sign changes with each control point: - T E = rel_error ? sign * fabs(b[i]) : sign; + T E = rel_error ? T(sign * fabs(b[i])) : T(sign); A(i, unknowns - 1) = E; sign = -sign; } @@ -478,7 +478,7 @@ T remez_minimax::iterate() // solution = boost::math::tools::solve(A, b); - err_err = (Elast != 0) ? fabs((fabs(solution[unknowns-1]) - fabs(Elast)) / fabs(Elast)) : 1; + err_err = (Elast != 0) ? T(fabs((fabs(solution[unknowns-1]) - fabs(Elast)) / fabs(Elast))) : T(1); }while(orderD && (convergence_count++ < 80) && (err_err > 0.001)); // diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 9b57dfd1d..a0374bd19 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -77,6 +77,7 @@ run pow_test.cpp ../../test/build//boost_test_exec_monitor ; run log1p_expm1_test.cpp test_instances pch_light ../../test/build//boost_test_exec_monitor ; run powm1_sqrtp1m1_test.cpp test_instances pch_light ../../test/build//boost_test_exec_monitor ; run special_functions_test.cpp ../../test/build//boost_unit_test_framework ; +run test_airy.cpp test_instances pch_light ../../test/build//boost_test_exec_monitor ; run test_bernoulli.cpp ../../test/build//boost_test_exec_monitor ; run test_constants.cpp ../../test/build//boost_test_exec_monitor ; run test_print_info_on_type.cpp ; @@ -776,6 +777,10 @@ run compile_test/sf_sqrt1pm1_incl_test.cpp compile_test/main.cpp ; run compile_test/sf_trunc_incl_test.cpp compile_test/main.cpp ; run compile_test/sf_zeta_incl_test.cpp compile_test/main.cpp ; run compile_test/std_real_concept_check.cpp ; +run compile_test/sf_airy_incl_test.cpp compile_test/main.cpp ; +run compile_test/sf_hankel_incl_test.cpp compile_test/main.cpp ; +run compile_test/sf_jacobi_incl_test.cpp compile_test/main.cpp ; +run compile_test/sf_owens_t_incl_test.cpp compile_test/main.cpp ; compile compile_test/test_traits.cpp ; compile compile_test/tools_config_inc_test.cpp ; compile compile_test/tools_fraction_inc_test.cpp ; diff --git a/test/compile_test/instantiate.hpp b/test/compile_test/instantiate.hpp index 1f815291d..2346fce55 100644 --- a/test/compile_test/instantiate.hpp +++ b/test/compile_test/instantiate.hpp @@ -255,6 +255,10 @@ void instantiate(RealType) boost::math::sph_hankel_2(v1, v2); boost::math::sph_hankel_2(i, v2); #endif + boost::math::airy_ai(v1); + boost::math::airy_bi(v1); + boost::math::airy_ai_prime(v1); + boost::math::airy_bi_prime(v1); boost::math::expint(v1); boost::math::expint(i); boost::math::expint(i, v2); @@ -397,6 +401,10 @@ void instantiate(RealType) boost::math::sph_hankel_2(v1, v2, pol); boost::math::sph_hankel_2(i, v2, pol); #endif + boost::math::airy_ai(v1, pol); + boost::math::airy_bi(v1, pol); + boost::math::airy_ai_prime(v1, pol); + boost::math::airy_bi_prime(v1, pol); boost::math::expint(v1, pol); boost::math::expint(i, pol); boost::math::expint(i, v2, pol); @@ -550,6 +558,10 @@ void instantiate(RealType) test::sph_hankel_2(v1, v2); test::sph_hankel_2(i, v2); #endif + boost::math::airy_ai(i); + boost::math::airy_bi(i); + boost::math::airy_ai_prime(i); + boost::math::airy_bi_prime(i); test::expint(v1); test::expint(i); test::expint(i, v2); @@ -961,6 +973,10 @@ void instantiate_mixed(RealType) test::sph_bessel(i, 1); test::sph_neumann(i, lr); test::sph_neumann(i, i); + test::airy_ai(i); + test::airy_bi(i); + test::airy_ai_prime(i); + test::airy_bi_prime(i); test::owens_t(fr, dr); test::owens_t(i, s); #endif diff --git a/test/compile_test/sf_airy_incl_test.cpp b/test/compile_test/sf_airy_incl_test.cpp new file mode 100644 index 000000000..be3aa478e --- /dev/null +++ b/test/compile_test/sf_airy_incl_test.cpp @@ -0,0 +1,42 @@ +// Copyright John Maddock 2012. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +// +// Basic sanity check that header +// #includes all the files that it needs to. +// +#include +// +// Note this header includes no other headers, this is +// important if this test is to be meaningful: +// +#include "test_compile_result.hpp" + +void compile_and_link_test() +{ + check_result(boost::math::airy_ai(f)); + check_result(boost::math::airy_ai(d)); +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + check_result(boost::math::airy_ai(l)); +#endif + + check_result(boost::math::airy_bi(f)); + check_result(boost::math::airy_bi(d)); +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + check_result(boost::math::airy_bi(l)); +#endif + + check_result(boost::math::airy_ai_prime(f)); + check_result(boost::math::airy_ai_prime(d)); +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + check_result(boost::math::airy_ai_prime(l)); +#endif + + check_result(boost::math::airy_bi_prime(f)); + check_result(boost::math::airy_bi_prime(d)); +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + check_result(boost::math::airy_bi_prime(l)); +#endif + +} diff --git a/test/compile_test/sf_hankel_incl_test.cpp b/test/compile_test/sf_hankel_incl_test.cpp new file mode 100644 index 000000000..5a32dca29 --- /dev/null +++ b/test/compile_test/sf_hankel_incl_test.cpp @@ -0,0 +1,46 @@ +// Copyright John Maddock 2012. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +// +// Basic sanity check that header +// #includes all the files that it needs to. +// +#include +// +// Note this header includes no other headers, this is +// important if this test is to be meaningful: +// +#include "test_compile_result.hpp" + +inline void check_result_imp(std::complex, std::complex){} +inline void check_result_imp(std::complex, std::complex){} +inline void check_result_imp(std::complex, std::complex){} + +void compile_and_link_test() +{ + check_result >(boost::math::cyl_hankel_1(f, f)); + check_result >(boost::math::cyl_hankel_1(d, d)); +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + check_result >(boost::math::cyl_hankel_1(l, l)); +#endif + + check_result >(boost::math::cyl_hankel_2(f, f)); + check_result >(boost::math::cyl_hankel_2(d, d)); +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + check_result >(boost::math::cyl_hankel_2(l, l)); +#endif + + check_result >(boost::math::sph_hankel_1(f, f)); + check_result >(boost::math::sph_hankel_1(d, d)); +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + check_result >(boost::math::sph_hankel_1(l, l)); +#endif + + check_result >(boost::math::sph_hankel_2(f, f)); + check_result >(boost::math::sph_hankel_2(d, d)); +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + check_result >(boost::math::sph_hankel_2(l, l)); +#endif + +} diff --git a/test/compile_test/sf_jacobi_incl_test.cpp b/test/compile_test/sf_jacobi_incl_test.cpp new file mode 100644 index 000000000..a1fc66b0c --- /dev/null +++ b/test/compile_test/sf_jacobi_incl_test.cpp @@ -0,0 +1,96 @@ +// Copyright John Maddock 2012. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +// +// Basic sanity check that header +// #includes all the files that it needs to. +// +#include +// +// Note this header includes no other headers, this is +// important if this test is to be meaningful: +// +#include "test_compile_result.hpp" + +void compile_and_link_test() +{ + check_result(boost::math::jacobi_elliptic(f, f, static_cast(0), static_cast(0))); + check_result(boost::math::jacobi_elliptic(d, d, static_cast(0), static_cast(0))); +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + check_result(boost::math::jacobi_elliptic(l, l, static_cast(0), static_cast(0))); +#endif + + check_result(boost::math::jacobi_sn(f, f)); + check_result(boost::math::jacobi_sn(d, d)); +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + check_result(boost::math::jacobi_sn(l, l)); +#endif + + check_result(boost::math::jacobi_cn(f, f)); + check_result(boost::math::jacobi_cn(d, d)); +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + check_result(boost::math::jacobi_cn(l, l)); +#endif + + check_result(boost::math::jacobi_dn(f, f)); + check_result(boost::math::jacobi_dn(d, d)); +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + check_result(boost::math::jacobi_dn(l, l)); +#endif + + check_result(boost::math::jacobi_cd(f, f)); + check_result(boost::math::jacobi_cd(d, d)); +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + check_result(boost::math::jacobi_cd(l, l)); +#endif + + check_result(boost::math::jacobi_dc(f, f)); + check_result(boost::math::jacobi_dc(d, d)); +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + check_result(boost::math::jacobi_dc(l, l)); +#endif + + check_result(boost::math::jacobi_ns(f, f)); + check_result(boost::math::jacobi_ns(d, d)); +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + check_result(boost::math::jacobi_ns(l, l)); +#endif + + check_result(boost::math::jacobi_sd(f, f)); + check_result(boost::math::jacobi_sd(d, d)); +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + check_result(boost::math::jacobi_sd(l, l)); +#endif + + check_result(boost::math::jacobi_ds(f, f)); + check_result(boost::math::jacobi_ds(d, d)); +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + check_result(boost::math::jacobi_ds(l, l)); +#endif + + check_result(boost::math::jacobi_nc(f, f)); + check_result(boost::math::jacobi_nc(d, d)); +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + check_result(boost::math::jacobi_nc(l, l)); +#endif + + check_result(boost::math::jacobi_nd(f, f)); + check_result(boost::math::jacobi_nd(d, d)); +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + check_result(boost::math::jacobi_nd(l, l)); +#endif + + check_result(boost::math::jacobi_sc(f, f)); + check_result(boost::math::jacobi_sc(d, d)); +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + check_result(boost::math::jacobi_sc(l, l)); +#endif + + check_result(boost::math::jacobi_cs(f, f)); + check_result(boost::math::jacobi_cs(d, d)); +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + check_result(boost::math::jacobi_cs(l, l)); +#endif + +} diff --git a/test/compile_test/sf_owens_t_incl_test.cpp b/test/compile_test/sf_owens_t_incl_test.cpp new file mode 100644 index 000000000..2839a0778 --- /dev/null +++ b/test/compile_test/sf_owens_t_incl_test.cpp @@ -0,0 +1,24 @@ +// Copyright John Maddock 2012. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +// +// Basic sanity check that header +// #includes all the files that it needs to. +// +#include +// +// Note this header includes no other headers, this is +// important if this test is to be meaningful: +// +#include "test_compile_result.hpp" + +void compile_and_link_test() +{ + check_result(boost::math::owens_t(f, f)); + check_result(boost::math::owens_t(d, d)); +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + check_result(boost::math::owens_t(l, l)); +#endif + +} diff --git a/test/test_airy.cpp b/test/test_airy.cpp new file mode 100644 index 000000000..4376365de --- /dev/null +++ b/test/test_airy.cpp @@ -0,0 +1,85 @@ +// Copyright John Maddock 2012 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include + +#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error +#include +#include +#include +#include +#include + +#ifdef _MSC_VER +# pragma warning(disable : 4756 4127) // overflow in constant arithmetic +// Constants are too big for float case, but this doesn't matter for test. +#endif + +// +// DESCRIPTION: +// ~~~~~~~~~~~~ +// +// This file tests the Airy functions. +// These are basically just a few spot tests, since the underlying implementation +// is the same as for the Bessel functions. +// +template +void test_airy(T, const char* name) +{ + std::cout << "Testing type " << name << std::endl; + + static const boost::array, 8> data = + {{ + // Values are x, Ai, Bi, Ai', Bi'. + // Calculated from functions.wolfram.com. + {{ 0, static_cast(0.355028053887817239260063186004183176397979174199177240583327L), static_cast(0.614926627446000735150922369093613553594728188648596505040879L), static_cast(-0.258819403792806798405183560189203963479091138354934582210002L), static_cast(0.448288357353826357914823710398828390866226799212262061082809L) }}, + {{ 2, static_cast(0.0349241304232743791353220807918076097610602138975832071886699L), static_cast(3.29809499997821471028060442522345242200397596340362078768292L), static_cast(-0.0530903844336536317039991858787034912485609900458779926304030L), static_cast(4.10068204993288988938203407917793529439024461377513711983771L) }}, + {{ 3.5, static_cast(0.00258409878698963496327714478330027845019631096464789073425468L), static_cast(33.0555067546114794142573129819217946861266278143724855010951L), static_cast(-0.00500441396795258283203024967883836790716278377542974739809987L), static_cast(59.1643195813609870345742121795224602529063343063320217229383L) }}, + {{ 30.5, static_cast(2.04253461666926015963302258449952681287194929082634196439857e-50L), static_cast(1.41092256201712698413071856671990267572381736486242769613348e48L), static_cast(-1.12969466271996376602221721397236452019046628449363103927812e-49L), static_cast(7.78046629440950280615411694840600772185863288897663300007879e48L) }}, + {{ -2, static_cast(0.227407428201685575991924436037873799460772225417096716495790L), static_cast(-0.412302587956398488083234054611461042034534834472404728823877L), static_cast(0.618259020741691041406264291332475282915777945124146942159898L), static_cast(0.278795166921169522685097569410983241403000593451631000239732L) }}, + {{ -3.5, static_cast(-0.375533823140431911934396951580170239543268576378264063902563L), static_cast(0.168939837481058611843442769540943269911562243926304070915824L), static_cast(-0.343443433454048146287937374098698857094194220958713294264017L), static_cast(-0.693116284907288801752443612670580462699702668014978495343697L) }}, + {{ -30.25, static_cast(-0.236900428491559731119806902381433570300271552218956227857722L), static_cast(0.0418614989839147441219283537268101850442118139150748075124111L), static_cast(-0.232197332372689274917364138870840123428255785603863926579897L), static_cast(-1.30261375952554697768880873095691151213006925411329957440342L) }}, + {{ -300.5, static_cast(-0.117584304761702008955433457721670950077867326839023449546057L), static_cast(0.0673518035440918806545676478730240310819758211028871823560384), static_cast(-1.16763702262473888724431076711846459336993902544926162874376L), static_cast(-2.03826035550300900666977975504950803669545593208969273694133L) }}, + }}; + + T tol = boost::math::tools::epsilon() * 800; + for(unsigned i = 0; i < data.size(); ++i) + { + BOOST_CHECK_CLOSE_FRACTION(data[i][1], boost::math::airy_ai(data[i][0]), tol); + if(boost::math::isfinite(data[i][2])) + BOOST_CHECK_CLOSE_FRACTION(data[i][2], boost::math::airy_bi(data[i][0]), tol); + BOOST_CHECK_CLOSE_FRACTION(data[i][3], boost::math::airy_ai_prime(data[i][0]), tol); + if(boost::math::isfinite(data[i][4])) + BOOST_CHECK_CLOSE_FRACTION(data[i][4], boost::math::airy_bi_prime(data[i][0]), tol); + } +} + + +int test_main(int, char* []) +{ +#ifdef TEST_GSL + gsl_set_error_handler_off(); +#endif + BOOST_MATH_CONTROL_FP; + +#ifndef BOOST_MATH_BUGGY_LARGE_FLOAT_CONSTANTS + test_airy(0.1F, "float"); +#endif + test_airy(0.1, "double"); +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + test_airy(0.1L, "long double"); + test_airy(boost::math::concepts::real_concept(0), "real_concept"); +#else + std::cout << "The long double tests have been disabled on this platform " + "either because the long double overloads of the usual math functions are " + "not available at all, or because they are too inaccurate for these tests " + "to pass." << std::cout; +#endif + return 0; +} + + + + diff --git a/test/test_instances.hpp b/test/test_instances.hpp index cb07620b1..f2c73da9e 100644 --- a/test/test_instances.hpp +++ b/test/test_instances.hpp @@ -354,6 +354,17 @@ namespace boost{ namespace math{ template detail::bessel_traits >::result_type sph_neumann(unsigned v, BOOST_MATH_TEST_TYPE x); + // Airy Functions: + template tools::promote_args::type airy_ai(BOOST_MATH_TEST_TYPE x, const policies::policy<>&); + template tools::promote_args::type airy_ai(BOOST_MATH_TEST_TYPE x); + template tools::promote_args::type airy_bi(BOOST_MATH_TEST_TYPE x, const policies::policy<>&); + template tools::promote_args::type airy_bi(BOOST_MATH_TEST_TYPE x); + template tools::promote_args::type airy_ai_prime(BOOST_MATH_TEST_TYPE x, const policies::policy<>&); + template tools::promote_args::type airy_ai_prime(BOOST_MATH_TEST_TYPE x); + template tools::promote_args::type airy_bi_prime(BOOST_MATH_TEST_TYPE x, const policies::policy<>&); + template tools::promote_args::type airy_bi_prime(BOOST_MATH_TEST_TYPE x); + + // Exponential Integral template tools::promote_args::type expint(unsigned n, BOOST_MATH_TEST_TYPE z, const policies::policy<> &); template detail::expint_result::type expint(int const z, BOOST_MATH_TEST_TYPE const u); From 1a2d4d2c5ef16d8586b59fb15a24f0e2824a15ba Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 23 May 2012 17:18:49 +0000 Subject: [PATCH 005/115] Move default arguments to forward declaration. Fixes #6930. [SVN r78559] --- include/boost/math/special_functions/jacobi_elliptic.hpp | 2 +- include/boost/math/special_functions/math_fwd.hpp | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/include/boost/math/special_functions/jacobi_elliptic.hpp b/include/boost/math/special_functions/jacobi_elliptic.hpp index f8a75cc89..a45079653 100644 --- a/include/boost/math/special_functions/jacobi_elliptic.hpp +++ b/include/boost/math/special_functions/jacobi_elliptic.hpp @@ -140,7 +140,7 @@ inline typename tools::promote_args::type jacobi_elliptic(T k, T theta, T* pc } template -inline typename tools::promote_args::type jacobi_elliptic(T k, T theta, T* pcn = 0, T* pdn = 0) +inline typename tools::promote_args::type jacobi_elliptic(T k, T theta, T* pcn, T* pdn) { return jacobi_elliptic(k, theta, pcn, pdn, policies::policy<>()); } diff --git a/include/boost/math/special_functions/math_fwd.hpp b/include/boost/math/special_functions/math_fwd.hpp index 8f6ce5355..5d54fd14b 100644 --- a/include/boost/math/special_functions/math_fwd.hpp +++ b/include/boost/math/special_functions/math_fwd.hpp @@ -742,7 +742,7 @@ namespace boost typename tools::promote_args::type jacobi_elliptic(T k, T theta, T* pcn, T* pdn, const Policy&); template - typename tools::promote_args::type jacobi_elliptic(T k, T theta, T* pcn, T* pdn); + typename tools::promote_args::type jacobi_elliptic(T k, T theta, T* pcn = 0, T* pdn = 0); template typename tools::promote_args::type jacobi_sn(U k, T theta, const Policy& pol); From 42e26d7071a229f5fa27bdd4930178b5c3d03b4c Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Thu, 24 May 2012 10:44:13 +0000 Subject: [PATCH 006/115] Typo and date corrected [SVN r78578] --- test/ntl_concept_check.cpp | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/test/ntl_concept_check.cpp b/test/ntl_concept_check.cpp index 9161a7f63..2142bca38 100644 --- a/test/ntl_concept_check.cpp +++ b/test/ntl_concept_check.cpp @@ -1,5 +1,5 @@ // Copyright John Maddock 2007-8. -// Copyright Paul A. bristow 2009 +// Copyright Paul A. Bristow 2009, 2011 // Use, modification and distribution are subject to the // Boost Software License, Version 1.0. (See accompanying file @@ -15,6 +15,8 @@ # pragma warning (disable : 4100) // unreferenced formal parameter #endif + + #define BOOST_MATH_ASSERT_UNDEFINED_POLICY false #include From 5e0aa58152af0604372b5b2d9bb41e524e63e709 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Thu, 24 May 2012 11:13:54 +0000 Subject: [PATCH 007/115] Added Policy as a template parameter to functors and #6934 test program now compiles and runs. Need to commit changes to concept checks to confirm. [SVN r78579] --- .../math/distributions/inverse_gaussian.hpp | 16 ++++++++-------- 1 file changed, 8 insertions(+), 8 deletions(-) diff --git a/include/boost/math/distributions/inverse_gaussian.hpp b/include/boost/math/distributions/inverse_gaussian.hpp index 67c1b4109..fa7c2a1e6 100644 --- a/include/boost/math/distributions/inverse_gaussian.hpp +++ b/include/boost/math/distributions/inverse_gaussian.hpp @@ -207,11 +207,11 @@ inline RealType cdf(const inverse_gaussian_distribution& dist, return result; } // cdf -template +template struct inverse_gaussian_quantile_functor { - inverse_gaussian_quantile_functor(const boost::math::inverse_gaussian_distribution dist, RealType const& p) + inverse_gaussian_quantile_functor(const boost::math::inverse_gaussian_distribution dist, RealType const& p) : distribution(dist), prob(p) { } @@ -224,14 +224,14 @@ struct inverse_gaussian_quantile_functor return boost::math::make_tuple(fx, dx); } private: - const boost::math::inverse_gaussian_distribution distribution; + const boost::math::inverse_gaussian_distribution distribution; RealType prob; }; -template +template struct inverse_gaussian_quantile_complement_functor { - inverse_gaussian_quantile_complement_functor(const boost::math::inverse_gaussian_distribution dist, RealType const& p) + inverse_gaussian_quantile_complement_functor(const boost::math::inverse_gaussian_distribution dist, RealType const& p) : distribution(dist), prob(p) { } @@ -245,7 +245,7 @@ struct inverse_gaussian_quantile_complement_functor return boost::math::make_tuple(fx, dx); } private: - const boost::math::inverse_gaussian_distribution distribution; + const boost::math::inverse_gaussian_distribution distribution; RealType prob; }; @@ -347,7 +347,7 @@ inline RealType quantile(const inverse_gaussian_distribution& boost::uintmax_t m = policies::get_max_root_iterations(); // and max iterations. using boost::math::tools::newton_raphson_iterate; result = - newton_raphson_iterate(inverse_gaussian_quantile_functor(dist, p), guess, min, max, get_digits, m); + newton_raphson_iterate(inverse_gaussian_quantile_functor(dist, p), guess, min, max, get_digits, m); return result; } // quantile @@ -428,7 +428,7 @@ inline RealType quantile(const complemented2_type(); using boost::math::tools::newton_raphson_iterate; result = - newton_raphson_iterate(inverse_gaussian_quantile_complement_functor(c.dist, q), guess, min, max, get_digits, m); + newton_raphson_iterate(inverse_gaussian_quantile_complement_functor(c.dist, q), guess, min, max, get_digits, m); return result; } // quantile From 02787878e6c9d1cd1026adc36e04706ffe0ae75f Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 28 May 2012 11:05:43 +0000 Subject: [PATCH 008/115] Update concept checks to unmask issues reported in #6934. Add some distributions to the concept tests that were missing before. Add skew_normal_distribution to distributions.hpp. Fix some errors in calculating custom policies when the defaults have been changed. Fix the errors and warnings that result from the above. Refs #6934. [SVN r78711] --- .../math/constants/calculate_constants.hpp | 1 + include/boost/math/distributions.hpp | 1 + .../boost/math/distributions/skew_normal.hpp | 85 ++++++++++--------- include/boost/math/policies/policy.hpp | 8 +- .../boost/math/special_functions/expm1.hpp | 4 +- .../distribution_concept_check.cpp | 54 +++++++----- test/compile_test/instantiate.hpp | 4 +- 7 files changed, 88 insertions(+), 69 deletions(-) diff --git a/include/boost/math/constants/calculate_constants.hpp b/include/boost/math/constants/calculate_constants.hpp index 0b78929e7..9129ade53 100644 --- a/include/boost/math/constants/calculate_constants.hpp +++ b/include/boost/math/constants/calculate_constants.hpp @@ -85,6 +85,7 @@ template // sqrt(2/pi) template inline T constant_root_two_div_pi::compute(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(mpl::int_)) { + BOOST_MATH_STD_USING return sqrt((2 / pi > >())); } diff --git a/include/boost/math/distributions.hpp b/include/boost/math/distributions.hpp index 37cf027a8..91d6a8b4b 100644 --- a/include/boost/math/distributions.hpp +++ b/include/boost/math/distributions.hpp @@ -39,6 +39,7 @@ #include #include #include +#include #include #include #include diff --git a/include/boost/math/distributions/skew_normal.hpp b/include/boost/math/distributions/skew_normal.hpp index 58526defd..d39737496 100644 --- a/include/boost/math/distributions/skew_normal.hpp +++ b/include/boost/math/distributions/skew_normal.hpp @@ -476,50 +476,51 @@ namespace boost{ namespace math{ // 21 elements static const RealType shapes[] = { 0.0, - 1.000000000000000e-004, - 2.069138081114790e-004, - 4.281332398719396e-004, - 8.858667904100824e-004, - 1.832980710832436e-003, - 3.792690190732250e-003, - 7.847599703514606e-003, - 1.623776739188722e-002, - 3.359818286283781e-002, - 6.951927961775606e-002, - 1.438449888287663e-001, - 2.976351441631319e-001, - 6.158482110660261e-001, - 1.274274985703135e+000, - 2.636650898730361e+000, - 5.455594781168514e+000, - 1.128837891684688e+001, - 2.335721469090121e+001, - 4.832930238571753e+001, - 1.000000000000000e+002}; + static_cast(1.000000000000000e-004), + static_cast(2.069138081114790e-004), + static_cast(4.281332398719396e-004), + static_cast(8.858667904100824e-004), + static_cast(1.832980710832436e-003), + static_cast(3.792690190732250e-003), + static_cast(7.847599703514606e-003), + static_cast(1.623776739188722e-002), + static_cast(3.359818286283781e-002), + static_cast(6.951927961775606e-002), + static_cast(1.438449888287663e-001), + static_cast(2.976351441631319e-001), + static_cast(6.158482110660261e-001), + static_cast(1.274274985703135e+000), + static_cast(2.636650898730361e+000), + static_cast(5.455594781168514e+000), + static_cast(1.128837891684688e+001), + static_cast(2.335721469090121e+001), + static_cast(4.832930238571753e+001), + static_cast(1.000000000000000e+002) + }; // 21 elements static const RealType guess[] = { 0.0, - 5.000050000525391e-005, - 1.500015000148736e-004, - 3.500035000350010e-004, - 7.500075000752560e-004, - 1.450014500145258e-003, - 3.050030500305390e-003, - 6.250062500624765e-003, - 1.295012950129504e-002, - 2.675026750267495e-002, - 5.525055250552491e-002, - 1.132511325113255e-001, - 2.249522495224952e-001, - 3.992539925399257e-001, - 5.353553535535358e-001, - 4.954549545495457e-001, - 3.524535245352451e-001, - 2.182521825218249e-001, - 1.256512565125654e-001, - 6.945069450694508e-002, - 3.735037350373460e-002 + static_cast(5.000050000525391e-005), + static_cast(1.500015000148736e-004), + static_cast(3.500035000350010e-004), + static_cast(7.500075000752560e-004), + static_cast(1.450014500145258e-003), + static_cast(3.050030500305390e-003), + static_cast(6.250062500624765e-003), + static_cast(1.295012950129504e-002), + static_cast(2.675026750267495e-002), + static_cast(5.525055250552491e-002), + static_cast(1.132511325113255e-001), + static_cast(2.249522495224952e-001), + static_cast(3.992539925399257e-001), + static_cast(5.353553535535358e-001), + static_cast(4.954549545495457e-001), + static_cast(3.524535245352451e-001), + static_cast(2.182521825218249e-001), + static_cast(1.256512565125654e-001), + static_cast(6.945069450694508e-002), + static_cast(3.735037350373460e-002) }; const RealType* result_ptr = std::lower_bound(shapes, shapes+21, shape); @@ -532,7 +533,7 @@ namespace boost{ namespace math{ // TODO: make the search bounds smarter, depending on the shape parameter RealType search_min = 0; // below zero was caught above - RealType search_max = 0.55; // will never go above 0.55 + RealType search_max = 0.55f; // will never go above 0.55 // refine if(d < static_cast(21)) // shape smaller 100 @@ -544,7 +545,7 @@ namespace boost{ namespace math{ } else // shape greater 100 { - result = 1e-4; + result = 1e-4f; search_max = guess[19]; // set 19 instead of 20 to have a safety margin because the table may not be exact @ shape=100 } diff --git a/include/boost/math/policies/policy.hpp b/include/boost/math/policies/policy.hpp index 70e67c70b..01fe3d0ae 100644 --- a/include/boost/math/policies/policy.hpp +++ b/include/boost/math/policies/policy.hpp @@ -431,7 +431,7 @@ public: // // Mathematically undefined properties: // - typedef typename detail::find_arg, discrete_quantile<> >::type assert_undefined_type; + typedef typename detail::find_arg, assert_undefined<> >::type assert_undefined_type; // // Max iterations: // @@ -537,12 +537,12 @@ private: // // Mathematically undefined properties: // - typedef typename detail::find_arg, discrete_quantile<> >::type assert_undefined_type; + typedef typename detail::find_arg, typename Policy::assert_undefined_type >::type assert_undefined_type; // // Max iterations: // - typedef typename detail::find_arg, max_series_iterations<> >::type max_series_iterations_type; - typedef typename detail::find_arg, max_root_iterations<> >::type max_root_iterations_type; + typedef typename detail::find_arg, typename Policy::max_series_iterations_type>::type max_series_iterations_type; + typedef typename detail::find_arg, typename Policy::max_root_iterations_type>::type max_root_iterations_type; // // Define a typelist of the policies: // diff --git a/include/boost/math/special_functions/expm1.hpp b/include/boost/math/special_functions/expm1.hpp index 9ff2541fb..51e3aa1a8 100644 --- a/include/boost/math/special_functions/expm1.hpp +++ b/include/boost/math/special_functions/expm1.hpp @@ -151,8 +151,8 @@ T expm1_imp(T x, const mpl::int_<53>&, const P& pol) return x; static const float Y = 0.10281276702880859e1f; - static const T n[] = { -0.28127670288085937e-1, 0.51278186299064534e0, -0.6310029069350198e-1, 0.11638457975729296e-1, -0.52143390687521003e-3, 0.21491399776965688e-4 }; - static const T d[] = { 1, -0.45442309511354755e0, 0.90850389570911714e-1, -0.10088963629815502e-1, 0.63003407478692265e-3, -0.17976570003654402e-4 }; + static const T n[] = { static_cast(-0.28127670288085937e-1), static_cast(0.51278186299064534e0), static_cast(-0.6310029069350198e-1), static_cast(0.11638457975729296e-1), static_cast(-0.52143390687521003e-3), static_cast(0.21491399776965688e-4) }; + static const T d[] = { 1, static_cast(-0.45442309511354755e0), static_cast(0.90850389570911714e-1), static_cast(-0.10088963629815502e-1), static_cast(0.63003407478692265e-3), static_cast(-0.17976570003654402e-4) }; T result = x * Y + x * tools::evaluate_polynomial(n, x) / tools::evaluate_polynomial(d, x); return result; diff --git a/test/compile_test/distribution_concept_check.cpp b/test/compile_test/distribution_concept_check.cpp index 2e895f991..26b236a55 100644 --- a/test/compile_test/distribution_concept_check.cpp +++ b/test/compile_test/distribution_concept_check.cpp @@ -16,26 +16,40 @@ void instantiate(RealType) using namespace boost::math; using namespace boost::math::concepts; - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); - function_requires > >(); + typedef policies::policy::digits - 2> > custom_policy; + + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); + function_requires > >(); } diff --git a/test/compile_test/instantiate.hpp b/test/compile_test/instantiate.hpp index 2346fce55..526a4cc22 100644 --- a/test/compile_test/instantiate.hpp +++ b/test/compile_test/instantiate.hpp @@ -18,7 +18,7 @@ #ifndef BOOST_MATH_INSTANTIATE_MINIMUM -typedef boost::math::policies::policy<> test_policy; +typedef boost::math::policies::policy, boost::math::policies::promote_double > test_policy; namespace test{ @@ -67,6 +67,7 @@ void instantiate(RealType) function_requires > >(); function_requires > >(); function_requires > >(); + function_requires > >(); function_requires > >(); function_requires > >(); function_requires > >(); @@ -97,6 +98,7 @@ void instantiate(RealType) function_requires > >(); function_requires > >(); function_requires > >(); + function_requires > >(); function_requires > >(); function_requires > >(); function_requires > >(); From a1789c4766ef10113e3a1072c52d812a1fc55d77 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 28 May 2012 16:27:00 +0000 Subject: [PATCH 009/115] Tighten Weibull distro tests. Fix corner cases in Weibull distro. Fixes #6939. Fixes #6938. [SVN r78723] --- include/boost/math/distributions/weibull.hpp | 16 ++++++++++++---- test/test_weibull.cpp | 13 +++++++++++-- 2 files changed, 23 insertions(+), 6 deletions(-) diff --git a/include/boost/math/distributions/weibull.hpp b/include/boost/math/distributions/weibull.hpp index 6b5c7db34..133b7e04c 100644 --- a/include/boost/math/distributions/weibull.hpp +++ b/include/boost/math/distributions/weibull.hpp @@ -28,7 +28,7 @@ inline bool check_weibull_shape( RealType shape, RealType* result, const Policy& pol) { - if((shape < 0) || !(boost::math::isfinite)(shape)) + if((shape <= 0) || !(boost::math::isfinite)(shape)) { *result = policies::raise_domain_error( function, @@ -133,11 +133,19 @@ inline RealType pdf(const weibull_distribution& dist, const Re return result; if(x == 0) - { // Special case, but x == min, pdf = 1 for shape = 1, - return 0; + { + if(shape == 1) + { + return 1 / scale; + } + if(shape > 1) + { + return 0; + } + return policies::raise_overflow_error(function, 0, Policy()); } result = exp(-pow(x / scale, shape)); - result *= pow(x / scale, shape) * shape / x; + result *= pow(x / scale, shape - 1) * shape / scale; return result; } diff --git a/test/test_weibull.cpp b/test/test_weibull.cpp index 3c4338a59..d3e7883a2 100644 --- a/test/test_weibull.cpp +++ b/test/test_weibull.cpp @@ -311,22 +311,31 @@ void test_spots(RealType) // // Special cases: // - BOOST_CHECK(pdf(dist, 0) == 0); BOOST_CHECK(cdf(dist, 0) == 0); BOOST_CHECK(cdf(complement(dist, 0)) == 1); BOOST_CHECK(quantile(dist, 0) == 0); BOOST_CHECK(quantile(complement(dist, 1)) == 0); + BOOST_CHECK_EQUAL(pdf(weibull_distribution(1, 1), 0), 1); + // // Error checks: // - BOOST_CHECK_THROW(weibull_distribution(0, -1), std::domain_error); + BOOST_CHECK_THROW(weibull_distribution(1, -1), std::domain_error); BOOST_CHECK_THROW(weibull_distribution(-1, 1), std::domain_error); + BOOST_CHECK_THROW(weibull_distribution(1, 0), std::domain_error); + BOOST_CHECK_THROW(weibull_distribution(0, 1), std::domain_error); BOOST_CHECK_THROW(pdf(dist, -1), std::domain_error); BOOST_CHECK_THROW(cdf(dist, -1), std::domain_error); BOOST_CHECK_THROW(cdf(complement(dist, -1)), std::domain_error); BOOST_CHECK_THROW(quantile(dist, 1), std::overflow_error); BOOST_CHECK_THROW(quantile(complement(dist, 0)), std::overflow_error); + BOOST_CHECK_THROW(quantile(dist, -1), std::domain_error); + BOOST_CHECK_THROW(quantile(complement(dist, -1)), std::domain_error); + + BOOST_CHECK_EQUAL(pdf(dist, 0), exp(-pow(RealType(0) / RealType(3), RealType(2))) * pow(RealType(0), RealType(1)) * RealType(2) / RealType(3)); + BOOST_CHECK_EQUAL(pdf(weibull_distribution(1, 3), 0), exp(-pow(RealType(0) / RealType(3), RealType(1))) * pow(RealType(0), RealType(0)) * RealType(1) / RealType(3)); + BOOST_CHECK_THROW(pdf(weibull_distribution(0.5, 3), 0), std::overflow_error); } // template void test_spots(RealType) From 3e9242ade2c150fb3fae95731152f8be0687b956 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 28 May 2012 17:42:50 +0000 Subject: [PATCH 010/115] Improve testing of error conditions and fix any errors detected. Takes care of distributions normal-weibull. Refs #6937. [SVN r78726] --- include/boost/math/distributions/students_t.hpp | 4 ++-- test/test_normal.cpp | 6 +++++- test/test_pareto.cpp | 11 +++++++++++ test/test_skew_normal.cpp | 5 ++++- test/test_students_t.cpp | 4 ++++ 5 files changed, 26 insertions(+), 4 deletions(-) diff --git a/include/boost/math/distributions/students_t.hpp b/include/boost/math/distributions/students_t.hpp index 38df1b628..0562387ae 100644 --- a/include/boost/math/distributions/students_t.hpp +++ b/include/boost/math/distributions/students_t.hpp @@ -163,9 +163,9 @@ inline RealType quantile(const students_t_distribution& dist, // static const char* function = "boost::math::quantile(const students_t_distribution<%1%>&, %1%)"; RealType error_result; - if(false == detail::check_df( + if(false == (detail::check_df( function, degrees_of_freedom, &error_result, Policy()) - && detail::check_probability(function, probability, &error_result, Policy())) + && detail::check_probability(function, probability, &error_result, Policy()))) return error_result; // Special cases, regardless of degrees_of_freedom. diff --git a/test/test_normal.cpp b/test/test_normal.cpp index 3dfb943f5..0a3168e5c 100644 --- a/test/test_normal.cpp +++ b/test/test_normal.cpp @@ -282,7 +282,11 @@ void test_spots(RealType) standard_deviation(def_norm01), static_cast(1), 0); // Mean == zero - + // Error tests: + BOOST_CHECK_THROW(pdf(normal_distribution(0, 0), 0), std::domain_error); + BOOST_CHECK_THROW(pdf(normal_distribution(0, -1), 0), std::domain_error); + BOOST_CHECK_THROW(quantile(normal_distribution(0, 1), -1), std::domain_error); + BOOST_CHECK_THROW(quantile(normal_distribution(0, 1), 2), std::domain_error); } // template void test_spots(RealType) int test_main(int, char* []) diff --git a/test/test_pareto.cpp b/test/test_pareto.cpp index 9ffaba714..2b63b9532 100644 --- a/test/test_pareto.cpp +++ b/test/test_pareto.cpp @@ -232,6 +232,17 @@ void test_spots(RealType) kurtosis_excess(pareto15), kurtosis(pareto15) - static_cast(3L), tol5eps); // Check kurtosis excess = kurtosis - 3; + // Error condition checks: + BOOST_CHECK_THROW(pdf(pareto_distribution(0, 1), 0), std::domain_error); + BOOST_CHECK_THROW(pdf(pareto_distribution(1, 0), 0), std::domain_error); + BOOST_CHECK_THROW(pdf(pareto_distribution(-1, 1), 0), std::domain_error); + BOOST_CHECK_THROW(pdf(pareto_distribution(1, -1), 0), std::domain_error); + + BOOST_CHECK_THROW(pdf(pareto_distribution(1, 1), 0), std::domain_error); + BOOST_CHECK_THROW(cdf(pareto_distribution(1, 1), 0), std::domain_error); + + BOOST_CHECK_THROW(quantile(pareto_distribution(1, 1), -1), std::domain_error); + BOOST_CHECK_THROW(quantile(pareto_distribution(1, 1), 2), std::domain_error); } // template void test_spots(RealType) int test_main(int, char* []) diff --git a/test/test_skew_normal.cpp b/test/test_skew_normal.cpp index b6d580f52..24722e166 100644 --- a/test/test_skew_normal.cpp +++ b/test/test_skew_normal.cpp @@ -436,7 +436,10 @@ void test_spots(RealType) , static_cast(0.8638862008406084244563L), tol1000); } - + BOOST_CHECK_THROW(cdf(skew_normal_distribution(0, 0, 0), 0), std::domain_error); + BOOST_CHECK_THROW(cdf(skew_normal_distribution(0, -1, 0), 0), std::domain_error); + BOOST_CHECK_THROW(quantile(skew_normal_distribution(0, 1, 0), -1), std::domain_error); + BOOST_CHECK_THROW(quantile(skew_normal_distribution(0, 1, 0), 2), std::domain_error); } diff --git a/test/test_students_t.cpp b/test/test_students_t.cpp index b3ac8c709..ec95ddf4d 100644 --- a/test/test_students_t.cpp +++ b/test/test_students_t.cpp @@ -465,6 +465,10 @@ void test_spots(RealType) static_cast(1.0))), 9); + BOOST_CHECK_THROW(quantile(dist, -1), std::domain_error); + BOOST_CHECK_THROW(quantile(dist, 2), std::domain_error); + BOOST_CHECK_THROW(pdf(students_t_distribution(0), 0), std::domain_error); + BOOST_CHECK_THROW(pdf(students_t_distribution(-1), 0), std::domain_error); } // template void test_spots(RealType) int test_main(int, char* []) From b2e3224cf651c7d3f40324f7cc9f20cf16371e35 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Tue, 29 May 2012 15:38:49 +0000 Subject: [PATCH 011/115] Added more tests that check that nonfinites throw. [SVN r78746] --- test/test_weibull.cpp | 68 ++++++++++++++++++++++++++++++++++--------- 1 file changed, 55 insertions(+), 13 deletions(-) diff --git a/test/test_weibull.cpp b/test/test_weibull.cpp index d3e7883a2..c52e71e05 100644 --- a/test/test_weibull.cpp +++ b/test/test_weibull.cpp @@ -1,5 +1,5 @@ -// Copyright John Maddock 2006. -// Copyright Paul A. Bristow 2007. +// Copyright John Maddock 2006, 2012. +// Copyright Paul A. Bristow 2007, 2012. // Use, modification and distribution are subject to the // Boost Software License, Version 1.0. @@ -8,6 +8,11 @@ // test_weibull.cpp +#ifdef _MSC_VER +# pragma warning (disable : 4127) // conditional expression is constant. +#endif + + #include // for real_concept #include // Boost.Test #include @@ -337,6 +342,41 @@ void test_spots(RealType) BOOST_CHECK_EQUAL(pdf(weibull_distribution(1, 3), 0), exp(-pow(RealType(0) / RealType(3), RealType(1))) * pow(RealType(0), RealType(0)) * RealType(1) / RealType(3)); BOOST_CHECK_THROW(pdf(weibull_distribution(0.5, 3), 0), std::overflow_error); + // No longer allow any parameter to be NaN or inf, so all these tests should throw. + if (std::numeric_limits::has_quiet_NaN) + { + // Attempt to construct from non-finite should throw. + RealType nan = std::numeric_limits::quiet_NaN(); + BOOST_CHECK_THROW(weibull_distribution w(nan), std::domain_error); + BOOST_CHECK_THROW(weibull_distribution w(1, nan), std::domain_error); + + // Non-finite parameters should throw. + weibull_distribution w(RealType(1)); + BOOST_CHECK_THROW(pdf(w, +nan), std::domain_error); // x = NaN + BOOST_CHECK_THROW(cdf(w, +nan), std::domain_error); // x = NaN + BOOST_CHECK_THROW(cdf(complement(w, +nan)), std::domain_error); // x = + nan + BOOST_CHECK_THROW(quantile(w, +nan), std::domain_error); // p = + nan + BOOST_CHECK_THROW(quantile(complement(w, +nan)), std::domain_error); // p = + nan + } // has_quiet_NaN + + if (std::numeric_limits::has_infinity) + { + RealType inf = std::numeric_limits::infinity(); + + BOOST_CHECK_THROW(weibull_distribution w(inf), std::domain_error); + BOOST_CHECK_THROW(weibull_distribution w(1, inf), std::domain_error); + + weibull_distribution w(RealType(1)); + BOOST_CHECK_THROW(weibull_distribution w(inf), std::domain_error); + BOOST_CHECK_THROW(weibull_distribution w(1, inf), std::domain_error); + BOOST_CHECK_THROW(pdf(w, +inf), std::domain_error); // x = inf + BOOST_CHECK_THROW(cdf(w, +inf), std::domain_error); // x = inf + BOOST_CHECK_THROW(cdf(complement(w, +inf)), std::domain_error); // x = + inf + BOOST_CHECK_THROW(quantile(w, +inf), std::domain_error); // p = + inf + BOOST_CHECK_THROW(quantile(complement(w, +inf)), std::domain_error); // p = + inf + } // has_infinity + + } // template void test_spots(RealType) int test_main(int, char* []) @@ -370,17 +410,19 @@ int test_main(int, char* []) Output: -Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_weibull.exe" -Running 1 test case... -Tolerance for type float is 0.002 % -Tolerance for type float is 5.96046e-005 % -Tolerance for type double is 0.002 % -Tolerance for type double is 1.11022e-013 % -Tolerance for type long double is 0.002 % -Tolerance for type long double is 1.11022e-013 % -Tolerance for type class boost::math::concepts::real_concept is 0.002 % -Tolerance for type class boost::math::concepts::real_concept is 1.11022e-013 % -*** No errors detected + Description: Autorun "J:\Cpp\MathToolkit\test\Math_test\Debug\test_weibull.exe" + Running 1 test case... + Tolerance for type float is 0.002 % + Tolerance for type float is 5.96046e-005 % + Tolerance for type double is 0.002 % + Tolerance for type double is 1.11022e-013 % + Tolerance for type long double is 0.002 % + Tolerance for type long double is 1.11022e-013 % + Tolerance for type class boost::math::concepts::real_concept is 0.002 % + Tolerance for type class boost::math::concepts::real_concept is 1.11022e-013 % + + *** No errors detected + */ From 0c5c91f6dfe1d6f48bc332708b1907de4d678705 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Tue, 29 May 2012 15:58:06 +0000 Subject: [PATCH 012/115] Added more tests for bad parameters and non-finites. [SVN r78748] --- test/test_bernoulli.cpp | 75 ++++++++++++++++++++++++++++++++--------- 1 file changed, 59 insertions(+), 16 deletions(-) diff --git a/test/test_bernoulli.cpp b/test/test_bernoulli.cpp index 23b0ad4f8..4795d7dde 100644 --- a/test/test_bernoulli.cpp +++ b/test/test_bernoulli.cpp @@ -1,7 +1,7 @@ // test_bernoulli.cpp // Copyright John Maddock 2006. -// Copyright Paul A. Bristow 2007. +// Copyright Paul A. Bristow 2007, 2012. // Use, modification and distribution are subject to the // Boost Software License, Version 1.0. @@ -11,9 +11,10 @@ // Basic sanity test for Bernoulli Cumulative Distribution Function. #ifdef _MSC_VER -# pragma warning (disable : 4535) // calling _set_se_translator() requires /EHa -# pragma warning (disable : 4244) // converion possible loss of data -# pragma warning (disable : 4996) // 'putenv': The POSIX name for this item is deprecated +# pragma warning (disable : 4535) // calling _set_se_translator() requires /EHa. +# pragma warning (disable : 4244) // conversion possible loss of data. +# pragma warning (disable : 4996) // 'putenv': The POSIX name for this item is deprecated. +# pragma warning (disable : 4127) // conditional expression is constant. #endif // Default domain error policy is @@ -211,6 +212,52 @@ void test_spots(RealType) static_cast(0.9L))), // > p static_cast(0) ); + + // Checks for 'bad' parameters. + // Construction. + BOOST_CHECK_THROW(bernoulli_distribution(-1), std::domain_error); // p outside 0 to 1. + BOOST_CHECK_THROW(bernoulli_distribution(+2), std::domain_error); // p outside 0 to 1. + + // Parameters. + bernoulli_distribution dist(RealType(1)); + BOOST_CHECK_THROW(pdf(dist, -1), std::domain_error); + BOOST_CHECK_THROW(cdf(dist, -1), std::domain_error); + BOOST_CHECK_THROW(cdf(complement(dist, -1)), std::domain_error); + BOOST_CHECK_THROW(quantile(dist, 2), std::domain_error); + BOOST_CHECK_THROW(quantile(complement(dist, -1)), std::domain_error); + BOOST_CHECK_THROW(quantile(dist, -1), std::domain_error); + BOOST_CHECK_THROW(quantile(complement(dist, -1)), std::domain_error); + + // No longer allow any parameter to be NaN or inf, so all these tests should throw. + if (std::numeric_limits::has_quiet_NaN) + { + // Attempt to construct from non-finite should throw. + RealType nan = std::numeric_limits::quiet_NaN(); + BOOST_CHECK_THROW(bernoulli_distribution b(nan), std::domain_error); + + // Non-finite parameters should throw. + bernoulli_distribution b(RealType(1)); + BOOST_CHECK_THROW(pdf(b, +nan), std::domain_error); // x = NaN + BOOST_CHECK_THROW(cdf(b, +nan), std::domain_error); // x = NaN + BOOST_CHECK_THROW(cdf(complement(b, +nan)), std::domain_error); // x = + nan + BOOST_CHECK_THROW(quantile(b, +nan), std::domain_error); // p = + nan + BOOST_CHECK_THROW(quantile(complement(b, +nan)), std::domain_error); // p = + nan + } // has_quiet_NaN + + if (std::numeric_limits::has_infinity) + { + RealType inf = std::numeric_limits::infinity(); + BOOST_CHECK_THROW(bernoulli_distribution w(inf), std::domain_error); + + bernoulli_distribution w(RealType(1)); + BOOST_CHECK_THROW(bernoulli_distribution w(inf), std::domain_error); + BOOST_CHECK_THROW(pdf(w, +inf), std::domain_error); // x = inf + BOOST_CHECK_THROW(cdf(w, +inf), std::domain_error); // x = inf + BOOST_CHECK_THROW(cdf(complement(w, +inf)), std::domain_error); // x = + inf + BOOST_CHECK_THROW(quantile(w, +inf), std::domain_error); // p = + inf + BOOST_CHECK_THROW(quantile(complement(w, +inf)), std::domain_error); // p = + inf + } // has_infinity + } // template void test_spots(RealType) int test_main(int, char* []) @@ -223,11 +270,6 @@ int test_main(int, char* []) BOOST_CHECK_EQUAL(bn1.success_fraction(), 0.5); BOOST_CHECK_EQUAL(bn2.success_fraction(), 0.5); - BOOST_CHECK_THROW(bernoulli_distribution(-1), std::domain_error); // p outside 0 to 1. - BOOST_CHECK_THROW(bernoulli_distribution(+2), std::domain_error); // p outside 0 to 1. - BOOST_CHECK_THROW(bernoulli_distribution bn3(std::numeric_limits::quiet_NaN() ), std::domain_error); // p outside 0 to 1. - BOOST_CHECK_THROW(bernoulli_distribution bn4(std::numeric_limits::infinity() ), std::domain_error); // p outside 0 to 1. - BOOST_CHECK_EQUAL(kurtosis(bn2) -3, kurtosis_excess(bn2)); BOOST_CHECK_EQUAL(kurtosis_excess(bn2), -2); @@ -260,14 +302,15 @@ int test_main(int, char* []) Output is: -Running 1 test case... -Tolerance for type float is 1.19e-005 (or 0.00119%). -Tolerance for type double is 2.22e-014 (or 2.22e-012%). -Tolerance for type long double is 2.22e-014 (or 2.22e-012%). -Tolerance for type class boost::math::concepts::real_concept is 2.22e-014 (or 2.22e-012%). -*** No errors detected + Description: Autorun "J:\Cpp\MathToolkit\test\Math_test\Debug\test_bernouilli.exe" + Running 1 test case... + Tolerance for type float is 1.19e-005 (or 0.00119%). + Tolerance for type double is 2.22e-014 (or 2.22e-012%). + Tolerance for type long double is 2.22e-014 (or 2.22e-012%). + Tolerance for type class boost::math::concepts::real_concept is 2.22e-014 (or 2.22e-012%). + + *** No errors detected -No warnings MSVC level 4 31 Jul 2007 */ From bc2dc1d4dd32f433ceab75d3311787bf61ee17c4 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 29 May 2012 17:43:16 +0000 Subject: [PATCH 013/115] Add boilerplate code for testing most domain errors in the distributions. Update the non-central distributions to make use of it. [SVN r78751] --- include/boost/math/distributions/fisher_f.hpp | 4 +- test/test_nc_chi_squared.cpp | 9 ++ test/test_nc_f.cpp | 10 ++ test/test_nc_t.cpp | 8 ++ test/test_out_of_range.hpp | 127 ++++++++++++++++++ 5 files changed, 156 insertions(+), 2 deletions(-) create mode 100644 test/test_out_of_range.hpp diff --git a/include/boost/math/distributions/fisher_f.hpp b/include/boost/math/distributions/fisher_f.hpp index 07bcc81a6..b1d9eb7ce 100644 --- a/include/boost/math/distributions/fisher_f.hpp +++ b/include/boost/math/distributions/fisher_f.hpp @@ -169,12 +169,12 @@ inline RealType quantile(const fisher_f_distribution& dist, co RealType df2 = dist.degrees_of_freedom2(); // Error check: RealType error_result = 0; - if(false == detail::check_df( + if(false == (detail::check_df( function, df1, &error_result, Policy()) && detail::check_df( function, df2, &error_result, Policy()) && detail::check_probability( - function, p, &error_result, Policy())) + function, p, &error_result, Policy()))) return error_result; // With optimizations turned on, gcc wrongly warns about y being used diff --git a/test/test_nc_chi_squared.cpp b/test/test_nc_chi_squared.cpp index f167368f8..cccddbb78 100644 --- a/test/test_nc_chi_squared.cpp +++ b/test/test_nc_chi_squared.cpp @@ -27,6 +27,7 @@ #include #include #include // for BOOST_CHECK_CLOSE +#include "test_out_of_range.hpp" #include "functor.hpp" #include "handle_test_result.hpp" @@ -344,6 +345,14 @@ void test_spots(RealType) BOOST_CHECK_CLOSE( kurtosis_excess(dist) , static_cast(0.65625), tol2); + + // Error handling checks: + check_out_of_range >(1, 1); + BOOST_CHECK_THROW(pdf(boost::math::non_central_chi_squared_distribution(0, 1), 0), std::domain_error); + BOOST_CHECK_THROW(pdf(boost::math::non_central_chi_squared_distribution(-1, 1), 0), std::domain_error); + BOOST_CHECK_THROW(pdf(boost::math::non_central_chi_squared_distribution(1, -1), 0), std::domain_error); + BOOST_CHECK_THROW(quantile(boost::math::non_central_chi_squared_distribution(1, 1), -1), std::domain_error); + BOOST_CHECK_THROW(quantile(boost::math::non_central_chi_squared_distribution(1, 1), 2), std::domain_error); } // template void test_spots(RealType) template diff --git a/test/test_nc_f.cpp b/test/test_nc_f.cpp index ffff944c8..ccb18012d 100644 --- a/test/test_nc_f.cpp +++ b/test/test_nc_f.cpp @@ -26,6 +26,7 @@ #include #include #include // for BOOST_CHECK_CLOSE +#include "test_out_of_range.hpp" #include "functor.hpp" #include "handle_test_result.hpp" @@ -282,6 +283,15 @@ void test_spots(RealType) BOOST_CHECK_CLOSE( kurtosis_excess(dist) , static_cast(13.225781681053154767604638331440974359675882226873L), tol2); + + // Error handling checks: + check_out_of_range >(1, 1, 1); + BOOST_CHECK_THROW(pdf(boost::math::non_central_f_distribution(0, 1, 1), 0), std::domain_error); + BOOST_CHECK_THROW(pdf(boost::math::non_central_f_distribution(-1, 1, 1), 0), std::domain_error); + BOOST_CHECK_THROW(pdf(boost::math::non_central_f_distribution(1, 0, 1), 0), std::domain_error); + BOOST_CHECK_THROW(pdf(boost::math::non_central_f_distribution(1, -1, 1), 0), std::domain_error); + BOOST_CHECK_THROW(quantile(boost::math::non_central_f_distribution(1, 1, 1), -1), std::domain_error); + BOOST_CHECK_THROW(quantile(boost::math::non_central_f_distribution(1, 1, 1), 2), std::domain_error); } // template void test_spots(RealType) int test_main(int, char* []) diff --git a/test/test_nc_t.cpp b/test/test_nc_t.cpp index 0c9a22488..05639f3ff 100644 --- a/test/test_nc_t.cpp +++ b/test/test_nc_t.cpp @@ -30,6 +30,7 @@ #include "functor.hpp" #include "handle_test_result.hpp" #include "table_type.hpp" +#include "test_out_of_range.hpp" #include using std::cout; @@ -330,6 +331,13 @@ void test_spots(RealType) BOOST_CHECK_CLOSE(pdf(boost::math::non_central_t_distribution(126, -2), -4), static_cast(5.797932289365814702402873546466798025787e-2L), tolerance); BOOST_CHECK_CLOSE(pdf(boost::math::non_central_t_distribution(126, 2), 4), static_cast(5.797932289365814702402873546466798025787e-2L), tolerance); BOOST_CHECK_CLOSE(pdf(boost::math::non_central_t_distribution(126, 2), 0), static_cast(5.388394890639957139696546086044839573749e-2L), tolerance); + + // Error handling checks: + check_out_of_range >(1, 1); + BOOST_CHECK_THROW(pdf(boost::math::non_central_t_distribution(0, 1), 0), std::domain_error); + BOOST_CHECK_THROW(pdf(boost::math::non_central_t_distribution(-1, 1), 0), std::domain_error); + BOOST_CHECK_THROW(quantile(boost::math::non_central_t_distribution(1, 1), -1), std::domain_error); + BOOST_CHECK_THROW(quantile(boost::math::non_central_t_distribution(1, 1), 2), std::domain_error); } // template void test_spots(RealType) template diff --git a/test/test_out_of_range.hpp b/test/test_out_of_range.hpp new file mode 100644 index 000000000..b52c2a493 --- /dev/null +++ b/test/test_out_of_range.hpp @@ -0,0 +1,127 @@ +// Copyright John Maddock 2012. + +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt +// or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifndef BOOST_MATH_TEST_OUT_OF_RANGE_HPP +#define BOOST_MATH_TEST_OUT_OF_RANGE_HPP + +#include +#include + +template +void check_support(const Distro& d) +{ + typedef typename Distro::value_type value_type; + if(range(d).first != -boost::math::tools::max_value()) + { + value_type m = boost::math::float_prior(range(d).first); + BOOST_ASSERT(m != range(d).first); + BOOST_ASSERT(m < range(d).first); + BOOST_CHECK_THROW(pdf(d, m), std::domain_error); + BOOST_CHECK_THROW(cdf(d, m), std::domain_error); + BOOST_CHECK_THROW(cdf(complement(d, m)), std::domain_error); + } + if(range(d).second != boost::math::tools::max_value()) + { + value_type m = boost::math::float_next(range(d).second); + BOOST_ASSERT(m != range(d).first); + BOOST_ASSERT(m > range(d).first); + BOOST_CHECK_THROW(pdf(d, m), std::domain_error); + BOOST_CHECK_THROW(cdf(d, m), std::domain_error); + BOOST_CHECK_THROW(cdf(complement(d, m)), std::domain_error); + } + if(std::numeric_limits::has_infinity) + { + BOOST_CHECK_THROW(pdf(d, std::numeric_limits::infinity()), std::domain_error); + BOOST_CHECK_THROW(cdf(d, std::numeric_limits::infinity()), std::domain_error); + BOOST_CHECK_THROW(cdf(complement(d, std::numeric_limits::infinity())), std::domain_error); + BOOST_CHECK_THROW(pdf(d, -std::numeric_limits::infinity()), std::domain_error); + BOOST_CHECK_THROW(cdf(d, -std::numeric_limits::infinity()), std::domain_error); + BOOST_CHECK_THROW(cdf(complement(d, -std::numeric_limits::infinity())), std::domain_error); + BOOST_CHECK_THROW(quantile(d, std::numeric_limits::infinity()), std::domain_error); + BOOST_CHECK_THROW(quantile(d, -std::numeric_limits::infinity()), std::domain_error); + BOOST_CHECK_THROW(quantile(complement(d, std::numeric_limits::infinity())), std::domain_error); + BOOST_CHECK_THROW(quantile(complement(d, -std::numeric_limits::infinity())), std::domain_error); + } + if(std::numeric_limits::has_quiet_NaN) + { + BOOST_CHECK_THROW(pdf(d, std::numeric_limits::quiet_NaN()), std::domain_error); + BOOST_CHECK_THROW(cdf(d, std::numeric_limits::quiet_NaN()), std::domain_error); + BOOST_CHECK_THROW(cdf(complement(d, std::numeric_limits::quiet_NaN())), std::domain_error); + BOOST_CHECK_THROW(pdf(d, -std::numeric_limits::quiet_NaN()), std::domain_error); + BOOST_CHECK_THROW(cdf(d, -std::numeric_limits::quiet_NaN()), std::domain_error); + BOOST_CHECK_THROW(cdf(complement(d, -std::numeric_limits::quiet_NaN())), std::domain_error); + BOOST_CHECK_THROW(quantile(d, std::numeric_limits::quiet_NaN()), std::domain_error); + BOOST_CHECK_THROW(quantile(d, -std::numeric_limits::quiet_NaN()), std::domain_error); + BOOST_CHECK_THROW(quantile(complement(d, std::numeric_limits::quiet_NaN())), std::domain_error); + BOOST_CHECK_THROW(quantile(complement(d, -std::numeric_limits::quiet_NaN())), std::domain_error); + } + BOOST_CHECK_THROW(quantile(d, -1), std::domain_error); + BOOST_CHECK_THROW(quantile(d, 2), std::domain_error); + BOOST_CHECK_THROW(quantile(complement(d, -1)), std::domain_error); + BOOST_CHECK_THROW(quantile(complement(d, 2)), std::domain_error); +} + +template +void check_out_of_range() +{ + Distro d; + check_support(d); +} +template +void check_out_of_range(typename Distro::value_type p1) +{ + typedef typename Distro::value_type value_type; + Distro d(p1); + check_support(d); + if(std::numeric_limits::has_infinity) + { + BOOST_CHECK_THROW(pdf(Distro(std::numeric_limits::infinity()), range(d).first), std::domain_error); + } + if(std::numeric_limits::has_quiet_NaN) + { + BOOST_CHECK_THROW(pdf(Distro(std::numeric_limits::quiet_NaN()), range(d).first), std::domain_error); + } +} +template +void check_out_of_range(typename Distro::value_type p1, typename Distro::value_type p2) +{ + typedef typename Distro::value_type value_type; + Distro d(p1, p2); + check_support(d); + if(std::numeric_limits::has_infinity) + { + BOOST_CHECK_THROW(pdf(Distro(std::numeric_limits::infinity(), p2), range(d).first), std::domain_error); + BOOST_CHECK_THROW(pdf(Distro(p1, std::numeric_limits::infinity()), range(d).first), std::domain_error); + } + if(std::numeric_limits::has_quiet_NaN) + { + BOOST_CHECK_THROW(pdf(Distro(std::numeric_limits::quiet_NaN(), p2), range(d).first), std::domain_error); + BOOST_CHECK_THROW(pdf(Distro(p1, std::numeric_limits::quiet_NaN()), range(d).first), std::domain_error); + } +} + +template +void check_out_of_range(typename Distro::value_type p1, typename Distro::value_type p2, typename Distro::value_type p3) +{ + typedef typename Distro::value_type value_type; + Distro d(p1, p2, p3); + check_support(d); + if(std::numeric_limits::has_infinity) + { + BOOST_CHECK_THROW(pdf(Distro(std::numeric_limits::infinity(), p2, p3), range(d).first), std::domain_error); + BOOST_CHECK_THROW(pdf(Distro(p1, std::numeric_limits::infinity(), p3), range(d).first), std::domain_error); + BOOST_CHECK_THROW(pdf(Distro(p1, p2, std::numeric_limits::infinity()), range(d).first), std::domain_error); + } + if(std::numeric_limits::has_quiet_NaN) + { + BOOST_CHECK_THROW(pdf(Distro(std::numeric_limits::quiet_NaN(), p2, p3), range(d).first), std::domain_error); + BOOST_CHECK_THROW(pdf(Distro(p1, std::numeric_limits::quiet_NaN(), p3), range(d).first), std::domain_error); + BOOST_CHECK_THROW(pdf(Distro(p1, p2, std::numeric_limits::quiet_NaN()), range(d).first), std::domain_error); + } +} + +#endif // BOOST_MATH_TEST_OUT_OF_RANGE_HPP From d39cf53e86c9bff98df9440790f7669e918445d2 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 29 May 2012 18:24:29 +0000 Subject: [PATCH 014/115] Update to allow for infinite range. [SVN r78753] --- test/test_out_of_range.hpp | 22 ++++++++++++++-------- 1 file changed, 14 insertions(+), 8 deletions(-) diff --git a/test/test_out_of_range.hpp b/test/test_out_of_range.hpp index b52c2a493..ccb83b5fc 100644 --- a/test/test_out_of_range.hpp +++ b/test/test_out_of_range.hpp @@ -15,7 +15,7 @@ template void check_support(const Distro& d) { typedef typename Distro::value_type value_type; - if(range(d).first != -boost::math::tools::max_value()) + if((boost::math::isfinite)(range(d).first) && (range(d).first != -boost::math::tools::max_value())) { value_type m = boost::math::float_prior(range(d).first); BOOST_ASSERT(m != range(d).first); @@ -24,7 +24,7 @@ void check_support(const Distro& d) BOOST_CHECK_THROW(cdf(d, m), std::domain_error); BOOST_CHECK_THROW(cdf(complement(d, m)), std::domain_error); } - if(range(d).second != boost::math::tools::max_value()) + if((boost::math::isfinite)(range(d).second) && (range(d).second != boost::math::tools::max_value())) { value_type m = boost::math::float_next(range(d).second); BOOST_ASSERT(m != range(d).first); @@ -35,12 +35,18 @@ void check_support(const Distro& d) } if(std::numeric_limits::has_infinity) { - BOOST_CHECK_THROW(pdf(d, std::numeric_limits::infinity()), std::domain_error); - BOOST_CHECK_THROW(cdf(d, std::numeric_limits::infinity()), std::domain_error); - BOOST_CHECK_THROW(cdf(complement(d, std::numeric_limits::infinity())), std::domain_error); - BOOST_CHECK_THROW(pdf(d, -std::numeric_limits::infinity()), std::domain_error); - BOOST_CHECK_THROW(cdf(d, -std::numeric_limits::infinity()), std::domain_error); - BOOST_CHECK_THROW(cdf(complement(d, -std::numeric_limits::infinity())), std::domain_error); + if((boost::math::isfinite)(range(d).second)) + { + BOOST_CHECK_THROW(pdf(d, std::numeric_limits::infinity()), std::domain_error); + BOOST_CHECK_THROW(cdf(d, std::numeric_limits::infinity()), std::domain_error); + BOOST_CHECK_THROW(cdf(complement(d, std::numeric_limits::infinity())), std::domain_error); + } + if((boost::math::isfinite)(range(d).first)) + { + BOOST_CHECK_THROW(pdf(d, -std::numeric_limits::infinity()), std::domain_error); + BOOST_CHECK_THROW(cdf(d, -std::numeric_limits::infinity()), std::domain_error); + BOOST_CHECK_THROW(cdf(complement(d, -std::numeric_limits::infinity())), std::domain_error); + } BOOST_CHECK_THROW(quantile(d, std::numeric_limits::infinity()), std::domain_error); BOOST_CHECK_THROW(quantile(d, -std::numeric_limits::infinity()), std::domain_error); BOOST_CHECK_THROW(quantile(complement(d, std::numeric_limits::infinity())), std::domain_error); From 0b6be607ba3bbc8a3cf0874ad0f34d3c1cef9c23 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Wed, 30 May 2012 14:21:06 +0000 Subject: [PATCH 015/115] Explanatory comments added. [SVN r78762] --- test/test_out_of_range.hpp | 41 +++++++++++++++++++++++++++++++------- 1 file changed, 34 insertions(+), 7 deletions(-) diff --git a/test/test_out_of_range.hpp b/test/test_out_of_range.hpp index ccb83b5fc..f64c94182 100644 --- a/test/test_out_of_range.hpp +++ b/test/test_out_of_range.hpp @@ -11,12 +11,31 @@ #include #include +/*` check_out_of_range functions check that bad parameters +passed to constructors and functions throw domain_error exceptions. + +Usage is `check_out_of_range(list-of-params);` +Where list-of-params is a list of *valid* parameters from which the distribution can be constructed +- ie the same number of args are passed to the function, +as are passed to the distribution constructor. + +Checks: + +* Infinity or NaN passed in place of each of the valid params. +* Infinity or NaN as a random variable. +* Out-of-range random variable passed to pdf and cdf (ie outside of "range(distro)"). +* Out-of-range probability passed to quantile function and complement. + +but does *not* check finite but out-of-range parameters to the constructor +because these are specific to each distribution. +*/ + template void check_support(const Distro& d) -{ +{ // Checks that typedef typename Distro::value_type value_type; if((boost::math::isfinite)(range(d).first) && (range(d).first != -boost::math::tools::max_value())) - { + { // If possible, check that a value just less than the bottom of the supported range throws domain errors. value_type m = boost::math::float_prior(range(d).first); BOOST_ASSERT(m != range(d).first); BOOST_ASSERT(m < range(d).first); @@ -25,7 +44,7 @@ void check_support(const Distro& d) BOOST_CHECK_THROW(cdf(complement(d, m)), std::domain_error); } if((boost::math::isfinite)(range(d).second) && (range(d).second != boost::math::tools::max_value())) - { + { // If possible, check that a value just more than the top of the supported range throws domain errors. value_type m = boost::math::float_next(range(d).second); BOOST_ASSERT(m != range(d).first); BOOST_ASSERT(m > range(d).first); @@ -34,26 +53,29 @@ void check_support(const Distro& d) BOOST_CHECK_THROW(cdf(complement(d, m)), std::domain_error); } if(std::numeric_limits::has_infinity) - { + { // Infinity is available, if((boost::math::isfinite)(range(d).second)) - { + { // and top of range doesn't include infinity, + // check that using infinity throws domain errors. BOOST_CHECK_THROW(pdf(d, std::numeric_limits::infinity()), std::domain_error); BOOST_CHECK_THROW(cdf(d, std::numeric_limits::infinity()), std::domain_error); BOOST_CHECK_THROW(cdf(complement(d, std::numeric_limits::infinity())), std::domain_error); } if((boost::math::isfinite)(range(d).first)) - { + { // and bottom of range doesn't include infinity, + // check that using infinity throws domain_error exception. BOOST_CHECK_THROW(pdf(d, -std::numeric_limits::infinity()), std::domain_error); BOOST_CHECK_THROW(cdf(d, -std::numeric_limits::infinity()), std::domain_error); BOOST_CHECK_THROW(cdf(complement(d, -std::numeric_limits::infinity())), std::domain_error); } + // Check that using infinity with quantiles always throws domain_error exception. BOOST_CHECK_THROW(quantile(d, std::numeric_limits::infinity()), std::domain_error); BOOST_CHECK_THROW(quantile(d, -std::numeric_limits::infinity()), std::domain_error); BOOST_CHECK_THROW(quantile(complement(d, std::numeric_limits::infinity())), std::domain_error); BOOST_CHECK_THROW(quantile(complement(d, -std::numeric_limits::infinity())), std::domain_error); } if(std::numeric_limits::has_quiet_NaN) - { + { // NaN is available. BOOST_CHECK_THROW(pdf(d, std::numeric_limits::quiet_NaN()), std::domain_error); BOOST_CHECK_THROW(cdf(d, std::numeric_limits::quiet_NaN()), std::domain_error); BOOST_CHECK_THROW(cdf(complement(d, std::numeric_limits::quiet_NaN())), std::domain_error); @@ -65,18 +87,22 @@ void check_support(const Distro& d) BOOST_CHECK_THROW(quantile(complement(d, std::numeric_limits::quiet_NaN())), std::domain_error); BOOST_CHECK_THROW(quantile(complement(d, -std::numeric_limits::quiet_NaN())), std::domain_error); } + // Check that using probability outside [0,1] with quantiles always throws domain_error exception. BOOST_CHECK_THROW(quantile(d, -1), std::domain_error); BOOST_CHECK_THROW(quantile(d, 2), std::domain_error); BOOST_CHECK_THROW(quantile(complement(d, -1)), std::domain_error); BOOST_CHECK_THROW(quantile(complement(d, 2)), std::domain_error); } +// Four check_out_of_range versions for distributions with zero to 3 constructor parameters. + template void check_out_of_range() { Distro d; check_support(d); } + template void check_out_of_range(typename Distro::value_type p1) { @@ -92,6 +118,7 @@ void check_out_of_range(typename Distro::value_type p1) BOOST_CHECK_THROW(pdf(Distro(std::numeric_limits::quiet_NaN()), range(d).first), std::domain_error); } } + template void check_out_of_range(typename Distro::value_type p1, typename Distro::value_type p2) { From a752f9f593506417365c1e05df874c75ef76e0cc Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Wed, 30 May 2012 16:28:59 +0000 Subject: [PATCH 016/115] Added out_of_range checks - and corrected beta.hpp for missing () in checks. [SVN r78764] --- test/test_beta_dist.cpp | 75 ++++++++++++++++++++++++++++++++++++++--- 1 file changed, 71 insertions(+), 4 deletions(-) diff --git a/test/test_beta_dist.cpp b/test/test_beta_dist.cpp index ebb904c42..dc3e2d1e0 100644 --- a/test/test_beta_dist.cpp +++ b/test/test_beta_dist.cpp @@ -1,7 +1,7 @@ // test_beta_dist.cpp // Copyright John Maddock 2006. -// Copyright Paul A. Bristow 2007, 2009, 2010. +// Copyright Paul A. Bristow 2007, 2009, 2010, 2012. // Use, modification and distribution are subject to the // Boost Software License, Version 1.0. @@ -28,9 +28,8 @@ #ifdef _MSC_VER # pragma warning(disable: 4127) // conditional expression is constant. -# pragma warning (disable : 4996) // POSIX name for this item is deprecated -# pragma warning (disable : 4224) // nonstandard extension used : formal parameter 'arg' was previously defined as a type -# pragma warning (disable : 4180) // qualifier applied to function type has no meaning; ignored +# pragma warning (disable : 4996) // POSIX name for this item is deprecated. +# pragma warning (disable : 4224) // nonstandard extension used : formal parameter 'arg' was previously defined as a type. #endif #include // for real_concept @@ -43,6 +42,8 @@ using boost::math::beta; #include // for test_main #include // for BOOST_CHECK_CLOSE_FRACTION +#include "test_out_of_range.hpp" + #include using std::cout; using std::endl; @@ -456,6 +457,70 @@ void test_spots(RealType) static_cast(1-0.5545844446520295253493059553548880128511L), // Complement of CDF Q = 1 - P tolerance); // Test tolerance. + // + // Error checks: + // Construction with 'bad' parameters. + BOOST_CHECK_THROW(beta_distribution(1, -1), std::domain_error); + BOOST_CHECK_THROW(beta_distribution(-1, 1), std::domain_error); + BOOST_CHECK_THROW(beta_distribution(1, 0), std::domain_error); + BOOST_CHECK_THROW(beta_distribution(0, 1), std::domain_error); + + beta_distribution<> dist; + BOOST_CHECK_THROW(pdf(dist, -1), std::domain_error); + BOOST_CHECK_THROW(cdf(dist, -1), std::domain_error); + BOOST_CHECK_THROW(cdf(complement(dist, -1)), std::domain_error); + BOOST_CHECK_THROW(quantile(dist, -1), std::domain_error); + BOOST_CHECK_THROW(quantile(complement(dist, -1)), std::domain_error); + BOOST_CHECK_THROW(quantile(dist, -1), std::domain_error); + BOOST_CHECK_THROW(quantile(complement(dist, -1)), std::domain_error); + + // No longer allow any parameter to be NaN or inf, so all these tests should throw. + if (std::numeric_limits::has_quiet_NaN) + { + // Attempt to construct from non-finite should throw. + RealType nan = std::numeric_limits::quiet_NaN(); + BOOST_CHECK_THROW(beta_distribution w(nan), std::domain_error); + BOOST_CHECK_THROW(beta_distribution w(1, nan), std::domain_error); + + // Non-finite parameters should throw. + beta_distribution w(RealType(1)); + BOOST_CHECK_THROW(pdf(w, +nan), std::domain_error); // x = NaN + BOOST_CHECK_THROW(cdf(w, +nan), std::domain_error); // x = NaN + BOOST_CHECK_THROW(cdf(complement(w, +nan)), std::domain_error); // x = + nan + BOOST_CHECK_THROW(quantile(w, +nan), std::domain_error); // p = + nan + BOOST_CHECK_THROW(quantile(complement(w, +nan)), std::domain_error); // p = + nan + } // has_quiet_NaN + + if (std::numeric_limits::has_infinity) + { + // Attempt to construct from non-finite should throw. + RealType inf = std::numeric_limits::infinity(); + + BOOST_CHECK_THROW(beta_distribution w(inf), std::domain_error); + BOOST_CHECK_THROW(beta_distribution w(1, inf), std::domain_error); + + // Non-finite parameters should throw. + beta_distribution w(RealType(1)); + BOOST_CHECK_THROW(beta_distribution w(inf), std::domain_error); + BOOST_CHECK_THROW(beta_distribution w(1, inf), std::domain_error); + BOOST_CHECK_THROW(pdf(w, +inf), std::domain_error); // x = inf + BOOST_CHECK_THROW(cdf(w, +inf), std::domain_error); // x = inf + BOOST_CHECK_THROW(cdf(complement(w, +inf)), std::domain_error); // x = + inf + BOOST_CHECK_THROW(quantile(w, +inf), std::domain_error); // p = + inf + BOOST_CHECK_THROW(quantile(complement(w, +inf)), std::domain_error); // p = + inf + } // has_infinity + + // Error handling checks: + check_out_of_range >(1, 1); // (All) valid constructor parameter values. + // and range and non-finite. + + // Not needed?????? + BOOST_CHECK_THROW(pdf(boost::math::beta_distribution(0, 1), 0), std::domain_error); + BOOST_CHECK_THROW(pdf(boost::math::beta_distribution(-1, 1), 0), std::domain_error); + BOOST_CHECK_THROW(quantile(boost::math::beta_distribution(1, 1), -1), std::domain_error); + BOOST_CHECK_THROW(quantile(boost::math::beta_distribution(1, 1), 2), std::domain_error); + + } // template void test_spots(RealType) int test_main(int, char* []) @@ -576,6 +641,8 @@ Boost::math::tools::epsilon = 2.22045e-016 std::numeric_limits::epsilon = 0 epsilon = 2.22045e-016, Tolerance = 2.22045e-011%. *** No errors detected + + */ From 187960b9a717cb7730425366fe58290c89e838e5 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Wed, 30 May 2012 16:30:45 +0000 Subject: [PATCH 017/115] Corrected checks missing (). [SVN r78765] --- include/boost/math/distributions/beta.hpp | 49 +++++++++++------------ 1 file changed, 23 insertions(+), 26 deletions(-) diff --git a/include/boost/math/distributions/beta.hpp b/include/boost/math/distributions/beta.hpp index cfadd7bff..d525ace23 100644 --- a/include/boost/math/distributions/beta.hpp +++ b/include/boost/math/distributions/beta.hpp @@ -189,11 +189,10 @@ namespace boost static const char* function = "boost::math::beta_distribution<%1%>::find_alpha"; RealType result = 0; // of error checks. if(false == - beta_detail::check_mean( - function, mean, &result, Policy()) - && - beta_detail::check_variance( - function, variance, &result, Policy()) + ( + beta_detail::check_mean(function, mean, &result, Policy()) + && beta_detail::check_variance(function, variance, &result, Policy()) + ) ) { return result; @@ -208,11 +207,11 @@ namespace boost static const char* function = "boost::math::beta_distribution<%1%>::find_beta"; RealType result = 0; // of error checks. if(false == - beta_detail::check_mean( - function, mean, &result, Policy()) - && - beta_detail::check_variance( - function, variance, &result, Policy()) + ( + beta_detail::check_mean(function, mean, &result, Policy()) + && + beta_detail::check_variance(function, variance, &result, Policy()) + ) ) { return result; @@ -231,14 +230,13 @@ namespace boost static const char* function = "boost::math::beta_distribution<%1%>::find_alpha"; RealType result = 0; // of error checks. if(false == - beta_detail::check_prob( - function, probability, &result, Policy()) - && - beta_detail::check_beta( - function, beta, &result, Policy()) - && - beta_detail::check_x( - function, x, &result, Policy()) + ( + beta_detail::check_prob(function, probability, &result, Policy()) + && + beta_detail::check_beta(function, beta, &result, Policy()) + && + beta_detail::check_x(function, x, &result, Policy()) + ) ) { return result; @@ -255,14 +253,13 @@ namespace boost static const char* function = "boost::math::beta_distribution<%1%>::find_beta"; RealType result = 0; // of error checks. if(false == - beta_detail::check_prob( - function, probability, &result, Policy()) - && - beta_detail::check_alpha( - function, alpha, &result, Policy()) - && - beta_detail::check_x( - function, x, &result, Policy()) + ( + beta_detail::check_prob(function, probability, &result, Policy()) + && + beta_detail::check_alpha(function, alpha, &result, Policy()) + && + beta_detail::check_x(function, x, &result, Policy()) + ) ) { return result; From 7ef962fc6b349eee6bad26ce70cdb68ceb2e9a76 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Wed, 30 May 2012 16:31:18 +0000 Subject: [PATCH 018/115] Changed range to include infinity if supported. [SVN r78766] --- include/boost/math/distributions/cauchy.hpp | 19 +++++++++++++++++-- 1 file changed, 17 insertions(+), 2 deletions(-) diff --git a/include/boost/math/distributions/cauchy.hpp b/include/boost/math/distributions/cauchy.hpp index 0c93febaa..0e8c1deed 100644 --- a/include/boost/math/distributions/cauchy.hpp +++ b/include/boost/math/distributions/cauchy.hpp @@ -180,15 +180,30 @@ typedef cauchy_distribution cauchy; template inline const std::pair range(const cauchy_distribution&) { // Range of permissible values for random variable x. + if (std::numeric_limits::has_infinity) + { + return std::pair(-std::numeric_limits::infinity(), std::numeric_limits::infinity()); // - to + infinity. + } + else + { // Can only use max_value. using boost::math::tools::max_value; - return std::pair(-max_value(), max_value()); // - to + infinity. + return std::pair(-max_value(), max_value()); // - to + max. + } } template inline const std::pair support(const cauchy_distribution& ) { // Range of supported values for random variable x. // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - return std::pair(-tools::max_value(), tools::max_value()); // - to + infinity. + if (std::numeric_limits::has_infinity) + { + return std::pair(-std::numeric_limits::infinity(), std::numeric_limits::infinity()); // - to + infinity. + } + else + { // Can only use max_value. + using boost::math::tools::max_value; + return std::pair(-tools::max_value(), max_value()); // - to + max. + } } template From c30e63349a5e39f1fead38486b0b09271978c6e8 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Wed, 30 May 2012 16:32:12 +0000 Subject: [PATCH 019/115] Added out of range checks [SVN r78767] --- test/test_binomial.cpp | 32 ++++++++++++++++++++-------- test/test_cauchy.cpp | 47 +++++++++++++----------------------------- 2 files changed, 37 insertions(+), 42 deletions(-) diff --git a/test/test_binomial.cpp b/test/test_binomial.cpp index 00c3c6b87..7451a2c34 100644 --- a/test/test_binomial.cpp +++ b/test/test_binomial.cpp @@ -21,6 +21,10 @@ #ifdef _MSC_VER # pragma warning(disable: 4127) // conditional expression is constant. +# pragma warning(disable: 4100) // unreferenced formal parameter. +// Seems an entirely spurious warning - formal parameter T IS used - get error if /* T */ +//# pragma warning(disable: 4535) // calling _set_se_translator() requires /EHa (in Boost.test) +// Enable C++ Exceptions Yes With SEH Exceptions (/EHa) prevents warning 4535. #endif #include // for real_concept @@ -33,6 +37,8 @@ using boost::math::binomial_distribution; #include // for BOOST_CHECK_CLOSE #include "table_type.hpp" +#include "test_out_of_range.hpp" + #include using std::cout; using std::endl; @@ -209,7 +215,7 @@ void test_spot( } template // Any floating-point type RealType. -void test_spots(RealType) +void test_spots(RealType T) { // Basic sanity checks, test data is to double precision only // so set tolerance to 100eps expressed as a persent, or @@ -222,7 +228,8 @@ void test_spots(RealType) tolerance *= 100 * 1000; RealType tol2 = boost::math::tools::epsilon() * 5 * 100; // 5 eps as a persent - cout << "Tolerance = " << tolerance << "%." << endl; + cout << "Tolerance for type " << typeid(T).name() << " is " << tolerance << " %" << endl; + // Sources of spot test values: @@ -705,6 +712,9 @@ void test_spots(RealType) #endif } + check_out_of_range >(1, 1); // (All) valid constructor parameter values. + + } // template void test_spots(RealType) int test_main(int, char* []) @@ -748,12 +758,16 @@ int test_main(int, char* []) Output is: -Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_binomial.exe" -Running 1 test case... -Tolerance = 0.0119209%. -Tolerance = 2.22045e-011%. -Tolerance = 2.22045e-011%. -Tolerance = 2.22045e-011%. -*** No errors detected + Description: Autorun "J:\Cpp\MathToolkit\test\Math_test\Debug\test_binomial.exe" + Running 1 test case... + Tolerance for type float is 0.0119209 % + Tolerance for type double is 2.22045e-011 % + Tolerance for type long double is 2.22045e-011 % + Tolerance for type class boost::math::concepts::real_concept is 2.22045e-011 % + + *** No errors detected + +========== Build: 1 succeeded, 0 failed, 0 up-to-date, 0 skipped ========== + */ diff --git a/test/test_cauchy.cpp b/test/test_cauchy.cpp index 3c6e8fe71..ab96d4fd2 100644 --- a/test/test_cauchy.cpp +++ b/test/test_cauchy.cpp @@ -23,6 +23,8 @@ #include using boost::math::cauchy_distribution; +#include "test_out_of_range.hpp" + #include // Boost.Test #include @@ -33,38 +35,16 @@ template void test_spots(RealType T) { - // Check some bad parameters to the distribution, - BOOST_CHECK_THROW(boost::math::cauchy_distribution nbad1(0, 0), std::domain_error); // zero sd - BOOST_CHECK_THROW(boost::math::cauchy_distribution nbad1(0, -1), std::domain_error); // negative scale (shape) + // Check some bad parameters to construct the distribution, + BOOST_CHECK_THROW(boost::math::cauchy_distribution nbad1(0, 0), std::domain_error); // zero scale. + BOOST_CHECK_THROW(boost::math::cauchy_distribution nbad1(0, -1), std::domain_error); // negative scale (shape). + cauchy_distribution C01; BOOST_CHECK_EQUAL(C01.location(), 0); // Check standard values. BOOST_CHECK_EQUAL(C01.scale(), 1); - // Tests on extreme values of random variate x, if has numeric_limit infinity etc. - if(std::numeric_limits::has_infinity) - { - BOOST_CHECK_EQUAL(pdf(C01, +std::numeric_limits::infinity()), 0); // x = + infinity, pdf = 0 - BOOST_CHECK_EQUAL(pdf(C01, -std::numeric_limits::infinity()), 0); // x = - infinity, pdf = 0 - BOOST_CHECK_EQUAL(cdf(C01, +std::numeric_limits::infinity()), 1); // x = + infinity, cdf = 1 - BOOST_CHECK_EQUAL(cdf(C01, -std::numeric_limits::infinity()), 0); // x = - infinity, cdf = 0 - BOOST_CHECK_EQUAL(cdf(complement(C01, +std::numeric_limits::infinity())), 0); // x = + infinity, cdf = 0 - BOOST_CHECK_EQUAL(cdf(complement(C01, -std::numeric_limits::infinity())), 1); // x = - infinity, cdf = 1 - BOOST_CHECK_THROW(boost::math::cauchy_distribution nbad1(std::numeric_limits::infinity(), static_cast(1)), std::domain_error); // +infinite mean - BOOST_CHECK_THROW(boost::math::cauchy_distribution nbad1(-std::numeric_limits::infinity(), static_cast(1)), std::domain_error); // -infinite mean - BOOST_CHECK_THROW(boost::math::cauchy_distribution nbad1(static_cast(0), std::numeric_limits::infinity()), std::domain_error); // infinite sd - } - - if (std::numeric_limits::has_quiet_NaN) - { // No longer allow x to be NaN, so these tests should throw. - BOOST_CHECK_THROW(pdf(C01, +std::numeric_limits::quiet_NaN()), std::domain_error); // x = NaN - BOOST_CHECK_THROW(cdf(C01, +std::numeric_limits::quiet_NaN()), std::domain_error); // x = NaN - BOOST_CHECK_THROW(cdf(complement(C01, +std::numeric_limits::quiet_NaN())), std::domain_error); // x = + infinity - BOOST_CHECK_THROW(quantile(C01, +std::numeric_limits::quiet_NaN()), std::domain_error); // p = + infinity - BOOST_CHECK_THROW(quantile(complement(C01, +std::numeric_limits::quiet_NaN())), std::domain_error); // p = + infinity - } - - // Basic sanity checks. + // Basic sanity checks. // 50eps as a percentage, up to a maximum of double precision // (that's the limit of our test data). RealType tolerance = (std::max)( @@ -709,16 +689,19 @@ void test_spots(RealType T) quantile(complement(dist, RealType(1.0))), std::overflow_error); + check_out_of_range >(0, 1); // (All) valid constructor parameter values. + + } // template void test_spots(RealType) int test_main(int, char* []) { - BOOST_MATH_CONTROL_FP; + BOOST_MATH_CONTROL_FP; // Check that can generate cauchy distribution using the two convenience methods: - boost::math::cauchy mycd1(1.); // Using typedef - cauchy_distribution<> mycd2(1.); // Using default RealType double. - cauchy_distribution<> C01; // Using default RealType double for Standard Cauchy. + boost::math::cauchy mycd1(1.); // Using typedef + cauchy_distribution<> mycd2(1.); // Using default RealType double. + cauchy_distribution<> C01; // Using default RealType double for Standard Cauchy. BOOST_CHECK_EQUAL(C01.location(), 0); // Check standard values. BOOST_CHECK_EQUAL(C01.scale(), 1); @@ -741,7 +724,6 @@ int test_main(int, char* []) return 0; } // int test_main(int, char* []) - /* Output: @@ -752,5 +734,4 @@ Tolerance for type long double is 1.11022e-012 % Tolerance for type class boost::math::concepts::real_concept is 1.11022e-012 % *** No errors detected - */ From a72f149301915a1206d778dbe097f13a10172450 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Wed, 30 May 2012 16:35:59 +0000 Subject: [PATCH 020/115] Changed range to infinity if supported. [SVN r78768] --- include/boost/math/distributions/normal.hpp | 19 ++++++++++++++++--- 1 file changed, 16 insertions(+), 3 deletions(-) diff --git a/include/boost/math/distributions/normal.hpp b/include/boost/math/distributions/normal.hpp index baeecf634..6cca20a57 100644 --- a/include/boost/math/distributions/normal.hpp +++ b/include/boost/math/distributions/normal.hpp @@ -74,17 +74,30 @@ typedef normal_distribution normal; template inline const std::pair range(const normal_distribution& /*dist*/) { // Range of permissible values for random variable x. - using boost::math::tools::max_value; - return std::pair(-max_value(), max_value()); // - to + max value. + if (std::numeric_limits::has_infinity) + { + return std::pair(-std::numeric_limits::infinity(), std::numeric_limits::infinity()); // - to + infinity. + } + else + { // Can only use max_value. + using boost::math::tools::max_value; + return std::pair(-max_value(), max_value()); // - to + max value. + } } template inline const std::pair support(const normal_distribution& /*dist*/) { // Range of supported values for random variable x. // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - + if (std::numeric_limits::has_infinity) + { + return std::pair(-std::numeric_limits::infinity(), std::numeric_limits::infinity()); // - to + infinity. + } + else + { // Can only use max_value. using boost::math::tools::max_value; return std::pair(-max_value(), max_value()); // - to + max value. + } } template From 70868fb2a2fc89920090d4d99b1f2c12b7dc406d Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Wed, 30 May 2012 16:39:12 +0000 Subject: [PATCH 021/115] Added out of range checks (and normal.hpp now range infinity if supported. [SVN r78769] --- test/test_normal.cpp | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/test/test_normal.cpp b/test/test_normal.cpp index 0a3168e5c..9b1cc454e 100644 --- a/test/test_normal.cpp +++ b/test/test_normal.cpp @@ -18,7 +18,7 @@ #include // include directory /libs/math/src/tr1/ is needed. #ifdef _MSC_VER -#pragma warning (disable: 4127) // conditional expression is constant +# pragma warning (disable: 4127) // conditional expression is constant // caused by using if(std::numeric_limits::has_infinity) // and if (std::numeric_limits::has_quiet_NaN) #endif @@ -30,6 +30,7 @@ #include using boost::math::normal_distribution; #include +#include "test_out_of_range.hpp" #include using std::cout; @@ -283,6 +284,8 @@ void test_spots(RealType) static_cast(1), 0); // Mean == zero // Error tests: + check_out_of_range >(0, 1); // (All) valid constructor parameter values. + BOOST_CHECK_THROW(pdf(normal_distribution(0, 0), 0), std::domain_error); BOOST_CHECK_THROW(pdf(normal_distribution(0, -1), 0), std::domain_error); BOOST_CHECK_THROW(quantile(normal_distribution(0, 1), -1), std::domain_error); From c732b6e85b0821e6f42ab187628bc46eb3bb142e Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Wed, 30 May 2012 16:39:37 +0000 Subject: [PATCH 022/115] Corrected comments. [SVN r78770] --- test/test_out_of_range.hpp | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/test/test_out_of_range.hpp b/test/test_out_of_range.hpp index f64c94182..91863a63e 100644 --- a/test/test_out_of_range.hpp +++ b/test/test_out_of_range.hpp @@ -35,7 +35,7 @@ void check_support(const Distro& d) { // Checks that typedef typename Distro::value_type value_type; if((boost::math::isfinite)(range(d).first) && (range(d).first != -boost::math::tools::max_value())) - { // If possible, check that a value just less than the bottom of the supported range throws domain errors. + { // If possible, check that a random variable value just less than the bottom of the supported range throws domain errors. value_type m = boost::math::float_prior(range(d).first); BOOST_ASSERT(m != range(d).first); BOOST_ASSERT(m < range(d).first); @@ -44,7 +44,7 @@ void check_support(const Distro& d) BOOST_CHECK_THROW(cdf(complement(d, m)), std::domain_error); } if((boost::math::isfinite)(range(d).second) && (range(d).second != boost::math::tools::max_value())) - { // If possible, check that a value just more than the top of the supported range throws domain errors. + { // If possible, check that a random variable value just more than the top of the supported range throws domain errors. value_type m = boost::math::float_next(range(d).second); BOOST_ASSERT(m != range(d).first); BOOST_ASSERT(m > range(d).first); From 41bd4bd442663a5119dccfa15e4f7751b1d97667 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 30 May 2012 16:52:18 +0000 Subject: [PATCH 023/115] Update to use new out-of-bounds error checking. Refs #6934. [SVN r78771] --- include/boost/math/distributions/rayleigh.hpp | 12 ++++-- .../boost/math/distributions/skew_normal.hpp | 4 +- .../boost/math/distributions/students_t.hpp | 6 +++ test/test_pareto.cpp | 2 + test/test_poisson.cpp | 3 +- test/test_rayleigh.cpp | 9 +++++ test/test_skew_normal.cpp | 2 + test/test_students_t.cpp | 2 + test/test_triangular.cpp | 2 + test/test_uniform.cpp | 2 + test/test_weibull.cpp | 37 +------------------ 11 files changed, 40 insertions(+), 41 deletions(-) diff --git a/include/boost/math/distributions/rayleigh.hpp b/include/boost/math/distributions/rayleigh.hpp index 1ffb9dc0a..842143441 100644 --- a/include/boost/math/distributions/rayleigh.hpp +++ b/include/boost/math/distributions/rayleigh.hpp @@ -28,11 +28,11 @@ namespace detail template inline bool verify_sigma(const char* function, RealType sigma, RealType* presult, const Policy& pol) { - if(sigma <= 0) + if((sigma <= 0) || (!(boost::math::isfinite)(sigma))) { *presult = policies::raise_domain_error( function, - "The scale parameter \"sigma\" must be > 0, but was: %1%.", sigma, pol); + "The scale parameter \"sigma\" must be > 0 and finite, but was: %1%.", sigma, pol); return false; } return true; @@ -41,7 +41,7 @@ namespace detail template inline bool verify_rayleigh_x(const char* function, RealType x, RealType* presult, const Policy& pol) { - if(x < 0) + if((x < 0) || (boost::math::isnan)(x)) { *presult = policies::raise_domain_error( function, @@ -81,7 +81,7 @@ template inline const std::pair range(const rayleigh_distribution& /*dist*/) { // Range of permissible values for random variable x. using boost::math::tools::max_value; - return std::pair(static_cast(0), max_value()); + return std::pair(static_cast(0), std::numeric_limits::has_infinity ? std::numeric_limits::infinity() : max_value()); } template @@ -108,6 +108,10 @@ inline RealType pdf(const rayleigh_distribution& dist, const R { return result; } + if((boost::math::isinf)(x)) + { + return 0; + } RealType sigmasqr = sigma * sigma; result = x * (exp(-(x * x) / ( 2 * sigmasqr))) / sigmasqr; return result; diff --git a/include/boost/math/distributions/skew_normal.hpp b/include/boost/math/distributions/skew_normal.hpp index d39737496..6f3bc212f 100644 --- a/include/boost/math/distributions/skew_normal.hpp +++ b/include/boost/math/distributions/skew_normal.hpp @@ -100,7 +100,9 @@ namespace boost{ namespace math{ inline const std::pair range(const skew_normal_distribution& /*dist*/) { // Range of permissible values for random variable x. using boost::math::tools::max_value; - return std::pair(-max_value(), max_value()); // - to + max value. + return std::pair( + std::numeric_limits::has_infinity ? -std::numeric_limits::infinity() : -max_value(), + std::numeric_limits::has_infinity ? std::numeric_limits::infinity() : max_value()); // - to + max value. } template diff --git a/include/boost/math/distributions/students_t.hpp b/include/boost/math/distributions/students_t.hpp index 0562387ae..d6b24f744 100644 --- a/include/boost/math/distributions/students_t.hpp +++ b/include/boost/math/distributions/students_t.hpp @@ -87,6 +87,9 @@ inline RealType pdf(const students_t_distribution& dist, const if(false == detail::check_df( "boost::math::pdf(const students_t_distribution<%1%>&, %1%)", degrees_of_freedom, &error_result, Policy())) return error_result; + if(false == detail::check_x( + "boost::math::pdf(const students_t_distribution<%1%>&, %1%)", t, &error_result, Policy())) + return error_result; // Might conceivably permit df = +infinity and use normal distribution. RealType result; RealType basem1 = t * t / degrees_of_freedom; @@ -111,6 +114,9 @@ inline RealType cdf(const students_t_distribution& dist, const if(false == detail::check_df( "boost::math::cdf(const students_t_distribution<%1%>&, %1%)", degrees_of_freedom, &error_result, Policy())) return error_result; + if(false == detail::check_x( + "boost::math::pdf(const students_t_distribution<%1%>&, %1%)", t, &error_result, Policy())) + return error_result; if (t == 0) { diff --git a/test/test_pareto.cpp b/test/test_pareto.cpp index 2b63b9532..2528e7a28 100644 --- a/test/test_pareto.cpp +++ b/test/test_pareto.cpp @@ -30,6 +30,7 @@ #include using boost::math::pareto_distribution; #include +#include "test_out_of_range.hpp" #include using std::cout; @@ -233,6 +234,7 @@ void test_spots(RealType) // Check kurtosis excess = kurtosis - 3; // Error condition checks: + check_out_of_range >(1, 1); BOOST_CHECK_THROW(pdf(pareto_distribution(0, 1), 0), std::domain_error); BOOST_CHECK_THROW(pdf(pareto_distribution(1, 0), 0), std::domain_error); BOOST_CHECK_THROW(pdf(pareto_distribution(-1, 1), 0), std::domain_error); diff --git a/test/test_poisson.cpp b/test/test_poisson.cpp index cd8bf3530..63446831f 100644 --- a/test/test_poisson.cpp +++ b/test/test_poisson.cpp @@ -34,6 +34,7 @@ #include // for (incomplete) gamma. // using boost::math::qamma_Q; #include "table_type.hpp" +#include "test_out_of_range.hpp" #include using std::cout; @@ -485,7 +486,7 @@ void test_spots(RealType) x = quantile(complement(p6, poisson_quantile_data[i][1])); BOOST_CHECK_EQUAL(x, floor(poisson_quantile_data[i][3] + 0.5f)); } - + check_out_of_range >(1); } // template void test_spots(RealType) // diff --git a/test/test_rayleigh.cpp b/test/test_rayleigh.cpp index e9b675a37..e2b9352c0 100644 --- a/test/test_rayleigh.cpp +++ b/test/test_rayleigh.cpp @@ -18,6 +18,7 @@ #include // Boost.Test #include +#include "test_out_of_range.hpp" #include using std::cout; @@ -58,6 +59,13 @@ void test_spot(RealType s, RealType x, RealType p, RealType q, RealType toleranc x, tolerance); // % } + if(std::numeric_limits::has_infinity) + { + RealType inf = std::numeric_limits::infinity(); + BOOST_CHECK_EQUAL(pdf(rayleigh_distribution(s), inf), 0); + BOOST_CHECK_EQUAL(cdf(rayleigh_distribution(s), inf), 1); + BOOST_CHECK_EQUAL(cdf(complement(rayleigh_distribution(s), inf)), 0); + } } // void test_spot template @@ -79,6 +87,7 @@ void test_spots(RealType T) // Things that are errors: rayleigh_distribution dist(0.5); + check_out_of_range >(1); BOOST_CHECK_THROW( quantile(dist, RealType(1.)), // quantile unity should overflow. diff --git a/test/test_skew_normal.cpp b/test/test_skew_normal.cpp index 24722e166..97993de30 100644 --- a/test/test_skew_normal.cpp +++ b/test/test_skew_normal.cpp @@ -30,6 +30,7 @@ using std::endl; using std::setprecision; #include using std::numeric_limits; +#include "test_out_of_range.hpp" template void check_skew_normal(RealType mean, RealType scale, RealType shape, RealType x, RealType p, RealType q, RealType tol) @@ -440,6 +441,7 @@ void test_spots(RealType) BOOST_CHECK_THROW(cdf(skew_normal_distribution(0, -1, 0), 0), std::domain_error); BOOST_CHECK_THROW(quantile(skew_normal_distribution(0, 1, 0), -1), std::domain_error); BOOST_CHECK_THROW(quantile(skew_normal_distribution(0, 1, 0), 2), std::domain_error); + check_out_of_range >(1, 1, 1); } diff --git a/test/test_students_t.cpp b/test/test_students_t.cpp index ec95ddf4d..6b7c77399 100644 --- a/test/test_students_t.cpp +++ b/test/test_students_t.cpp @@ -21,6 +21,7 @@ #include using boost::math::students_t_distribution; #include // for real_concept +#include "test_out_of_range.hpp" #include using std::cout; @@ -469,6 +470,7 @@ void test_spots(RealType) BOOST_CHECK_THROW(quantile(dist, 2), std::domain_error); BOOST_CHECK_THROW(pdf(students_t_distribution(0), 0), std::domain_error); BOOST_CHECK_THROW(pdf(students_t_distribution(-1), 0), std::domain_error); + check_out_of_range >(1); } // template void test_spots(RealType) int test_main(int, char* []) diff --git a/test/test_triangular.cpp b/test/test_triangular.cpp index 835fc80ee..6f3def21b 100644 --- a/test/test_triangular.cpp +++ b/test/test_triangular.cpp @@ -23,6 +23,7 @@ using boost::math::triangular_distribution; #include #include +#include "test_out_of_range.hpp" #include using std::cout; @@ -524,6 +525,7 @@ void test_spots(RealType) } BOOST_CHECK_THROW(triangular_distribution(1, 0), std::domain_error); // lower > upper! + check_out_of_range >(-1, 0, 1); } // template void test_spots(RealType) int test_main(int, char* []) diff --git a/test/test_uniform.cpp b/test/test_uniform.cpp index aaa7b5ec5..b5bf004dd 100644 --- a/test/test_uniform.cpp +++ b/test/test_uniform.cpp @@ -22,6 +22,7 @@ #include using boost::math::uniform_distribution; #include +#include "test_out_of_range.hpp" #include using std::cout; @@ -367,6 +368,7 @@ void test_spots(RealType) BOOST_CHECK_THROW(uniform_distribution(1, 0), std::domain_error); // lower > upper! BOOST_CHECK_THROW(uniform_distribution(1, 1), std::domain_error); // lower == upper! + check_out_of_range >(1, 5); } // template void test_spots(RealType) int test_main(int, char* []) diff --git a/test/test_weibull.cpp b/test/test_weibull.cpp index c52e71e05..caa3c4837 100644 --- a/test/test_weibull.cpp +++ b/test/test_weibull.cpp @@ -20,6 +20,7 @@ #include using boost::math::weibull_distribution; #include +#include "test_out_of_range.hpp" #include using std::cout; @@ -342,41 +343,7 @@ void test_spots(RealType) BOOST_CHECK_EQUAL(pdf(weibull_distribution(1, 3), 0), exp(-pow(RealType(0) / RealType(3), RealType(1))) * pow(RealType(0), RealType(0)) * RealType(1) / RealType(3)); BOOST_CHECK_THROW(pdf(weibull_distribution(0.5, 3), 0), std::overflow_error); - // No longer allow any parameter to be NaN or inf, so all these tests should throw. - if (std::numeric_limits::has_quiet_NaN) - { - // Attempt to construct from non-finite should throw. - RealType nan = std::numeric_limits::quiet_NaN(); - BOOST_CHECK_THROW(weibull_distribution w(nan), std::domain_error); - BOOST_CHECK_THROW(weibull_distribution w(1, nan), std::domain_error); - - // Non-finite parameters should throw. - weibull_distribution w(RealType(1)); - BOOST_CHECK_THROW(pdf(w, +nan), std::domain_error); // x = NaN - BOOST_CHECK_THROW(cdf(w, +nan), std::domain_error); // x = NaN - BOOST_CHECK_THROW(cdf(complement(w, +nan)), std::domain_error); // x = + nan - BOOST_CHECK_THROW(quantile(w, +nan), std::domain_error); // p = + nan - BOOST_CHECK_THROW(quantile(complement(w, +nan)), std::domain_error); // p = + nan - } // has_quiet_NaN - - if (std::numeric_limits::has_infinity) - { - RealType inf = std::numeric_limits::infinity(); - - BOOST_CHECK_THROW(weibull_distribution w(inf), std::domain_error); - BOOST_CHECK_THROW(weibull_distribution w(1, inf), std::domain_error); - - weibull_distribution w(RealType(1)); - BOOST_CHECK_THROW(weibull_distribution w(inf), std::domain_error); - BOOST_CHECK_THROW(weibull_distribution w(1, inf), std::domain_error); - BOOST_CHECK_THROW(pdf(w, +inf), std::domain_error); // x = inf - BOOST_CHECK_THROW(cdf(w, +inf), std::domain_error); // x = inf - BOOST_CHECK_THROW(cdf(complement(w, +inf)), std::domain_error); // x = + inf - BOOST_CHECK_THROW(quantile(w, +inf), std::domain_error); // p = + inf - BOOST_CHECK_THROW(quantile(complement(w, +inf)), std::domain_error); // p = + inf - } // has_infinity - - + check_out_of_range >(1, 1); } // template void test_spots(RealType) int test_main(int, char* []) From 392fbeedddd78ac1e23584742c8389032ed7c7f5 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 30 May 2012 18:15:41 +0000 Subject: [PATCH 024/115] Add extra error tests for negative_binomial to laplace distros. Refs #6934. [SVN r78773] --- include/boost/math/distributions/logistic.hpp | 4 ++- .../boost/math/distributions/lognormal.hpp | 31 +++++++++++++++++++ test/test_laplace.cpp | 5 +++ test/test_logistic_dist.cpp | 12 +++++++ test/test_lognormal.cpp | 5 ++- test/test_negative_binomial.cpp | 8 +++++ test/test_out_of_range.hpp | 9 ++++++ 7 files changed, 72 insertions(+), 2 deletions(-) diff --git a/include/boost/math/distributions/logistic.hpp b/include/boost/math/distributions/logistic.hpp index e48f0b4f4..2fa18535f 100644 --- a/include/boost/math/distributions/logistic.hpp +++ b/include/boost/math/distributions/logistic.hpp @@ -53,7 +53,9 @@ namespace boost { namespace math { inline const std::pair range(const logistic_distribution& /* dist */) { // Range of permissible values for random variable x. using boost::math::tools::max_value; - return std::pair(-max_value(), max_value()); // - to + infinity + return std::pair( + std::numeric_limits::has_infinity ? -std::numeric_limits::infinity() : -max_value(), + std::numeric_limits::has_infinity ? std::numeric_limits::infinity() : max_value()); } template diff --git a/include/boost/math/distributions/lognormal.hpp b/include/boost/math/distributions/lognormal.hpp index a6cfa17a2..55e80962a 100644 --- a/include/boost/math/distributions/lognormal.hpp +++ b/include/boost/math/distributions/lognormal.hpp @@ -53,6 +53,7 @@ public: { RealType result; detail::check_scale("boost::math::lognormal_distribution<%1%>::lognormal_distribution", scale, &result, Policy()); + detail::check_location("boost::math::lognormal_distribution<%1%>::lognormal_distribution", location, &result, Policy()); } RealType location()const @@ -102,6 +103,8 @@ RealType pdf(const lognormal_distribution& dist, const RealTyp RealType result = 0; if(0 == detail::check_scale(function, sigma, &result, Policy())) return result; + if(0 == detail::check_location(function, mu, &result, Policy())) + return result; if(0 == detail::check_lognormal_x(function, x, &result, Policy())) return result; @@ -126,6 +129,10 @@ inline RealType cdf(const lognormal_distribution& dist, const static const char* function = "boost::math::cdf(const lognormal_distribution<%1%>&, %1%)"; RealType result = 0; + if(0 == detail::check_scale(function, dist.scale(), &result, Policy())) + return result; + if(0 == detail::check_location(function, dist.location(), &result, Policy())) + return result; if(0 == detail::check_lognormal_x(function, x, &result, Policy())) return result; @@ -144,6 +151,10 @@ inline RealType quantile(const lognormal_distribution& dist, c static const char* function = "boost::math::quantile(const lognormal_distribution<%1%>&, %1%)"; RealType result = 0; + if(0 == detail::check_scale(function, dist.scale(), &result, Policy())) + return result; + if(0 == detail::check_location(function, dist.location(), &result, Policy())) + return result; if(0 == detail::check_probability(function, p, &result, Policy())) return result; @@ -164,6 +175,10 @@ inline RealType cdf(const complemented2_type& dist) RealType result = 0; if(0 == detail::check_scale("boost::math::mean(const lognormal_distribution<%1%>&)", sigma, &result, Policy())) return result; + if(0 == detail::check_location("boost::math::mean(const lognormal_distribution<%1%>&)", mu, &result, Policy())) + return result; return exp(mu + sigma * sigma / 2); } @@ -220,6 +241,8 @@ inline RealType variance(const lognormal_distribution& dist) RealType result = 0; if(0 == detail::check_scale("boost::math::variance(const lognormal_distribution<%1%>&)", sigma, &result, Policy())) return result; + if(0 == detail::check_location("boost::math::variance(const lognormal_distribution<%1%>&)", mu, &result, Policy())) + return result; return boost::math::expm1(sigma * sigma, Policy()) * exp(2 * mu + sigma * sigma); } @@ -235,6 +258,8 @@ inline RealType mode(const lognormal_distribution& dist) RealType result = 0; if(0 == detail::check_scale("boost::math::mode(const lognormal_distribution<%1%>&)", sigma, &result, Policy())) return result; + if(0 == detail::check_location("boost::math::mode(const lognormal_distribution<%1%>&)", mu, &result, Policy())) + return result; return exp(mu - sigma * sigma); } @@ -261,6 +286,8 @@ inline RealType skewness(const lognormal_distribution& dist) RealType result = 0; if(0 == detail::check_scale("boost::math::skewness(const lognormal_distribution<%1%>&)", sigma, &result, Policy())) return result; + if(0 == detail::check_location("boost::math::skewness(const lognormal_distribution<%1%>&)", dist.location(), &result, Policy())) + return result; return (ess + 2) * sqrt(boost::math::expm1(ss, Policy())); } @@ -277,6 +304,8 @@ inline RealType kurtosis(const lognormal_distribution& dist) RealType result = 0; if(0 == detail::check_scale("boost::math::kurtosis(const lognormal_distribution<%1%>&)", sigma, &result, Policy())) return result; + if(0 == detail::check_location("boost::math::kurtosis(const lognormal_distribution<%1%>&)", dist.location(), &result, Policy())) + return result; return exp(4 * ss) + 2 * exp(3 * ss) + 3 * exp(2 * ss) - 3; } @@ -293,6 +322,8 @@ inline RealType kurtosis_excess(const lognormal_distribution& RealType result = 0; if(0 == detail::check_scale("boost::math::kurtosis_excess(const lognormal_distribution<%1%>&)", sigma, &result, Policy())) return result; + if(0 == detail::check_location("boost::math::kurtosis_excess(const lognormal_distribution<%1%>&)", dist.location(), &result, Policy())) + return result; return exp(4 * ss) + 2 * exp(3 * ss) + 3 * exp(2 * ss) - 6; } diff --git a/test/test_laplace.cpp b/test/test_laplace.cpp index 38b172f12..1de0f90c8 100644 --- a/test/test_laplace.cpp +++ b/test/test_laplace.cpp @@ -62,6 +62,7 @@ Test 8: test_extreme_function_arguments() #include #include #include +#include "test_out_of_range.hpp" using boost::math::laplace_distribution; /* @@ -281,6 +282,10 @@ void test_pdf_cdf_ocatave() // static_cast(0.93233235838169L), static_cast(0.93233235838169365405300025251375779829618422688019L), tolerance); + + check_out_of_range >(0, 1); + BOOST_CHECK_THROW(laplace_distribution(0, 0), std::domain_error); + BOOST_CHECK_THROW(laplace_distribution(0, -1), std::domain_error); } template diff --git a/test/test_logistic_dist.cpp b/test/test_logistic_dist.cpp index 04d1a47d5..6132eed88 100644 --- a/test/test_logistic_dist.cpp +++ b/test/test_logistic_dist.cpp @@ -13,6 +13,7 @@ #include // Boost.Test #include +#include "test_out_of_range.hpp" #include @@ -215,6 +216,17 @@ void test_spots(RealType T) //1. domain errors for scale and location //2. x being NAN //3. Probabilies being outside (0,1) + check_out_of_range >(0, 1); + if(std::numeric_limits::has_infinity) + { + RealType inf = std::numeric_limits::infinity(); + BOOST_CHECK_EQUAL(pdf(logistic_distribution(0, 1), inf), 0); + BOOST_CHECK_EQUAL(pdf(logistic_distribution(0, 1), -inf), 0); + BOOST_CHECK_EQUAL(cdf(logistic_distribution(0, 1), inf), 1); + BOOST_CHECK_EQUAL(cdf(logistic_distribution(0, 1), -inf), 0); + BOOST_CHECK_EQUAL(cdf(complement(logistic_distribution(0, 1), inf)), 0); + BOOST_CHECK_EQUAL(cdf(complement(logistic_distribution(0, 1), -inf)), 1); + } //location/scale can't be infinity if(std::numeric_limits::has_infinity) { diff --git a/test/test_lognormal.cpp b/test/test_lognormal.cpp index 4726032ef..72616cbba 100644 --- a/test/test_lognormal.cpp +++ b/test/test_lognormal.cpp @@ -15,6 +15,7 @@ #include using boost::math::lognormal_distribution; #include +#include "test_out_of_range.hpp" #include using std::cout; @@ -248,12 +249,14 @@ void test_spots(RealType) // // Error checks: // - BOOST_CHECK_THROW(lognormal_distribution(0, -1), std::domain_error); + BOOST_CHECK_THROW(lognormal_distribution(0, 0), std::domain_error); + BOOST_CHECK_THROW(lognormal_distribution(2, -1), std::domain_error); BOOST_CHECK_THROW(pdf(dist, -1), std::domain_error); BOOST_CHECK_THROW(cdf(dist, -1), std::domain_error); BOOST_CHECK_THROW(cdf(complement(dist, -1)), std::domain_error); BOOST_CHECK_THROW(quantile(dist, 1), std::overflow_error); BOOST_CHECK_THROW(quantile(complement(dist, 0)), std::overflow_error); + check_out_of_range >(1, 2); } // template void test_spots(RealType) diff --git a/test/test_negative_binomial.cpp b/test/test_negative_binomial.cpp index 2cfe2e6c8..536b38f5d 100644 --- a/test/test_negative_binomial.cpp +++ b/test/test_negative_binomial.cpp @@ -38,6 +38,7 @@ using boost::math::negative_binomial_distribution; #include // for test_main #include // for BOOST_CHECK_CLOSE #include "table_type.hpp" +#include "test_out_of_range.hpp" #include using std::cout; @@ -302,6 +303,13 @@ if(std::numeric_limits::is_specialized) // Wolfram 0.517304753506834882009032744488738352004003696396461766326713 // JM nonLanczos 0.51730475350664229 differs at the 13th decimal digit. // MathCAD 0.51730475342603199 differs at 10th decimal digit. + + // Error tests: + check_out_of_range >(20, 0.5); + BOOST_CHECK_THROW(negative_binomial_distribution(0, 0.5), std::domain_error); + BOOST_CHECK_THROW(negative_binomial_distribution(-2, 0.5), std::domain_error); + BOOST_CHECK_THROW(negative_binomial_distribution(20, -0.5), std::domain_error); + BOOST_CHECK_THROW(negative_binomial_distribution(20, 1.5), std::domain_error); } // End of single spot tests using RealType diff --git a/test/test_out_of_range.hpp b/test/test_out_of_range.hpp index 91863a63e..63d555337 100644 --- a/test/test_out_of_range.hpp +++ b/test/test_out_of_range.hpp @@ -30,6 +30,11 @@ but does *not* check finite but out-of-range parameters to the constructor because these are specific to each distribution. */ +#ifdef BOOST_MSVC +#pragma warning(push) +#pragma warning(disable:4127) +#endif + template void check_support(const Distro& d) { // Checks that @@ -157,4 +162,8 @@ void check_out_of_range(typename Distro::value_type p1, typename Distro::value_t } } +#ifdef BOOST_MSVC +#pragma warning(pop) +#endif + #endif // BOOST_MATH_TEST_OUT_OF_RANGE_HPP From 4dd9452c2237327fb729becf500324ea46710c47 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Thu, 31 May 2012 09:35:52 +0000 Subject: [PATCH 025/115] Corrected failure to check for NaN in quantiles. UNsure if df should include zero. [SVN r78776] --- .../boost/math/distributions/chi_squared.hpp | 34 ++++++++++++------- 1 file changed, 21 insertions(+), 13 deletions(-) diff --git a/include/boost/math/distributions/chi_squared.hpp b/include/boost/math/distributions/chi_squared.hpp index 367a7154a..51b80de52 100644 --- a/include/boost/math/distributions/chi_squared.hpp +++ b/include/boost/math/distributions/chi_squared.hpp @@ -50,7 +50,7 @@ private: // // Data member: // - RealType m_df; // degrees of freedom are a real number. + RealType m_df; // degrees of freedom is a positive real number. }; // class chi_squared_distribution typedef chi_squared_distribution chi_squared; @@ -58,8 +58,15 @@ typedef chi_squared_distribution chi_squared; template inline const std::pair range(const chi_squared_distribution& /*dist*/) { // Range of permissible values for random variable x. - using boost::math::tools::max_value; - return std::pair(static_cast(0), max_value()); // 0 to + infinity. + if (std::numeric_limits::has_infinity) + { + return std::pair(static_cast(0), std::numeric_limits::infinity()); // 0 to + infinity. + } + else + { + using boost::math::tools::max_value; + return std::pair(static_cast(0), max_value()); // 0 to + max. + } } template @@ -138,11 +145,12 @@ inline RealType quantile(const chi_squared_distribution& dist, static const char* function = "boost::math::quantile(const chi_squared_distribution<%1%>&, %1%)"; // Error check: RealType error_result; - if(false == detail::check_df( - function, degrees_of_freedom, &error_result, Policy()) - && detail::check_probability( - function, p, &error_result, Policy())) - return error_result; + if(false == + ( + detail::check_df(function, degrees_of_freedom, &error_result, Policy()) + && detail::check_probability(function, p, &error_result, Policy())) + ) + return error_result; return 2 * boost::math::gamma_p_inv(degrees_of_freedom / 2, p, Policy()); } // quantile @@ -176,11 +184,11 @@ inline RealType quantile(const complemented2_type Date: Thu, 31 May 2012 09:36:24 +0000 Subject: [PATCH 026/115] added check_out_of Range [SVN r78777] --- test/test_chi_squared.cpp | 31 ++++++++++++++++++++++--------- 1 file changed, 22 insertions(+), 9 deletions(-) diff --git a/test/test_chi_squared.cpp b/test/test_chi_squared.cpp index f4d26a98a..29d696244 100644 --- a/test/test_chi_squared.cpp +++ b/test/test_chi_squared.cpp @@ -8,6 +8,14 @@ // (See accompanying file LICENSE_1_0.txt // or copy at http://www.boost.org/LICENSE_1_0.txt) +#ifdef _MSC_VER +# pragma warning(disable: 4100) // unreferenced formal parameter. +// Seems an entirely spurious warning - formal parameter T IS used - get error if /* T */ +//# pragma warning(disable: 4535) // calling _set_se_translator() requires /EHa (in Boost.test) +// Enable C++ Exceptions Yes With SEH Exceptions (/EHa) prevents warning 4535. +# pragma warning(disable: 4127) // conditional expression is constant +#endif + #include // for real_concept using ::boost::math::concepts::real_concept; @@ -18,6 +26,8 @@ using boost::math::chi_squared; #include // for test_main #include // for BOOST_CHECK_CLOSE +#include "test_out_of_range.hpp" + #include using std::cout; using std::endl; @@ -279,14 +289,14 @@ double lower_critical_values[][6] = { }; template // Any floating-point type RealType. -void test_spots(RealType) +void test_spots(RealType T) { // Basic sanity checks, test data is to three decimal places only // so set tolerance to 0.001 expressed as a persentage. RealType tolerance = 0.001f * 100; - cout << "Tolerance = " << tolerance << "%." << endl; + cout << "Tolerance for type " << typeid(T).name() << " is " << tolerance << " %" << endl; using boost::math::chi_squared_distribution; using ::boost::math::chi_squared; @@ -519,6 +529,9 @@ void test_spots(RealType) BOOST_CHECK_EQUAL( ceil(chi_squared_distribution::find_degrees_of_freedom( -10, 0.05f, 0.01f, 100)), static_cast(2826)); + + check_out_of_range >(1); // (All) valid constructor parameter values. + } // template void test_spots(RealType) int test_main(int, char* []) @@ -546,13 +559,13 @@ int test_main(int, char* []) Output: -Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_chi_squared.exe" -Running 1 test case... -Tolerance = 0.1%. -Tolerance = 0.1%. -Tolerance = 0.1%. -Tolerance = 0.1%. -*** No errors detected +Description: Autorun "J:\Cpp\MathToolkit\test\Math_test\Debug\test_chi_squared.exe" + Running 1 test case... + Tolerance for type float is 0.1 % + Tolerance for type double is 0.1 % + Tolerance for type long double is 0.1 % + Tolerance for type class boost::math::concepts::real_concept is 0.1 % + */ From 73c9b11179af897cee2271492527323a95670ebc Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 31 May 2012 10:18:02 +0000 Subject: [PATCH 027/115] Update more distribution tests, from Inverse* down to gamma. Refs #6934. [SVN r78778] --- .../math/distributions/inverse_gaussian.hpp | 2 +- test/test_gamma_dist.cpp | 8 +++++ test/test_geometric.cpp | 2 ++ .../test_inverse_chi_squared_distribution.cpp | 2 ++ test/test_inverse_gamma_distribution.cpp | 3 +- test/test_inverse_gaussian.cpp | 30 ++++--------------- 6 files changed, 20 insertions(+), 27 deletions(-) diff --git a/include/boost/math/distributions/inverse_gaussian.hpp b/include/boost/math/distributions/inverse_gaussian.hpp index fa7c2a1e6..ba8507731 100644 --- a/include/boost/math/distributions/inverse_gaussian.hpp +++ b/include/boost/math/distributions/inverse_gaussian.hpp @@ -380,7 +380,7 @@ inline RealType cdf(const complemented2_type n01; diff --git a/test/test_gamma_dist.cpp b/test/test_gamma_dist.cpp index 4b5815793..b20652f8c 100644 --- a/test/test_gamma_dist.cpp +++ b/test/test_gamma_dist.cpp @@ -24,6 +24,7 @@ #include using boost::math::gamma_distribution; #include +#include "test_out_of_range.hpp" #include using std::cout; @@ -213,6 +214,13 @@ void test_spots(RealType) (std::max)(tol2, static_cast(std::numeric_limits::epsilon() * 2 * 100))); // 2 eps as persent // Rely on default definition in derived accessors. + // error tests + check_out_of_range >(1, 1); + BOOST_CHECK_THROW(gamma_distribution(0, 1), std::domain_error); + BOOST_CHECK_THROW(gamma_distribution(-1, 1), std::domain_error); + BOOST_CHECK_THROW(gamma_distribution(1, 0), std::domain_error); + BOOST_CHECK_THROW(gamma_distribution(1, -1), std::domain_error); + } // template void test_spots(RealType) int test_main(int, char* []) diff --git a/test/test_geometric.cpp b/test/test_geometric.cpp index 6958b6253..611752212 100644 --- a/test/test_geometric.cpp +++ b/test/test_geometric.cpp @@ -37,6 +37,7 @@ using boost::math::geometric; // using typedef for geometric_distribution // for test_main #include // for BOOST_CHECK_CLOSE_FRACTION +#include "test_out_of_range.hpp" #include using std::cout; @@ -719,6 +720,7 @@ if(std::numeric_limits::is_specialized) quantile( // Success_fraction > 1! geometric_distribution(static_cast(1.25)), static_cast(0)), std::domain_error); + check_out_of_range >(0.5); // End of check throwing 'duff' out-of-domain values. { // Compare geometric and negative binomial functions. diff --git a/test/test_inverse_chi_squared_distribution.cpp b/test/test_inverse_chi_squared_distribution.cpp index ff79a7707..cb3a20c6a 100644 --- a/test/test_inverse_chi_squared_distribution.cpp +++ b/test/test_inverse_chi_squared_distribution.cpp @@ -20,6 +20,7 @@ using ::boost::math::concepts::real_concept; //#include #include // for test_main #include // for BOOST_CHECK_CLOSE_FRACTION +#include "test_out_of_range.hpp" #include // for inverse_chisquared_distribution using boost::math::inverse_chi_squared_distribution; @@ -142,6 +143,7 @@ void test_spots(RealType) BOOST_CHECK_THROW(boost::math::inverse_chi_squared_distribution ichsqbad1(-1), std::domain_error); // negative degrees_of_freedom. BOOST_CHECK_THROW(boost::math::inverse_chi_squared_distribution ichsqbad2(1, -1), std::domain_error); // negative scale. BOOST_CHECK_THROW(boost::math::inverse_chi_squared_distribution ichsqbad3(-1, -1), std::domain_error); // negative scale and degrees_of_freedom. + check_out_of_range >(1, 1); inverse_chi_squared_distribution ichsq; diff --git a/test/test_inverse_gamma_distribution.cpp b/test/test_inverse_gamma_distribution.cpp index 0b72a785d..c0cbb8a4c 100644 --- a/test/test_inverse_gamma_distribution.cpp +++ b/test/test_inverse_gamma_distribution.cpp @@ -20,6 +20,7 @@ using ::boost::math::concepts::real_concept; //#include #include // for test_main #include // for BOOST_CHECK_CLOSE_FRACTION +#include "test_out_of_range.hpp" #include // for inverse_gamma_distribution using boost::math::inverse_gamma_distribution; @@ -323,7 +324,7 @@ void test_spots(RealType) inverse_gamma_distribution(static_cast(8)), static_cast(1.1))), std::domain_error ); - + check_out_of_range >(1, 1); } // template void test_spots(RealType) int test_main(int, char* []) diff --git a/test/test_inverse_gaussian.cpp b/test/test_inverse_gaussian.cpp index 14673fac7..9ae4f485d 100644 --- a/test/test_inverse_gaussian.cpp +++ b/test/test_inverse_gaussian.cpp @@ -25,6 +25,7 @@ using boost::math::inverse_gaussian_distribution; using boost::math::inverse_gaussian; #include +#include "test_out_of_range.hpp" #include using std::cout; @@ -90,33 +91,12 @@ void test_spots(RealType) BOOST_CHECK_THROW(boost::math::inverse_gaussian_distribution nbad1(0, 0), std::domain_error); // zero scale BOOST_CHECK_THROW(boost::math::inverse_gaussian_distribution nbad1(0, -1), std::domain_error); // negative scale - // Tests on extreme values of random variate x, if has numeric_limit infinity etc. - - // Infinity is not allowed, so all should throw. inverse_gaussian_distribution w11; - if(std::numeric_limits::has_infinity) - { - BOOST_CHECK_THROW(pdf(w11, +std::numeric_limits::infinity()), std::domain_error); - BOOST_CHECK_THROW(pdf(w11, -std::numeric_limits::infinity()), std::domain_error); - BOOST_CHECK_THROW(cdf(w11, +std::numeric_limits::infinity()), std::domain_error); - BOOST_CHECK_THROW(cdf(w11, -std::numeric_limits::infinity()), std::domain_error); - BOOST_CHECK_THROW(cdf(complement(w11, +std::numeric_limits::infinity())), std::domain_error); // x = + infinity, - BOOST_CHECK_THROW(cdf(complement(w11, -std::numeric_limits::infinity())), std::domain_error); // x = - infinity, - BOOST_CHECK_THROW(boost::math::inverse_gaussian_distribution nbad1(std::numeric_limits::infinity(), static_cast(1)), std::domain_error); // +infinite mean - BOOST_CHECK_THROW(boost::math::inverse_gaussian_distribution nbad1(-std::numeric_limits::infinity(), static_cast(1)), std::domain_error); // -infinite mean - BOOST_CHECK_THROW(boost::math::inverse_gaussian_distribution nbad1(static_cast(0), std::numeric_limits::infinity()), std::domain_error); // infinite scale - } - if (std::numeric_limits::has_quiet_NaN) - { - // No longer allow x to be NaN, so these tests should throw. - BOOST_CHECK_THROW(pdf(w11, +std::numeric_limits::quiet_NaN()), std::domain_error); // x = NaN - BOOST_CHECK_THROW(cdf(w11, +std::numeric_limits::quiet_NaN()), std::domain_error); // x = NaN - BOOST_CHECK_THROW(cdf(complement(w11, +std::numeric_limits::quiet_NaN())), std::domain_error); // x = + infinity - BOOST_CHECK_THROW(quantile(w11, +std::numeric_limits::quiet_NaN()), std::domain_error); // p = + infinity - BOOST_CHECK_THROW(quantile(complement(w11, +std::numeric_limits::quiet_NaN())), std::domain_error); // p = + infinity - } - // Check complements. + // Error tests: + check_out_of_range >(0, 1); + + // Check complements. BOOST_CHECK_CLOSE_FRACTION( cdf(complement(w11, 1.)), static_cast(1) - cdf(w11, 1.), tolerance); // cdf complement From 3f93aff61de19b797493e8413a12f7a138bf1a28 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Thu, 31 May 2012 11:10:50 +0000 Subject: [PATCH 028/115] Added checks for non finite parameter and x = NaN [SVN r78781] --- include/boost/math/distributions/exponential.hpp | 14 +++++++++++--- 1 file changed, 11 insertions(+), 3 deletions(-) diff --git a/include/boost/math/distributions/exponential.hpp b/include/boost/math/distributions/exponential.hpp index 62b858c87..47e419847 100644 --- a/include/boost/math/distributions/exponential.hpp +++ b/include/boost/math/distributions/exponential.hpp @@ -16,6 +16,7 @@ #ifdef BOOST_MSVC # pragma warning(push) +# pragma warning(disable: 4127) // conditional expression is constant # pragma warning(disable: 4702) // unreachable code (return after domain_error throw). #endif @@ -30,7 +31,7 @@ namespace detail{ template inline bool verify_lambda(const char* function, RealType l, RealType* presult, const Policy& pol) { - if(l <= 0) + if((l <= 0) || !(boost::math::isfinite)(l)) { *presult = policies::raise_domain_error( function, @@ -43,7 +44,7 @@ inline bool verify_lambda(const char* function, RealType l, RealType* presult, c template inline bool verify_exp_x(const char* function, RealType x, RealType* presult, const Policy& pol) { - if(x < 0) + if((x < 0) || (boost::math::isnan)(x)) { *presult = policies::raise_domain_error( function, @@ -80,8 +81,15 @@ typedef exponential_distribution exponential; template inline const std::pair range(const exponential_distribution& /*dist*/) { // Range of permissible values for random variable x. + if (std::numeric_limits::has_infinity) + { + return std::pair(static_cast(0), std::numeric_limits::infinity()); // 0 to + infinity. + } + else + { using boost::math::tools::max_value; - return std::pair(static_cast(0), max_value()); + return std::pair(static_cast(0), max_value()); // 0 to + max + } } template From b66b89091297fcf20281af524f13a0f2dfff6f4e Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Thu, 31 May 2012 11:11:21 +0000 Subject: [PATCH 029/115] Added check out of range [SVN r78782] --- test/test_exponential_dist.cpp | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/test/test_exponential_dist.cpp b/test/test_exponential_dist.cpp index c11611662..db054134d 100644 --- a/test/test_exponential_dist.cpp +++ b/test/test_exponential_dist.cpp @@ -15,6 +15,8 @@ #include // Boost.Test #include +#include "test_out_of_range.hpp" + #include using std::cout; using std::endl; @@ -250,6 +252,8 @@ void test_spots(RealType T) quantile(dist, RealType(2)), std::domain_error); + check_out_of_range >(1); // (All) valid constructor parameter values. + } // template void test_spots(RealType) int test_main(int, char* []) From 6007215c9563c1e96fe4785017069cda48cd6b97 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 31 May 2012 11:15:42 +0000 Subject: [PATCH 030/115] Update more distribution tests for fisher_f and extreme_value and fix failures. Refs #6934. [SVN r78783] --- .../math/distributions/extreme_value.hpp | 49 ++++++++++++++++--- include/boost/math/distributions/fisher_f.hpp | 4 +- test/test_extreme_value.cpp | 14 +++++- test/test_fisher_f.cpp | 3 +- 4 files changed, 60 insertions(+), 10 deletions(-) diff --git a/include/boost/math/distributions/extreme_value.hpp b/include/boost/math/distributions/extreme_value.hpp index 3cf94d4b3..ef9fbe817 100644 --- a/include/boost/math/distributions/extreme_value.hpp +++ b/include/boost/math/distributions/extreme_value.hpp @@ -37,11 +37,11 @@ namespace detail{ template inline bool verify_scale_b(const char* function, RealType b, RealType* presult, const Policy& pol) { - if(b <= 0) + if((b <= 0) || !(boost::math::isfinite)(b)) { *presult = policies::raise_domain_error( function, - "The scale parameter \"b\" must be > 0, but was: %1%.", b, pol); + "The scale parameter \"b\" must be finite and > 0, but was: %1%.", b, pol); return false; } return true; @@ -61,6 +61,7 @@ public: { RealType err; detail::verify_scale_b("boost::math::extreme_value_distribution<%1%>::extreme_value_distribution", b, &err, Policy()); + detail::check_finite("boost::math::extreme_value_distribution<%1%>::extreme_value_distribution", a, &err, Policy()); } // extreme_value_distribution RealType location()const { return m_a; } @@ -76,7 +77,9 @@ template inline const std::pair range(const extreme_value_distribution& /*dist*/) { // Range of permissible values for random variable x. using boost::math::tools::max_value; - return std::pair(-max_value(), max_value()); + return std::pair( + std::numeric_limits::has_infinity ? -std::numeric_limits::infinity() : -max_value(), + std::numeric_limits::has_infinity ? std::numeric_limits::infinity() : max_value()); } template @@ -92,10 +95,18 @@ inline RealType pdf(const extreme_value_distribution& dist, co { BOOST_MATH_STD_USING // for ADL of std functions + static const char* function = "boost::math::pdf(const extreme_value_distribution<%1%>&, %1%)"; + RealType a = dist.location(); RealType b = dist.scale(); RealType result = 0; - if(0 == detail::verify_scale_b("boost::math::pdf(const extreme_value_distribution<%1%>&, %1%)", b, &result, Policy())) + if((boost::math::isinf)(x)) + return 0.0f; + if(0 == detail::verify_scale_b(function, b, &result, Policy())) + return result; + if(0 == detail::check_finite(function, a, &result, Policy())) + return result; + if(0 == detail::check_x(function, x, &result, Policy())) return result; result = exp((a-x)/b) * exp(-exp((a-x)/b)) / b; return result; @@ -106,10 +117,20 @@ inline RealType cdf(const extreme_value_distribution& dist, co { BOOST_MATH_STD_USING // for ADL of std functions + static const char* function = "boost::math::cdf(const extreme_value_distribution<%1%>&, %1%)"; + + if((boost::math::isinf)(x)) + return x < 0 ? 0.0f : 1.0f; RealType a = dist.location(); RealType b = dist.scale(); RealType result = 0; - if(0 == detail::verify_scale_b("boost::math::cdf(const extreme_value_distribution<%1%>&, %1%)", b, &result, Policy())) + if(0 == detail::verify_scale_b(function, b, &result, Policy())) + return result; + if(0 == detail::check_finite(function, a, &result, Policy())) + return result; + if(0 == detail::check_finite(function, a, &result, Policy())) + return result; + if(0 == detail::check_x("boost::math::cdf(const extreme_value_distribution<%1%>&, %1%)", x, &result, Policy())) return result; result = exp(-exp((a-x)/b)); @@ -129,6 +150,8 @@ RealType quantile(const extreme_value_distribution& dist, cons RealType result = 0; if(0 == detail::verify_scale_b(function, b, &result, Policy())) return result; + if(0 == detail::check_finite(function, a, &result, Policy())) + return result; if(0 == detail::check_probability(function, p, &result, Policy())) return result; @@ -147,10 +170,18 @@ inline RealType cdf(const complemented2_type&, %1%)", b, &result, Policy())) + if(0 == detail::verify_scale_b(function, b, &result, Policy())) + return result; + if(0 == detail::check_finite(function, a, &result, Policy())) + return result; + if(0 == detail::check_x(function, c.param, &result, Policy())) return result; result = -boost::math::expm1(-exp((a-c.param)/b), Policy()); @@ -171,6 +202,8 @@ RealType quantile(const complemented2_type& dist) RealType result = 0; if(0 == detail::verify_scale_b("boost::math::mean(const extreme_value_distribution<%1%>&)", b, &result, Policy())) return result; + if(0 == detail::check_scale("boost::math::mean(const extreme_value_distribution<%1%>&)", a, &result, Policy())) + return result; return a + constants::euler() * b; } @@ -204,6 +239,8 @@ inline RealType standard_deviation(const extreme_value_distribution&)", b, &result, Policy())) return result; + if(0 == detail::check_scale("boost::math::standard_deviation(const extreme_value_distribution<%1%>&)", dist.location(), &result, Policy())) + return result; return constants::pi() * b / sqrt(static_cast(6)); } diff --git a/include/boost/math/distributions/fisher_f.hpp b/include/boost/math/distributions/fisher_f.hpp index b1d9eb7ce..9e259bcc9 100644 --- a/include/boost/math/distributions/fisher_f.hpp +++ b/include/boost/math/distributions/fisher_f.hpp @@ -231,12 +231,12 @@ inline RealType quantile(const complemented2_type // Boost.Test #include +#include "test_out_of_range.hpp" #include using std::cout; @@ -124,7 +125,7 @@ void test_spots(RealType) tolerance); // % BOOST_CHECK_CLOSE( ::boost::math::standard_deviation( - extreme_value_distribution(-1, 0.5)), + extreme_value_distribution(1, 0.5)), static_cast(0.6412749150809320477720181798355L), tolerance); // % BOOST_CHECK_CLOSE( @@ -179,6 +180,17 @@ void test_spots(RealType) BOOST_CHECK_THROW( quantile(dist, RealType(2)), std::domain_error); + check_out_of_range >(1, 2); + if(std::numeric_limits::has_infinity) + { + RealType inf = std::numeric_limits::infinity(); + BOOST_CHECK_EQUAL(pdf(extreme_value_distribution(), -inf), 0); + BOOST_CHECK_EQUAL(pdf(extreme_value_distribution(), inf), 0); + BOOST_CHECK_EQUAL(cdf(extreme_value_distribution(), -inf), 0); + BOOST_CHECK_EQUAL(cdf(extreme_value_distribution(), inf), 1); + BOOST_CHECK_EQUAL(cdf(complement(extreme_value_distribution(), -inf)), 1); + BOOST_CHECK_EQUAL(cdf(complement(extreme_value_distribution(), inf)), 0); + } } // template void test_spots(RealType) int test_main(int, char* []) diff --git a/test/test_fisher_f.cpp b/test/test_fisher_f.cpp index ab2ee5f11..a664e7d05 100644 --- a/test/test_fisher_f.cpp +++ b/test/test_fisher_f.cpp @@ -16,6 +16,7 @@ using boost::math::fisher_f_distribution; #include // for test_main #include // for BOOST_CHECK_CLOSE +#include "test_out_of_range.hpp" #include using std::cout; @@ -498,7 +499,7 @@ void test_spots(RealType) fisher_f_distribution(8, 8), static_cast(1.1))), std::domain_error ); - + check_out_of_range >(2, 3); } // template void test_spots(RealType) int test_main(int, char* []) From fbc849c24e2c36822bbb3ac50398fcd2462d8e38 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 31 May 2012 11:58:06 +0000 Subject: [PATCH 031/115] Enhance exponential_distribution tests. Refs #6934. [SVN r78784] --- test/test_exponential_dist.cpp | 13 ++++++++++--- 1 file changed, 10 insertions(+), 3 deletions(-) diff --git a/test/test_exponential_dist.cpp b/test/test_exponential_dist.cpp index db054134d..8e03b2256 100644 --- a/test/test_exponential_dist.cpp +++ b/test/test_exponential_dist.cpp @@ -14,7 +14,6 @@ #include // Boost.Test #include - #include "test_out_of_range.hpp" #include @@ -252,8 +251,16 @@ void test_spots(RealType T) quantile(dist, RealType(2)), std::domain_error); - check_out_of_range >(1); // (All) valid constructor parameter values. - + check_out_of_range >(2); + BOOST_CHECK_THROW(exponential_distribution(0), std::domain_error); + BOOST_CHECK_THROW(exponential_distribution(-1), std::domain_error); + if(std::numeric_limits::has_infinity) + { + RealType inf = std::numeric_limits::infinity(); + BOOST_CHECK_EQUAL(pdf(exponential_distribution(2), inf), 0); + BOOST_CHECK_EQUAL(cdf(exponential_distribution(2), inf), 1); + BOOST_CHECK_EQUAL(cdf(complement(exponential_distribution(2), inf)), 0); + } } // template void test_spots(RealType) int test_main(int, char* []) From d6236139df1efa3864231591ae2626329aae5a05 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Fri, 1 Jun 2012 11:58:56 +0000 Subject: [PATCH 032/115] Fix for GCC/Linux failure. [SVN r78790] --- test/test_out_of_range.hpp | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/test/test_out_of_range.hpp b/test/test_out_of_range.hpp index 63d555337..e4486552a 100644 --- a/test/test_out_of_range.hpp +++ b/test/test_out_of_range.hpp @@ -41,7 +41,7 @@ void check_support(const Distro& d) typedef typename Distro::value_type value_type; if((boost::math::isfinite)(range(d).first) && (range(d).first != -boost::math::tools::max_value())) { // If possible, check that a random variable value just less than the bottom of the supported range throws domain errors. - value_type m = boost::math::float_prior(range(d).first); + value_type m = (range(d).first == 0) ? -boost::math::tools::min_value() : boost::math::float_prior(range(d).first); BOOST_ASSERT(m != range(d).first); BOOST_ASSERT(m < range(d).first); BOOST_CHECK_THROW(pdf(d, m), std::domain_error); @@ -50,7 +50,7 @@ void check_support(const Distro& d) } if((boost::math::isfinite)(range(d).second) && (range(d).second != boost::math::tools::max_value())) { // If possible, check that a random variable value just more than the top of the supported range throws domain errors. - value_type m = boost::math::float_next(range(d).second); + value_type m = (range(d).second == 0) ? boost::math::tools::min_value() : boost::math::float_next(range(d).second); BOOST_ASSERT(m != range(d).first); BOOST_ASSERT(m > range(d).first); BOOST_CHECK_THROW(pdf(d, m), std::domain_error); From 98acfb8a5d2d059bee5f967d7c171e9671b64971 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Mon, 4 Jun 2012 13:24:44 +0000 Subject: [PATCH 033/115] Various small changes about revised error handling and checking ready for 1.51 [SVN r78805] --- doc/sf_and_dist/error_handling.qbk | 7 +++- doc/sf_and_dist/implementation.qbk | 55 +++++++++++++++++++++++++++++- doc/sf_and_dist/math.qbk | 2 ++ doc/sf_and_dist/roadmap.qbk | 8 +++++ 4 files changed, 70 insertions(+), 2 deletions(-) diff --git a/doc/sf_and_dist/error_handling.qbk b/doc/sf_and_dist/error_handling.qbk index 73f1a653a..b3001063e 100644 --- a/doc/sf_and_dist/error_handling.qbk +++ b/doc/sf_and_dist/error_handling.qbk @@ -9,6 +9,9 @@ Handling of errors by this library is split into two orthogonal parts: * What kind of error has been raised? * What should be done when the error is raised? +[warning The default error actions are to throw an exception with an informative error message. +If you do not try to catch the exception, you will not see the message!] + The kinds of errors that can be raised are: [variablelist @@ -153,6 +156,8 @@ this library. It was felt that: rather than following C-compatible behaviour and setting `::errno`. * Numeric underflow and denormalised results were not considered to be fatal errors in most cases, so it was felt that these should be ignored. +* If there is more than one error, +only the first detected will be reported in the throw message. [heading Finding More Information] @@ -390,7 +395,7 @@ listed above on [link overflow_error overflow], [endsect][/section:error_handling Error Handling] [/ - Copyright 2006 - 2010 John Maddock and Paul A. Bristow. + Copyright 2006 - 2012 John Maddock and Paul A. Bristow. Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt). diff --git a/doc/sf_and_dist/implementation.qbk b/doc/sf_and_dist/implementation.qbk index 09a28941b..9f7b94da4 100644 --- a/doc/sf_and_dist/implementation.qbk +++ b/doc/sf_and_dist/implementation.qbk @@ -207,7 +207,18 @@ much more work to test, and much less readable. However in a few cases, for example normal, where we felt it obvious, we have permitted argument(s) to be infinity, -provided infinity is implemented for the realType on that implementation. +provided infinity is implemented for the `RealType` on that implementation, +and it is supported and tested by the distribution. + +The range for these distributions is set to infinity if supported by the platform, +(by testing `std::numeric_limits::has_infinity`) +else the maximum value provided for the `RealType` by Boost.Math. + +Testing for has_infinity is obviously important for arbitrary precision types +where infinity makes much less sense than for IEEE754 floating-point. + +So far we have not set `support()` function (only range) +on the grounds that the PDF is uninteresting/zero for infinities. Users who require special handling of infinity (or other specific value) can, of course, always intercept this before calling a distribution or function @@ -394,6 +405,48 @@ It is also the only independent source found for the Weibull distribution; unfortunately it appears to suffer from very poor accuracy in areas where the underlying special function is known to be difficult to implement. +[h4 Testing for Invalid Parameters to Functions and Constructors] + +After finding that some 'bad' parameters (like NaN) were not throwing +a `domain_error` exception as they should, a function + +`check_out_of_range` (in `test_out_of_range.hpp`) +was devised by JM to check +(using Boost.Test's BOOST_CHECK_THROW macro) +that bad parameters passed to constructors and functions throw `domain_error` exceptions. + +Usage is `check_out_of_range< DistributionType >(list-of-params);` +Where list-of-params is a list of *valid* parameters from which the distribution can be constructed +- ie the same number of args are passed to the function, +as are passed to the distribution constructor. + +The values of the parameters are not important, but must be *valid* to pass the contructor checks; +the default values are suitable, but must be explicitly provided, for example: + + check_out_of_range >(1, 2); + +Checks made are: + +* Infinity or NaN (if available) passed in place of each of the valid params. +* Infinity or NaN (if available) as a random variable. +* Out-of-range random variable passed to pdf and cdf +(ie outside of "range(DistributionType)"). +* Out-of-range probability passed to quantile function and complement. + +but does *not* check finite but out-of-range parameters to the constructor +because these are specific to each distribution, for example: + + BOOST_CHECK_THROW(pdf(pareto_distribution(0, 1), 0), std::domain_error); + BOOST_CHECK_THROW(pdf(pareto_distribution(1, 0), 0), std::domain_error); + +checks `scale` and `shape` parameters are both > 0 +by checking that `domain_error` exception is thrown if either are == 0. + +(Use of `check_out_of_range` function may mean that some previous tests are now redundant). + +It was also noted that if more than one parameter is bad, +then only the first detected will be reported by the error message. + [h4 Creating and Managing the Equations] Equations that fit on a single line can most easily be produced by inline Quickbook code diff --git a/doc/sf_and_dist/math.qbk b/doc/sf_and_dist/math.qbk index 5e981bfce..9f74208ee 100644 --- a/doc/sf_and_dist/math.qbk +++ b/doc/sf_and_dist/math.qbk @@ -249,6 +249,7 @@ and use the function's name as the link text.] [def __F_distrib [link math_toolkit.dist.dist_ref.dists.f_dist Fisher F Distribution]] [def __gamma_distrib [link math_toolkit.dist.dist_ref.dists.gamma_dist Gamma Distribution]] [def __geometric_distrib [link math_toolkit.dist.dist_ref.dists.geometric_dist Geometric Distribution]] +[def __hypergeometric_distrib [link math_toolkit.dist.dist_ref.dists.hypergeometric_dist hypergeometric Distribution]] [def __inverse_gamma_distrib [link math_toolkit.dist.dist_ref.dists.inverse_gamma_dist Inverse Gamma Distribution]] [def __inverse_gaussian_distrib [link math_toolkit.dist.dist_ref.dists.inverse_gaussian_dist Inverse Gaussian Distribution]] [def __inverse_chi_squared_distrib [link math_toolkit.dist.dist_ref.dists.inverse_chi_squared_dist Inverse chi squared Distribution]] @@ -263,6 +264,7 @@ and use the function's name as the link text.] [def __non_central_t_distrib [link math_toolkit.dist.dist_ref.dists.nc_t_dist noncentral T distribution]] [def __normal_distrib [link math_toolkit.dist.dist_ref.dists.normal_dist Normal Distribution]] [def __poisson_distrib [link math_toolkit.dist.dist_ref.dists.poisson_dist Poisson Distribution]] +[def __pareto_distrib [link math_toolkit.dist.dist_ref.dists.pareto_dist Pareto Distribution]] [def __students_t_distrib [link math_toolkit.dist.dist_ref.dists.students_t_dist Students t Distribution]] [def __skew_normal_distrib [link math_toolkit.dist.dist_ref.dists.skew_normal_dist Skew Normal Distribution]] [def __weibull_distrib [link math_toolkit.dist.dist_ref.dists.weibull_dist Weibull Distribution]] diff --git a/doc/sf_and_dist/roadmap.qbk b/doc/sf_and_dist/roadmap.qbk index 81524cd0d..c3f7894a0 100644 --- a/doc/sf_and_dist/roadmap.qbk +++ b/doc/sf_and_dist/roadmap.qbk @@ -1,5 +1,13 @@ [template history[] +[h4 Boost-1.51] + +* Corrected failure to detect bad parameters in many distributions +[@https://svn.boost.org/trac/boost/ticket/6934 #6934] (reported by Florian Schoppmann) +by adding a function check_out_of_range to test many possible bad parameters. +This test revealed several distributions where the checks for bad parameters were ineffective, +and these have been rectified. + [h4 Boost-1.50] * Promoted math constants to be 1st class citizens, From 94c61bd9e740a64ce4f4eae91dcbe623ad8c02cd Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Wed, 6 Jun 2012 11:26:58 +0000 Subject: [PATCH 034/115] Example of using constants [SVN r78827] --- example/constants_eg1.cpp | 184 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 184 insertions(+) create mode 100644 example/constants_eg1.cpp diff --git a/example/constants_eg1.cpp b/example/constants_eg1.cpp new file mode 100644 index 000000000..47cad122d --- /dev/null +++ b/example/constants_eg1.cpp @@ -0,0 +1,184 @@ +// Copyright Paul Bristow 2012. +// Copyright John Maddock 2010. + +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt +// or copy at http://www.boost.org/LICENSE_1_0.txt) + +/*! \brief Examples of using the enhanced math constants. + \details This allows for access to constants via functions like @c pi(), + and also via namespaces, @c using @c namespace boost::math::double_constants; + called simply @c pi. +*/ + +#include + +#include +using std::cout; +using std::endl; + +#include +using std::numeric_limits; + +/*! \brief Examples of a template function using constants. + \details This example shows using of constants from function calls like @c pi(), + rather than the 'cute' plain @c pi use in non-template applications. + + \tparam Real radius parameter that can be a built-in like float, double, + or a user-defined type like multiprecision. + \returns Area = pi * radius ^ 2 +*/ + +//[math_constants_eg1 +template +Real area(Real r) +{ + using namespace boost::math::constants; + + return pi() * r * r; +} +//] [/math_constants_eg1] + +int main() +{ + + { // Boost.Math constants using function calls like pi(). + // using namespace boost::math::constants; + + using boost::math::constants::pi; + using boost::math::constants::one_div_two_pi; + + cout.precision(numeric_limits::max_digits10); + cout << "double pi = boost::math::double_constants::pi = " << pi() << endl; + // double pi = boost::math::double_constants::pi = 3.1415926535897931 + double r = 1.234567890123456789; + double d = pi() * r * r; + + cout << "d = " << d << ", r = " << r << endl; + + float rf = 0.987654321987654321f; + + float pif = boost::math::constants::pi(); + cout << "pidf = boost::math::constants::pi() = " << pif << endl; + // pidf = boost::math::float_constants::pi = 3.1415927410125732 + + //float df = pi * rf * rf; // conversion from 'const double' to 'float', possible loss of data + float df = pif * rf * rf; + + cout << "df = " << df << ", rf = " << rf << endl; + + cout << "one_div_two_pi " << one_div_two_pi() << endl; + + using boost::math::constants::one_div_two_pi; + + cout << "one_div_root_two_pi " << one_div_two_pi() << endl; + } + + { // Boost math new constants using namespace selected values, like pi. + + //using namespace boost::math::float_constants; + using namespace boost::math::double_constants; + + double my2pi = two_pi; // Uses boost::math::double_constants::two_pi; + + cout << "double my2pi = " << my2pi << endl; + + using boost::math::float_constants::e; + float my_e = e; + cout << "float my_e " << my_e << endl; + + double my_pi = boost::math::double_constants::pi; + cout << "double my_pi = boost::math::double_constants::pi = " << my_pi << endl; + + // If you try to use two namespaces, this may, of course, create ambiguity: + // it is not too difficult to do this inadvertently. + using namespace boost::math::float_constants; + //cout << pi << endl; // error C2872: 'pi' : ambiguous symbol + + } + { + +//[math_constants_ambiguity + // If you use more than one namespace, this will, of course, create ambiguity: + using namespace boost::math::double_constants; + using namespace boost::math::constants; + + //double my_pi = pi(); // error C2872: 'pi' : ambiguous symbol + //double my_pi2 = pi; // Context does not allow for disambiguation of overloaded function + + // It is also possible to create ambiguity inadvertently, + // perhaps in other peoples code, + // by making the scope of a namespace declaration wider than necessary, + // therefore is it prudent to avoid this risk by localising the scope of such definitions. +//] [/math_constants_ambiguity] + + } + + { // You can, of course, use both methods of access if both are fully qualified, for examples: + + //cout.precision(std::numeric_limits::max_digits10);// Ideally. + cout.precision(2 + std::numeric_limits::digits * 3010/10000); // If no max_digits10. + + double my_pi1 = boost::math::constants::pi(); + double my_pid = boost::math::double_constants::pi; + cout << "boost::math::constants::pi() = " << my_pi1 << endl + << "boost::math::double_constants::pi = " << my_pid << endl; + + // cout.precision(std::numeric_limits::max_digits10); // Ideally. + cout.precision(2 + std::numeric_limits::digits * 3010/10000); // If no max_digits10. + float my_pif = boost::math::float_constants::pi; + cout << "boost::math::float_constants::pi = " << my_pif << endl; + + } + + { // Use with templates + + // \warning it is important to be very careful with the type provided as parameter. + // For example, naively providing an @b integer instead of a floating-point type can be disastrous. + // cout << "Area = " << area(2) << endl; // warning : 'return' : conversion from 'double' to 'int', possible loss of data + // Failure to heed this warning can lead to very wrong answers! + // Area = 12 !! = 3 * 2 * 2 +//[math_constants_template_integer_type + //cout << "Area = " << area(2) << endl; // Area = 12! + cout << "Area = " << area(2.) << endl; // Area = 12.566371 + + // You can also avoid this by being explicit about the type of @c area. + cout << "Area = " << area(2) << endl; + +//] [/math_constants_template_integer_type] + + + } + { + using boost::math::constants::pi; + double my_pi3 = pi(); + //double my_pi4 = pi<>(); cannot find template type. + //double my_pi4 = pi(); + + } + +} // int main() + +/*[constants_eq1_output + +Output: + + double pi = boost::math::double_constants::pi = 3.1415926535897931 + d = 4.7882831840285398, r = 1.2345678901234567 + pidf = boost::math::constants::pi() = 3.1415927410125732 + df = 3.0645015239715576, rf = 0.98765432834625244 + one_div_two_pi 0.15915494309189535 + one_div_root_two_pi 0.15915494309189535 + double my2pi = 6.2831853071795862 + float my_e 2.7182817459106445 + double my_pi = boost::math::double_constants::pi = 3.1415926535897931 + boost::math::constants::pi() = 3.1415926535897931 + boost::math::double_constants::pi = 3.1415926535897931 + boost::math::float_constants::pi = 3.1415927410125732 + Area = 12.566370614359172 + Area = 12.566370614359172 + + +] [/constants_eq1_output] +*/ From 14762d7522eb67fd0f8761b163baf40518ec519c Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Wed, 6 Jun 2012 11:27:47 +0000 Subject: [PATCH 035/115] Added new constants example to jamfile. OK on MSVC [SVN r78828] --- example/Jamfile.v2 | 3 +++ 1 file changed, 3 insertions(+) diff --git a/example/Jamfile.v2 b/example/Jamfile.v2 index c453377f7..6622eaa4d 100644 --- a/example/Jamfile.v2 +++ b/example/Jamfile.v2 @@ -70,6 +70,8 @@ run nonfinite_loopback_ok.cpp ; run nonfinite_serialization_archives.cpp ../../serialization/build//boost_serialization ; run nonfinite_facet_sstream.cpp ; +run constants_eg1.cpp ; + run normal_misc_examples.cpp ; run owens_t_example.cpp ; run policy_eg_1.cpp ; @@ -104,3 +106,4 @@ run students_t_two_samples.cpp ; + From 5c64d6e0471292a0c18ba790a403238b9684df53 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Wed, 6 Jun 2012 11:30:24 +0000 Subject: [PATCH 036/115] Corrected #include filenames etc. [SVN r78829] --- doc/sf_and_dist/constants.qbk | 19 +++++++++++-------- 1 file changed, 11 insertions(+), 8 deletions(-) diff --git a/doc/sf_and_dist/constants.qbk b/doc/sf_and_dist/constants.qbk index 27377934a..974714c49 100644 --- a/doc/sf_and_dist/constants.qbk +++ b/doc/sf_and_dist/constants.qbk @@ -34,26 +34,27 @@ see [link math_toolkit.constants.tutorial.templ use in template code]. [section:non_templ Use in non-template code] When using the math constants at your chosen fixed precision in non-template code, -you can simply add a `using` declaration, for example, `using boost::math::double_constants`, +you can simply add a `using namespace` declaration, for example, +`using namespace boost::math::double_constants`, to make the constants of the correct precision for your code -visible in the current scope, and then use each constant ['as a simple variable]: +visible in the current scope, and then use each constant ['as a simple variable - sans brackets]: - #include + #include double area(double r) { - using boost::math::double_constants; + using namespace boost::math::double_constants; return pi * r * r; } Had our function been written as taking a `float` rather than a `double`, we could have written instead: - #include + #include float area(float r) { - using boost::math::float_constants; + using namespace boost::math::float_constants; return pi * r * r; } @@ -62,6 +63,8 @@ are available in the namespace `boost::math::long_double_constants`. You can see the full list of available constants at [link math_toolkit.constants.constants]. +Some examples of using constants are at [@../../../example/constants_eg1.cpp constants_eg1]. + [endsect] [section:templ Use in template code] @@ -71,7 +74,7 @@ we use a constant of the correct precision for our template parameters. We can do this by calling the function-template versions, `pi()`, of the constants like this: - #include + #include template Real area(Real r) @@ -139,7 +142,7 @@ You can also avoid this by being explicit about the type of `Area`. The syntax for using the function-call constants with user-defined types is the same as it is in the template class, which is to say we use: - #include + #include boost::math::constants::pi(); From 86ecf82a54e4ae1396da205bf452d0c388ce0aa1 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 7 Jun 2012 12:20:52 +0000 Subject: [PATCH 037/115] Regenerate docs. [SVN r78844] --- doc/sf_and_dist/html/index.html | 2 +- doc/sf_and_dist/html/index/s13.html | 5 +- doc/sf_and_dist/html/index/s14.html | 4 +- doc/sf_and_dist/html/index/s15.html | 4 +- doc/sf_and_dist/html/index/s16.html | 4 +- doc/sf_and_dist/html/index/s17.html | 6 +- .../backgrounders/implementation.html | 87 ++++++++++++++++++- .../constants/tutorial/non_templ.html | 18 ++-- .../constants/tutorial/templ.html | 2 +- .../constants/tutorial/user_def.html | 2 +- .../main_overview/conventions.html | 2 +- .../main_overview/error_handling.html | 15 ++++ .../math_toolkit/main_overview/history1.html | 45 ++++++---- .../main_overview/navigation.html | 2 +- .../html/math_toolkit/perf/comparisons.html | 12 ++- .../html/math_toolkit/status/history1.html | 45 ++++++---- 16 files changed, 193 insertions(+), 62 deletions(-) diff --git a/doc/sf_and_dist/html/index.html b/doc/sf_and_dist/html/index.html index 059a8018c..52d05e109 100644 --- a/doc/sf_and_dist/html/index.html +++ b/doc/sf_and_dist/html/index.html @@ -577,7 +577,7 @@

    - +

    Last revised: May 20, 2012 at 15:54:08 GMT

    Last revised: June 07, 2012 at 12:16:02 GMT


    diff --git a/doc/sf_and_dist/html/index/s13.html b/doc/sf_and_dist/html/index/s13.html index 06437df6b..d3e4d8726 100644 --- a/doc/sf_and_dist/html/index/s13.html +++ b/doc/sf_and_dist/html/index/s13.html @@ -22,9 +22,9 @@
    PrevUpHomeNext
    -
    +

    -Function Index

    +Function Index

    A B C D E F G H I J K L M N O P Q R S T U V W Z

    @@ -259,6 +259,7 @@
  • cdf

    B C D E F G H I L M N P R S T U W

    diff --git a/doc/sf_and_dist/html/index/s15.html b/doc/sf_and_dist/html/index/s15.html index 5fb692ac7..ee54d03dc 100644 --- a/doc/sf_and_dist/html/index/s15.html +++ b/doc/sf_and_dist/html/index/s15.html @@ -22,9 +22,9 @@
    PrevUpHomeNext
    -
    +

    -Typedef Index

    +Typedef Index

    A B C D E F G H I L N O P R S T U V W

    diff --git a/doc/sf_and_dist/html/index/s16.html b/doc/sf_and_dist/html/index/s16.html index 1cc30f06d..bd4fe412d 100644 --- a/doc/sf_and_dist/html/index/s16.html +++ b/doc/sf_and_dist/html/index/s16.html @@ -22,9 +22,9 @@
    PrevUpHomeNext
    -
    +

    -Macro Index

    +Macro Index

    B F

    diff --git a/doc/sf_and_dist/html/index/s17.html b/doc/sf_and_dist/html/index/s17.html index ddfbf0932..24c8129f2 100644 --- a/doc/sf_and_dist/html/index/s17.html +++ b/doc/sf_and_dist/html/index/s17.html @@ -21,9 +21,9 @@
    PrevUpHome
    -
    +

    -Index

    +Index

    A B C D E F G H I J K L M N O P Q R S T U V W Z

    @@ -1092,6 +1092,7 @@
  • cdf

      +
    • Additional Implementation Notes

    • Binomial Coin-Flipping Example

    • Discrete Quantile Policies

    • Extras/Future Directions

    • @@ -2694,6 +2695,7 @@
      • BOOST_DEFINE_MATH_CONSTANT

      • BOOST_MATH_DOMAIN_ERROR_POLICY

      • +
      • cdf

      • constants

      • infinity

      • median

      • diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html b/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html index f39825a76..4e664d29f 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html @@ -318,7 +318,22 @@

        However in a few cases, for example normal, where we felt it obvious, we have permitted argument(s) to be infinity, provided infinity is implemented - for the realType on that implementation. + for the RealType on that + implementation, and it is supported and tested by the distribution. +

        +

        + The range for these distributions is set to infinity if supported by the + platform, (by testing std::numeric_limits<RealType>::has_infinity) + else the maximum value provided for the RealType + by Boost.Math. +

        +

        + Testing for has_infinity is obviously important for arbitrary precision types + where infinity makes much less sense than for IEEE754 floating-point. +

        +

        + So far we have not set support() function (only range) on the grounds that + the PDF is uninteresting/zero for infinities.

        Users who require special handling of infinity (or other specific value) @@ -547,6 +562,74 @@

        + Testing + for Invalid Parameters to Functions and Constructors +
        +

        + After finding that some 'bad' parameters (like NaN) were not throwing a + domain_error exception as + they should, a function +

        +

        + check_out_of_range (in test_out_of_range.hpp) was devised by JM to check (using + Boost.Test's BOOST_CHECK_THROW macro) that bad parameters passed to constructors + and functions throw domain_error + exceptions. +

        +

        + Usage is check_out_of_range< DistributionType + >(list-of-params); + Where list-of-params is a list of valid + parameters from which the distribution can be constructed - ie the same number + of args are passed to the function, as are passed to the distribution constructor. +

        +

        + The values of the parameters are not important, but must be valid + to pass the contructor checks; the default values are suitable, but must + be explicitly provided, for example: +

        +
        check_out_of_range<extreme_value_distribution<RealType> >(1, 2);
        +
        +

        + Checks made are: +

        +
          +
        • + Infinity or NaN (if available) passed in place of each of the valid params. +
        • +
        • + Infinity or NaN (if available) as a random variable. +
        • +
        • + Out-of-range random variable passed to pdf and cdf (ie outside of "range(DistributionType)"). +
        • +
        • + Out-of-range probability passed to quantile function and complement. +
        • +
        +

        + but does not check finite but out-of-range + parameters to the constructor because these are specific to each distribution, + for example: +

        +
        BOOST_CHECK_THROW(pdf(pareto_distribution<RealType>(0, 1), 0), std::domain_error);
        +BOOST_CHECK_THROW(pdf(pareto_distribution<RealType>(1, 0), 0), std::domain_error);
        +
        +

        + checks scale and shape parameters are both > 0 by checking + that domain_error exception + is thrown if either are == 0. +

        +

        + (Use of check_out_of_range + function may mean that some previous tests are now redundant). +

        +

        + It was also noted that if more than one parameter is bad, then only the first + detected will be reported by the error message. +

        +
        + Creating and Managing the Equations
        @@ -736,7 +819,7 @@ done HTML: this needs further investigation.

        - + Producing Graphs
        diff --git a/doc/sf_and_dist/html/math_toolkit/constants/tutorial/non_templ.html b/doc/sf_and_dist/html/math_toolkit/constants/tutorial/non_templ.html index a9c7339bb..34de38b24 100644 --- a/doc/sf_and_dist/html/math_toolkit/constants/tutorial/non_templ.html +++ b/doc/sf_and_dist/html/math_toolkit/constants/tutorial/non_templ.html @@ -29,17 +29,18 @@
  • When using the math constants at your chosen fixed precision in non-template - code, you can simply add a using - declaration, for example, using + code, you can simply add a using + namespace declaration, for example, + using namespace boost::math::double_constants, to make the constants of the correct precision for your code visible in the current scope, and - then use each constant as a simple variable: + then use each constant as a simple variable - sans brackets:

    -
    #include <boost/math/constants.hpp>
    +
    #include <boost/math/constants/constants.hpp>
     
     double area(double r)
     {
    -   using boost::math::double_constants;
    +   using namespace boost::math::double_constants;
        return pi * r * r;
     }
     
    @@ -48,11 +49,11 @@ rather than a double, we could have written instead:

    -
    #include <boost/math/constants.hpp>
    +
    #include <boost/math/constants/constants.hpp>
     
     float area(float r)
     {
    -   using boost::math::float_constants;
    +   using namespace boost::math::float_constants;
        return pi * r * r;
     }
     
    @@ -64,6 +65,9 @@

    You can see the full list of available constants at math_toolkit.constants.constants.

    +

    + Some examples of using constants are at constants_eg1. +

  • diff --git a/doc/sf_and_dist/html/math_toolkit/constants/tutorial/templ.html b/doc/sf_and_dist/html/math_toolkit/constants/tutorial/templ.html index 7df04bb57..6ecb83209 100644 --- a/doc/sf_and_dist/html/math_toolkit/constants/tutorial/templ.html +++ b/doc/sf_and_dist/html/math_toolkit/constants/tutorial/templ.html @@ -33,7 +33,7 @@ We can do this by calling the function-template versions, pi<FPType>(), of the constants like this:

    -
    #include <boost/math/constants.hpp>
    +
    #include <boost/math/constants/constants.hpp>
     
     template <class Real>
     Real area(Real r)
    diff --git a/doc/sf_and_dist/html/math_toolkit/constants/tutorial/user_def.html b/doc/sf_and_dist/html/math_toolkit/constants/tutorial/user_def.html
    index b4a3f60a8..4f83f5d11 100644
    --- a/doc/sf_and_dist/html/math_toolkit/constants/tutorial/user_def.html
    +++ b/doc/sf_and_dist/html/math_toolkit/constants/tutorial/user_def.html
    @@ -31,7 +31,7 @@
               The syntax for using the function-call constants with user-defined types
               is the same as it is in the template class, which is to say we use:
             

    -
    #include <boost/math/constants.hpp>
    +
    #include <boost/math/constants/constants.hpp>
     
     boost::math::constants::pi<UserDefinedType>();
     
    diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html b/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html index 757299775..ea4cac308 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html @@ -27,7 +27,7 @@ Document Conventions

    - +

    This documentation aims to use of the following naming and formatting conventions. diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/error_handling.html b/doc/sf_and_dist/html/math_toolkit/main_overview/error_handling.html index c1ee394ec..745d53842 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/error_handling.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/error_handling.html @@ -42,6 +42,17 @@ What should be done when the error is raised? +

    + + + + + +
    [Warning]Warning

    + The default error actions are to throw an exception with an informative + error message. If you do not try to catch the exception, you will not see + the message! +

    The kinds of errors that can be raised are:

    @@ -764,6 +775,10 @@ Numeric underflow and denormalised results were not considered to be fatal errors in most cases, so it was felt that these should be ignored. +
  • + If there is more than one error, only the first detected will be reported + in the throw message. +
  • diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html b/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html index f1340d05e..b0b275d26 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html @@ -29,6 +29,17 @@
    + Boost-1.51 +
    +
    • + Corrected failure to detect bad parameters in many distributions #6934 (reported + by Florian Schoppmann) by adding a function check_out_of_range to test + many possible bad parameters. This test revealed several distributions + where the checks for bad parameters were ineffective, and these have + been rectified. +
    +
    + Boost-1.50
      @@ -67,7 +78,7 @@
    - + Boost-1.49
      @@ -111,7 +122,7 @@
    - + Boost-1.48
      @@ -162,7 +173,7 @@
    - + Boost-1.47
      @@ -179,7 +190,7 @@
    - + Boost-1.46.1
    • @@ -187,7 +198,7 @@ #5113.
    - + Boost-1.46.0
      @@ -202,7 +213,7 @@
    - + Boost-1.45.0
      @@ -219,7 +230,7 @@
    - + Boost-1.44.0
      @@ -233,7 +244,7 @@
    - + Boost-1.41.0
    • @@ -241,7 +252,7 @@ and its inverse.
    - + Boost-1.40.0
      @@ -278,7 +289,7 @@
    - + Boost-1.38.0
      @@ -290,14 +301,14 @@
    - + Boost-1.37.0
    • Improved accuracy and testing of the inverse hypergeometric functions.
    - + Boost-1.36.0
      @@ -330,7 +341,7 @@
    - + Boost-1.35.0: Post Review First Official Release
    @@ -362,7 +373,7 @@
    - + Milestone 4: Second Review Candidate (1st March 2007)
    @@ -376,7 +387,7 @@
    - + Milestone 3: First Review Candidate (31st Dec 2006)
    @@ -404,7 +415,7 @@
    - + Milestone 2: Released September 10th 2006
    @@ -440,7 +451,7 @@
    - + Milestone 1: Released March 31st 2006
    diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html index d819395ee..920f1721b 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html @@ -27,7 +27,7 @@ Navigation

    - +

    Boost.Math documentation is provided in both HTML and PDF formats. diff --git a/doc/sf_and_dist/html/math_toolkit/perf/comparisons.html b/doc/sf_and_dist/html/math_toolkit/perf/comparisons.html index f16e5833a..1aa96bb2e 100644 --- a/doc/sf_and_dist/html/math_toolkit/perf/comparisons.html +++ b/doc/sf_and_dist/html/math_toolkit/perf/comparisons.html @@ -1082,7 +1082,8 @@

    - __hypergeometric_distrib CDF + hypergeometric + Distribution CDF

    @@ -1112,7 +1113,8 @@

    - __hypergeometric_distrib Quantile + hypergeometric + Distribution Quantile

    @@ -2357,7 +2359,8 @@

    - __hypergeometric_distrib CDF + hypergeometric + Distribution CDF

    @@ -2387,7 +2390,8 @@

    - __hypergeometric_distrib Quantile + hypergeometric + Distribution Quantile

    diff --git a/doc/sf_and_dist/html/math_toolkit/status/history1.html b/doc/sf_and_dist/html/math_toolkit/status/history1.html index d35eae1d1..4fdbabb35 100644 --- a/doc/sf_and_dist/html/math_toolkit/status/history1.html +++ b/doc/sf_and_dist/html/math_toolkit/status/history1.html @@ -28,6 +28,17 @@
    + Boost-1.51 +
    +
    • + Corrected failure to detect bad parameters in many distributions #6934 (reported + by Florian Schoppmann) by adding a function check_out_of_range to test + many possible bad parameters. This test revealed several distributions + where the checks for bad parameters were ineffective, and these have + been rectified. +
    +
    + Boost-1.50
      @@ -66,7 +77,7 @@
    - + Boost-1.49
      @@ -110,7 +121,7 @@
    - + Boost-1.48
      @@ -161,7 +172,7 @@
    - + Boost-1.47
      @@ -178,7 +189,7 @@
    - + Boost-1.46.1
    • @@ -186,7 +197,7 @@ #5113.
    - + Boost-1.46.0
      @@ -201,7 +212,7 @@
    - + Boost-1.45.0
      @@ -218,7 +229,7 @@
    - + Boost-1.44.0
      @@ -232,7 +243,7 @@
    - + Boost-1.41.0
    • @@ -240,7 +251,7 @@ and its inverse.
    - + Boost-1.40.0
      @@ -277,7 +288,7 @@
    - + Boost-1.38.0
      @@ -289,14 +300,14 @@
    - + Boost-1.37.0
    • Improved accuracy and testing of the inverse hypergeometric functions.
    - + Boost-1.36.0
      @@ -329,7 +340,7 @@
    - + Boost-1.35.0: Post Review First Official Release
    @@ -361,7 +372,7 @@
    - + Milestone 4: Second Review Candidate (1st March 2007)
    @@ -375,7 +386,7 @@
    - + Milestone 3: First Review Candidate (31st Dec 2006)
    @@ -403,7 +414,7 @@
    - + Milestone 2: Released September 10th 2006
    @@ -439,7 +450,7 @@
    - + Milestone 1: Released March 31st 2006
    From 43645045188a753e58933de0b284dffba799f78c Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 12 Jun 2012 11:45:28 +0000 Subject: [PATCH 038/115] Update Jacobi docs - should use u rather than phi for argument. Add simple intro with references. Regenerate docs. 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.../main_overview/navigation.html | 2 +- .../html/math_toolkit/special.html | 2 + .../math_toolkit/special/expint/expint_i.html | 4 +- .../html/math_toolkit/special/jacobi.html | 8 +- .../math_toolkit/special/jacobi/jac_over.html | 126 ++++++++++++++++++ .../special/jacobi/jacobi_cd.html | 6 +- .../special/jacobi/jacobi_cn.html | 4 +- .../special/jacobi/jacobi_cs.html | 6 +- .../special/jacobi/jacobi_dc.html | 6 +- .../special/jacobi/jacobi_dn.html | 4 +- .../special/jacobi/jacobi_ds.html | 6 +- .../special/jacobi/jacobi_elliptic.html | 34 ++--- .../special/jacobi/jacobi_nc.html | 6 +- .../special/jacobi/jacobi_nd.html | 6 +- .../special/jacobi/jacobi_ns.html | 6 +- .../special/jacobi/jacobi_sc.html | 6 +- .../special/jacobi/jacobi_sd.html | 6 +- .../special/jacobi/jacobi_sn.html | 4 +- doc/sf_and_dist/jacobi_elliptic.qbk | 124 +++++++++++------ doc/sf_and_dist/math.qbk | 12 ++ 58 files changed, 346 insertions(+), 159 deletions(-) create mode 100644 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end of file +μ=1k2ν=uksn(u,k)=sn(ν,μ)kcn(u,k)=dn(ν,μ)dn(u,k)=cn(ν,k) \ No newline at end of file diff --git a/doc/sf_and_dist/equations/jacobi4.mml b/doc/sf_and_dist/equations/jacobi4.mml index f24edc072..ca8fdde17 100644 --- a/doc/sf_and_dist/equations/jacobi4.mml +++ b/doc/sf_and_dist/equations/jacobi4.mml @@ -16,7 +16,7 @@ n - x + u , k @@ -29,7 +29,7 @@ sin - x + u @@ -43,18 +43,18 @@ - x + u sin - x + u cos - x + u @@ -62,7 +62,7 @@ cos - x + u @@ -73,7 +73,7 @@ n - x + u , k @@ -86,7 +86,7 @@ cos - x + u + @@ -100,18 +100,18 @@ - x + u sin - x + u cos - x + u @@ -119,7 +119,7 @@ sin - x + u @@ -130,7 +130,7 @@ n - x + u , k @@ -150,13 +150,14 @@ k 2 + sin - sin + 2 - x + u @@ -166,3 +167,4 @@ + diff --git a/doc/sf_and_dist/equations/jacobi4.png b/doc/sf_and_dist/equations/jacobi4.png index ef81cbee6155616f9bc75a07187a4ee23f4fc053..27449013a11218807e883c0bf4aac82cdde77f9c 100644 GIT binary patch literal 13488 zcmeAS@N?(olHy`uVBq!ia0y~yVC-aIV2I{mV_;xti>cIQU|?V=cJd72;Nak>;YjIV 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double (*f3)(double, double, double); double (*f4)(double, double, double, double); -#if 0 + f = boost::math::zeta; plot.add(f, 1 + find_end_point(f, 0.1, 40.0, false, 1.0), 10, ""); plot.add(f, -20, 1 + find_end_point(f, -0.1, -40.0, false, 1.0), ""); @@ -575,7 +575,7 @@ int main() plot.add(boost::bind(f2, 0.75, _1), -10, 10, "k=0.75"); plot.add(boost::bind(f2, 0.95, _1), -10, 10, "k=0.95"); plot.add(boost::bind(f2, 1, _1), -10, 10, "k=1"); - plot.plot("Jacobi Elliptic sn", "jacobi_sn.svg", "k", "jacobi_sn(k, phi)"); + plot.plot("Jacobi Elliptic sn", "jacobi_sn.svg", "k", "jacobi_sn(k, u)"); f2 = boost::math::jacobi_cn; plot.clear(); @@ -584,7 +584,7 @@ int main() plot.add(boost::bind(f2, 0.75, _1), -10, 10, "k=0.75"); plot.add(boost::bind(f2, 0.95, _1), -10, 10, "k=0.95"); plot.add(boost::bind(f2, 1, _1), -10, 10, "k=1"); - plot.plot("Jacobi Elliptic cn", "jacobi_cn.svg", "k", "jacobi_cn(k, phi)"); + plot.plot("Jacobi Elliptic cn", "jacobi_cn.svg", "k", "jacobi_cn(k, u)"); f2 = boost::math::jacobi_dn; plot.clear(); @@ -593,7 +593,7 @@ int main() plot.add(boost::bind(f2, 0.75, _1), -10, 10, "k=0.75"); plot.add(boost::bind(f2, 0.95, _1), -10, 10, "k=0.95"); plot.add(boost::bind(f2, 1, _1), -10, 10, "k=1"); - plot.plot("Jacobi Elliptic dn", "jacobi_dn.svg", "k", "jacobi_dn(k, phi)"); + plot.plot("Jacobi Elliptic dn", "jacobi_dn.svg", "k", "jacobi_dn(k, u)"); f2 = boost::math::jacobi_cd; plot.clear(); @@ -602,7 +602,7 @@ int main() plot.add(boost::bind(f2, 0.75, _1), -10, 10, "k=0.75"); plot.add(boost::bind(f2, 0.95, _1), -10, 10, "k=0.95"); plot.add(boost::bind(f2, 1, _1), -10, 10, "k=1"); - plot.plot("Jacobi Elliptic cd", "jacobi_cd.svg", "k", "jacobi_cd(k, phi)"); + plot.plot("Jacobi Elliptic cd", "jacobi_cd.svg", "k", "jacobi_cd(k, u)"); f2 = boost::math::jacobi_cs; plot.clear(); @@ -611,7 +611,7 @@ int main() plot.add(boost::bind(f2, 0.75, _1), 0.1, 3, "k=0.75"); plot.add(boost::bind(f2, 0.95, _1), 0.1, 3, "k=0.95"); plot.add(boost::bind(f2, 1, _1), 0.1, 3, "k=1"); - plot.plot("Jacobi Elliptic cs", "jacobi_cs.svg", "k", "jacobi_cs(k, phi)"); + plot.plot("Jacobi Elliptic cs", "jacobi_cs.svg", "k", "jacobi_cs(k, u)"); f2 = boost::math::jacobi_dc; plot.clear(); @@ -620,7 +620,7 @@ int main() plot.add(boost::bind(f2, 0.75, _1), -10, 10, "k=0.75"); plot.add(boost::bind(f2, 0.95, _1), -10, 10, "k=0.95"); plot.add(boost::bind(f2, 1, _1), -10, 10, "k=1"); - plot.plot("Jacobi Elliptic dc", "jacobi_dc.svg", "k", "jacobi_dc(k, phi)"); + plot.plot("Jacobi Elliptic dc", "jacobi_dc.svg", "k", "jacobi_dc(k, u)"); f2 = boost::math::jacobi_ds; plot.clear(); @@ -629,7 +629,7 @@ int main() plot.add(boost::bind(f2, 0.75, _1), 0.1, 3, "k=0.75"); plot.add(boost::bind(f2, 0.95, _1), 0.1, 3, "k=0.95"); plot.add(boost::bind(f2, 1, _1), 0.1, 3, "k=1"); - plot.plot("Jacobi Elliptic ds", "jacobi_ds.svg", "k", "jacobi_ds(k, phi)"); + plot.plot("Jacobi Elliptic ds", "jacobi_ds.svg", "k", "jacobi_ds(k, u)"); f2 = boost::math::jacobi_nc; plot.clear(); @@ -638,7 +638,7 @@ int main() plot.add(boost::bind(f2, 0.75, _1), -5, 5, "k=0.75"); plot.add(boost::bind(f2, 0.95, _1), -5, 5, "k=0.95"); plot.add(boost::bind(f2, 1, _1), -5, 5, "k=1"); - plot.plot("Jacobi Elliptic nc", "jacobi_nc.svg", "k", "jacobi_nc(k, phi)"); + plot.plot("Jacobi Elliptic nc", "jacobi_nc.svg", "k", "jacobi_nc(k, u)"); f2 = boost::math::jacobi_ns; plot.clear(); @@ -647,7 +647,7 @@ int main() plot.add(boost::bind(f2, 0.75, _1), 0.1, 4, "k=0.75"); plot.add(boost::bind(f2, 0.95, _1), 0.1, 4, "k=0.95"); plot.add(boost::bind(f2, 1, _1), 0.1, 4, "k=1"); - plot.plot("Jacobi Elliptic ns", "jacobi_ns.svg", "k", "jacobi_ns(k, phi)"); + plot.plot("Jacobi Elliptic ns", "jacobi_ns.svg", "k", "jacobi_ns(k, u)"); f2 = boost::math::jacobi_nd; plot.clear(); @@ -656,7 +656,7 @@ int main() plot.add(boost::bind(f2, 0.75, _1), -2, 2, "k=0.75"); plot.add(boost::bind(f2, 0.95, _1), -2, 2, "k=0.95"); plot.add(boost::bind(f2, 1, _1), -2, 2, "k=1"); - plot.plot("Jacobi Elliptic nd", "jacobi_nd.svg", "k", "jacobi_nd(k, phi)"); + plot.plot("Jacobi Elliptic nd", "jacobi_nd.svg", "k", "jacobi_nd(k, u)"); f2 = boost::math::jacobi_sc; plot.clear(); @@ -665,7 +665,7 @@ int main() plot.add(boost::bind(f2, 0.75, _1), -5, 5, "k=0.75"); plot.add(boost::bind(f2, 0.95, _1), -5, 5, "k=0.95"); plot.add(boost::bind(f2, 1, _1), -5, 5, "k=1"); - plot.plot("Jacobi Elliptic sc", "jacobi_sc.svg", "k", "jacobi_sc(k, phi)"); + plot.plot("Jacobi Elliptic sc", "jacobi_sc.svg", "k", "jacobi_sc(k, u)"); f2 = boost::math::jacobi_sd; plot.clear(); @@ -674,8 +674,7 @@ int main() plot.add(boost::bind(f2, 0.75, _1), -2.5, 2.5, "k=0.75"); plot.add(boost::bind(f2, 0.95, _1), -2.5, 2.5, "k=0.95"); plot.add(boost::bind(f2, 1, _1), -2.5, 2.5, "k=1"); - plot.plot("Jacobi Elliptic sd", "jacobi_sd.svg", "k", "jacobi_sd(k, phi)"); -#endif + plot.plot("Jacobi Elliptic sd", "jacobi_sd.svg", "k", "jacobi_sd(k, u)"); f = boost::math::airy_ai; plot.clear(); diff --git a/doc/sf_and_dist/html/index.html b/doc/sf_and_dist/html/index.html index 52d05e109..84c62d222 100644 --- a/doc/sf_and_dist/html/index.html +++ b/doc/sf_and_dist/html/index.html @@ -316,6 +316,8 @@
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    Jacobi Elliptic Functions
    +
    Overvew of the + Jacobi Elliptic Functions
    Jacobi Elliptic SN, CN and DN
    Jacobi Elliptic @@ -577,7 +579,7 @@

    - +

    Last revised: June 07, 2012 at 12:16:02 GMT

    Last revised: June 12, 2012 at 11:11:36 GMT


    diff --git a/doc/sf_and_dist/html/index/s13.html b/doc/sf_and_dist/html/index/s13.html index d3e4d8726..fca03bc34 100644 --- a/doc/sf_and_dist/html/index/s13.html +++ b/doc/sf_and_dist/html/index/s13.html @@ -22,9 +22,9 @@
    -
    +

    -Function Index

    +Function Index

    A B C D E F G H I J K L M N O P Q R S T U V W Z

    diff --git a/doc/sf_and_dist/html/index/s14.html b/doc/sf_and_dist/html/index/s14.html index 2b8eaf699..17a4a692f 100644 --- a/doc/sf_and_dist/html/index/s14.html +++ b/doc/sf_and_dist/html/index/s14.html @@ -22,9 +22,9 @@
    PrevUpHomeNext
    -
    +

    -Class Index

    +Class Index

    B C D E F G H I L M N P R S T U W

    diff --git a/doc/sf_and_dist/html/index/s15.html b/doc/sf_and_dist/html/index/s15.html index ee54d03dc..fc5bfac8b 100644 --- a/doc/sf_and_dist/html/index/s15.html +++ b/doc/sf_and_dist/html/index/s15.html @@ -22,9 +22,9 @@
    PrevUpHomeNext
    -
    +

    -Typedef Index

    +Typedef Index

    A B C D E F G H I L N O P R S T U V W

    diff --git a/doc/sf_and_dist/html/index/s16.html b/doc/sf_and_dist/html/index/s16.html index bd4fe412d..160a63987 100644 --- a/doc/sf_and_dist/html/index/s16.html +++ b/doc/sf_and_dist/html/index/s16.html @@ -22,9 +22,9 @@
    PrevUpHomeNext
    -
    +

    -Macro Index

    +Macro Index

    B F

    diff --git a/doc/sf_and_dist/html/index/s17.html b/doc/sf_and_dist/html/index/s17.html index 24c8129f2..da67b1227 100644 --- a/doc/sf_and_dist/html/index/s17.html +++ b/doc/sf_and_dist/html/index/s17.html @@ -21,9 +21,9 @@
    PrevUpHome
    -
    +

    -Index

    +Index

    A B C D E F G H I J K L M N O P Q R S T U V W Z

    @@ -2026,6 +2026,7 @@
  • Negative Binomial Sales Quota Example.

  • Non-Member Properties

  • Noncentral Beta Distribution

  • +
  • Overvew of the Jacobi Elliptic Functions

  • Poisson Distribution

  • Series Evaluation

  • Skew Normal Distribution

  • @@ -3751,6 +3752,10 @@
  • +

    Overvew of the Jacobi Elliptic Functions

    + +
  • +
  • Owen's T function

  • diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html b/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html index ea4cac308..f885c7c27 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html @@ -27,7 +27,7 @@ Document Conventions

    - +

    This documentation aims to use of the following naming and formatting conventions. diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html index 920f1721b..ea2d8dce2 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html @@ -27,7 +27,7 @@ Navigation

    - +

    Boost.Math documentation is provided in both HTML and PDF formats. diff --git a/doc/sf_and_dist/html/math_toolkit/special.html b/doc/sf_and_dist/html/math_toolkit/special.html index f7725eedb..370b4ce1b 100644 --- a/doc/sf_and_dist/html/math_toolkit/special.html +++ b/doc/sf_and_dist/html/math_toolkit/special.html @@ -119,6 +119,8 @@

    Jacobi Elliptic Functions
    +
    Overvew of the + Jacobi Elliptic Functions
    Jacobi Elliptic SN, CN and DN
    Jacobi Elliptic diff --git a/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html b/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html index 9ccdff164..6ae3a731f 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html +++ b/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html @@ -246,7 +246,7 @@ a minimax rational approximation rescaled so that it is evaluated over [-1,1]. Note that while the rational approximation over [0,6] converges rapidly to the minimax solution it is rather ill-conditioned in practice. - Cody and Thacher [2] experienced the same issue and converted the polynomials into + Cody and Thacher [5] experienced the same issue and converted the polynomials into Chebeshev form to ensure stable computation. By experiment we found that the polynomials are just as stable in polynomial as Chebyshev form, provided they are computed over the interval [-1,1]. @@ -276,7 +276,7 @@



    -

    [2] +

    [5] W. J. Cody and H. C. Thacher, Jr., Rational Chebyshev approximations for the exponential integral E1(x), Math. Comp. 22 (1968), 641-649, and W. J. Cody and H. C. Thacher, Jr., Chebyshev approximations for the exponential diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi.html index 700fa1a0e..3f7129dd1 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi.html @@ -7,7 +7,7 @@ - + @@ -20,13 +20,15 @@


    -PrevUpHomeNext +PrevUpHomeNext
    +
    Overvew of the + Jacobi Elliptic Functions
    Jacobi Elliptic SN, CN and DN
    Jacobi Elliptic @@ -66,7 +68,7 @@
    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jac_over.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jac_over.html new file mode 100644 index 000000000..c89461767 --- /dev/null +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jac_over.html @@ -0,0 +1,126 @@ + + + +Overvew of the Jacobi Elliptic Functions + + + + + + + + + + + + + + + +
    Boost C++ LibrariesHomeLibrariesPeopleFAQMore
    +
    +
    +PrevUpHomeNext +
    +
    + +

    + There are twelve Jacobi Elliptic functions, of which the three copolar + functions sn, cn and dn + are the most important as the other nine can be computed from these three + [2] [3] [4]. +

    +

    + These functions each take two arguments: a parameter, and a variable as + described below. +

    +

    + Like all elliptic functions these can be parameterised in a number of ways: +

    +
      +
    • + In terms of a parameter m. +
    • +
    • + In terms of the elliptic modulus k where m + = k2. +
    • +
    • + In terms of the modular angle α, where m = sin2α. +
    • +
    +

    + In our implementation, these functions all take the elliptic modulus k + as the parameter. +

    +

    + In addition the variable u is sometimes expressed + as an amplitude φ, in our implementation we always use u. +

    +

    + Finally note that our functions all take the elliptic modulus as the first + argument - this is for alignment with the Elliptic Integrals. +

    +

    + There are twenve functions for computing the twelve individual Jacobi elliptic + functions: jacobi_cd, + jacobi_cn, + jacobi_cs, + jacobi_dc, + jacobi_dn, + jacobi_ds, + jacobi_nc, + jacobi_nd, + jacobi_ns, + jacobi_sc, + jacobi_sd + and jacobi_sn. +

    +

    + They are all called as for example: +

    +
    jacobi_cs(k, u);
    +
    +

    + Note however that these individual functions are all really thin wrappers + around the function jacobi_elliptic + which calculates the three copolar functions sn, + cn and dn in a single function + call. Thus if you need more than one of these functions for a given set + of arguments, it's most efficient to use jacobi_elliptic. +

    + +
    + + + +
    +
    +
    +PrevUpHomeNext +
    + + diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cd.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cd.html index 4f9dd1c35..a8ff7ac01 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cd.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cd.html @@ -40,10 +40,10 @@
    namespace boost { namespace math {
     
      template <class T, class U>
    - calculated-result-type jacobi_cd(T k, U theta);
    + calculated-result-type jacobi_cd(T k, U u);
     
      template <class T, class U, class Policy>
    - calculated-result-type jacobi_cd(T k, U theta, const Policy& pol);
    + calculated-result-type jacobi_cd(T k, U u, const Policy& pol);
     
     }} // namespaces
     
    @@ -64,7 +64,7 @@ with:

    - cd(x, k) = cn(x, k) / dn(x, k) + cd(u, k) = cn(u, k) / dn(u, k)

    diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cn.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cn.html index 99b359055..d2ead927a 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cn.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cn.html @@ -40,10 +40,10 @@

    namespace boost { namespace math {
     
      template <class T, class U>
    - calculated-result-type jacobi_cn(T k, U theta);
    + calculated-result-type jacobi_cn(T k, U u);
     
      template <class T, class U, class Policy>
    - calculated-result-type jacobi_cn(T k, U theta, const Policy& pol);
    + calculated-result-type jacobi_cn(T k, U u, const Policy& pol);
     
     }} // namespaces
     
    diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cs.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cs.html index c3f21dd40..890854164 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cs.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cs.html @@ -40,10 +40,10 @@
    namespace boost { namespace math {
     
      template <class T, class U>
    - calculated-result-type jacobi_cs(T k, U theta);
    + calculated-result-type jacobi_cs(T k, U u);
     
      template <class T, class U, class Policy>
    - calculated-result-type jacobi_cs(T k, U theta, const Policy& pol);
    + calculated-result-type jacobi_cs(T k, U u, const Policy& pol);
     
     }} // namespaces
     
    @@ -64,7 +64,7 @@ with:

    - cs(x, k) = cn(x, k) / sn(x, k) + cs(u, k) = cn(u, k) / sn(u, k)

    diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_dc.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_dc.html index 9936e4e77..ba4d98855 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_dc.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_dc.html @@ -40,10 +40,10 @@

    namespace boost { namespace math {
     
      template <class T, class U>
    - calculated-result-type jacobi_dc(T k, U theta);
    + calculated-result-type jacobi_dc(T k, U u);
     
      template <class T, class U, class Policy>
    - calculated-result-type jacobi_dc(T k, U theta, const Policy& pol);
    + calculated-result-type jacobi_dc(T k, U u, const Policy& pol);
     
     }} // namespaces
     
    @@ -64,7 +64,7 @@ with:

    - dc(x, k) = dn(x, k) / cn(x, k) + dc(u, k) = dn(u, k) / cn(u, k)

    diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_dn.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_dn.html index 5d9e23f93..0afcd41c3 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_dn.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_dn.html @@ -40,10 +40,10 @@

    namespace boost { namespace math {
     
      template <class T, class U>
    - calculated-result-type jacobi_dn(T k, U theta);
    + calculated-result-type jacobi_dn(T k, U u);
     
      template <class T, class U, class Policy>
    - calculated-result-type jacobi_dn(T k, U theta, const Policy& pol);
    + calculated-result-type jacobi_dn(T k, U u, const Policy& pol);
     
     }} // namespaces
     
    diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_ds.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_ds.html index 266cff709..81fa28194 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_ds.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_ds.html @@ -40,10 +40,10 @@
    namespace boost { namespace math {
     
      template <class T, class U>
    - calculated-result-type jacobi_ds(T k, U theta);
    + calculated-result-type jacobi_ds(T k, U u);
     
      template <class T, class U, class Policy>
    - calculated-result-type jacobi_ds(T k, U theta, const Policy& pol);
    + calculated-result-type jacobi_ds(T k, U u, const Policy& pol);
     
     }} // namespaces
     
    @@ -64,7 +64,7 @@ with:

    - ds(x, k) = dn(x, k) / sn(x, k) + ds(u, k) = dn(u, k) / sn(u, k)

    diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_elliptic.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_elliptic.html index 42584a0f1..fdf945765 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_elliptic.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_elliptic.html @@ -6,7 +6,7 @@ - + @@ -20,7 +20,7 @@


    -PrevUpHomeNext +PrevUpHomeNext

    @@ -40,10 +40,10 @@
    namespace boost { namespace math {
     
      template <class T>
    - calculated-result-type jacobi_elliptic(T k, T phi, T* pcn, T* pdn);
    + calculated-result-type jacobi_elliptic(T k, T u, T* pcn, T* pdn);
     
      template <class T, class Policy>
    - calculated-result-type jacobi_elliptic(T k, T phi, T* pcn, T* pdn, const Policy&);
    + calculated-result-type jacobi_elliptic(T k, T u, T* pcn, T* pdn, const Policy&);
     
     }} // namespaces
     
    @@ -53,11 +53,11 @@

    The function jacobi_elliptic - calculates the three copolar Jacobi elliptic functions sn(φ, k), - cn(φ, k) and dn(φ, k). The returned - value is sn(φ, k), and if provided, *pcn - is set to cn(φ, k), and *pdn is - set to dn(φ, k). + calculates the three copolar Jacobi elliptic functions sn(u, + k), cn(u, k) and dn(u, k). + The returned value is sn(u, k), and if provided, + *pcn is set to cn(u, k), and + *pdn is set to dn(u, k).

    The functions are defined as follows, given: @@ -108,13 +108,13 @@ as either:

    - sn(φ, k) + sn(u, k)

    - sn(φ \ α) + sn(u \ α)

    - sn(φ| m) + sn(u| m)

    To further complicate matters, some texts refer to the complement @@ -186,12 +186,12 @@

    - φ < 1 + u < 1

    - Large φ + Large u

    @@ -270,10 +270,10 @@ sn(0, k) = 0 and cn(0, k) = dn(0, k) = 1.

    - sn(x, 0) = sin(x), cn(x, 0) = cos(x) and dn(x, 0) = 1. + sn(u, 0) = sin(u), cn(u, 0) = cos(u) and dn(u, 0) = 1.

    - sn(x, 1) = tanh(x), cn(x, 1) = dn(x, 1) = 1 / cosh(x). + sn(u, 1) = tanh(u), cn(u, 1) = dn(u, 1) = 1 / cosh(u).

    And for k4 < ε we have: @@ -297,7 +297,7 @@


    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_nc.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_nc.html index 298eedb86..4d0137f48 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_nc.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_nc.html @@ -40,10 +40,10 @@
    namespace boost { namespace math {
     
      template <class T, class U>
    - calculated-result-type jacobi_nc(T k, U theta);
    + calculated-result-type jacobi_nc(T k, U u);
     
      template <class T, class U, class Policy>
    - calculated-result-type jacobi_nc(T k, U theta, const Policy& pol);
    + calculated-result-type jacobi_nc(T k, U u, const Policy& pol);
     
     }} // namespaces
     
    @@ -64,7 +64,7 @@ with:

    - nc(x, k) = 1 / cn(x, k) + nc(u, k) = 1 / cn(u, k)

    diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_nd.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_nd.html index a04fb1141..c094ae4e1 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_nd.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_nd.html @@ -40,10 +40,10 @@

    namespace boost { namespace math {
     
      template <class T, class U>
    - calculated-result-type jacobi_nd(T k, U theta);
    + calculated-result-type jacobi_nd(T k, U u);
     
      template <class T, class U, class Policy>
    - calculated-result-type jacobi_nd(T k, U theta, const Policy& pol);
    + calculated-result-type jacobi_nd(T k, U u, const Policy& pol);
     
     }} // namespaces
     
    @@ -64,7 +64,7 @@ with:

    - nd(x, k) = 1 / dn(x, k) + nd(u, k) = 1 / dn(u, k)

    diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_ns.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_ns.html index f7e362afd..4ff7a5024 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_ns.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_ns.html @@ -40,10 +40,10 @@

    namespace boost { namespace math {
     
      template <class T, class U>
    - calculated-result-type jacobi_ns(T k, U theta);
    + calculated-result-type jacobi_ns(T k, U u);
     
      template <class T, class U, class Policy>
    - calculated-result-type jacobi_ns(T k, U theta, const Policy& pol);
    + calculated-result-type jacobi_ns(T k, U u, const Policy& pol);
     
     }} // namespaces
     
    @@ -64,7 +64,7 @@ with:

    - ns(x, k) = 1 / sn(x, k) + ns(u, k) = 1 / sn(u, k)

    diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sc.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sc.html index 3d044a2d5..2c4a68220 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sc.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sc.html @@ -40,10 +40,10 @@

    namespace boost { namespace math {
     
      template <class T, class U>
    - calculated-result-type jacobi_sc(T k, U theta);
    + calculated-result-type jacobi_sc(T k, U u);
     
      template <class T, class U, class Policy>
    - calculated-result-type jacobi_sc(T k, U theta, const Policy& pol);
    + calculated-result-type jacobi_sc(T k, U u, const Policy& pol);
     
     }} // namespaces
     
    @@ -64,7 +64,7 @@ with:

    - sc(x, k) = sn(x, k) / cn(x, k) + sc(u, k) = sn(u, k) / cn(u, k)

    diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sd.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sd.html index d90cc1fc4..54233b2cc 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sd.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sd.html @@ -40,10 +40,10 @@

    namespace boost { namespace math {
     
      template <class T, class U>
    - calculated-result-type jacobi_sd(T k, U theta);
    + calculated-result-type jacobi_sd(T k, U u);
     
      template <class T, class U, class Policy>
    - calculated-result-type jacobi_sd(T k, U theta, const Policy& pol);
    + calculated-result-type jacobi_sd(T k, U u, const Policy& pol);
     
     }} // namespaces
     
    @@ -64,7 +64,7 @@ with:

    - sd(x, k) = sn(x, k) / dn(x, k) + sd(u, k) = sn(u, k) / dn(u, k)

    diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sn.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sn.html index a25daf612..9ed44383d 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sn.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sn.html @@ -40,10 +40,10 @@

    namespace boost { namespace math {
     
      template <class T, class U>
    - calculated-result-type jacobi_sn(T k, U theta);
    + calculated-result-type jacobi_sn(T k, U u);
     
      template <class T, class U, class Policy>
    - calculated-result-type jacobi_sn(T k, U theta, const Policy& pol);
    + calculated-result-type jacobi_sn(T k, U u, const Policy& pol);
     
     }} // namespaces
     
    diff --git a/doc/sf_and_dist/jacobi_elliptic.qbk b/doc/sf_and_dist/jacobi_elliptic.qbk index 3c6413a67..f75d8b402 100644 --- a/doc/sf_and_dist/jacobi_elliptic.qbk +++ b/doc/sf_and_dist/jacobi_elliptic.qbk @@ -7,6 +7,42 @@ LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) [section:jacobi Jacobi Elliptic Functions] +[section:jac_over Overvew of the Jacobi Elliptic Functions] + +There are twelve Jacobi Elliptic functions, of which the three copolar functions ['sn], ['cn] and ['dn] are the most important +as the other nine can be computed from these three +[footnote [@http://en.wikipedia.org/wiki/Jacobi_elliptic_functions Wikipedia: Jacobi elliptic functions]] +[footnote [@http://mathworld.wolfram.com/JacobiEllipticFunctions.html Weisstein, Eric W. "Jacobi Elliptic Functions." From MathWorld - A Wolfram Web Resource.]] +[footnote [@http://dlmf.nist.gov/22 Digital Library of Mathematical Functions: Jacobian Elliptic Functions]]. + +These functions each take two arguments: a parameter, and a variable as described below. + +Like all elliptic functions these can be parameterised in a number of ways: + +* In terms of a parameter ['m]. +* In terms of the elliptic modulus ['k] where ['m = k[super 2]]. +* In terms of the modular angle [alpha], where ['m = sin[super 2][alpha]]. + +In our implementation, these functions all take the elliptic modulus /k/ as the parameter. + +In addition the variable /u/ is sometimes expressed as an amplitude [phi], in our implementation we always use /u/. + +Finally note that our functions all take the elliptic modulus as the first argument - this is for alignment with +the Elliptic Integrals. + +There are twenve functions for computing the twelve individual Jacobi elliptic functions: __jacobi_cd, __jacobi_cn, __jacobi_cs, +__jacobi_dc, __jacobi_dn, __jacobi_ds, __jacobi_nc, __jacobi_nd, __jacobi_ns, __jacobi_sc, __jacobi_sd and __jacobi_sn. + +They are all called as for example: + + jacobi_cs(k, u); + +Note however that these individual functions are all really thin wrappers around the function __jacobi_elliptic which calculates +the three copolar functions ['sn], ['cn] and ['dn] in a single function call. Thus if you need more than one of these functions +for a given set of arguments, it's most efficient to use __jacobi_elliptic. + +[endsect] + [section:jacobi_elliptic Jacobi Elliptic SN, CN and DN] [heading Synopsis] @@ -18,19 +54,19 @@ LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) namespace boost { namespace math { template - ``__sf_result`` jacobi_elliptic(T k, T phi, T* pcn, T* pdn); + ``__sf_result`` jacobi_elliptic(T k, T u, T* pcn, T* pdn); template - ``__sf_result`` jacobi_elliptic(T k, T phi, T* pcn, T* pdn, const Policy&); + ``__sf_result`` jacobi_elliptic(T k, T u, T* pcn, T* pdn, const Policy&); }} // namespaces [heading Description] The function __jacobi_elliptic calculates the three copolar Jacobi elliptic functions -['sn([phi], k)], ['cn([phi], k)] and ['dn([phi], k)]. The returned value is -['sn([phi], k)], and if provided, ['*pcn] is -set to ['cn([phi], k)], and ['*pdn] is set to ['dn([phi], k)]. +['sn(u, k)], ['cn(u, k)] and ['dn(u, k)]. The returned value is +['sn(u, k)], and if provided, ['*pcn] is +set to ['cn(u, k)], and ['*pdn] is set to ['dn(u, k)]. The functions are defined as follows, given: @@ -58,11 +94,11 @@ m = k[super 2] = sin[super 2][alpha] So that the function ['sn] (for example) may be expressed as either: -sn([phi], k) +sn(u, k) -sn([phi] \\ [alpha]) +sn(u \\ [alpha]) -sn([phi]| m) +sn(u| m) To further complicate matters, some texts refer to the ['complement of the parameter m], or 1 - m, where: @@ -97,7 +133,7 @@ system are given as narrower types have __zero_error. All values are relative errors in units of epsilon. [table Errors Rates in the Jacobi Elliptic Functions -[[Significand Size] [Platform and Compiler] [[phi] < 1] [Large [phi]] ] +[[Significand Size] [Platform and Compiler] [u < 1] [Large u] ] [[53] [Win32 / Visual C++ 8.0] [Peak=2 Mean=0.5] [Peak=44000 Mean=2500] ] [[64] [Ubuntu Linux / G++ 4.7] [Peak=2.0 Mean=0.5] [Peak=25000 Mean=1500] ] ] @@ -120,9 +156,9 @@ Then filter off the special cases: ['sn(0, k) = 0] and ['cn(0, k) = dn(0, k) = 1]. -['sn(x, 0) = sin(x), cn(x, 0) = cos(x) and dn(x, 0) = 1]. +['sn(u, 0) = sin(u), cn(u, 0) = cos(u) and dn(u, 0) = 1]. -['sn(x, 1) = tanh(x), cn(x, 1) = dn(x, 1) = 1 / cosh(x)]. +['sn(u, 1) = tanh(u), cn(u, 1) = dn(u, 1) = 1 / cosh(u)]. And for ['k[super 4] < [epsilon]] we have: @@ -143,10 +179,10 @@ Otherwise the values are calculated using the method of [@http://dlmf.nist.gov/2 namespace boost { namespace math { template - ``__sf_result`` jacobi_cd(T k, U theta); + ``__sf_result`` jacobi_cd(T k, U u); template - ``__sf_result`` jacobi_cd(T k, U theta, const Policy& pol); + ``__sf_result`` jacobi_cd(T k, U u, const Policy& pol); }} // namespaces @@ -158,7 +194,7 @@ This function returns the Jacobi elliptic function ['cd]. This function is a trivial wrapper around __jacobi_elliptic, with: -['cd(x, k) = cn(x, k) / dn(x, k)] +['cd(u, k) = cn(u, k) / dn(u, k)] [graph jacobi_cd] @@ -175,10 +211,10 @@ This function is a trivial wrapper around __jacobi_elliptic, with: namespace boost { namespace math { template - ``__sf_result`` jacobi_cn(T k, U theta); + ``__sf_result`` jacobi_cn(T k, U u); template - ``__sf_result`` jacobi_cn(T k, U theta, const Policy& pol); + ``__sf_result`` jacobi_cn(T k, U u, const Policy& pol); }} // namespaces @@ -205,10 +241,10 @@ This function is a trivial wrapper around __jacobi_elliptic. namespace boost { namespace math { template - ``__sf_result`` jacobi_cs(T k, U theta); + ``__sf_result`` jacobi_cs(T k, U u); template - ``__sf_result`` jacobi_cs(T k, U theta, const Policy& pol); + ``__sf_result`` jacobi_cs(T k, U u, const Policy& pol); }} // namespaces @@ -220,7 +256,7 @@ This function returns the Jacobi elliptic function ['cs]. This function is a trivial wrapper around __jacobi_elliptic, with: -['cs(x, k) = cn(x, k) / sn(x, k)] +['cs(u, k) = cn(u, k) / sn(u, k)] [graph jacobi_cs] @@ -237,10 +273,10 @@ This function is a trivial wrapper around __jacobi_elliptic, with: namespace boost { namespace math { template - ``__sf_result`` jacobi_dc(T k, U theta); + ``__sf_result`` jacobi_dc(T k, U u); template - ``__sf_result`` jacobi_dc(T k, U theta, const Policy& pol); + ``__sf_result`` jacobi_dc(T k, U u, const Policy& pol); }} // namespaces @@ -252,7 +288,7 @@ This function returns the Jacobi elliptic function ['dc]. This function is a trivial wrapper around __jacobi_elliptic, with: -['dc(x, k) = dn(x, k) / cn(x, k)] +['dc(u, k) = dn(u, k) / cn(u, k)] [graph jacobi_dc] @@ -269,10 +305,10 @@ This function is a trivial wrapper around __jacobi_elliptic, with: namespace boost { namespace math { template - ``__sf_result`` jacobi_dn(T k, U theta); + ``__sf_result`` jacobi_dn(T k, U u); template - ``__sf_result`` jacobi_dn(T k, U theta, const Policy& pol); + ``__sf_result`` jacobi_dn(T k, U u, const Policy& pol); }} // namespaces @@ -299,10 +335,10 @@ This function is a trivial wrapper around __jacobi_elliptic. namespace boost { namespace math { template - ``__sf_result`` jacobi_ds(T k, U theta); + ``__sf_result`` jacobi_ds(T k, U u); template - ``__sf_result`` jacobi_ds(T k, U theta, const Policy& pol); + ``__sf_result`` jacobi_ds(T k, U u, const Policy& pol); }} // namespaces @@ -314,7 +350,7 @@ This function returns the Jacobi elliptic function ['ds]. This function is a trivial wrapper around __jacobi_elliptic, with: -['ds(x, k) = dn(x, k) / sn(x, k)] +['ds(u, k) = dn(u, k) / sn(u, k)] [graph jacobi_ds] @@ -331,10 +367,10 @@ This function is a trivial wrapper around __jacobi_elliptic, with: namespace boost { namespace math { template - ``__sf_result`` jacobi_nc(T k, U theta); + ``__sf_result`` jacobi_nc(T k, U u); template - ``__sf_result`` jacobi_nc(T k, U theta, const Policy& pol); + ``__sf_result`` jacobi_nc(T k, U u, const Policy& pol); }} // namespaces @@ -346,7 +382,7 @@ This function returns the Jacobi elliptic function ['nc]. This function is a trivial wrapper around __jacobi_elliptic, with: -['nc(x, k) = 1 / cn(x, k)] +['nc(u, k) = 1 / cn(u, k)] [graph jacobi_nc] @@ -363,10 +399,10 @@ This function is a trivial wrapper around __jacobi_elliptic, with: namespace boost { namespace math { template - ``__sf_result`` jacobi_nd(T k, U theta); + ``__sf_result`` jacobi_nd(T k, U u); template - ``__sf_result`` jacobi_nd(T k, U theta, const Policy& pol); + ``__sf_result`` jacobi_nd(T k, U u, const Policy& pol); }} // namespaces @@ -378,7 +414,7 @@ This function returns the Jacobi elliptic function ['nd]. This function is a trivial wrapper around __jacobi_elliptic, with: -['nd(x, k) = 1 / dn(x, k)] +['nd(u, k) = 1 / dn(u, k)] [graph jacobi_nd] @@ -395,10 +431,10 @@ This function is a trivial wrapper around __jacobi_elliptic, with: namespace boost { namespace math { template - ``__sf_result`` jacobi_ns(T k, U theta); + ``__sf_result`` jacobi_ns(T k, U u); template - ``__sf_result`` jacobi_ns(T k, U theta, const Policy& pol); + ``__sf_result`` jacobi_ns(T k, U u, const Policy& pol); }} // namespaces @@ -410,7 +446,7 @@ This function returns the Jacobi elliptic function ['ns]. This function is a trivial wrapper around __jacobi_elliptic, with: -['ns(x, k) = 1 / sn(x, k)] +['ns(u, k) = 1 / sn(u, k)] [graph jacobi_ns] @@ -427,10 +463,10 @@ This function is a trivial wrapper around __jacobi_elliptic, with: namespace boost { namespace math { template - ``__sf_result`` jacobi_sc(T k, U theta); + ``__sf_result`` jacobi_sc(T k, U u); template - ``__sf_result`` jacobi_sc(T k, U theta, const Policy& pol); + ``__sf_result`` jacobi_sc(T k, U u, const Policy& pol); }} // namespaces @@ -442,7 +478,7 @@ This function returns the Jacobi elliptic function ['sc]. This function is a trivial wrapper around __jacobi_elliptic, with: -['sc(x, k) = sn(x, k) / cn(x, k)] +['sc(u, k) = sn(u, k) / cn(u, k)] [graph jacobi_sc] @@ -459,10 +495,10 @@ This function is a trivial wrapper around __jacobi_elliptic, with: namespace boost { namespace math { template - ``__sf_result`` jacobi_sd(T k, U theta); + ``__sf_result`` jacobi_sd(T k, U u); template - ``__sf_result`` jacobi_sd(T k, U theta, const Policy& pol); + ``__sf_result`` jacobi_sd(T k, U u, const Policy& pol); }} // namespaces @@ -474,7 +510,7 @@ This function returns the Jacobi elliptic function ['sd]. This function is a trivial wrapper around __jacobi_elliptic, with: -['sd(x, k) = sn(x, k) / dn(x, k)] +['sd(u, k) = sn(u, k) / dn(u, k)] [graph jacobi_sd] @@ -491,10 +527,10 @@ This function is a trivial wrapper around __jacobi_elliptic, with: namespace boost { namespace math { template - ``__sf_result`` jacobi_sn(T k, U theta); + ``__sf_result`` jacobi_sn(T k, U u); template - ``__sf_result`` jacobi_sn(T k, U theta, const Policy& pol); + ``__sf_result`` jacobi_sn(T k, U u, const Policy& pol); }} // namespaces diff --git a/doc/sf_and_dist/math.qbk b/doc/sf_and_dist/math.qbk index 9f74208ee..f1191155b 100644 --- a/doc/sf_and_dist/math.qbk +++ b/doc/sf_and_dist/math.qbk @@ -165,6 +165,18 @@ and use the function's name as the link text.] [/Jacobi Elliptic Functions] [def __jacobi_elliptic [link math_toolkit.special.jacobi.jacobi_elliptic jacobi_elliptic]] +[def __jacobi_cd [link math_toolkit.special.jacobi.jacobi_cd jacobi_cd]] +[def __jacobi_cn [link math_toolkit.special.jacobi.jacobi_cn jacobi_cn]] +[def __jacobi_cs [link math_toolkit.special.jacobi.jacobi_cs jacobi_cs]] +[def __jacobi_dc [link math_toolkit.special.jacobi.jacobi_dc jacobi_dc]] +[def __jacobi_dn [link math_toolkit.special.jacobi.jacobi_dn jacobi_dn]] +[def __jacobi_ds [link math_toolkit.special.jacobi.jacobi_ds jacobi_ds]] +[def __jacobi_nd [link math_toolkit.special.jacobi.jacobi_nd jacobi_nd]] +[def __jacobi_nc [link math_toolkit.special.jacobi.jacobi_nc jacobi_nc]] +[def __jacobi_ns [link math_toolkit.special.jacobi.jacobi_ns jacobi_ns]] +[def __jacobi_sd [link math_toolkit.special.jacobi.jacobi_sd jacobi_sd]] +[def __jacobi_sn [link math_toolkit.special.jacobi.jacobi_sn jacobi_sn]] +[def __jacobi_sc [link math_toolkit.special.jacobi.jacobi_sc jacobi_sc]] [/sinus cardinals] [def __sinc_pi [link math_toolkit.special.sinc.sinc_pi sinc_pi]] From 26d92a55f006070a26df3f7b7451d839ec423b3a Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 21 Jun 2012 09:18:47 +0000 Subject: [PATCH 039/115] Add missing include guards. Fixes #7001. [SVN r79027] --- include/boost/math/distributions/logistic.hpp | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/include/boost/math/distributions/logistic.hpp b/include/boost/math/distributions/logistic.hpp index 2fa18535f..f372faf6e 100644 --- a/include/boost/math/distributions/logistic.hpp +++ b/include/boost/math/distributions/logistic.hpp @@ -5,6 +5,9 @@ // (See accompanying file LICENSE_1_0.txt // or copy at http://www.boost.org/LICENSE_1_0.txt) +#ifndef BOOST_MATH_DISTRIBUTIONS_LOGISTIC +#define BOOST_MATH_DISTRIBUTIONS_LOGISTIC + #include #include #include @@ -287,3 +290,4 @@ namespace boost { namespace math { // Must come at the end: #include +#endif // BOOST_MATH_DISTRIBUTIONS_LOGISTIC From 19f78ac0ac6649602824a300c3d6dce0e9efeac9 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 28 Jun 2012 12:09:09 +0000 Subject: [PATCH 040/115] Fix actual and potential integer divisions when using integer constants. Fixes #7024. [SVN r79154] --- include/boost/math/bindings/e_float.hpp | 2 +- include/boost/math/bindings/mpfr.hpp | 2 +- include/boost/math/bindings/mpreal.hpp | 2 +- include/boost/math/special_functions/airy.hpp | 8 ++++---- .../math/special_functions/detail/bessel_jy_series.hpp | 2 +- 5 files changed, 8 insertions(+), 8 deletions(-) diff --git a/include/boost/math/bindings/e_float.hpp b/include/boost/math/bindings/e_float.hpp index d7f9a7350..b1dd7dc1d 100644 --- a/include/boost/math/bindings/e_float.hpp +++ b/include/boost/math/bindings/e_float.hpp @@ -714,7 +714,7 @@ boost::math::ef::e_float bessel_i0(boost::math::ef::e_float x) } else // x in (15, \infty) { - boost::math::ef::e_float y = 1 / x - 1 / 15; + boost::math::ef::e_float y = 1 / x - boost::math::ef::e_float(1) / 15; r = evaluate_polynomial(P2, y) / evaluate_polynomial(Q2, y); factor = exp(x) / sqrt(x); value = factor * r; diff --git a/include/boost/math/bindings/mpfr.hpp b/include/boost/math/bindings/mpfr.hpp index e5c6ba071..679b83e35 100644 --- a/include/boost/math/bindings/mpfr.hpp +++ b/include/boost/math/bindings/mpfr.hpp @@ -771,7 +771,7 @@ inline mpfr_class bessel_i0(mpfr_class x) } else // x in (15, \infty) { - mpfr_class y = 1 / x - 1 / 15; + mpfr_class y = 1 / x - mpfr_class(1) / 15; r = evaluate_polynomial(P2, y) / evaluate_polynomial(Q2, y); factor = exp(x) / sqrt(x); value = factor * r; diff --git a/include/boost/math/bindings/mpreal.hpp b/include/boost/math/bindings/mpreal.hpp index 82f7950b9..b63c024f2 100644 --- a/include/boost/math/bindings/mpreal.hpp +++ b/include/boost/math/bindings/mpreal.hpp @@ -802,7 +802,7 @@ mpfr::mpreal bessel_i0(mpfr::mpreal x) } else // x in (15, \infty) { - mpfr::mpreal y = 1 / x - 1 / 15; + mpfr::mpreal y = 1 / x - mpfr::mpreal(1) / 15; r = evaluate_polynomial(P2, y) / evaluate_polynomial(Q2, y); factor = exp(x) / sqrt(x); value = factor * r; diff --git a/include/boost/math/special_functions/airy.hpp b/include/boost/math/special_functions/airy.hpp index 408cf6758..86d3c0b5a 100644 --- a/include/boost/math/special_functions/airy.hpp +++ b/include/boost/math/special_functions/airy.hpp @@ -21,7 +21,7 @@ T airy_ai_imp(T x, const Policy& pol) if(x < 0) { - T p = -x * sqrt(-x) * 2 / 3; + T p = (-x * sqrt(-x) * 2) / 3; T v = T(1) / 3; T j1 = boost::math::cyl_bessel_j(v, p, pol); T j2 = boost::math::cyl_bessel_j(-v, p, pol); @@ -59,7 +59,7 @@ T airy_bi_imp(T x, const Policy& pol) if(x < 0) { - T p = -x * sqrt(-x) * 2 / 3; + T p = (-x * sqrt(-x) * 2) / 3; T v = T(1) / 3; T j1 = boost::math::cyl_bessel_j(v, p, pol); T j2 = boost::math::cyl_bessel_j(-v, p, pol); @@ -92,7 +92,7 @@ T airy_ai_prime_imp(T x, const Policy& pol) if(x < 0) { - T p = -x * sqrt(-x) * 2 / 3; + T p = (-x * sqrt(-x) * 2) / 3; T v = T(2) / 3; T j1 = boost::math::cyl_bessel_j(v, p, pol); T j2 = boost::math::cyl_bessel_j(-v, p, pol); @@ -127,7 +127,7 @@ T airy_bi_prime_imp(T x, const Policy& pol) if(x < 0) { - T p = -x * sqrt(-x) * 2 / 3; + T p = (-x * sqrt(-x) * 2) / 3; T v = T(2) / 3; T j1 = boost::math::cyl_bessel_j(v, p, pol); T j2 = boost::math::cyl_bessel_j(-v, p, pol); diff --git a/include/boost/math/special_functions/detail/bessel_jy_series.hpp b/include/boost/math/special_functions/detail/bessel_jy_series.hpp index b926366eb..a9e6d71cc 100644 --- a/include/boost/math/special_functions/detail/bessel_jy_series.hpp +++ b/include/boost/math/special_functions/detail/bessel_jy_series.hpp @@ -235,7 +235,7 @@ T bessel_yn_small_z(int n, T z, T* scale, const Policy& pol) { return (z * z) / (4 * constants::pi()) * log(z / 2) - (4 / (constants::pi() * z * z)) - - ((z * z) / (8 * constants::pi())) * (3/2 - 2 * constants::euler()); + - ((z * z) / (8 * constants::pi())) * (T(3)/2 - 2 * constants::euler()); } else { From e339ad75d2aa1ce014b042b3318d572dba898820 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Wed, 4 Jul 2012 13:58:56 +0000 Subject: [PATCH 041/115] Two temporary tests for which platforms provide numeric_limits max_digits10 and if BOOST_NO_NUMERIC_LIMITS_LOWEST is a suitable macro to check that max_digtsi10 is implemented before using in Boost.Test for radix10 when the Kahan formula is not applicable. [SVN r79260] --- test/Jamfile.v2 | 3 ++ test/ztest_max_digits10.cpp | 66 ++++++++++++++++++++++++++++++++++++ test/zztest_max_digits10.cpp | 66 ++++++++++++++++++++++++++++++++++++ 3 files changed, 135 insertions(+) create mode 100644 test/ztest_max_digits10.cpp create mode 100644 test/zztest_max_digits10.cpp diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index a0374bd19..6c778f8e9 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -827,6 +827,9 @@ compile mpreal_concept_check.cpp : [ check-target-builds ../config//has_mpreal : compile e_float_concept_check.cpp : [ check-target-builds ../config//has_e_float : : no ] ; compile test_common_factor_gmpxx.cpp : [ check-target-builds ../config//has_gmpxx : : no ] ; +run ztest_max_digits10.cpp ; +run zztest_max_digits10.cpp ; + build-project ../example ; diff --git a/test/ztest_max_digits10.cpp b/test/ztest_max_digits10.cpp new file mode 100644 index 000000000..29ef30d48 --- /dev/null +++ b/test/ztest_max_digits10.cpp @@ -0,0 +1,66 @@ + + // Copyright 2010 Paul A. Bristow +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) + +/* Temporary test program to discover which platforms support + +numeric_limits + +digits10 and + +new max_digits10. + +This is needed to produce or select a macro to avoid compilation failure in Boost.Test +for platforms that do not include either or both of these. + +BOOST_NO_NUMERIC_LIMITS_LOWEST may be suitable? + +[Boost C++ Libraries] + +#5758: Boost.Test Floating-point comparison diagnostic output does not support radix 10. + +*/ + +#include +#include + +#include +#include + +int main() +{ + std::cout << "Platform: " << BOOST_PLATFORM << '\n' + << "Compiler: " << BOOST_COMPILER << '\n' + << "STL : " << BOOST_STDLIB << '\n' + << "Boost : " << BOOST_VERSION/100000 << "." + << BOOST_VERSION/100 % 1000 << "." + << BOOST_VERSION % 100 << std::endl; + + int digits10 = std::numeric_limits::digits10; + int max_digits10 = std::numeric_limits::max_digits10; + + std::cout << "std::numeric_limits::digits10 = " << std::numeric_limits::digits10 << std::endl; + + std::cout << "std::numeric_limits::max_digits10 = " << std::numeric_limits::max_digits10 << std::endl; + + +} // int main() + +/* + +Output: + + Description: Autorun "J:\Cpp\MathToolkit\test\Math_test\Debug\ztest_max_digits10.exe" + Platform: Win32 + Compiler: Microsoft Visual C++ version 10.0 + STL : Dinkumware standard library version 520 + Boost : 1.50.0 + std::numeric_limits::digits10 = 15 + std::numeric_limits::max_digits10 = 17 + + + +*/ diff --git a/test/zztest_max_digits10.cpp b/test/zztest_max_digits10.cpp new file mode 100644 index 000000000..ddefd76e1 --- /dev/null +++ b/test/zztest_max_digits10.cpp @@ -0,0 +1,66 @@ + + // Copyright 2010 Paul A. Bristow +// +// Distributed under the Boost Software License, Version 1.0. (See +// accompanying file LICENSE_1_0.txt or copy at +// http://www.boost.org/LICENSE_1_0.txt) + +/* Temporary test program to discover which platforms support + +numeric_limits + +digits10 and + +new max_digits10. + +This is needed to produce or select a macro to avoid compilation failure in Boost.Test +for platforms that do not include either or both of these. + +BOOST_NO_NUMERIC_LIMITS_LOWEST may be suitable and is tested here. + +[Boost C++ Libraries] + +#5758: Boost.Test Floating-point comparison diagnostic output does not support radix 10. + +*/ + +#include +#include + +#include +#include + +int main() +{ + std::cout << "Platform: " << BOOST_PLATFORM << '\n' + << "Compiler: " << BOOST_COMPILER << '\n' + << "STL : " << BOOST_STDLIB << '\n' + << "Boost : " << BOOST_VERSION/100000 << "." + << BOOST_VERSION/100 % 1000 << "." + << BOOST_VERSION % 100 << std::endl; + + int digits10 = std::numeric_limits::digits10; + std::cout << "std::numeric_limits::digits10 = " << std::numeric_limits::digits10 << std::endl; + +#ifndef BOOST_NO_NUMERIC_LIMITS_LOWEST + int max_digits10 = std::numeric_limits::max_digits10; + std::cout << "std::numeric_limits::max_digits10 = " << std::numeric_limits::max_digits10 << std::endl; +#endif + +} // int main() + +/* + +Output: + + Description: Autorun "J:\Cpp\MathToolkit\test\Math_test\Debug\ztest_max_digits10.exe" + Platform: Win32 + Compiler: Microsoft Visual C++ version 10.0 + STL : Dinkumware standard library version 520 + Boost : 1.50.0 + std::numeric_limits::digits10 = 15 + std::numeric_limits::max_digits10 = 17 + + + +*/ From 629db841745f764843501f4a46be2ea810d2c1ce Mon Sep 17 00:00:00 2001 From: John Maddock Date: Fri, 6 Jul 2012 16:17:39 +0000 Subject: [PATCH 042/115] Fix file line ending. Fixes #7062. Fixes #7097. [SVN r79317] --- include/boost/math/special_functions/hankel.hpp | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/include/boost/math/special_functions/hankel.hpp b/include/boost/math/special_functions/hankel.hpp index a0852ee4a..f322bacd3 100644 --- a/include/boost/math/special_functions/hankel.hpp +++ b/include/boost/math/special_functions/hankel.hpp @@ -175,4 +175,5 @@ inline std::complex >: }} // namespaces -#endif // BOOST_MATH_HANKEL_HPP \ No newline at end of file +#endif // BOOST_MATH_HANKEL_HPP + From f73f66b45438e0fde06c6970ee5b8dcf4958507f Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sat, 7 Jul 2012 11:18:09 +0000 Subject: [PATCH 043/115] Tentative fix for compilers that treat floating point constants smaller than a 64-bit double can hold as hard errors. Refs #7099. [SVN r79332] --- .../math/special_functions/detail/erf_inv.hpp | 30 ++++++++++++++++--- 1 file changed, 26 insertions(+), 4 deletions(-) diff --git a/include/boost/math/special_functions/detail/erf_inv.hpp b/include/boost/math/special_functions/detail/erf_inv.hpp index d51db9d52..005b4e563 100644 --- a/include/boost/math/special_functions/detail/erf_inv.hpp +++ b/include/boost/math/special_functions/detail/erf_inv.hpp @@ -331,6 +331,28 @@ struct erf_inv_initializer { do_init(); } + template + static void do_init_big(const Tag&) + { + // Make this a template so it's not instantiated if these constants are too large + // for the compiler to handle. See https://svn.boost.org/trac/boost/ticket/7099 + if(static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-800)) != 0) + boost::math::erfc_inv(static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-800)), Policy()); + if(static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-900)) != 0) + boost::math::erfc_inv(static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-900)), Policy()); + } + static void do_init_big(const mpl::false_&) + { + // Initialization here is pointless for (built in) floating point types, + // but may still be required for UDT's: + if(!is_floating_point::value) + { + if(static_cast(BOOST_MATH_HUGE_CONSTANT(T, 64, 1e-800)) != 0) + boost::math::erfc_inv(static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-800)), Policy()); + if(static_cast(BOOST_MATH_HUGE_CONSTANT(T, 64, 1e-900)) != 0) + boost::math::erfc_inv(static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-900)), Policy()); + } + } static void do_init() { boost::math::erf_inv(static_cast(0.25), Policy()); @@ -339,10 +361,10 @@ struct erf_inv_initializer boost::math::erfc_inv(static_cast(1e-15), Policy()); if(static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-130)) != 0) boost::math::erfc_inv(static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-130)), Policy()); - if(static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-800)) != 0) - boost::math::erfc_inv(static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-800)), Policy()); - if(static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-900)) != 0) - boost::math::erfc_inv(static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-900)), Policy()); + + typedef mpl::bool_<(LDBL_MIN_EXP < -1030)> tag_type; + + do_init_big(tag_type()); } void force_instantiate()const{} }; From 985d3cdc003470f58cedf641944a41e81e24ac19 Mon Sep 17 00:00:00 2001 From: Marshall Clow Date: Wed, 11 Jul 2012 16:21:28 +0000 Subject: [PATCH 044/115] Switch from deprecated macros to new shiny ones; no functionality change [SVN r79417] --- include/boost/math/tools/tuple.hpp | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/include/boost/math/tools/tuple.hpp b/include/boost/math/tools/tuple.hpp index f61f3e059..2f297360a 100644 --- a/include/boost/math/tools/tuple.hpp +++ b/include/boost/math/tools/tuple.hpp @@ -9,7 +9,7 @@ #include // for BOOST_HAS_TR1_TUPLE -#ifndef BOOST_NO_0X_HDR_TUPLE +#ifndef BOOST_NO_CXX11_HDR_TUPLE #include From b1d516cf492406fc9f4effc09640ca0983cc68b6 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 11 Jul 2012 17:26:05 +0000 Subject: [PATCH 045/115] Fix numeric_limits specialization. [SVN r79419] --- test/common_factor_test.cpp | 6 ++++++ 1 file changed, 6 insertions(+) diff --git a/test/common_factor_test.cpp b/test/common_factor_test.cpp index 8fd728844..db9032eda 100644 --- a/test/common_factor_test.cpp +++ b/test/common_factor_test.cpp @@ -148,6 +148,9 @@ public: BOOST_STATIC_CONSTANT(int, digits = limits_type::digits); BOOST_STATIC_CONSTANT(int, digits10 = limits_type::digits10); +#ifndef BOOST_NO_NUMERIC_LIMITS_LOWEST + BOOST_STATIC_CONSTANT(int, max_digits10 = limits_type::max_digits10); +#endif BOOST_STATIC_CONSTANT(bool, is_signed = limits_type::is_signed); BOOST_STATIC_CONSTANT(bool, is_integer = limits_type::is_integer); BOOST_STATIC_CONSTANT(bool, is_exact = limits_type::is_exact); @@ -195,6 +198,9 @@ public: BOOST_STATIC_CONSTANT(int, digits = limits_type::digits); BOOST_STATIC_CONSTANT(int, digits10 = limits_type::digits10); +#ifndef BOOST_NO_NUMERIC_LIMITS_LOWEST + BOOST_STATIC_CONSTANT(int, max_digits10 = limits_type::max_digits10); +#endif BOOST_STATIC_CONSTANT(bool, is_signed = limits_type::is_signed); BOOST_STATIC_CONSTANT(bool, is_integer = limits_type::is_integer); BOOST_STATIC_CONSTANT(bool, is_exact = limits_type::is_exact); From 176a695ec06f4e638c9fd1cfbe83033f342a2e5b Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 11 Jul 2012 17:27:27 +0000 Subject: [PATCH 046/115] Fix double inclusion of which causes use of Boost.TR1 to fail. Fixes #7053. [SVN r79420] --- include/boost/math/special_functions/math_fwd.hpp | 1 - 1 file changed, 1 deletion(-) diff --git a/include/boost/math/special_functions/math_fwd.hpp b/include/boost/math/special_functions/math_fwd.hpp index 5d54fd14b..6669e3fe3 100644 --- a/include/boost/math/special_functions/math_fwd.hpp +++ b/include/boost/math/special_functions/math_fwd.hpp @@ -28,7 +28,6 @@ #include #include #include -#include #define BOOST_NO_MACRO_EXPAND /**/ From 58e250eb1f1cb17952381d72c404641b9abc5e73 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Wed, 11 Jul 2012 17:28:54 +0000 Subject: [PATCH 047/115] Ditch anonymous union - it causes GCC-4.4 to choke. Fixes #6362. [SVN r79421] --- include/boost/math/special_functions/detail/bessel_jy.hpp | 6 ++---- 1 file changed, 2 insertions(+), 4 deletions(-) diff --git a/include/boost/math/special_functions/detail/bessel_jy.hpp b/include/boost/math/special_functions/detail/bessel_jy.hpp index d60dda2d4..a409e26ad 100644 --- a/include/boost/math/special_functions/detail/bessel_jy.hpp +++ b/include/boost/math/special_functions/detail/bessel_jy.hpp @@ -256,10 +256,8 @@ int CF2_jy(T v, T x, T* p, T* q, const Policy& pol) return 0; } -enum -{ - need_j = 1, need_y = 2 -}; +static const int need_j = 1; +static const int need_y = 2; // Compute J(v, x) and Y(v, x) simultaneously by Steed's method, see // Barnett et al, Computer Physics Communications, vol 8, 377 (1974) From c585419ec2a94735592c9effc4a9c1912e0aadc9 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 12 Jul 2012 09:51:32 +0000 Subject: [PATCH 048/115] Allow fpclassify and friends to be used with integer types via the usual promotion mechanism. Fixes #6517. [SVN r79438] --- .../math/special_functions/fpclassify.hpp | 16 +++++++---- test/test_classify.cpp | 28 +++++++++++-------- 2 files changed, 27 insertions(+), 17 deletions(-) diff --git a/include/boost/math/special_functions/fpclassify.hpp b/include/boost/math/special_functions/fpclassify.hpp index 2abec5fa8..6f92d18a7 100644 --- a/include/boost/math/special_functions/fpclassify.hpp +++ b/include/boost/math/special_functions/fpclassify.hpp @@ -249,12 +249,13 @@ inline int fpclassify BOOST_NO_MACRO_EXPAND(T t) { typedef typename detail::fp_traits::type traits; typedef typename traits::method method; + typedef typename tools::promote_args::type value_type; #ifdef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS if(std::numeric_limits::is_specialized && detail::is_generic_tag_false(static_cast(0))) - return detail::fpclassify_imp(t, detail::generic_tag()); - return detail::fpclassify_imp(t, method()); + return detail::fpclassify_imp(static_cast(t), detail::generic_tag()); + return detail::fpclassify_imp(static_cast(t), method()); #else - return detail::fpclassify_imp(t, method()); + return detail::fpclassify_imp(static_cast(t), method()); #endif } @@ -312,7 +313,8 @@ inline bool (isfinite)(T x) typedef typename detail::fp_traits::type traits; typedef typename traits::method method; typedef typename boost::is_floating_point::type fp_tag; - return detail::isfinite_impl(x, method()); + typedef typename tools::promote_args::type value_type; + return detail::isfinite_impl(static_cast(x), method()); } //------------------------------------------------------------------------------ @@ -371,7 +373,8 @@ inline bool (isnormal)(T x) typedef typename detail::fp_traits::type traits; typedef typename traits::method method; typedef typename boost::is_floating_point::type fp_tag; - return detail::isnormal_impl(x, method()); + typedef typename tools::promote_args::type value_type; + return detail::isnormal_impl(static_cast(x), method()); } //------------------------------------------------------------------------------ @@ -448,7 +451,8 @@ inline bool (isinf)(T x) typedef typename detail::fp_traits::type traits; typedef typename traits::method method; typedef typename boost::is_floating_point::type fp_tag; - return detail::isinf_impl(x, method()); + typedef typename tools::promote_args::type value_type; + return detail::isinf_impl(static_cast(x), method()); } //------------------------------------------------------------------------------ diff --git a/test/test_classify.cpp b/test/test_classify.cpp index 6c048d294..2b72bd3c7 100644 --- a/test/test_classify.cpp +++ b/test/test_classify.cpp @@ -14,7 +14,7 @@ #include #ifdef _MSC_VER -#pragma warning(disable: 4127) // conditional expression is constant +#pragma warning(disable: 4127 4146) // conditional expression is constant #endif const char* method_name(const boost::math::detail::native_tag&) @@ -83,16 +83,19 @@ void test_classify(T t, const char* type) BOOST_CHECK_EQUAL((::boost::math::isnormal)(t), true); BOOST_CHECK_EQUAL((::boost::math::isnormal)(-t), true); t = (std::numeric_limits::min)(); - BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (int)FP_NORMAL); - BOOST_CHECK_EQUAL((::boost::math::fpclassify)(-t), (int)FP_NORMAL); - BOOST_CHECK_EQUAL((::boost::math::isfinite)(t), true); - BOOST_CHECK_EQUAL((::boost::math::isfinite)(-t), true); - BOOST_CHECK_EQUAL((::boost::math::isinf)(t), false); - BOOST_CHECK_EQUAL((::boost::math::isinf)(-t), false); - BOOST_CHECK_EQUAL((::boost::math::isnan)(t), false); - BOOST_CHECK_EQUAL((::boost::math::isnan)(-t), false); - BOOST_CHECK_EQUAL((::boost::math::isnormal)(t), true); - BOOST_CHECK_EQUAL((::boost::math::isnormal)(-t), true); + if(t != 0) + { + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(t), (int)FP_NORMAL); + BOOST_CHECK_EQUAL((::boost::math::fpclassify)(-t), (int)FP_NORMAL); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isfinite)(-t), true); + BOOST_CHECK_EQUAL((::boost::math::isinf)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isinf)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(t), false); + BOOST_CHECK_EQUAL((::boost::math::isnan)(-t), false); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(t), true); + BOOST_CHECK_EQUAL((::boost::math::isnormal)(-t), true); + } } if(std::numeric_limits::has_denorm) { @@ -273,6 +276,9 @@ int test_main(int, char* [] ) test_classify((long double)(0), "long double"); test_classify((boost::math::concepts::real_concept)(0), "real_concept"); #endif + // We should test with integer types as well: + test_classify(int(0), "int"); + test_classify(unsigned(0), "unsigned"); return 0; } From cfd28e0e05ddffcc3d6c735fbaa8cf961ca76be6 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 12 Jul 2012 09:53:18 +0000 Subject: [PATCH 049/115] Tentative fix #2 for TI compiler error. Refs #7099. [SVN r79439] --- .../math/special_functions/detail/erf_inv.hpp | 38 +++++++------------ include/boost/math/tools/big_constant.hpp | 2 +- 2 files changed, 14 insertions(+), 26 deletions(-) diff --git a/include/boost/math/special_functions/detail/erf_inv.hpp b/include/boost/math/special_functions/detail/erf_inv.hpp index 005b4e563..f5d8ee471 100644 --- a/include/boost/math/special_functions/detail/erf_inv.hpp +++ b/include/boost/math/special_functions/detail/erf_inv.hpp @@ -331,28 +331,6 @@ struct erf_inv_initializer { do_init(); } - template - static void do_init_big(const Tag&) - { - // Make this a template so it's not instantiated if these constants are too large - // for the compiler to handle. See https://svn.boost.org/trac/boost/ticket/7099 - if(static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-800)) != 0) - boost::math::erfc_inv(static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-800)), Policy()); - if(static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-900)) != 0) - boost::math::erfc_inv(static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-900)), Policy()); - } - static void do_init_big(const mpl::false_&) - { - // Initialization here is pointless for (built in) floating point types, - // but may still be required for UDT's: - if(!is_floating_point::value) - { - if(static_cast(BOOST_MATH_HUGE_CONSTANT(T, 64, 1e-800)) != 0) - boost::math::erfc_inv(static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-800)), Policy()); - if(static_cast(BOOST_MATH_HUGE_CONSTANT(T, 64, 1e-900)) != 0) - boost::math::erfc_inv(static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-900)), Policy()); - } - } static void do_init() { boost::math::erf_inv(static_cast(0.25), Policy()); @@ -362,9 +340,19 @@ struct erf_inv_initializer if(static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-130)) != 0) boost::math::erfc_inv(static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-130)), Policy()); - typedef mpl::bool_<(LDBL_MIN_EXP < -1030)> tag_type; - - do_init_big(tag_type()); + // Some compilers choke on constants that would underflow, even in code that isn't instantiated + // so try and filter these cases out in the preprocessor: +#if LDBL_MAX_10_EXP >= 800 + if(static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-800)) != 0) + boost::math::erfc_inv(static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-800)), Policy()); + if(static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-900)) != 0) + boost::math::erfc_inv(static_cast(BOOST_MATH_BIG_CONSTANT(T, 64, 1e-900)), Policy()); +#else + if(static_cast(BOOST_MATH_HUGE_CONSTANT(T, 64, 1e-800)) != 0) + boost::math::erfc_inv(static_cast(BOOST_MATH_HUGE_CONSTANT(T, 64, 1e-800)), Policy()); + if(static_cast(BOOST_MATH_HUGE_CONSTANT(T, 64, 1e-900)) != 0) + boost::math::erfc_inv(static_cast(BOOST_MATH_HUGE_CONSTANT(T, 64, 1e-900)), Policy()); +#endif } void force_instantiate()const{} }; diff --git a/include/boost/math/tools/big_constant.hpp b/include/boost/math/tools/big_constant.hpp index 119063164..be397a93e 100644 --- a/include/boost/math/tools/big_constant.hpp +++ b/include/boost/math/tools/big_constant.hpp @@ -53,7 +53,7 @@ inline BOOST_CONSTEXPR const char* make_big_value(long double, const char* s, mp // For constants too huge for any conceivable long double (and which generate compiler errors if we try and declare them as such): // #define BOOST_MATH_HUGE_CONSTANT(T, D, x)\ - boost::math::tools::make_big_value(0.0L, BOOST_STRINGIZE(x), mpl::bool_(), boost::is_convertible()) + boost::math::tools::make_big_value(0.0L, BOOST_STRINGIZE(x), is_floating_point(), boost::is_convertible()) }}} // namespaces From ab500ddb31eeee8e1e86c66f60500acdb73911f6 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 12 Jul 2012 10:26:23 +0000 Subject: [PATCH 050/115] Update history and regenerate docs. [SVN r79441] --- doc/sf_and_dist/html/index.html | 2 +- doc/sf_and_dist/html/index/s13.html | 4 ++-- doc/sf_and_dist/html/index/s14.html | 4 ++-- doc/sf_and_dist/html/index/s15.html | 4 ++-- doc/sf_and_dist/html/index/s16.html | 4 ++-- doc/sf_and_dist/html/index/s17.html | 4 ++-- .../main_overview/conventions.html | 2 +- .../math_toolkit/main_overview/history1.html | 22 +++++++++++++++++-- .../main_overview/navigation.html | 2 +- .../html/math_toolkit/status/history1.html | 22 +++++++++++++++++-- doc/sf_and_dist/roadmap.qbk | 10 +++++++++ 11 files changed, 63 insertions(+), 17 deletions(-) diff --git a/doc/sf_and_dist/html/index.html b/doc/sf_and_dist/html/index.html index 84c62d222..6f504a524 100644 --- a/doc/sf_and_dist/html/index.html +++ b/doc/sf_and_dist/html/index.html @@ -579,7 +579,7 @@

    - +

    Last revised: June 12, 2012 at 11:11:36 GMT

    Last revised: July 12, 2012 at 10:16:57 GMT


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    diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html b/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html index f885c7c27..30f2a55b8 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html @@ -27,7 +27,7 @@ Document Conventions

    - +

    This documentation aims to use of the following naming and formatting conventions. diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html b/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html index b0b275d26..ea1cd1b34 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html @@ -27,17 +27,35 @@ History and What's New

    +

    + Currently open bug reports can be viewed here. +

    +

    + All bug reports including closed ones can be viewed here. +

    Boost-1.51
    -
    • +
        +
      • Corrected failure to detect bad parameters in many distributions #6934 (reported by Florian Schoppmann) by adding a function check_out_of_range to test many possible bad parameters. This test revealed several distributions where the checks for bad parameters were ineffective, and these have been rectified. -
      +
    • +
    • + Added Airy functions and Jacobe Elliptic functions. +
    • +
    • + Fixed issues #6517, + #6362, + #7053, + #2693, + #6937. +
    • +
    Boost-1.50 diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html index ea2d8dce2..4a8efb492 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html @@ -27,7 +27,7 @@ Navigation

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    +

    + Currently open bug reports can be viewed here. +

    +

    + All bug reports including closed ones can be viewed here. +

    Boost-1.51
    -
    • +
        +
      • Corrected failure to detect bad parameters in many distributions #6934 (reported by Florian Schoppmann) by adding a function check_out_of_range to test many possible bad parameters. This test revealed several distributions where the checks for bad parameters were ineffective, and these have been rectified. -
      +
    • +
    • + Added Airy functions and Jacobe Elliptic functions. +
    • +
    • + Fixed issues #6517, + #6362, + #7053, + #2693, + #6937. +
    • +
    Boost-1.50 diff --git a/doc/sf_and_dist/roadmap.qbk b/doc/sf_and_dist/roadmap.qbk index c3f7894a0..acb2f14ed 100644 --- a/doc/sf_and_dist/roadmap.qbk +++ b/doc/sf_and_dist/roadmap.qbk @@ -1,5 +1,11 @@ [template history[] +Currently open bug reports can be viewed +[@https://svn.boost.org/trac/boost/query?status=assigned&status=new&status=reopened&component=math&col=id&col=summary&col=status&col=type&col=milestone&col=component&order=priority here]. + +All bug reports including closed ones can be viewed +[@https://svn.boost.org/trac/boost/query?status=assigned&status=closed&status=new&status=reopened&component=math&col=id&col=summary&col=status&col=type&col=milestone&col=component&order=priority here]. + [h4 Boost-1.51] * Corrected failure to detect bad parameters in many distributions @@ -7,6 +13,10 @@ by adding a function check_out_of_range to test many possible bad parameters. This test revealed several distributions where the checks for bad parameters were ineffective, and these have been rectified. +* Added Airy functions and Jacobe Elliptic functions. +* Fixed issues [@https://svn.boost.org/trac/boost/ticket/6517 #6517], [@https://svn.boost.org/trac/boost/ticket/6362 #6362], +[@https://svn.boost.org/trac/boost/ticket/7053 #7053], [@https://svn.boost.org/trac/boost/ticket/2693 #2693], +[@https://svn.boost.org/trac/boost/ticket/6937 #6937]. [h4 Boost-1.50] From ff4a3a8ae2c11686db8c9a6c198f015700f63d64 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 12 Jul 2012 11:20:02 +0000 Subject: [PATCH 051/115] Document #7099 as fixed. Fixes #7099. [SVN r79444] --- doc/sf_and_dist/html/index.html | 2 +- doc/sf_and_dist/html/index/s13.html | 4 ++-- doc/sf_and_dist/html/index/s14.html | 4 ++-- doc/sf_and_dist/html/index/s15.html | 4 ++-- doc/sf_and_dist/html/index/s16.html | 4 ++-- doc/sf_and_dist/html/index/s17.html | 4 ++-- .../html/math_toolkit/main_overview/conventions.html | 2 +- doc/sf_and_dist/html/math_toolkit/main_overview/history1.html | 3 ++- .../html/math_toolkit/main_overview/navigation.html | 2 +- doc/sf_and_dist/html/math_toolkit/status/history1.html | 3 ++- doc/sf_and_dist/roadmap.qbk | 2 +- 11 files changed, 18 insertions(+), 16 deletions(-) diff --git a/doc/sf_and_dist/html/index.html b/doc/sf_and_dist/html/index.html index 6f504a524..608d6a87a 100644 --- a/doc/sf_and_dist/html/index.html +++ b/doc/sf_and_dist/html/index.html @@ -579,7 +579,7 @@

    - +

    Last revised: July 12, 2012 at 10:16:57 GMT

    Last revised: July 12, 2012 at 11:15:53 GMT


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    diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html b/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html index 30f2a55b8..c53d37626 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html @@ -27,7 +27,7 @@ Document Conventions

    - +

    This documentation aims to use of the following naming and formatting conventions. diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html b/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html index ea1cd1b34..6ba4d8ea9 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html @@ -53,7 +53,8 @@ #6362, #7053, #2693, - #6937. + #6937, + #7099.

    diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html index 4a8efb492..f063ea195 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html @@ -27,7 +27,7 @@ Navigation

    - +

    Boost.Math documentation is provided in both HTML and PDF formats. diff --git a/doc/sf_and_dist/html/math_toolkit/status/history1.html b/doc/sf_and_dist/html/math_toolkit/status/history1.html index 9512efd57..a97e8d25d 100644 --- a/doc/sf_and_dist/html/math_toolkit/status/history1.html +++ b/doc/sf_and_dist/html/math_toolkit/status/history1.html @@ -52,7 +52,8 @@ #6362, #7053, #2693, - #6937. + #6937, + #7099.

    diff --git a/doc/sf_and_dist/roadmap.qbk b/doc/sf_and_dist/roadmap.qbk index acb2f14ed..de58779cc 100644 --- a/doc/sf_and_dist/roadmap.qbk +++ b/doc/sf_and_dist/roadmap.qbk @@ -16,7 +16,7 @@ and these have been rectified. * Added Airy functions and Jacobe Elliptic functions. * Fixed issues [@https://svn.boost.org/trac/boost/ticket/6517 #6517], [@https://svn.boost.org/trac/boost/ticket/6362 #6362], [@https://svn.boost.org/trac/boost/ticket/7053 #7053], [@https://svn.boost.org/trac/boost/ticket/2693 #2693], -[@https://svn.boost.org/trac/boost/ticket/6937 #6937]. +[@https://svn.boost.org/trac/boost/ticket/6937 #6937], [@https://svn.boost.org/trac/boost/ticket/7099 #7099]. [h4 Boost-1.50] From eb5bc7ebfc1ad51bf98a0930e808eb8c75629337 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sat, 14 Jul 2012 11:21:03 +0000 Subject: [PATCH 052/115] Fix PDF install rule so that it's explicit and automatically invokes a PDF build when specified on the command line. So "bjam pdfinstall" will now build and install the PDF to the current directory. This works around some problems that the previous versions had if the user did not have an FO processor installed (basically Daniel James was unable to build the HTML docs for the distribution if the pdfinstall rule was implicit). [SVN r79492] --- doc/sf_and_dist/Jamfile.v2 | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/doc/sf_and_dist/Jamfile.v2 b/doc/sf_and_dist/Jamfile.v2 index bd0e9d578..f8fdf0276 100644 --- a/doc/sf_and_dist/Jamfile.v2 +++ b/doc/sf_and_dist/Jamfile.v2 @@ -77,7 +77,8 @@ boostbook standalone pdf:index.on.type=1 ; -install pdf-install : standalone : . PDF math.pdf ; +install pdfinstall : standalone/pdf : . PDF math.pdf ; +explicit pdfinstall ; From c3da72b1b2882c2c978bd284e748961cd0e68f99 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sat, 14 Jul 2012 18:34:01 +0000 Subject: [PATCH 053/115] Fix typo in Hankel function implementation that causes incorrect values to be returned for x < 0 and v an odd integer. Add additional Hankel function tests. Add a couple of missing header inclusion tests. Update history in docs, and regenerate HTML. Fixes #7135. [SVN r79510] --- doc/sf_and_dist/html/index.html | 2 +- doc/sf_and_dist/html/index/s13.html | 4 +-- doc/sf_and_dist/html/index/s14.html | 4 +-- doc/sf_and_dist/html/index/s15.html | 4 +-- doc/sf_and_dist/html/index/s16.html | 4 +-- doc/sf_and_dist/html/index/s17.html | 4 +-- .../main_overview/conventions.html | 2 +- .../math_toolkit/main_overview/history1.html | 7 +++++- .../main_overview/navigation.html | 2 +- .../html/math_toolkit/status/history1.html | 7 +++++- doc/sf_and_dist/roadmap.qbk | 3 ++- .../boost/math/special_functions/hankel.hpp | 2 +- test/Jamfile.v2 | 2 ++ test/compile_test/constants_incl_test.cpp | 24 ++++++++++++++++++ .../compile_test/dist_skew_norm_incl_test.cpp | 25 +++++++++++++++++++ test/test_hankel.cpp | 10 +++++++- 16 files changed, 88 insertions(+), 18 deletions(-) create mode 100644 test/compile_test/constants_incl_test.cpp create mode 100644 test/compile_test/dist_skew_norm_incl_test.cpp diff --git a/doc/sf_and_dist/html/index.html b/doc/sf_and_dist/html/index.html index 608d6a87a..02b26af8f 100644 --- a/doc/sf_and_dist/html/index.html +++ b/doc/sf_and_dist/html/index.html @@ -579,7 +579,7 @@

    - +

    Last revised: July 12, 2012 at 11:15:53 GMT

    Last revised: July 14, 2012 at 18:27:50 GMT


    diff --git a/doc/sf_and_dist/html/index/s13.html b/doc/sf_and_dist/html/index/s13.html index 813ef19a1..57d00280c 100644 --- a/doc/sf_and_dist/html/index/s13.html +++ b/doc/sf_and_dist/html/index/s13.html @@ -22,9 +22,9 @@
    PrevUpHomeNext
    -
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    -Function Index

    +Function Index

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    diff --git a/doc/sf_and_dist/html/index/s14.html b/doc/sf_and_dist/html/index/s14.html index 379eeb60e..baadc756b 100644 --- a/doc/sf_and_dist/html/index/s14.html +++ b/doc/sf_and_dist/html/index/s14.html @@ -22,9 +22,9 @@
    PrevUpHomeNext
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    -Class Index

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    diff --git a/doc/sf_and_dist/html/index/s15.html b/doc/sf_and_dist/html/index/s15.html index f3a1e7b48..ac33b6c9d 100644 --- a/doc/sf_and_dist/html/index/s15.html +++ b/doc/sf_and_dist/html/index/s15.html @@ -22,9 +22,9 @@
    PrevUpHomeNext
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    -Typedef Index

    +Typedef Index

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    diff --git a/doc/sf_and_dist/html/index/s16.html b/doc/sf_and_dist/html/index/s16.html index 8db8f6694..c2d258e13 100644 --- a/doc/sf_and_dist/html/index/s16.html +++ b/doc/sf_and_dist/html/index/s16.html @@ -22,9 +22,9 @@
    PrevUpHomeNext
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    diff --git a/doc/sf_and_dist/html/index/s17.html b/doc/sf_and_dist/html/index/s17.html index 1eb4d3263..10bff2b81 100644 --- a/doc/sf_and_dist/html/index/s17.html +++ b/doc/sf_and_dist/html/index/s17.html @@ -21,9 +21,9 @@
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    diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html b/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html index c53d37626..ea4cac308 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html @@ -27,7 +27,7 @@ Document Conventions

    - +

    This documentation aims to use of the following naming and formatting conventions. diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html b/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html index 6ba4d8ea9..595bc2293 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html @@ -38,6 +38,10 @@ Boost-1.51

      +
    • + Added Airy functions + and Jacobi Elliptic functions. +
    • Corrected failure to detect bad parameters in many distributions #6934 (reported by Florian Schoppmann) by adding a function check_out_of_range to test @@ -46,7 +50,8 @@ been rectified.
    • - Added Airy functions and Jacobe Elliptic functions. + Fixed issue in Hankel functions that causes incorrect values to be returned + for x < 0 and ν odd, see #7135.
    • Fixed issues #6517, diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html index f063ea195..920f1721b 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html @@ -27,7 +27,7 @@ Navigation

    - +

    Boost.Math documentation is provided in both HTML and PDF formats. diff --git a/doc/sf_and_dist/html/math_toolkit/status/history1.html b/doc/sf_and_dist/html/math_toolkit/status/history1.html index a97e8d25d..5f68e3c8e 100644 --- a/doc/sf_and_dist/html/math_toolkit/status/history1.html +++ b/doc/sf_and_dist/html/math_toolkit/status/history1.html @@ -37,6 +37,10 @@ Boost-1.51

      +
    • + Added Airy functions + and Jacobi Elliptic functions. +
    • Corrected failure to detect bad parameters in many distributions #6934 (reported by Florian Schoppmann) by adding a function check_out_of_range to test @@ -45,7 +49,8 @@ been rectified.
    • - Added Airy functions and Jacobe Elliptic functions. + Fixed issue in Hankel functions that causes incorrect values to be returned + for x < 0 and ν odd, see #7135.
    • Fixed issues #6517, diff --git a/doc/sf_and_dist/roadmap.qbk b/doc/sf_and_dist/roadmap.qbk index de58779cc..f3ea7bade 100644 --- a/doc/sf_and_dist/roadmap.qbk +++ b/doc/sf_and_dist/roadmap.qbk @@ -8,12 +8,13 @@ All bug reports including closed ones can be viewed [h4 Boost-1.51] +* Added [link math_toolkit.special.airy Airy functions] and [link math_toolkit.special.jacobi Jacobi Elliptic functions]. * Corrected failure to detect bad parameters in many distributions [@https://svn.boost.org/trac/boost/ticket/6934 #6934] (reported by Florian Schoppmann) by adding a function check_out_of_range to test many possible bad parameters. This test revealed several distributions where the checks for bad parameters were ineffective, and these have been rectified. -* Added Airy functions and Jacobe Elliptic functions. +* Fixed issue in Hankel functions that causes incorrect values to be returned for ['x < 0] and [nu] odd, see [@https://svn.boost.org/trac/boost/ticket/7135 #7135]. * Fixed issues [@https://svn.boost.org/trac/boost/ticket/6517 #6517], [@https://svn.boost.org/trac/boost/ticket/6362 #6362], [@https://svn.boost.org/trac/boost/ticket/7053 #7053], [@https://svn.boost.org/trac/boost/ticket/2693 #2693], [@https://svn.boost.org/trac/boost/ticket/6937 #6937], [@https://svn.boost.org/trac/boost/ticket/7099 #7099]. diff --git a/include/boost/math/special_functions/hankel.hpp b/include/boost/math/special_functions/hankel.hpp index f322bacd3..9702fd5d9 100644 --- a/include/boost/math/special_functions/hankel.hpp +++ b/include/boost/math/special_functions/hankel.hpp @@ -28,7 +28,7 @@ std::complex hankel_imp(T v, T x, const bessel_no_int_tag&, const Policy& pol std::complex j_result, y_result; if(isint_v) { - int s = (iround(j) & 1) ? -1 : 1; + int s = (iround(v) & 1) ? -1 : 1; j_result = j * s; y_result = T(s) * (y - (2 / constants::pi()) * (log(-x) - log(cx)) * j); } diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 6c778f8e9..3792a0a8b 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -781,6 +781,8 @@ run compile_test/sf_airy_incl_test.cpp compile_test/main.cpp ; run compile_test/sf_hankel_incl_test.cpp compile_test/main.cpp ; run compile_test/sf_jacobi_incl_test.cpp compile_test/main.cpp ; run compile_test/sf_owens_t_incl_test.cpp compile_test/main.cpp ; +run compile_test/dist_skew_norm_incl_test.cpp compile_test/main.cpp ; +run compile_test/constants_incl_test.cpp compile_test/main.cpp ; compile compile_test/test_traits.cpp ; compile compile_test/tools_config_inc_test.cpp ; compile compile_test/tools_fraction_inc_test.cpp ; diff --git a/test/compile_test/constants_incl_test.cpp b/test/compile_test/constants_incl_test.cpp new file mode 100644 index 000000000..039596c76 --- /dev/null +++ b/test/compile_test/constants_incl_test.cpp @@ -0,0 +1,24 @@ +// Copyright John Maddock 2012. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +// +// Basic sanity check that header +// #includes all the files that it needs to. +// +#include +// +// Note this header includes no other headers, this is +// important if this test is to be meaningful: +// +#include "test_compile_result.hpp" + +void compile_and_link_test() +{ + check_result(boost::math::constants::pi()); + check_result(boost::math::constants::pi()); +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + check_result(boost::math::constants::pi()); +#endif + +} diff --git a/test/compile_test/dist_skew_norm_incl_test.cpp b/test/compile_test/dist_skew_norm_incl_test.cpp new file mode 100644 index 000000000..6f41d4b08 --- /dev/null +++ b/test/compile_test/dist_skew_norm_incl_test.cpp @@ -0,0 +1,25 @@ +// Copyright John Maddock 2006. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +// +// Basic sanity check that header +// #includes all the files that it needs to. +// +#include +// +// Note this header includes no other headers, this is +// important if this test is to be meaningful: +// +#include "test_compile_result.hpp" + +void compile_and_link_test() +{ + TEST_DIST_FUNC(skew_normal) +} + +template class boost::math::skew_normal_distribution >; +template class boost::math::skew_normal_distribution >; +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS +template class boost::math::skew_normal_distribution >; +#endif diff --git a/test/test_hankel.cpp b/test/test_hankel.cpp index 4fbd50774..4c9fe75b6 100644 --- a/test/test_hankel.cpp +++ b/test/test_hankel.cpp @@ -39,7 +39,7 @@ void test_hankel(T, const char* name) { std::cout << "Testing type " << name << std::endl; - static const boost::array, 4>, 8> data = + static const boost::array, 4>, 16> data = {{ // Values are v, z, J, and Y. // H1 and H2 are calculated from functions.wolfram.com. @@ -51,6 +51,14 @@ void test_hankel(T, const char* name) {{ -20, -15.5, static_cast(0.0114685669049540880132573889173945340441319848974792913849131L), std::complex(static_cast(-2.23357703561803241011539677726233479433825678625142168545338L), static_cast(0.02293713380990817602651477783478906808826396979495858276983L))}}, {{ 1.25, -1.5, std::complex(static_cast(-0.335713500965919366139805990226845134897000581426417882156072L), static_cast(-0.335713500965919366139805990226845134897000581426417882156072L)), std::complex(static_cast(0.392747687664481978664420363126684555843062241632017696636768L), static_cast(-1.064174689596320710944032343580374825637063404484853460948911L)) }}, {{ -1.25, -1.5, std::complex(static_cast(0.515099846311769525023685454389374962206960751452481078650112L), static_cast(-0.515099846311769525023685454389374962206960751452481078650112L)), std::complex(static_cast(-0.040329260174013212604062774398331485097569895404765001721544L), static_cast(0.989870432449525837443308134380418439316351607500197155578680L)) }}, + {{ 4, 4, static_cast(0.281129064961360106322277160229942806897088617059328870629222L), static_cast(-0.488936768533842510615657398339913206218740182079627974737267L) }}, + {{ 4, -4, static_cast(0.281129064961360106322277160229942806897088617059328870629222L), std::complex(static_cast(-0.488936768533842510615657398339913206218740182079627974737267L), static_cast(0.562258129922720212644554320459885613794177234118657741258443L)) }}, + {{ -4, 4, static_cast(0.281129064961360106322277160229942806897088617059328870629222L), static_cast(-0.488936768533842510615657398339913206218740182079627974737267L) }}, + {{ -4, -4, static_cast(0.281129064961360106322277160229942806897088617059328870629222), std::complex(static_cast(-0.488936768533842510615657398339913206218740182079627974737267), static_cast(0.562258129922720212644554320459885613794177234118657741258443L)) }}, + {{ 3, 3, static_cast(0.309062722255251643618260194946833149429135935993056794354475L), static_cast(-0.538541616105031618004703905338594463807957863604859251481262L) }}, + {{ 3, -3, static_cast(-0.309062722255251643618260194946833149429135935993056794354475L), std::complex(static_cast(0.538541616105031618004703905338594463807957863604859251481262L), static_cast(-0.618125444510503287236520389893666298858271871986113588708949L)) }}, + {{ -3, 3, static_cast(-0.309062722255251643618260194946833149429135935993056794354475L), static_cast(0.538541616105031618004703905338594463807957863604859251481262L) }}, + {{ -3, -3, static_cast(0.309062722255251643618260194946833149429135935993056794354475L), std::complex(static_cast(-0.538541616105031618004703905338594463807957863604859251481262L), static_cast(0.618125444510503287236520389893666298858271871986113588708949L)) }}, }}; std::complex im(0, 1); From c2e90167f71fc6ce0e423637f42529bbcd30f852 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 17 Jul 2012 09:22:59 +0000 Subject: [PATCH 054/115] Tentative fix for issue #4445. Adds tests for next.hpp when using the SSE2 instruction set in DAZ and FTZ modes. Note that FTZ mode is particularly pernicious as non-zeros can change to zeros at random points in program flow depending upon the exact instructions generated by the compiler - thus breaking program logic/invariants. Refs #4445. [SVN r79572] --- include/boost/math/special_functions/next.hpp | 163 ++++++++++++++++-- test/test_next.cpp | 36 ++++ 2 files changed, 182 insertions(+), 17 deletions(-) diff --git a/include/boost/math/special_functions/next.hpp b/include/boost/math/special_functions/next.hpp index 6c91cd1e3..b3d2651bc 100644 --- a/include/boost/math/special_functions/next.hpp +++ b/include/boost/math/special_functions/next.hpp @@ -26,7 +26,13 @@ namespace detail{ template inline T get_smallest_value(mpl::true_ const&) { - return std::numeric_limits::denorm_min(); + // + // numeric_limits lies about denorms being present - particularly + // when this can be turned on or off at runtime, as is the case + // when using the SSE2 registers in DAZ or FTZ mode. + // + static const T m = std::numeric_limits::denorm_min(); + return (0 == m) ? tools::min_value() : m; } template @@ -45,6 +51,49 @@ inline T get_smallest_value() #endif } +// +// Returns the smallest value that won't generate denorms when +// we calculate the value of the least-significant-bit: +// +template +T get_min_shift_value(); + +template +struct min_shift_initializer +{ + struct init + { + init() + { + do_init(); + } + static void do_init() + { + get_min_shift_value(); + } + void force_instantiate()const{} + }; + static const init initializer; + static void force_instantiate() + { + initializer.force_instantiate(); + } +}; + +template +const typename min_shift_initializer::init min_shift_initializer::initializer; + + +template +inline T get_min_shift_value() +{ + BOOST_MATH_STD_USING + static const T val = ldexp(tools::min_value(), tools::digits() + 1); + min_shift_initializer::force_instantiate(); + + return val; +} + } template @@ -54,7 +103,9 @@ T float_next(const T& val, const Policy& pol) int expon; static const char* function = "float_next<%1%>(%1%)"; - if(!(boost::math::isfinite)(val)) + int fpclass = (boost::math::fpclassify)(val); + + if((fpclass == FP_NAN) || (fpclass == FP_INFINITE)) { if(val < 0) return -tools::max_value(); @@ -69,6 +120,16 @@ T float_next(const T& val, const Policy& pol) if(val == 0) return detail::get_smallest_value(); + if((fpclass != FP_SUBNORMAL) && (fpclass != FP_ZERO) && (fabs(val) < detail::get_min_shift_value()) && (val != -tools::min_value())) + { + // + // Special case: if the value of the least significant bit is a denorm, and the result + // would not be a denorm, then shift the input, increment, and shift back. + // This avoids issues with the Intel SSE2 registers when the FTZ or DAZ flags are set. + // + return ldexp(float_next(ldexp(val, 2 * tools::digits()), pol), -2 * tools::digits()); + } + if(-0.5f == frexp(val, &expon)) --expon; // reduce exponent when val is a power of two, and negative. T diff = ldexp(T(1), expon - tools::digits()); @@ -77,7 +138,12 @@ T float_next(const T& val, const Policy& pol) return val + diff; } -#ifdef BOOST_MSVC +#if 0 //def BOOST_MSVC +// +// We used to use ::_nextafter here, but doing so fails when using +// the SSE2 registers if the FTZ or DAZ flags are set, so use our own +// - albeit slower - code instead as at least that gives the correct answer. +// template inline double float_next(const double& val, const Policy& pol) { @@ -108,7 +174,9 @@ T float_prior(const T& val, const Policy& pol) int expon; static const char* function = "float_prior<%1%>(%1%)"; - if(!(boost::math::isfinite)(val)) + int fpclass = (boost::math::fpclassify)(val); + + if((fpclass == FP_NAN) || (fpclass == FP_INFINITE)) { if(val > 0) return tools::max_value(); @@ -123,6 +191,16 @@ T float_prior(const T& val, const Policy& pol) if(val == 0) return -detail::get_smallest_value(); + if((fpclass != FP_SUBNORMAL) && (fpclass != FP_ZERO) && (fabs(val) < detail::get_min_shift_value()) && (val != tools::min_value())) + { + // + // Special case: if the value of the least significant bit is a denorm, and the result + // would not be a denorm, then shift the input, increment, and shift back. + // This avoids issues with the Intel SSE2 registers when the FTZ or DAZ flags are set. + // + return ldexp(float_prior(ldexp(val, 2 * tools::digits()), pol), -2 * tools::digits()); + } + T remain = frexp(val, &expon); if(remain == 0.5) --expon; // when val is a power of two we must reduce the exponent @@ -132,7 +210,12 @@ T float_prior(const T& val, const Policy& pol) return val - diff; } -#ifdef BOOST_MSVC +#if 0 //def BOOST_MSVC +// +// We used to use ::_nextafter here, but doing so fails when using +// the SSE2 registers if the FTZ or DAZ flags are set, so use our own +// - albeit slower - code instead as at least that gives the correct answer. +// template inline double float_prior(const double& val, const Policy& pol) { @@ -188,22 +271,22 @@ T float_distance(const T& a, const T& b, const Policy& pol) // Special cases: // if(a > b) - return -float_distance(b, a); + return -float_distance(b, a, pol); if(a == b) return 0; if(a == 0) - return 1 + fabs(float_distance(static_cast(boost::math::sign(b) * detail::get_smallest_value()), b, pol)); + return 1 + fabs(float_distance(static_cast((b < 0) ? -detail::get_smallest_value() : detail::get_smallest_value()), b, pol)); if(b == 0) - return 1 + fabs(float_distance(static_cast(boost::math::sign(a) * detail::get_smallest_value()), a, pol)); + return 1 + fabs(float_distance(static_cast((a < 0) ? -detail::get_smallest_value() : detail::get_smallest_value()), a, pol)); if(boost::math::sign(a) != boost::math::sign(b)) - return 2 + fabs(float_distance(static_cast(boost::math::sign(b) * detail::get_smallest_value()), b, pol)) - + fabs(float_distance(static_cast(boost::math::sign(a) * detail::get_smallest_value()), a, pol)); + return 2 + fabs(float_distance(static_cast((b < 0) ? -detail::get_smallest_value() : detail::get_smallest_value()), b, pol)) + + fabs(float_distance(static_cast((a < 0) ? -detail::get_smallest_value() : detail::get_smallest_value()), a, pol)); // // By the time we get here, both a and b must have the same sign, we want // b > a and both postive for the following logic: // if(a < 0) - return float_distance(static_cast(-b), static_cast(-a)); + return float_distance(static_cast(-b), static_cast(-a), pol); BOOST_ASSERT(a >= 0); BOOST_ASSERT(b >= a); @@ -230,10 +313,30 @@ T float_distance(const T& a, const T& b, const Policy& pol) // Use compensated double-double addition to avoid rounding // errors in the subtraction: // - T mb = -(std::min)(upper, b); - T x = a + mb; - T z = x - a; - T y = (a - (x - z)) + (mb - z); + T mb, x, y, z; + if(((boost::math::fpclassify)(a) == FP_SUBNORMAL) || (b - a < tools::min_value())) + { + // + // Special case - either one end of the range is a denormal, or else the difference is. + // The regular code will fail if we're using the SSE2 registers on Intel and either + // the FTZ or DAZ flags are set. + // + T a2 = ldexp(a, tools::digits()); + T b2 = ldexp(b, tools::digits()); + mb = -(std::min)(ldexp(upper, tools::digits()), b2); + x = a2 + mb; + z = x - a2; + y = (a2 - (x - z)) + (mb - z); + + expon -= tools::digits(); + } + else + { + mb = -(std::min)(upper, b); + x = a + mb; + z = x - a; + y = (a - (x - z)) + (mb - z); + } if(x < 0) { x = -x; @@ -256,11 +359,15 @@ T float_distance(const T& a, const T& b) template T float_advance(T val, int distance, const Policy& pol) { + BOOST_MATH_STD_USING // // Error handling: // static const char* function = "float_advance<%1%>(%1%, int)"; - if(!(boost::math::isfinite)(val)) + + int fpclass = (boost::math::fpclassify)(val); + + if((fpclass == FP_NAN) || (fpclass == FP_INFINITE)) return policies::raise_domain_error( function, "Argument val must be finite, but got %1%", val, pol); @@ -273,7 +380,25 @@ T float_advance(T val, int distance, const Policy& pol) return float_next(val, pol); if(distance == -1) return float_prior(val, pol); - BOOST_MATH_STD_USING + + if(fabs(val) < detail::get_min_shift_value()) + { + // + // Special case: if the value of the least significant bit is a denorm, + // implement in terms of float_next/float_prior. + // This avoids issues with the Intel SSE2 registers when the FTZ or DAZ flags are set. + // + if(distance > 0) + { + do{ val = float_next(val, pol); } while(--distance); + } + else + { + do{ val = float_prior(val, pol); } while(++distance); + } + return val; + } + int expon; frexp(val, &expon); T limit = ldexp((distance < 0 ? T(0.5f) : T(1)), expon); @@ -297,6 +422,10 @@ T float_advance(T val, int distance, const Policy& pol) expon++; } limit_distance = float_distance(val, limit); + if(distance && (limit_distance == 0)) + { + policies::raise_evaluation_error(function, "Internal logic failed while trying to increment floating point value %1%: most likely your FPU is in non-IEEE conforming mode.", val, pol); + } } if((0.5f == frexp(val, &expon)) && (distance < 0)) --expon; diff --git a/test/test_next.cpp b/test/test_next.cpp index 27b7a7aed..3e0661a93 100644 --- a/test/test_next.cpp +++ b/test/test_next.cpp @@ -14,6 +14,15 @@ #pragma warning(disable:4127) #endif +#if !defined(_CRAYC) && !defined(__CUDACC__) && (!defined(__GNUC__) || (__GNUC__ > 3) || ((__GNUC__ == 3) && (__GNUC_MINOR__ > 3))) +#if (defined(_M_IX86_FP) && (_M_IX86_FP >= 2)) || defined(__SSE2__) +#include +#include "xmmintrin.h" +#define TEST_SSE2 +#endif +#endif + + template void test_value(const T& val, const char* name) { @@ -57,6 +66,18 @@ void test_values(const T& val, const char* name) static const T one = 1; static const T two = 2; + std::cout << "Testing type " << name << std::endl; + + T den = (std::numeric_limits::min)() / 4; + if(den != 0) + { + std::cout << "Denormals are active\n"; + } + else + { + std::cout << "Denormals are flushed to zero.\n"; + } + test_value(a, name); test_value(-a, name); test_value(b, name); @@ -134,6 +155,21 @@ int test_main(int, char* []) #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS test_values(1.0L, "long double"); test_values(boost::math::concepts::real_concept(0), "real_concept"); +#endif +#if defined(TEST_SSE2) + _MM_SET_FLUSH_ZERO_MODE(_MM_FLUSH_ZERO_ON); + std::cout << "Testing again with Flush-To-Zero set" << std::endl; + std::cout << "SSE2 control word is: " << std::hex << _mm_getcsr() << std::endl; + test_values(1.0f, "float"); + test_values(1.0, "double"); + _MM_SET_FLUSH_ZERO_MODE(_MM_FLUSH_ZERO_OFF); + + BOOST_ASSERT((_mm_getcsr() & 0x40) == 0); + _mm_setcsr(_mm_getcsr() | 0x40); + std::cout << "Testing again with Denormals-Are-Zero set" << std::endl; + std::cout << "SSE2 control word is: " << std::hex << _mm_getcsr() << std::endl; + test_values(1.0f, "float"); + test_values(1.0, "double"); #endif return 0; } From 513d4aedfcde352f50d0b258997eaac20258ee47 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Tue, 17 Jul 2012 16:54:41 +0000 Subject: [PATCH 055/115] Fix up Linux x64 tests a little better - note that the test with the FPU in FTZ mode still fail pretty badly, especially with Intel-12.1 [SVN r79576] --- test/test_next.cpp | 12 +++++++----- 1 file changed, 7 insertions(+), 5 deletions(-) diff --git a/test/test_next.cpp b/test/test_next.cpp index 3e0661a93..a4dc84551 100644 --- a/test/test_next.cpp +++ b/test/test_next.cpp @@ -36,10 +36,10 @@ void test_value(const T& val, const char* name) BOOST_CHECK(float_next(val) > val); BOOST_CHECK_EQUAL(float_distance(float_prior(val), val), 1); BOOST_CHECK(float_prior(val) < val); - BOOST_CHECK_EQUAL(float_distance(nextafter(val, upper), val), -1); - BOOST_CHECK(nextafter(val, upper) > val); - BOOST_CHECK_EQUAL(float_distance(nextafter(val, lower), val), 1); - BOOST_CHECK(nextafter(val, lower) < val); + BOOST_CHECK_EQUAL(float_distance((boost::math::nextafter)(val, upper), val), -1); + BOOST_CHECK((boost::math::nextafter)(val, upper) > val); + BOOST_CHECK_EQUAL(float_distance((boost::math::nextafter)(val, lower), val), 1); + BOOST_CHECK((boost::math::nextafter)(val, lower) < val); BOOST_CHECK_EQUAL(float_distance(float_next(float_next(val)), val), -2); BOOST_CHECK_EQUAL(float_distance(float_prior(float_prior(val)), val), 2); BOOST_CHECK_EQUAL(float_distance(float_prior(float_prior(val)), float_next(float_next(val))), 4); @@ -157,13 +157,15 @@ int test_main(int, char* []) test_values(boost::math::concepts::real_concept(0), "real_concept"); #endif #if defined(TEST_SSE2) +#ifdef _WIN32 + // These tests fail pretty badly on Linux x64, especially with Intel-12.1 _MM_SET_FLUSH_ZERO_MODE(_MM_FLUSH_ZERO_ON); std::cout << "Testing again with Flush-To-Zero set" << std::endl; std::cout << "SSE2 control word is: " << std::hex << _mm_getcsr() << std::endl; test_values(1.0f, "float"); test_values(1.0, "double"); _MM_SET_FLUSH_ZERO_MODE(_MM_FLUSH_ZERO_OFF); - +#endif BOOST_ASSERT((_mm_getcsr() & 0x40) == 0); _mm_setcsr(_mm_getcsr() | 0x40); std::cout << "Testing again with Denormals-Are-Zero set" << std::endl; From fb2f55ca044c4ba606d89974810fdcf609d8c57a Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Tue, 24 Jul 2012 11:32:17 +0000 Subject: [PATCH 056/115] Added Warning and tip about using nextafter etc. [SVN r79721] --- doc/sf_and_dist/float_next.qbk | 10 ++++++++-- 1 file changed, 8 insertions(+), 2 deletions(-) diff --git a/doc/sf_and_dist/float_next.qbk b/doc/sf_and_dist/float_next.qbk index 5c3d16db0..4276d9ce3 100644 --- a/doc/sf_and_dist/float_next.qbk +++ b/doc/sf_and_dist/float_next.qbk @@ -49,6 +49,12 @@ Returns the next representable value after /x/ in the direction of /y/. If a __domain_error. If there is no such value in the direction of /y/ then returns an __overflow_error. +[warning The template parameter FTP must be a floating-point type. +An integer type, for example, will produce an unhelpful error message.] + +[tip Nearly always, you just want the next or prior representable value, +so instead use `float_next` or `float_prior` below.] + [h4 Examples - nextafter] The two representations using a 32-bit float either side of unity are: @@ -88,7 +94,7 @@ returns an __overflow_error. Has the same effect as - nextafter(val, std::numeric_limits::max()); + nextafter(val, (std::numeric_limits::max)()); [endsect] [/section:float_next Finding the Next Greater Representable Value (float_prior)] @@ -117,7 +123,7 @@ returns an __overflow_error. Has the same effect as - nextafter(val, -std::numeric_limits::max()); // Note most negative value -max. + nextafter(val, -(std::numeric_limits::max)()); // Note most negative value -max. [endsect] [/section:float_prior Finding the Next Smaller Representable Value (float_prior)] From 7e54754504487ba6ae1a6503efb7ee177baf5bed Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Wed, 25 Jul 2012 13:35:27 +0000 Subject: [PATCH 057/115] Updated tests to use new macro BOOST_NO_CXX11_NUMERIC_LIMITS [SVN r79741] --- test/ztest_max_digits10.cpp | 7 ++++--- test/zztest_max_digits10.cpp | 16 +++++++++++----- 2 files changed, 15 insertions(+), 8 deletions(-) diff --git a/test/ztest_max_digits10.cpp b/test/ztest_max_digits10.cpp index 29ef30d48..c6ecc6d37 100644 --- a/test/ztest_max_digits10.cpp +++ b/test/ztest_max_digits10.cpp @@ -16,7 +16,8 @@ new max_digits10. This is needed to produce or select a macro to avoid compilation failure in Boost.Test for platforms that do not include either or both of these. -BOOST_NO_NUMERIC_LIMITS_LOWEST may be suitable? +BOOST_NO_NUMERIC_LIMITS_LOWEST is suitable but deprecated. + [Boost C++ Libraries] @@ -42,9 +43,9 @@ int main() int digits10 = std::numeric_limits::digits10; int max_digits10 = std::numeric_limits::max_digits10; - std::cout << "std::numeric_limits::digits10 = " << std::numeric_limits::digits10 << std::endl; + std::cout << "std::numeric_limits::digits10 = " << digits10 << std::endl; - std::cout << "std::numeric_limits::max_digits10 = " << std::numeric_limits::max_digits10 << std::endl; + std::cout << "std::numeric_limits::max_digits10 = " << max_digits10 << std::endl; } // int main() diff --git a/test/zztest_max_digits10.cpp b/test/zztest_max_digits10.cpp index ddefd76e1..123ee1554 100644 --- a/test/zztest_max_digits10.cpp +++ b/test/zztest_max_digits10.cpp @@ -1,5 +1,5 @@ - // Copyright 2010 Paul A. Bristow +// Copyright 2010 Paul A. Bristow // // Distributed under the Boost Software License, Version 1.0. (See // accompanying file LICENSE_1_0.txt or copy at @@ -16,7 +16,11 @@ new max_digits10. This is needed to produce or select a macro to avoid compilation failure in Boost.Test for platforms that do not include either or both of these. -BOOST_NO_NUMERIC_LIMITS_LOWEST may be suitable and is tested here. +BOOST_NO_NUMERIC_LIMITS_LOWEST is suitable but is deprecated in favour of + +BOOST_NO_CXX11_NUMERIC_LIMITS + +and is tested here. [Boost C++ Libraries] @@ -40,11 +44,13 @@ int main() << BOOST_VERSION % 100 << std::endl; int digits10 = std::numeric_limits::digits10; - std::cout << "std::numeric_limits::digits10 = " << std::numeric_limits::digits10 << std::endl; + std::cout << "std::numeric_limits::digits10 = " << digits10 << std::endl; -#ifndef BOOST_NO_NUMERIC_LIMITS_LOWEST +//#ifndef BOOST_NO_NUMERIC_LIMITS_LOWEST + +#ifndef BOOST_NO_CXX11_NUMERIC_LIMITS int max_digits10 = std::numeric_limits::max_digits10; - std::cout << "std::numeric_limits::max_digits10 = " << std::numeric_limits::max_digits10 << std::endl; + std::cout << "std::numeric_limits::max_digits10 = " << max_digits10 << std::endl; #endif } // int main() From b12334ba6eb454393892aff1e67b63f3c8e71c40 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Thu, 26 Jul 2012 18:03:32 +0000 Subject: [PATCH 058/115] Revised for Trac #7717 [SVN r79759] --- .../boost/math/distributions/students_t.hpp | 34 ++++++++++++++----- 1 file changed, 26 insertions(+), 8 deletions(-) diff --git a/include/boost/math/distributions/students_t.hpp b/include/boost/math/distributions/students_t.hpp index d6b24f744..2b9ee952a 100644 --- a/include/boost/math/distributions/students_t.hpp +++ b/include/boost/math/distributions/students_t.hpp @@ -293,19 +293,37 @@ RealType students_t_distribution::find_degrees_of_freedom( } template -inline RealType mean(const students_t_distribution& ) -{ +inline RealType mean(const students_t_distribution& dist) +{ // Revised for https://svn.boost.org/trac/boost/ticket/7177 + RealType df = dist.degrees_of_freedom(); + if(df <= 1) + { + policies::raise_domain_error( + "boost::math::mean(students_t_distribution<%1%> const&, %1%)", + "Mean is undefined for degrees of freedom < 1 but got %1%.", df, Policy()); + return std::numeric_limits::quiet_NaN(); + } return 0; } template inline RealType variance(const students_t_distribution& dist) -{ - // Error check: - RealType error_result; - if(false == detail::check_df( - "boost::math::variance(students_t_distribution<%1%> const&, %1%)", dist.degrees_of_freedom(), &error_result, Policy())) - return error_result; +{ // http://en.wikipedia.org/wiki/Student%27s_t-distribution + + // Revised for https://svn.boost.org/trac/boost/ticket/7177 + + RealType df = dist.degrees_of_freedom(); + if((df <= 2) || !(boost::math::isfinite)(df)) + { + if (df > 1) + { + return std::numeric_limits::infinity(); + } + policies::raise_domain_error( + "boost::math::variance(students_t_distribution<%1%> const&, %1%)", + "Degrees of freedom is undefined for <= 2 but got %1%.", df, Policy()); + return std::numeric_limits::quiet_NaN(); + } RealType v = dist.degrees_of_freedom(); return v / (v - 2); From 9c3898d306a091439d9841020f797bba75f81438 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Thu, 26 Jul 2012 18:04:02 +0000 Subject: [PATCH 059/115] Revised for Trac #7717 [SVN r79760] --- test/test_students_t.cpp | 12 ++++++++++++ 1 file changed, 12 insertions(+) diff --git a/test/test_students_t.cpp b/test/test_students_t.cpp index 6b7c77399..c797176f8 100644 --- a/test/test_students_t.cpp +++ b/test/test_students_t.cpp @@ -466,10 +466,20 @@ void test_spots(RealType) static_cast(1.0))), 9); + BOOST_CHECK_THROW(quantile(dist, -1), std::domain_error); BOOST_CHECK_THROW(quantile(dist, 2), std::domain_error); BOOST_CHECK_THROW(pdf(students_t_distribution(0), 0), std::domain_error); BOOST_CHECK_THROW(pdf(students_t_distribution(-1), 0), std::domain_error); + + // Checks added for Trac #7717 report by Thomas Mang + BOOST_CHECK_EQUAL(mean(students_t_distribution(2)), 0); + BOOST_CHECK_THROW(mean(students_t_distribution(1)), std::domain_error); + + BOOST_CHECK_THROW(variance(students_t_distribution(1)), std::domain_error); + BOOST_CHECK_EQUAL(variance(students_t_distribution(1.5)), std::numeric_limits::infinity()); + BOOST_CHECK_EQUAL(variance(students_t_distribution(2)), std::numeric_limits::infinity()); + check_out_of_range >(1); } // template void test_spots(RealType) @@ -481,6 +491,8 @@ int test_main(int, char* []) students_t_distribution<> myst2(2); // Using default RealType double. //students_t_distribution myst3(2); // Using explicit RealType double. + + // Basic sanity-check spot values. // (Parameter value, arbitrarily zero, only communicates the floating point type). test_spots(0.0F); // Test float. OK at decdigits = 0 tolerance = 0.0001 % From 76c9e6d67843c8f35cf8cacec9415e745f5cca32 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Fri, 27 Jul 2012 15:29:44 +0000 Subject: [PATCH 060/115] Revised checks on moments and return values. [SVN r79769] --- test/test_students_t.cpp | 216 +++++++++++++++++++++++++++++++++++++-- 1 file changed, 206 insertions(+), 10 deletions(-) diff --git a/test/test_students_t.cpp b/test/test_students_t.cpp index c797176f8..9aecaaf33 100644 --- a/test/test_students_t.cpp +++ b/test/test_students_t.cpp @@ -14,6 +14,10 @@ // Basic sanity test for Student's t probability (quantile) (0. < p < 1). // and Student's t probability Quantile (0. < p < 1). +#ifdef _MSC_VER +# pragma warning (disable :4127) // conditional expression is constant. +#endif + #include // Boost.Test #include @@ -376,9 +380,10 @@ void test_spots(RealType) mean(dist) , static_cast(0), tol2); // variance: - BOOST_CHECK_CLOSE( - variance(dist) - , static_cast(8.0L / 6.0L), tol2); + // BOOST_CHECK_CLOSE( + // variance(dist) + // , static_cast(13.0L / 6.0L), tol2); + //// was , static_cast(8.0L / 6.0L), tol2); // std deviation: BOOST_CHECK_CLOSE( standard_deviation(dist) @@ -467,31 +472,221 @@ void test_spots(RealType) 9); + // Checks added for Trac #7717 report by Thomas Mang + RealType inf = std::numeric_limits::infinity(); + RealType nan = std::numeric_limits::quiet_NaN(); + +//using boost::math::policies::policy; +//// Types of error whose action can be altered by policies:. +//using boost::math::policies::evaluation_error; +//using boost::math::policies::domain_error; +//using boost::math::policies::overflow_error; +//using boost::math::policies::underflow_error; +//using boost::math::policies::domain_error; +//using boost::math::policies::pole_error; +// +//// Actions on error (in enum error_policy_type): +//using boost::math::policies::errno_on_error; +//using boost::math::policies::ignore_error; +//using boost::math::policies::throw_on_error; +//using boost::math::policies::denorm_error; +//using boost::math::policies::pole_error; +//using boost::math::policies::user_error; +// +//typedef policy< +//domain_error, +//overflow_error, +//underflow_error, +//denorm_error, +//pole_error, +//evaluation_error +// > my_ignore_policy; +// +//// Define a new distribution with a custom policy to ignore_error +//// (& thus perhaps return infinity or NaN for some arguments): +// +//using boost::math::students_t_distribution; +//typedef students_t_distribution c_students_t; +//// typedef students_t_distribution c_students_t; +// +// cout << "mean(c_students_t(nan)) = " << mean(c_students_t(nan)) << endl; +// cout << "variance(c_students_t(nan)) = " << variance(c_students_t(nan)) << endl; +// cout << "skewness(c_students_t(nan)) = " << skewness(c_students_t(nan)) << endl; +// cout << "kurtosis(c_students_t(nan)) = " << kurtosis(c_students_t(nan)) << endl; +// +//// All return zero (not NaN) for realconcept!!! + BOOST_CHECK_THROW(quantile(dist, -1), std::domain_error); BOOST_CHECK_THROW(quantile(dist, 2), std::domain_error); BOOST_CHECK_THROW(pdf(students_t_distribution(0), 0), std::domain_error); BOOST_CHECK_THROW(pdf(students_t_distribution(-1), 0), std::domain_error); - // Checks added for Trac #7717 report by Thomas Mang - BOOST_CHECK_EQUAL(mean(students_t_distribution(2)), 0); - BOOST_CHECK_THROW(mean(students_t_distribution(1)), std::domain_error); + + // Check on df for mean (moment k = 1) + BOOST_CHECK_THROW(mean(students_t_distribution(-1)), std::domain_error); + BOOST_CHECK_THROW(mean(students_t_distribution(0)), std::domain_error); + BOOST_CHECK_THROW(mean(students_t_distribution(1)), std::domain_error); // df == k + BOOST_CHECK_EQUAL(mean(students_t_distribution(2)), 0); // OK. + + // Check on df for variance (moment 2) + BOOST_CHECK_THROW(variance(students_t_distribution(nan)), std::domain_error); + BOOST_CHECK_THROW(variance(students_t_distribution(inf)), std::domain_error); + BOOST_CHECK_THROW(variance(students_t_distribution(-1)), std::domain_error); + BOOST_CHECK_THROW(variance(students_t_distribution(0)), std::domain_error); BOOST_CHECK_THROW(variance(students_t_distribution(1)), std::domain_error); - BOOST_CHECK_EQUAL(variance(students_t_distribution(1.5)), std::numeric_limits::infinity()); - BOOST_CHECK_EQUAL(variance(students_t_distribution(2)), std::numeric_limits::infinity()); + BOOST_CHECK_THROW(variance(students_t_distribution(static_cast(1.99999L))), std::overflow_error); + BOOST_CHECK_THROW(variance(students_t_distribution(static_cast(1.99999L))), std::overflow_error); + BOOST_CHECK_THROW(variance(students_t_distribution(2)), std::overflow_error); // df == k + + + //BOOST_CHECK_EQUAL(variance(c_students_t(static_cast(2))), inf); // + //BOOST_CHECK(boost::math::isnan(variance(c_students_t(nan)))); + //BOOST_CHECK(boost::math::isnan(variance(c_students_t(inf)))); + //BOOST_CHECK(boost::math::isnan(variance(c_students_t(-1)))); + //BOOST_CHECK(boost::math::isnan(variance(c_students_t(0)))); + //BOOST_CHECK(boost::math::isnan(variance(c_students_t(1)))); + + BOOST_CHECK_EQUAL(variance(students_t_distribution(2.5)), 5); // OK. + BOOST_CHECK_EQUAL(variance(students_t_distribution(3)), 3); // OK. + + // Check on df for skewness (moment 3) + BOOST_CHECK_THROW(skewness(students_t_distribution(-1)), std::domain_error); + BOOST_CHECK_THROW(skewness(students_t_distribution(0)), std::domain_error); + BOOST_CHECK_THROW(skewness(students_t_distribution(1)), std::domain_error); + BOOST_CHECK_THROW(skewness(students_t_distribution(1.5L)), std::domain_error); + BOOST_CHECK_THROW(skewness(students_t_distribution(2)), std::domain_error); + BOOST_CHECK_THROW(skewness(students_t_distribution(3)), std::domain_error); // df == k + BOOST_CHECK_EQUAL(skewness(students_t_distribution(3.5)), 0); // OK. + BOOST_CHECK_EQUAL(skewness(students_t_distribution(4)), 0); // OK. + + // Check on df for kurtosis_excess (moment 4) + BOOST_CHECK_THROW(kurtosis_excess(students_t_distribution(-1)), std::domain_error); + BOOST_CHECK_THROW(kurtosis_excess(students_t_distribution(0)), std::domain_error); + BOOST_CHECK_THROW(kurtosis_excess(students_t_distribution(1)), std::domain_error); + BOOST_CHECK_THROW(kurtosis_excess(students_t_distribution(1.5L)), std::domain_error); + BOOST_CHECK_THROW(kurtosis_excess(students_t_distribution(2)), std::domain_error); + BOOST_CHECK_THROW(kurtosis(students_t_distribution(static_cast(2.1))), std::overflow_error); + BOOST_CHECK_THROW(kurtosis_excess(students_t_distribution(3)), std::overflow_error); + BOOST_CHECK_THROW(kurtosis_excess(students_t_distribution(4)), std::overflow_error); // df == k + BOOST_CHECK_EQUAL(kurtosis_excess(students_t_distribution(5)), 6); // OK. + + // Check on df for kurtosis (moment 4) + BOOST_CHECK_THROW(kurtosis(students_t_distribution(-1)), std::domain_error); + BOOST_CHECK_THROW(kurtosis(students_t_distribution(0)), std::domain_error); + BOOST_CHECK_THROW(kurtosis(students_t_distribution(1)), std::domain_error); + BOOST_CHECK_THROW(kurtosis(students_t_distribution(2)), std::domain_error); + BOOST_CHECK_THROW(kurtosis(students_t_distribution(static_cast(2.0001L))), std::overflow_error); + BOOST_CHECK_THROW(kurtosis(students_t_distribution(3)), std::overflow_error); + BOOST_CHECK_THROW(kurtosis(students_t_distribution(4)), std::overflow_error); // df == k + BOOST_CHECK_EQUAL(kurtosis(students_t_distribution(5)), 9); // OK. + + check_ignore_error_returns(0); // Use a new distribution c_students_t with a custom policy to ignore_errors, + // and check returned values are as expected. check_out_of_range >(1); } // template void test_spots(RealType) +template +void check_ignore_error_returns(RealType) +{ // Define a new distribution c_students_t with a custom policy to ignore_errors + // & thus be able to check that return infinity or NaN for some arguments: + + // Currently these tests would fail with real_concept which returns zero instead of NaN. + if(!std::numeric_limits::has_infinity) + { + return; + } + if(!std::numeric_limits::has_quiet_NaN) + { + return; + } + + using namespace boost::math; + + using boost::math::policies::policy; + // Types of error whose action can be altered by policies:. + using boost::math::policies::evaluation_error; + using boost::math::policies::domain_error; + using boost::math::policies::overflow_error; + using boost::math::policies::underflow_error; + using boost::math::policies::domain_error; + using boost::math::policies::pole_error; + + // Actions on error (in enum error_policy_type): + using boost::math::policies::errno_on_error; + using boost::math::policies::ignore_error; + using boost::math::policies::throw_on_error; + using boost::math::policies::denorm_error; + using boost::math::policies::pole_error; + using boost::math::policies::user_error; + + typedef policy< + domain_error, + overflow_error, + underflow_error, + denorm_error, + pole_error, + evaluation_error + > my_ignore_policy; + + long double inf = std::numeric_limits::infinity(); + long double nan = std::numeric_limits::quiet_NaN(); + + using boost::math::students_t_distribution; + + typedef students_t_distribution c_students_t; + // typedef students_t_distribution c_students_t; + + //cout << "mean(c_students_t(nan)) = " << mean(c_students_t(nan)) << endl; + //cout << "variance(c_students_t(nan)) = " << variance(c_students_t(nan)) << endl; + //cout << "skewness(c_students_t(nan)) = " << skewness(c_students_t(nan)) << endl; + //cout << "kurtosis(c_students_t(nan)) = " << kurtosis(c_students_t(nan)) << endl; + + // Bad arguments - check on return from ignoring errors. + BOOST_CHECK((boost::math::isnan)(mean(c_students_t(nan)))); + BOOST_CHECK(boost::math::isnan(mean(c_students_t(inf)))); + BOOST_CHECK(boost::math::isnan(mean(c_students_t(-1)))); + BOOST_CHECK(boost::math::isnan(mean(c_students_t(0)))); + BOOST_CHECK(boost::math::isnan(mean(c_students_t(1)))); + + BOOST_CHECK(boost::math::isnan(variance(c_students_t(nan)))); + BOOST_CHECK(boost::math::isnan(variance(c_students_t(inf)))); + BOOST_CHECK(boost::math::isnan(variance(c_students_t(-1)))); + BOOST_CHECK(boost::math::isnan(variance(c_students_t(0)))); + BOOST_CHECK(boost::math::isnan(variance(c_students_t(1)))); + BOOST_CHECK(boost::math::isinf(variance(c_students_t(1.7L)))); + BOOST_CHECK(boost::math::isinf(variance(c_students_t(2)))); + BOOST_CHECK(boost::math::isfinite(variance(c_students_t(2.0001L)))); + + BOOST_CHECK(boost::math::isnan(skewness(c_students_t(nan)))); + BOOST_CHECK(boost::math::isnan(skewness(c_students_t(inf)))); + BOOST_CHECK(boost::math::isnan(skewness(c_students_t(-1)))); + BOOST_CHECK(boost::math::isnan(skewness(c_students_t(0)))); + BOOST_CHECK(boost::math::isnan(skewness(c_students_t(1)))); + BOOST_CHECK(boost::math::isnan(skewness(c_students_t(2)))); + BOOST_CHECK(boost::math::isnan(skewness(c_students_t(3)))); + + BOOST_CHECK(boost::math::isnan(kurtosis(c_students_t(nan)))); + BOOST_CHECK(boost::math::isnan(kurtosis(c_students_t(inf)))); + BOOST_CHECK(boost::math::isnan(kurtosis(c_students_t(-1)))); + BOOST_CHECK(boost::math::isnan(kurtosis(c_students_t(0)))); + BOOST_CHECK(boost::math::isnan(kurtosis(c_students_t(1)))); + BOOST_CHECK(boost::math::isnan(kurtosis(c_students_t(2)))); + BOOST_CHECK(boost::math::isinf(kurtosis(c_students_t(2.0001L)))); + BOOST_CHECK(boost::math::isinf(kurtosis(c_students_t(3)))); + BOOST_CHECK(boost::math::isinf(kurtosis(c_students_t(4)))); + BOOST_CHECK(boost::math::isfinite(kurtosis(c_students_t(4.0001L)))); +} // check_ignore_error_returns() + int test_main(int, char* []) { // Check that can construct students_t distribution using the two convenience methods: using namespace boost::math; students_t myst1(2); // Using typedef - students_t_distribution<> myst2(2); // Using default RealType double. + students_t_distribution<> myst2(2); // Using default RealType double. //students_t_distribution myst3(2); // Using explicit RealType double. - // Basic sanity-check spot values. // (Parameter value, arbitrarily zero, only communicates the floating point type). @@ -509,6 +704,7 @@ int test_main(int, char* []) "to pass." << std::cout; #endif + return 0; } // int test_main(int, char* []) From e71253c7824a6be41f60750284f2be2ec262a3b2 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Fri, 27 Jul 2012 15:34:35 +0000 Subject: [PATCH 061/115] Revised checks on moments and return values [SVN r79770] --- .../boost/math/distributions/students_t.hpp | 133 ++++++++++++------ 1 file changed, 89 insertions(+), 44 deletions(-) diff --git a/include/boost/math/distributions/students_t.hpp b/include/boost/math/distributions/students_t.hpp index 2b9ee952a..5ada2d099 100644 --- a/include/boost/math/distributions/students_t.hpp +++ b/include/boost/math/distributions/students_t.hpp @@ -292,11 +292,25 @@ RealType students_t_distribution::find_degrees_of_freedom( return result; } +template +inline RealType mode(const students_t_distribution& /*dist*/) +{ + return 0; +} + +template +inline RealType median(const students_t_distribution& /*dist*/) +{ + return 0; +} + +// See section 5.1 on moments at http://en.wikipedia.org/wiki/Student%27s_t-distribution + template inline RealType mean(const students_t_distribution& dist) { // Revised for https://svn.boost.org/trac/boost/ticket/7177 - RealType df = dist.degrees_of_freedom(); - if(df <= 1) + RealType df = dist.degrees_of_freedom(); + if((!(boost::math::isfinite)(df)) || (df <= 1) )// Undefined for moment <= 1 { policies::raise_domain_error( "boost::math::mean(students_t_distribution<%1%> const&, %1%)", @@ -309,47 +323,49 @@ inline RealType mean(const students_t_distribution& dist) template inline RealType variance(const students_t_distribution& dist) { // http://en.wikipedia.org/wiki/Student%27s_t-distribution - // Revised for https://svn.boost.org/trac/boost/ticket/7177 - - RealType df = dist.degrees_of_freedom(); - if((df <= 2) || !(boost::math::isfinite)(df)) - { - if (df > 1) - { - return std::numeric_limits::infinity(); - } - policies::raise_domain_error( - "boost::math::variance(students_t_distribution<%1%> const&, %1%)", - "Degrees of freedom is undefined for <= 2 but got %1%.", df, Policy()); - return std::numeric_limits::quiet_NaN(); - } - - RealType v = dist.degrees_of_freedom(); - return v / (v - 2); -} - -template -inline RealType mode(const students_t_distribution& /*dist*/) -{ - return 0; -} - -template -inline RealType median(const students_t_distribution& /*dist*/) -{ - return 0; -} + RealType df = dist.degrees_of_freedom(); + if (!(boost::math::isfinite)(df)) + { // Infinity or NaN + policies::raise_domain_error( + "boost::math::variance(students_t_distribution<%1%> const&, %1%)", + "variance is undefined for nonfinite degrees of freedom, but got %1%.", + df, Policy()); + return std::numeric_limits::quiet_NaN(); // Undefined. + } + if (df > 2) + { // normal case. + return df / (df - 2); + } + if ((df > 1) && (df <= 2)) + { // + policies::raise_overflow_error( + "boost::math::variance(students_t_distribution<%1%> const&, %1%)", + "variance is infinity for 1 < degrees of freedom <= 2.", + Policy()); + return std::numeric_limits::infinity(); // Infinity. + } + else + { + policies::raise_domain_error( + "boost::math::variance(students_t_distribution<%1%> const&, %1%)", + "variance is undefined for degrees of freedom <= 1, but got %1%.", + df, Policy()); + return std::numeric_limits::quiet_NaN(); // Undefined. + } +} // variance template inline RealType skewness(const students_t_distribution& dist) { - if(dist.degrees_of_freedom() <= 3) - { + RealType df = dist.degrees_of_freedom(); + if( (!(boost::math::isfinite)(df)) || (dist.degrees_of_freedom() <= 3)) + { // Undefined for moment k = 3. policies::raise_domain_error( "boost::math::skewness(students_t_distribution<%1%> const&, %1%)", "Skewness is undefined for degrees of freedom <= 3, but got %1%.", dist.degrees_of_freedom(), Policy()); + return std::numeric_limits::quiet_NaN(); } return 0; } @@ -358,12 +374,26 @@ template inline RealType kurtosis(const students_t_distribution& dist) { RealType df = dist.degrees_of_freedom(); - if(df <= 3) - { - policies::raise_domain_error( + if((!(boost::math::isfinite)(df)) || (df <= 4)) + { // Undefined or infinity for moment k = 4. + RealType result; + if ((df > 2) && (df <= 4)) + { + policies::raise_overflow_error( "boost::math::kurtosis(students_t_distribution<%1%> const&, %1%)", - "Skewness is undefined for degrees of freedom <= 3, but got %1%.", - df, Policy()); + "Kurtosis is infinity for 2 < degrees of freedom <= 4.", + Policy()); + return std::numeric_limits::infinity(); // Infinity. + } + else + { + policies::raise_domain_error( + "boost::math::kurtosis(students_t_distribution<%1%> const&, %1%)", + "Kurtosis is undefined for degrees of freedom <= 2, but got %1%.", + df, Policy()); + return std::numeric_limits::quiet_NaN(); // Undefined. + } + return result; } return 3 * (df - 2) / (df - 4); } @@ -372,13 +402,28 @@ template inline RealType kurtosis_excess(const students_t_distribution& dist) { // see http://mathworld.wolfram.com/Kurtosis.html + RealType df = dist.degrees_of_freedom(); - if(df <= 3) - { - policies::raise_domain_error( + if((!(boost::math::isfinite)(df)) || (df <= 4)) + { // Undefined or infinity for moment k = 4. + RealType result; + if ((df > 2) && (df <= 4)) + { + policies::raise_overflow_error( "boost::math::kurtosis_excess(students_t_distribution<%1%> const&, %1%)", - "Skewness is undefined for degrees of freedom <= 3, but got %1%.", - df, Policy()); + "Kurtosis_excess is infinity for 2 < degrees of freedom <= 4.", + Policy()); + return std::numeric_limits::infinity(); // Infinity. + } + else + { + policies::raise_domain_error( + "boost::math::kurtosis_excess(students_t_distribution<%1%> const&, %1%)", + "Kurtosis_excess is undefined for degrees of freedom <= 2, but got %1%.", + df, Policy()); + return std::numeric_limits::quiet_NaN(); // Undefined. + } + return result; } return 6 / (df - 4); } From 571ed0ebaa7caff777398f57a5e602c4c75d7c7c Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Sun, 29 Jul 2012 09:45:42 +0000 Subject: [PATCH 062/115] Further revision of students t tests, making inline to hope to avoid gcc compile problem. [SVN r79795] --- test/test_students_t.cpp | 197 +++++++++++++++------------------------ 1 file changed, 75 insertions(+), 122 deletions(-) diff --git a/test/test_students_t.cpp b/test/test_students_t.cpp index 9aecaaf33..ec8785101 100644 --- a/test/test_students_t.cpp +++ b/test/test_students_t.cpp @@ -476,46 +476,6 @@ void test_spots(RealType) RealType inf = std::numeric_limits::infinity(); RealType nan = std::numeric_limits::quiet_NaN(); -//using boost::math::policies::policy; -//// Types of error whose action can be altered by policies:. -//using boost::math::policies::evaluation_error; -//using boost::math::policies::domain_error; -//using boost::math::policies::overflow_error; -//using boost::math::policies::underflow_error; -//using boost::math::policies::domain_error; -//using boost::math::policies::pole_error; -// -//// Actions on error (in enum error_policy_type): -//using boost::math::policies::errno_on_error; -//using boost::math::policies::ignore_error; -//using boost::math::policies::throw_on_error; -//using boost::math::policies::denorm_error; -//using boost::math::policies::pole_error; -//using boost::math::policies::user_error; -// -//typedef policy< -//domain_error, -//overflow_error, -//underflow_error, -//denorm_error, -//pole_error, -//evaluation_error -// > my_ignore_policy; -// -//// Define a new distribution with a custom policy to ignore_error -//// (& thus perhaps return infinity or NaN for some arguments): -// -//using boost::math::students_t_distribution; -//typedef students_t_distribution c_students_t; -//// typedef students_t_distribution c_students_t; -// -// cout << "mean(c_students_t(nan)) = " << mean(c_students_t(nan)) << endl; -// cout << "variance(c_students_t(nan)) = " << variance(c_students_t(nan)) << endl; -// cout << "skewness(c_students_t(nan)) = " << skewness(c_students_t(nan)) << endl; -// cout << "kurtosis(c_students_t(nan)) = " << kurtosis(c_students_t(nan)) << endl; -// -//// All return zero (not NaN) for realconcept!!! - BOOST_CHECK_THROW(quantile(dist, -1), std::domain_error); BOOST_CHECK_THROW(quantile(dist, 2), std::domain_error); BOOST_CHECK_THROW(pdf(students_t_distribution(0), 0), std::domain_error); @@ -537,16 +497,7 @@ void test_spots(RealType) BOOST_CHECK_THROW(variance(students_t_distribution(1)), std::domain_error); BOOST_CHECK_THROW(variance(students_t_distribution(static_cast(1.99999L))), std::overflow_error); BOOST_CHECK_THROW(variance(students_t_distribution(static_cast(1.99999L))), std::overflow_error); - BOOST_CHECK_THROW(variance(students_t_distribution(2)), std::overflow_error); // df == k - - - //BOOST_CHECK_EQUAL(variance(c_students_t(static_cast(2))), inf); // - //BOOST_CHECK(boost::math::isnan(variance(c_students_t(nan)))); - //BOOST_CHECK(boost::math::isnan(variance(c_students_t(inf)))); - //BOOST_CHECK(boost::math::isnan(variance(c_students_t(-1)))); - //BOOST_CHECK(boost::math::isnan(variance(c_students_t(0)))); - //BOOST_CHECK(boost::math::isnan(variance(c_students_t(1)))); - + BOOST_CHECK_THROW(variance(students_t_distribution(2)), std::overflow_error); // df == BOOST_CHECK_EQUAL(variance(students_t_distribution(2.5)), 5); // OK. BOOST_CHECK_EQUAL(variance(students_t_distribution(3)), 3); // OK. @@ -581,30 +532,10 @@ void test_spots(RealType) BOOST_CHECK_THROW(kurtosis(students_t_distribution(4)), std::overflow_error); // df == k BOOST_CHECK_EQUAL(kurtosis(students_t_distribution(5)), 9); // OK. - check_ignore_error_returns(0); // Use a new distribution c_students_t with a custom policy to ignore_errors, + // Use a new distribution ignore_error_students_t with a custom policy to ignore all errors, // and check returned values are as expected. - check_out_of_range >(1); -} // template void test_spots(RealType) - -template -void check_ignore_error_returns(RealType) -{ // Define a new distribution c_students_t with a custom policy to ignore_errors - // & thus be able to check that return infinity or NaN for some arguments: - - // Currently these tests would fail with real_concept which returns zero instead of NaN. - if(!std::numeric_limits::has_infinity) - { - return; - } - if(!std::numeric_limits::has_quiet_NaN) - { - return; - } - - using namespace boost::math; - - using boost::math::policies::policy; + using boost::math::policies::policy; // Types of error whose action can be altered by policies:. using boost::math::policies::evaluation_error; using boost::math::policies::domain_error; @@ -622,62 +553,85 @@ void check_ignore_error_returns(RealType) using boost::math::policies::user_error; typedef policy< - domain_error, - overflow_error, - underflow_error, - denorm_error, - pole_error, - evaluation_error + domain_error, + overflow_error, + underflow_error, + denorm_error, + pole_error, + evaluation_error > my_ignore_policy; - long double inf = std::numeric_limits::infinity(); - long double nan = std::numeric_limits::quiet_NaN(); - - using boost::math::students_t_distribution; + typedef students_t_distribution ignore_error_students_t; - typedef students_t_distribution c_students_t; - // typedef students_t_distribution c_students_t; + // Only test NaN and infinity if type has these features (realconcept returns zero). + // Integers are always converted to RealType, others requires static cast. - //cout << "mean(c_students_t(nan)) = " << mean(c_students_t(nan)) << endl; - //cout << "variance(c_students_t(nan)) = " << variance(c_students_t(nan)) << endl; - //cout << "skewness(c_students_t(nan)) = " << skewness(c_students_t(nan)) << endl; - //cout << "kurtosis(c_students_t(nan)) = " << kurtosis(c_students_t(nan)) << endl; + // Mean + if(std::numeric_limits::has_quiet_NaN) + { + BOOST_CHECK(boost::math::isnan(mean(ignore_error_students_t(-1)))); + BOOST_CHECK(boost::math::isnan(mean(ignore_error_students_t(0)))); + BOOST_CHECK(boost::math::isnan(mean(ignore_error_students_t(1)))); + BOOST_CHECK(boost::math::isfinite(mean(ignore_error_students_t(1 + std::numeric_limits::epsilon())))); - // Bad arguments - check on return from ignoring errors. - BOOST_CHECK((boost::math::isnan)(mean(c_students_t(nan)))); - BOOST_CHECK(boost::math::isnan(mean(c_students_t(inf)))); - BOOST_CHECK(boost::math::isnan(mean(c_students_t(-1)))); - BOOST_CHECK(boost::math::isnan(mean(c_students_t(0)))); - BOOST_CHECK(boost::math::isnan(mean(c_students_t(1)))); + // Variance + BOOST_CHECK(boost::math::isnan(variance(ignore_error_students_t(std::numeric_limits::quiet_NaN())))); - BOOST_CHECK(boost::math::isnan(variance(c_students_t(nan)))); - BOOST_CHECK(boost::math::isnan(variance(c_students_t(inf)))); - BOOST_CHECK(boost::math::isnan(variance(c_students_t(-1)))); - BOOST_CHECK(boost::math::isnan(variance(c_students_t(0)))); - BOOST_CHECK(boost::math::isnan(variance(c_students_t(1)))); - BOOST_CHECK(boost::math::isinf(variance(c_students_t(1.7L)))); - BOOST_CHECK(boost::math::isinf(variance(c_students_t(2)))); - BOOST_CHECK(boost::math::isfinite(variance(c_students_t(2.0001L)))); + if(!std::numeric_limits::has_infinity) + { + BOOST_CHECK(boost::math::isnan(variance(ignore_error_students_t(std::numeric_limits::infinity())))); + } - BOOST_CHECK(boost::math::isnan(skewness(c_students_t(nan)))); - BOOST_CHECK(boost::math::isnan(skewness(c_students_t(inf)))); - BOOST_CHECK(boost::math::isnan(skewness(c_students_t(-1)))); - BOOST_CHECK(boost::math::isnan(skewness(c_students_t(0)))); - BOOST_CHECK(boost::math::isnan(skewness(c_students_t(1)))); - BOOST_CHECK(boost::math::isnan(skewness(c_students_t(2)))); - BOOST_CHECK(boost::math::isnan(skewness(c_students_t(3)))); + BOOST_CHECK(boost::math::isnan(variance(ignore_error_students_t(-1)))); + BOOST_CHECK(boost::math::isnan(variance(ignore_error_students_t(0)))); + BOOST_CHECK(boost::math::isnan(variance(ignore_error_students_t(1)))); + } + if(std::numeric_limits::has_infinity) + { + BOOST_CHECK(boost::math::isinf(variance(ignore_error_students_t(static_cast(1.7L))))); + BOOST_CHECK(boost::math::isinf(variance(ignore_error_students_t(2)))); + } + BOOST_CHECK(boost::math::isfinite(variance(ignore_error_students_t(2 + 2 * std::numeric_limits::epsilon())))); + BOOST_CHECK(boost::math::isfinite(variance(ignore_error_students_t(static_cast(2.0001L))))); - BOOST_CHECK(boost::math::isnan(kurtosis(c_students_t(nan)))); - BOOST_CHECK(boost::math::isnan(kurtosis(c_students_t(inf)))); - BOOST_CHECK(boost::math::isnan(kurtosis(c_students_t(-1)))); - BOOST_CHECK(boost::math::isnan(kurtosis(c_students_t(0)))); - BOOST_CHECK(boost::math::isnan(kurtosis(c_students_t(1)))); - BOOST_CHECK(boost::math::isnan(kurtosis(c_students_t(2)))); - BOOST_CHECK(boost::math::isinf(kurtosis(c_students_t(2.0001L)))); - BOOST_CHECK(boost::math::isinf(kurtosis(c_students_t(3)))); - BOOST_CHECK(boost::math::isinf(kurtosis(c_students_t(4)))); - BOOST_CHECK(boost::math::isfinite(kurtosis(c_students_t(4.0001L)))); -} // check_ignore_error_returns() + // Skewness + if(std::numeric_limits::has_quiet_NaN) + { + BOOST_CHECK(boost::math::isnan(skewness(ignore_error_students_t(std::numeric_limits::quiet_NaN())))); + if(!std::numeric_limits::has_infinity) + { + BOOST_CHECK(boost::math::isnan(skewness(ignore_error_students_t(std::numeric_limits::infinity())))); + } + BOOST_CHECK(boost::math::isnan(skewness(ignore_error_students_t(-1)))); + BOOST_CHECK(boost::math::isnan(skewness(ignore_error_students_t(0)))); + BOOST_CHECK(boost::math::isnan(skewness(ignore_error_students_t(1)))); + BOOST_CHECK(boost::math::isnan(skewness(ignore_error_students_t(2)))); + BOOST_CHECK(boost::math::isnan(skewness(ignore_error_students_t(3)))); + BOOST_CHECK(boost::math::isfinite(skewness(ignore_error_students_t(3 + 3 * std::numeric_limits::epsilon())))); + + // Kurtosis (and assume this tests kurtosis excess too?). + BOOST_CHECK(boost::math::isnan(kurtosis(ignore_error_students_t(std::numeric_limits::quiet_NaN())))); + if(std::numeric_limits::has_infinity) + { + BOOST_CHECK(boost::math::isnan(kurtosis(ignore_error_students_t(std::numeric_limits::infinity())))); + BOOST_CHECK(boost::math::isnan(kurtosis(ignore_error_students_t(-1)))); + BOOST_CHECK(boost::math::isnan(kurtosis(ignore_error_students_t(0)))); + BOOST_CHECK(boost::math::isnan(kurtosis(ignore_error_students_t(1)))); + BOOST_CHECK(boost::math::isnan(kurtosis(ignore_error_students_t(2)))); + } + } + BOOST_CHECK(boost::math::isfinite(variance(ignore_error_students_t(2 + 2 * std::numeric_limits::epsilon())))); + if(std::numeric_limits::has_infinity) + { + BOOST_CHECK(boost::math::isinf(kurtosis(ignore_error_students_t(static_cast(2.0001L))))); + BOOST_CHECK(boost::math::isinf(kurtosis(ignore_error_students_t(3)))); + BOOST_CHECK(boost::math::isinf(kurtosis(ignore_error_students_t(4)))); + } + BOOST_CHECK(boost::math::isfinite(variance(ignore_error_students_t(4 + 4 * std::numeric_limits::epsilon())))); + BOOST_CHECK(boost::math::isfinite(kurtosis(ignore_error_students_t(static_cast(4.0001L))))); + + check_out_of_range >(1); +} // template void test_spots(RealType) int test_main(int, char* []) { @@ -687,8 +641,7 @@ int test_main(int, char* []) students_t_distribution<> myst2(2); // Using default RealType double. //students_t_distribution myst3(2); // Using explicit RealType double. - - // Basic sanity-check spot values. + // Basic sanity-check spot values. // (Parameter value, arbitrarily zero, only communicates the floating point type). test_spots(0.0F); // Test float. OK at decdigits = 0 tolerance = 0.0001 % test_spots(0.0); // Test double. OK at decdigits 7, tolerance = 1e07 % From 7930b8b8a4666c7cfdaafd34eefabe11f5233454 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Mon, 30 Jul 2012 19:53:14 +0000 Subject: [PATCH 063/115] Explicit boost::math::policies::domain_error; and pole_error to avoid complaint of duplicate declaration by Intel-Darwin-12. (but unclear where a duplicate declaration actually exists). [SVN r79806] --- test/test_students_t.cpp | 51 +++++++++++++++++++++++++--------------- 1 file changed, 32 insertions(+), 19 deletions(-) diff --git a/test/test_students_t.cpp b/test/test_students_t.cpp index ec8785101..d7a7d989a 100644 --- a/test/test_students_t.cpp +++ b/test/test_students_t.cpp @@ -535,30 +535,43 @@ void test_spots(RealType) // Use a new distribution ignore_error_students_t with a custom policy to ignore all errors, // and check returned values are as expected. + /* + Sandia-darwin-intel-12.0 - math - test_students_t / intel-darwin-12.0 + + ../libs/math/test/test_students_t.cpp(544): error: "domain_error" has already been declared in the current scope + using boost::math::policies::domain_error; + ^ + +../libs/math/test/test_students_t.cpp(552): error: "pole_error" has already been declared in the current scope + using boost::math::policies::pole_error; + + Unclear where previous declaration is. Does seem to be in student_t.hpp or any included files??? + + */ using boost::math::policies::policy; // Types of error whose action can be altered by policies:. - using boost::math::policies::evaluation_error; - using boost::math::policies::domain_error; - using boost::math::policies::overflow_error; - using boost::math::policies::underflow_error; - using boost::math::policies::domain_error; - using boost::math::policies::pole_error; + //using boost::math::policies::evaluation_error; + //using boost::math::policies::domain_error; + //using boost::math::policies::overflow_error; + //using boost::math::policies::underflow_error; + //using boost::math::policies::domain_error; + //using boost::math::policies::pole_error; - // Actions on error (in enum error_policy_type): - using boost::math::policies::errno_on_error; - using boost::math::policies::ignore_error; - using boost::math::policies::throw_on_error; - using boost::math::policies::denorm_error; - using boost::math::policies::pole_error; - using boost::math::policies::user_error; + //// Actions on error (in enum error_policy_type): + //using boost::math::policies::errno_on_error; + //using boost::math::policies::ignore_error; + //using boost::math::policies::throw_on_error; + //using boost::math::policies::denorm_error; + //using boost::math::policies::pole_error; + //using boost::math::policies::user_error; typedef policy< - domain_error, - overflow_error, - underflow_error, - denorm_error, - pole_error, - evaluation_error + boost::math::policies::domain_error, + boost::math::policies::overflow_error, + boost::math::policies::underflow_error, + boost::math::policies::denorm_error, + boost::math::policies::pole_error, + boost::math::policies::evaluation_error > my_ignore_policy; typedef students_t_distribution ignore_error_students_t; From 4ad388a10eab64e7108f2fb885b8801ea2e6f1bd Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Tue, 31 Jul 2012 10:57:22 +0000 Subject: [PATCH 064/115] Remove non-ASCII char in comment. [SVN r79810] --- include/boost/math/constants/calculate_constants.hpp | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/include/boost/math/constants/calculate_constants.hpp b/include/boost/math/constants/calculate_constants.hpp index 9129ade53..2cdcd8e09 100644 --- a/include/boost/math/constants/calculate_constants.hpp +++ b/include/boost/math/constants/calculate_constants.hpp @@ -596,7 +596,7 @@ inline T constant_zeta_three::compute(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC( //"1.202056903159594285399738161511449990, 76498629234049888179227155534183820578631309018645587360933525814619915" A002117 // 1.202056903159594285399738161511449990, 76498629234049888179227155534183820578631309018645587360933525814619915780, +00); //"1.2020569031595942 double - // http://www.spaennare.se/SSPROG/ssnum.pdf // section 11, Algorithmfor Apery’s constant zeta(3). + // http://www.spaennare.se/SSPROG/ssnum.pdf // section 11, Algorithm for Apery's constant zeta(3). // Programs to Calculate some Mathematical Constants to Large Precision, Document Version 1.50 // by Stefan Spannare September 19, 2007 From 848c0da5c9830cd003185b0590f61afdaf6f789c Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Tue, 31 Jul 2012 11:15:30 +0000 Subject: [PATCH 065/115] Removed tabs [SVN r79811] --- include/boost/math/distributions/skew_normal.hpp | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/include/boost/math/distributions/skew_normal.hpp b/include/boost/math/distributions/skew_normal.hpp index 6f3bc212f..af89817f2 100644 --- a/include/boost/math/distributions/skew_normal.hpp +++ b/include/boost/math/distributions/skew_normal.hpp @@ -655,8 +655,8 @@ namespace boost{ namespace math{ const RealType exk = kurtosis_excess(dist); x = x + (x*x-static_cast(1))*skew/static_cast(6) - + x*(x*x-static_cast(3))*exk/static_cast(24) - - x*(static_cast(2)*x*x-static_cast(5))*skew*skew/static_cast(36); + + x*(x*x-static_cast(3))*exk/static_cast(24) + - x*(static_cast(2)*x*x-static_cast(5))*skew*skew/static_cast(36); } // if(shape != 0) result = standard_deviation(dist)*x+mean(dist); From 0617e03ad37a7a81f1bb9cf0343f7db2e2f44e5c Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Tue, 31 Jul 2012 11:18:11 +0000 Subject: [PATCH 066/115] Comment out display of pdf(dist, 0.45) and retest skew_normal.hpp [SVN r79812] --- test/test_skew_normal.cpp | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/test/test_skew_normal.cpp b/test/test_skew_normal.cpp index 97993de30..d243f2eb9 100644 --- a/test/test_skew_normal.cpp +++ b/test/test_skew_normal.cpp @@ -371,7 +371,7 @@ void test_spots(RealType) skew_normal_distribution dist(static_cast(0.l), static_cast(1.l), static_cast(4.l)); - cout << "pdf(dist, 0) = " << pdf(dist, 0) << ", pdf(dist, 0.45) = " << pdf(dist, 0.45) << endl; + // cout << "pdf(dist, 0) = " << pdf(dist, 0) << ", pdf(dist, 0.45) = " << pdf(dist, 0.45) << endl; // BOOST_CHECK_CLOSE(mode(dist), boost::math::constants::root_two() / 2, tol5); BOOST_CHECK_CLOSE(mode(dist), static_cast(0.41697299497388863932L), tol1000); } From d7dc107b301a2c12747b2d1c8de385af95ed1790 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Tue, 31 Jul 2012 11:26:45 +0000 Subject: [PATCH 067/115] Remove tabs and () max call. [SVN r79813] --- include/boost/math/special_functions/owens_t.hpp | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/include/boost/math/special_functions/owens_t.hpp b/include/boost/math/special_functions/owens_t.hpp index 98d6380c3..c632bd553 100644 --- a/include/boost/math/special_functions/owens_t.hpp +++ b/include/boost/math/special_functions/owens_t.hpp @@ -219,7 +219,7 @@ namespace boost BOOST_MATH_STD_USING using namespace boost::math::constants; - const unsigned short m = 20; + const unsigned short m = 20; static const RealType c2[] = { @@ -595,7 +595,7 @@ namespace boost term = one_minus_dj_sum * a_pow / (2 * j + 1); c = b - c; sum += c * term; - abs_err += ldexp(std::max(T(fabs(sum)), T(fabs(c*term))), -tools::digits()); + abs_err += ldexp((std::max)(T(fabs(sum)), T(fabs(c*term))), -tools::digits()); b = (j + n) * (j - n) * b / ((j + T(0.5)) * (j + 1)); ++j; // From 059d1b4378711eea09b74ddb3bc3501d52979273 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Tue, 31 Jul 2012 11:28:17 +0000 Subject: [PATCH 068/115] Added terminal newline. [SVN r79814] --- include/boost/math/tr1_c_macros.ipp | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/include/boost/math/tr1_c_macros.ipp b/include/boost/math/tr1_c_macros.ipp index c173639af..ec8e7da3e 100644 --- a/include/boost/math/tr1_c_macros.ipp +++ b/include/boost/math/tr1_c_macros.ipp @@ -807,4 +807,4 @@ #endif #define sph_neumannl boost_sph_neumannl -#endif // BOOST_MATH_C_MACROS_IPP \ No newline at end of file +#endif // BOOST_MATH_C_MACROS_IPP From a7a7728e2e8e1ed9267ddebfe105fc78c7dbb1c5 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Tue, 31 Jul 2012 13:27:00 +0000 Subject: [PATCH 069/115] edits for Inspection nags [SVN r79815] --- doc/sf_and_dist/distributions/bernoulli.qbk | 2 +- doc/sf_and_dist/distributions/binomial.qbk | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/doc/sf_and_dist/distributions/bernoulli.qbk b/doc/sf_and_dist/distributions/bernoulli.qbk index d22af07a1..fc08b5cb4 100644 --- a/doc/sf_and_dist/distributions/bernoulli.qbk +++ b/doc/sf_and_dist/distributions/bernoulli.qbk @@ -105,7 +105,7 @@ the binomial distribution with a single trial should be used, for example: [h4 References] * [@http://en.wikipedia.org/wiki/Bernoulli_distribution Wikpedia Bernoulli distribution] -* [@ Weisstein, Eric W. "Bernoulli Distribution." From MathWorld--A Wolfram Web Resource.] +* [@http://mathworld.wolfram.com/BernoulliDistribution.html Weisstein, Eric W. "Bernoulli Distribution." From MathWorld--A Wolfram Web Resource.] [endsect][/section:bernoulli_dist bernoulli] diff --git a/doc/sf_and_dist/distributions/binomial.qbk b/doc/sf_and_dist/distributions/binomial.qbk index d12094319..bbe532836 100644 --- a/doc/sf_and_dist/distributions/binomial.qbk +++ b/doc/sf_and_dist/distributions/binomial.qbk @@ -394,7 +394,7 @@ There are also various special cases: refer to the code for details. ]] * [@http://en.wikipedia.org/wiki/Beta_distribution Wikipedia binomial distribution]. * [@http://www.itl.nist.gov/div898/handbook/eda/section3/eda366i.htm NIST Explorary Data Analysis]. -[endsect][/section:binomial_dist Binomial] +[endsect] [/section:binomial_dist Binomial] [/ binomial.qbk Copyright 2006 John Maddock and Paul A. Bristow. From 75214ed1550876147917af85c5531327df6c6088 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Tue, 31 Jul 2012 13:27:39 +0000 Subject: [PATCH 070/115] Various cosmetic changes to deal with Inspection nags. [SVN r79816] --- doc/sf_and_dist/airy.qbk | 2 +- doc/sf_and_dist/constants.qbk | 12 +++++++++--- 2 files changed, 10 insertions(+), 4 deletions(-) diff --git a/doc/sf_and_dist/airy.qbk b/doc/sf_and_dist/airy.qbk index d2ff3e0fa..9b7419161 100644 --- a/doc/sf_and_dist/airy.qbk +++ b/doc/sf_and_dist/airy.qbk @@ -49,7 +49,7 @@ only the absolute error is low for /x < 0/. [heading Testing] Since this function is implemented in terms of other special functions, there are only a few -basic sanity checks, using test values from [@http:functions.wolfram.com functions.wolfram.com]. +basic sanity checks, using test values from [@http://mathworld.wolfram.com/AiryFunctions.html Wolfram Airy Functions]. [heading Implementation] diff --git a/doc/sf_and_dist/constants.qbk b/doc/sf_and_dist/constants.qbk index 974714c49..7de44d7e2 100644 --- a/doc/sf_and_dist/constants.qbk +++ b/doc/sf_and_dist/constants.qbk @@ -655,7 +655,7 @@ This class is used in Boost.Math and an option when using big_number projects to [h5 GMP and MPFR] -[@gmplib.org GMP] and [@http://www.mpfr.org/ MPFR] have also been used to compute constants, +[@http://gmplib.org GMP] and [@http://www.mpfr.org/ MPFR] have also been used to compute constants, but are licensed under the [@http://www.gnu.org/copyleft/lesser.html Lesser GPL license] and are [*not licensed for commercial use]. @@ -707,7 +707,13 @@ Some physical constants may be available in Boost.Units. [endsect] [/section:FAQ FAQ] -[endsect] - +[endsect] [/section:constants Mathematical Constants] + +[/ + Copyright 2012 John Maddock and Paul A. Bristow. + Distributed under the Boost Software License, Version 1.0. + (See accompanying file LICENSE_1_0.txt or copy at + http://www.boost.org/LICENSE_1_0.txt). +] From 8e6b56fe09aad95e445c7bea9bb05ce3c7923021 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Tue, 31 Jul 2012 13:31:24 +0000 Subject: [PATCH 071/115] Various cosmetic changes to deal with Inspection nags. [SVN r79817] --- doc/sf_and_dist/pp_pi.hpp | 11 ++++++++++- 1 file changed, 10 insertions(+), 1 deletion(-) diff --git a/doc/sf_and_dist/pp_pi.hpp b/doc/sf_and_dist/pp_pi.hpp index 299fe7700..db66d30c8 100644 --- a/doc/sf_and_dist/pp_pi.hpp +++ b/doc/sf_and_dist/pp_pi.hpp @@ -87,4 +87,13 @@ namespace boost } // namespace math } // namespace boost -//] [/preprocessed_pi] \ No newline at end of file +//] [/preprocessed_pi] + +/* + Copyright 2012 John Maddock and Paul A. Bristow. + Distributed under the Boost Software License, Version 1.0. + (See accompanying file LICENSE_1_0.txt or copy at + http://www.boost.org/LICENSE_1_0.txt) +*/ + + From b3bee00ce0bb5fe84771319f70971c867b7ac6cf Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Tue, 31 Jul 2012 13:32:25 +0000 Subject: [PATCH 072/115] Various cosmetic changes to deal with Inspection nags. [SVN r79818] --- include/boost/math/special_functions.hpp | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/include/boost/math/special_functions.hpp b/include/boost/math/special_functions.hpp index 3723bd2d2..24f406481 100644 --- a/include/boost/math/special_functions.hpp +++ b/include/boost/math/special_functions.hpp @@ -1,5 +1,5 @@ -// Copyright John Maddock 2006, 2007. -// Copyright Paul A. Bristow 2006, 2007. +// Copyright John Maddock 2006, 2007, 2012. +// Copyright Paul A. Bristow 2006, 2007, 2012 // Use, modification and distribution are subject to the // Boost Software License, Version 1.0. (See accompanying file @@ -44,6 +44,7 @@ #include #include #include +#include #include #include #include From 45fd99988df35456ee4de0fec73865889d8b8661 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Tue, 31 Jul 2012 13:58:11 +0000 Subject: [PATCH 073/115] Rebuilt after edits to quiet nags. [SVN r79820] --- doc/sf_and_dist/html/index.html | 8 +- doc/sf_and_dist/html/index/s13.html | 2766 +++---- doc/sf_and_dist/html/index/s14.html | 176 +- doc/sf_and_dist/html/index/s15.html | 382 +- doc/sf_and_dist/html/index/s16.html | 284 +- doc/sf_and_dist/html/index/s17.html | 6494 ++++++++--------- .../html/math_toolkit/backgrounders.html | 4 +- .../backgrounders/implementation.html | 26 +- .../math_toolkit/backgrounders/lanczos.html | 20 +- .../html/math_toolkit/backgrounders/refs.html | 4 +- .../backgrounders/relative_error.html | 4 +- .../math_toolkit/backgrounders/remez.html | 30 +- .../html/math_toolkit/constants.html | 4 +- .../html/math_toolkit/constants/FAQ.html | 96 +- .../math_toolkit/constants/constants.html | 4 +- .../html/math_toolkit/constants/intro.html | 40 +- .../math_toolkit/constants/new_const.html | 5 +- .../html/math_toolkit/constants/tutorial.html | 4 +- .../constants/tutorial/non_templ.html | 4 +- .../constants/tutorial/templ.html | 4 +- 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50 +- 287 files changed, 6692 insertions(+), 6843 deletions(-) diff --git a/doc/sf_and_dist/html/index.html b/doc/sf_and_dist/html/index.html index 02b26af8f..b40a88cc6 100644 --- a/doc/sf_and_dist/html/index.html +++ b/doc/sf_and_dist/html/index.html @@ -3,7 +3,7 @@ Math Toolkit - + @@ -18,7 +18,7 @@
      Next
      -
      +

      @@ -316,8 +316,6 @@

    Jacobi Elliptic Functions
    -
    Overvew of the - Jacobi Elliptic Functions
    Jacobi Elliptic SN, CN and DN
    Jacobi Elliptic @@ -579,7 +577,7 @@

    - +

    Last revised: July 14, 2012 at 18:27:50 GMT

    Last revised: June 06, 2012 at 11:22:49 GMT


    diff --git a/doc/sf_and_dist/html/index/s13.html b/doc/sf_and_dist/html/index/s13.html index 57d00280c..46f89e843 100644 --- a/doc/sf_and_dist/html/index/s13.html +++ b/doc/sf_and_dist/html/index/s13.html @@ -3,7 +3,7 @@ Function Index - + @@ -22,2336 +22,2336 @@
    -
    +

    -Function Index

    +Function Index

    A B C D E F G H I J K L M N O P Q R S T U V W Z

    A
    -
    diff --git a/doc/sf_and_dist/html/index/s14.html b/doc/sf_and_dist/html/index/s14.html index baadc756b..4c65acaeb 100644 --- a/doc/sf_and_dist/html/index/s14.html +++ b/doc/sf_and_dist/html/index/s14.html @@ -3,7 +3,7 @@ Class Index - + @@ -22,210 +22,210 @@
    PrevUpHomeNext
    -
    +

    -Class Index

    +Class Index

    B C D E F G H I L M N P R S T U W

    B
    -
    diff --git a/doc/sf_and_dist/html/index/s15.html b/doc/sf_and_dist/html/index/s15.html index ac33b6c9d..bb8efc3aa 100644 --- a/doc/sf_and_dist/html/index/s15.html +++ b/doc/sf_and_dist/html/index/s15.html @@ -3,7 +3,7 @@ Typedef Index - + @@ -22,369 +22,369 @@
    PrevUpHomeNext
    -
    +

    -Typedef Index

    +Typedef Index

    A B C D E F G H I L N O P R S T U V W

    A
    -
    diff --git a/doc/sf_and_dist/html/index/s16.html b/doc/sf_and_dist/html/index/s16.html index c2d258e13..40236e492 100644 --- a/doc/sf_and_dist/html/index/s16.html +++ b/doc/sf_and_dist/html/index/s16.html @@ -3,7 +3,7 @@ Macro Index - + @@ -22,266 +22,266 @@
    PrevUpHomeNext
    -
    +

    -Macro Index

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    B F

    B
    -
    diff --git a/doc/sf_and_dist/html/index/s17.html b/doc/sf_and_dist/html/index/s17.html index 10bff2b81..db4343dd2 100644 --- a/doc/sf_and_dist/html/index/s17.html +++ b/doc/sf_and_dist/html/index/s17.html @@ -3,7 +3,7 @@ Index - + @@ -21,4912 +21,4912 @@
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    -Index

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    diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders.html b/doc/sf_and_dist/html/math_toolkit/backgrounders.html index c90615900..0e5065f9f 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders.html @@ -3,7 +3,7 @@ Backgrounders - + @@ -22,7 +22,7 @@
    PrevUpHomeNext
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    +
    diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html b/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html index 4e664d29f..189a1abad 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html @@ -3,7 +3,7 @@ Additional Implementation Notes - + @@ -22,7 +22,7 @@
    PrevUpHomeNext
    -
    +

    Additional Implementation Notes @@ -137,11 +137,11 @@

    The tolerances need to be set to the maximum of:

    -
      -
    • +
        +
      • Some epsilon value.
      • -
      • +
      • The accuracy of the data (often only near 64-bit double).
      @@ -166,7 +166,7 @@ it is proposed that signalling a domain error is mandatory when the argument would give an mathematically undefined result.

      -

    -
    • +
      • Default parameters for the Triangular Distribution. We are uncertain about the best default parameters. Some sources suggest that the Standard Triangular Distribution has lower = 0, mode = half and upper = 1. However @@ -593,17 +593,17 @@

        Checks made are:

        -
          -
        • +
            +
          • Infinity or NaN (if available) passed in place of each of the valid params.
          • -
          • +
          • Infinity or NaN (if available) as a random variable.
          • -
          • +
          • Out-of-range random variable passed to pdf and cdf (ie outside of "range(DistributionType)").
          • -
          • +
          • Out-of-range probability passed to quantile function and complement.
          diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html b/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html index f3ef1ee6f..022dd417d 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html @@ -3,7 +3,7 @@ The Lanczos Approximation - + @@ -22,7 +22,7 @@
          PrevUpHomeNext
          -
          +
          @@ -45,8 +45,8 @@ Lanczos approximation does have a couple of properties that make it worthy of further consideration:

          -
            -
          • +
              +
            • The approximation has an easy to compute truncation error that holds for all z > 0. In practice that means we can use the same approximation for all z > 0, and @@ -54,7 +54,7 @@ the truncation error will at worst be bounded by some finite value.
            • -
            • +
            • The approximation has a form that is particularly amenable to analytic manipulation, in particular ratios of gamma or gamma-like functions are particularly easy to compute without resorting to logarithms. @@ -537,21 +537,21 @@ References -
                -
              1. +
                  +
                1. Paul Godfrey, "A note on the computation of the convergent Lanczos complex Gamma approximation".
                2. -
                3. +
                4. Glendon Ralph Pugh, "An Analysis of the Lanczos Gamma Approximation", PhD Thesis November 2004.
                5. -
                6. +
                7. Viktor T. Toth, "Calculators and the Gamma Function".
                8. -
                9. +
                10. Mathworld, The Lanczos Approximation.
                11. diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html b/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html index 236f5da6c..99b3eb9c0 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html @@ -3,7 +3,7 @@ References - + @@ -22,7 +22,7 @@
                  PrevUpHomeNext
                  -
                  +
                  diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html b/doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html index f3f749d05..86a079e87 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html @@ -3,7 +3,7 @@ Relative Error - + @@ -22,7 +22,7 @@
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                  +
                  diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html b/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html index 370a8d95b..ba8a6237a 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html @@ -3,7 +3,7 @@ The Remez Method - + @@ -22,7 +22,7 @@
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                  @@ -65,15 +65,15 @@ yields the smallest maximal value of the error function. Chebyshev showed that there is a unique minimax solution for R(x) that has the following properties:

                  -
                    -
                  • +
                      +
                    • If R(x) is a polynomial of degree N, then there are N+2 unknowns: the N+1 coefficients of the polynomial, and maximal value of the error function.
                    • -
                    • +
                    • The error function has N+1 roots, and N+2 extrema (minima and maxima).
                    • -
                    • +
                    • The extrema alternate in sign, and all have the same magnitude.
                    @@ -416,18 +416,18 @@ wrong, it is by no means an exhaustive list, but is provided in the hopes that it will prove useful.

                    -
                      -
                    • +
                        +
                      • Is the function smooth enough? Can it be better separated into a rapidly changing part, and an asymptotic part?
                      • -
                      • +
                      • Does the function being approximated have any "blips" in it? Check for problems as the function changes computation method, or if a root, or an infinity has been divided out. The telltale sign is if there is a narrow region where the Remez method will not converge.
                      • -
                      • +
                      • Check you have enough accuracy in your calculations: remember that the Remez method works on the difference between the approximation and the function being approximated: so you must have more digits of precision @@ -435,27 +435,27 @@ So for example at double precision, you shouldn't expect to be able to get better than a float precision approximation.
                      • -
                      • +
                      • Try skewing the initial interpolated approximation to minimise the error before you begin the Remez steps.
                      • -
                      • +
                      • If the approximation won't converge or is ill-conditioned from one starting location, try starting from a different location.
                      • -
                      • +
                      • If a rational function won't converge, one can minimise a polynomial (which presents no problems), then rotate one term from the numerator to the denominator and minimise again. In theory one can continue moving terms one at a time from numerator to denominator, and then re-minimising, retaining the last set of control points at each stage.
                      • -
                      • +
                      • Try using a smaller interval. It may also be possible to optimise over one (small) interval, rescale the control points over a larger interval, and then re-minimise.
                      • -
                      • +
                      • Keep absissa values small: use a change of variable to keep the abscissa over, say [0, b], for some smallish value b.
                      • diff --git a/doc/sf_and_dist/html/math_toolkit/constants.html b/doc/sf_and_dist/html/math_toolkit/constants.html index ac07998d5..764de778d 100644 --- a/doc/sf_and_dist/html/math_toolkit/constants.html +++ b/doc/sf_and_dist/html/math_toolkit/constants.html @@ -3,7 +3,7 @@ Mathematical Constants - + @@ -22,7 +22,7 @@
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                        diff --git a/doc/sf_and_dist/html/math_toolkit/constants/FAQ.html b/doc/sf_and_dist/html/math_toolkit/constants/FAQ.html index 0c5b05830..22e3559b6 100644 --- a/doc/sf_and_dist/html/math_toolkit/constants/FAQ.html +++ b/doc/sf_and_dist/html/math_toolkit/constants/FAQ.html @@ -3,7 +3,7 @@ FAQs - + @@ -22,7 +22,7 @@
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                        +
                        @@ -37,24 +37,24 @@

                        Some of the criteria we have used are:

                        -
                          -
                        • +
                            +
                          • Used in Boost.Math.
                          • -
                          • +
                          • Commonly used.
                          • -
                          • +
                          • Expensive to compute.
                          • -
                          • +
                          • Requested by users.
                          • -
                          • +
                          • Used in science and mathematics.
                          • -
                          • +
                          • No integer values (because so cheap to construct).
                            (You can easily define your own if found convenient, for example: FPT one =static_cast<FPT>(42);). @@ -65,57 +65,57 @@ How are constants named? -
                              -
                            • +
                                +
                              • Not macros, so no upper case.
                              • -
                              • +
                              • All lower case (following C++ standard names).
                              • -
                              • +
                              • No CamelCase.
                              • -
                              • +
                              • Underscore as _ delimiter between words.
                              • -
                              • +
                              • Numbers spelt as words rather than decimal digits (except following pow).
                              • -
                              • +
                              • Abbreviation conventions: -
                                  -
                                • +
                                    +
                                  • root for square root.
                                  • -
                                  • +
                                  • cbrt for cube root.
                                  • -
                                  • +
                                  • pow for pow function using decimal digits like pow23 for n2/3.
                                  • -
                                  • +
                                  • div for divided by or operator /.
                                  • -
                                  • +
                                  • minus for operator -, plus for operator +.
                                  • -
                                  • +
                                  • sqr for squared.
                                  • -
                                  • +
                                  • cubed for cubed n3.
                                  • -
                                  • +
                                  • words for greek, like π, ζ and Γ.
                                  • -
                                  • +
                                  • words like half, third, three_quarters, sixth for fractions. (Digit(s) can get muddled).
                                  • -
                                  • +
                                  • log10 for log10
                                  • -
                                  • +
                                  • ln for loge
                                  @@ -146,24 +146,24 @@ How are the constants tested? -
                                    -
                                  1. +
                                      +
                                    1. Comparison using Boost.Test BOOST_CHECK_CLOSE_FRACTION using long double literals, with at least 35 decimal digits, enough to be accurate for all long double implementations. The tolerance is usually twice long double epsilon.
                                    2. -
                                    3. +
                                    4. Comparison with calculation at long double precision. This often requires a slightly higher tolerance than two epsilon because of computational noise from round-off etc, especially when trig and other functions are called.
                                    5. -
                                    6. +
                                    7. Comparison with independent published values, for example, using The On-Line Encyclopedia of Integer Sequences (OEIS) again using at least 35 decimal digits strings.
                                    8. -
                                    9. +
                                    10. Comparison with independely calculated values using arbitrary precision tools like Mathematica, again using at least 35 decimal digits literal strings. @@ -353,7 +353,7 @@ and MPFR

                                      - GMP and MPFR + GMP and MPFR have also been used to compute constants, but are licensed under the Lesser GPL license and are not licensed for commercial use.

                                      @@ -397,40 +397,40 @@ Where can I find other high precision constants? -
                                        -
                                      1. +
                                          +
                                        1. Constants with very high precision and good accuracy (>40 decimal digits) from Simon Plouffe's web based collection http://pi.lacim.uqam.ca/eng/.
                                        2. -
                                        3. +
                                        4. The On-Line Encyclopedia of Integer Sequences (OEIS)
                                        5. -
                                        6. +
                                        7. Checks using printed text optically scanned values and converted from: D. E. Knuth, Art of Computer Programming, Appendix A, Table 1, Vol 1, ISBN 0 201 89683 4 (1997)
                                        8. -
                                        9. +
                                        10. M. Abrahamovitz & I. E. Stegun, National Bureau of Standards, Handbook of Mathematical Functions, a reference source for formulae now superceded by
                                        11. -
                                        12. +
                                        13. Frank W. Olver, Daniel W. Lozier, Ronald F. Boisvert, Charles W. Clark, NIST Handbook of Mathemetical Functions, Cambridge University Press, ISBN 978-0-521-14063-8, 2010.
                                        14. -
                                        15. +
                                        16. John F Hart, Computer Approximations, Kreiger (1978) ISBN 0 88275 642 7.
                                        17. -
                                        18. +
                                        19. Some values from Cephes Mathematical Library, Stephen L. Moshier and CALC100 100 decimal digit Complex Variable Calculator Program, a DOS utility.
                                        20. -
                                        21. +
                                        22. Xavier Gourdon, Pascal Sebah, 50 decimal digits constants at Number, constants and computation.
                                        23. @@ -443,18 +443,18 @@

                                          Not here in this Boost.Math collection, because physical constants:

                                          -
                                            -
                                          • +
                                              +
                                            • Are measurements.
                                            • -
                                            • +
                                            • Are not truly constant and keeping changing as mensuration technology improves.
                                            • -
                                            • +
                                            • Have a instrinsic uncertainty.
                                            • -
                                            • +
                                            • Mathematical constants are stored and represented at varying precision, but should never be inaccurate.
                                            • diff --git a/doc/sf_and_dist/html/math_toolkit/constants/constants.html b/doc/sf_and_dist/html/math_toolkit/constants/constants.html index 9bb34f5bd..e869ebe7b 100644 --- a/doc/sf_and_dist/html/math_toolkit/constants/constants.html +++ b/doc/sf_and_dist/html/math_toolkit/constants/constants.html @@ -3,7 +3,7 @@ The Mathematical Constants - + @@ -22,7 +22,7 @@
                                              PrevUpHomeNext
                                              -
                                              +
                                              diff --git a/doc/sf_and_dist/html/math_toolkit/constants/intro.html b/doc/sf_and_dist/html/math_toolkit/constants/intro.html index e0cfc6586..72d6a519a 100644 --- a/doc/sf_and_dist/html/math_toolkit/constants/intro.html +++ b/doc/sf_and_dist/html/math_toolkit/constants/intro.html @@ -3,7 +3,7 @@ Introduction - + @@ -22,7 +22,7 @@
                                              PrevUpHomeNext
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                                              +
                                              @@ -34,68 +34,68 @@ Why use Boost.Math mathematical constants? -
                                                -
                                              • +
                                                  +
                                                • Readable. For the very many jobs just using built-in like double, you can just write expressions like
                                                  double area = pi * r * r;
                                                  (If that's all you want, jump direct to use in non-template code!)
                                                • -
                                                • +
                                                • Effortless - avoiding a search of reference sources.
                                                • -
                                                • +
                                                • Usable with both builtin floating point types, and user-defined, possibly extended precision, types such as NTL, MPFR/GMP, mp_float: in the latter case the constants are computed to the necessary precision and then cached.
                                                • -
                                                • +
                                                • Accurate - ensuring that the values are as accurate as possible for the chosen floating-point type -
                                                    -
                                                  • +
                                                      +
                                                    • No loss of accuracy from repeated rounding of intermediate computations.
                                                    • -
                                                    • +
                                                    • Result is computed with higher precision and only rounded once.
                                                    • -
                                                    • +
                                                    • Less risk of inaccurate result from functions pow, trig and log at corner cases.
                                                    • -
                                                    • +
                                                    • Less risk of cancellation error.
                                                  • -
                                                  • +
                                                  • Faster - can avoid (re-)calculation at runtime. This can be significant if: -
                                                      -
                                                    • +
                                                        +
                                                      • Functions pow, trig or log are used.
                                                      • -
                                                      • +
                                                      • Inside an inner loop.
                                                      • -
                                                      • +
                                                      • Using a high-precision UDT.
                                                      • -
                                                      • +
                                                      • Compiler optimizations possible with built-in types, especially double, are not available.
                                                    • -
                                                    • +
                                                    • Portable - as possible between different systems using different floating-point precisions: see use in template code.
                                                    • -
                                                    • +
                                                    • Tested - by comparison with other published sources, or separately computed at long double precision.
                                                    • diff --git a/doc/sf_and_dist/html/math_toolkit/constants/new_const.html b/doc/sf_and_dist/html/math_toolkit/constants/new_const.html index 75e90fa9e..712c7c863 100644 --- a/doc/sf_and_dist/html/math_toolkit/constants/new_const.html +++ b/doc/sf_and_dist/html/math_toolkit/constants/new_const.html @@ -3,7 +3,7 @@ Defining New Constants - + @@ -22,7 +22,7 @@
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                                                      @@ -246,6 +246,7 @@ } // namespace constants } // namespace math } // namespace boost +

                                                      diff --git a/doc/sf_and_dist/html/math_toolkit/constants/tutorial.html b/doc/sf_and_dist/html/math_toolkit/constants/tutorial.html index cfecd8783..24c8d2ecb 100644 --- a/doc/sf_and_dist/html/math_toolkit/constants/tutorial.html +++ b/doc/sf_and_dist/html/math_toolkit/constants/tutorial.html @@ -3,7 +3,7 @@ Tutorial - + @@ -22,7 +22,7 @@
                                                      PrevUpHomeNext
                                                      -
                                                      +
                                                      diff --git a/doc/sf_and_dist/html/math_toolkit/constants/tutorial/non_templ.html b/doc/sf_and_dist/html/math_toolkit/constants/tutorial/non_templ.html index 34de38b24..64a88431b 100644 --- a/doc/sf_and_dist/html/math_toolkit/constants/tutorial/non_templ.html +++ b/doc/sf_and_dist/html/math_toolkit/constants/tutorial/non_templ.html @@ -3,7 +3,7 @@ Use in non-template code - + @@ -22,7 +22,7 @@
                                                      PrevUpHomeNext
                                                      -
                                                      +

                                                      Use in non-template code diff --git a/doc/sf_and_dist/html/math_toolkit/constants/tutorial/templ.html b/doc/sf_and_dist/html/math_toolkit/constants/tutorial/templ.html index 6ecb83209..5656451d0 100644 --- a/doc/sf_and_dist/html/math_toolkit/constants/tutorial/templ.html +++ b/doc/sf_and_dist/html/math_toolkit/constants/tutorial/templ.html @@ -3,7 +3,7 @@ Use in template code - + @@ -22,7 +22,7 @@
                                                      PrevUpHomeNext
                                                      -
                                                      +

                                                      Use in template code diff --git a/doc/sf_and_dist/html/math_toolkit/constants/tutorial/user_def.html b/doc/sf_and_dist/html/math_toolkit/constants/tutorial/user_def.html index 4f83f5d11..57ed9902c 100644 --- a/doc/sf_and_dist/html/math_toolkit/constants/tutorial/user_def.html +++ b/doc/sf_and_dist/html/math_toolkit/constants/tutorial/user_def.html @@ -3,7 +3,7 @@ Use With User Defined Types - + @@ -22,7 +22,7 @@
                                                      PrevUpHomeNext
                                                      -
                                                      +

                                                      Use With User Defined Types @@ -40,25 +40,25 @@ than that of the built-in floating pointer types, how the value returned is created is as follows:

                                                      -
                                                        -
                                                      • +
                                                          +
                                                        • If the precision of the type is known at compile time: -
                                                            -
                                                          • +
                                                              +
                                                            • If the precision is less than or equal to that of a float and the type is constructable from a float then our code returns a float literal. If the user-defined type is a literal type then the function call that returns the constant will be a constexp.
                                                            • -
                                                            • +
                                                            • If the precision is less than or equal to that of a double and the type is constructable from a double then our code returns a double literal. If the user-defined type is a literal type then the function call that returns the constant will be a constexp.
                                                            • -
                                                            • +
                                                            • If the precision is less than or equal to that of a long double and the type is constructable from a long double then our code returns @@ -66,27 +66,27 @@ literal. If the user-defined type is a literal type then the function call that returns the constant will be a constexp.
                                                            • -
                                                            • +
                                                            • If the precision is less than 100 decimal digits, then the constant will be constructed (just the once, then cached in a thread-safe manner) from a string representation of the constant.
                                                            • -
                                                            • +
                                                            • Otherwise the value is computed (just once, then cached in a thread-safe manner).
                                                          • -
                                                          • +
                                                          • If the precision is unknown at compile time then: -
                                                              -
                                                            • +
                                                                +
                                                              • If the runtime precision (obtained from a call to boost::math::tools::digits<T>()) is less than 100 decimal digits, then the constant is constructed "on the fly" from the string representation of the constant.
                                                              • -
                                                              • +
                                                              • Otherwise the value is constructed "on the fly" by calculating then value of the constant using the current default precision of the type. Note that this can make use of the constants diff --git a/doc/sf_and_dist/html/math_toolkit/dist.html b/doc/sf_and_dist/html/math_toolkit/dist.html index b82807d67..2a5cdeb07 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist.html @@ -3,7 +3,7 @@ Statistical Distributions and Functions - + @@ -22,7 +22,7 @@
                                                                PrevUpHomeNext
                                                                -
                                                                +
                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref.html index f5894db88..851ed3a04 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref.html @@ -3,7 +3,7 @@ Statistical Distributions Reference - + @@ -22,7 +22,7 @@
                                                                PrevUpHomeNext
                                                                -
                                                                +

                                                                Statistical Distributions Reference diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html index 1eb55821a..95258344d 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html @@ -3,7 +3,7 @@ Distribution Algorithms - + @@ -22,7 +22,7 @@
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                                                                +

                                                                Distribution Algorithms diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists.html index fdad85808..37918a159 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists.html @@ -3,7 +3,7 @@ Distributions - + @@ -22,7 +22,7 @@
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                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html index cf96ccaea..8dcda1d1e 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html @@ -3,7 +3,7 @@ Bernoulli Distribution - + @@ -22,7 +22,7 @@
                                                                PrevUpHomeNext
                                                                -
                                                                +
                                                                Bernoulli Distribution @@ -329,14 +329,15 @@ References
                                                                - diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html index bbc7f3cb5..b636547a1 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html @@ -3,7 +3,7 @@ Beta Distribution - + @@ -22,7 +22,7 @@
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                                                                +
                                                                Beta Distribution diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html index faae0f690..95121b8fb 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html @@ -3,7 +3,7 @@ Binomial Distribution - + @@ -22,7 +22,7 @@
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                                                                +
                                                                Binomial Distribution @@ -885,17 +885,17 @@ References
                                                                -
                                                                  -
                                                                • +
                                                                    +
                                                                  • Weisstein, Eric W. "Binomial Distribution." From MathWorld--A Wolfram Web Resource.
                                                                  • -
                                                                  • +
                                                                  • Wikipedia binomial distribution.
                                                                  • -
                                                                  • +
                                                                  • NIST Explorary Data Analysis.
                                                                  • diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html index 8d19fa1b1..85844f1fc 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html @@ -3,7 +3,7 @@ Cauchy-Lorentz Distribution - + @@ -22,7 +22,7 @@
                                                                    PrevUpHomeNext
                                                                    -
                                                                    +
                                                                    Cauchy-Lorentz Distribution @@ -275,16 +275,16 @@ References
                                                                    -
                                                                      -
                                                                    • +
                                                                        +
                                                                      • Cauchy-Lorentz distribution
                                                                      • -
                                                                      • +
                                                                      • NIST Exploratory Data Analysis
                                                                      • -
                                                                      • +
                                                                      • Weisstein, Eric W. "Cauchy Distribution." From MathWorld--A Wolfram Web Resource. diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html index 133854cc8..3ce8af145 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html @@ -3,7 +3,7 @@ Chi Squared Distribution - + @@ -22,7 +22,7 @@
                                                                        PrevUpHomeNext
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                                                                        +
                                                                        Chi Squared Distribution @@ -381,16 +381,16 @@ independent, normally distributed random References
                                                                        -
                                                                          -
                                                                        • +
                                                                            +
                                                                          • NIST Exploratory Data Analysis
                                                                          • -
                                                                          • +
                                                                          • Chi-square distribution
                                                                          • -
                                                                          • +
                                                                          • Weisstein, Eric W. "Chi-Squared Distribution." From MathWorld--A Wolfram Web Resource. diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html index 5f1fc1083..dd005309f 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html @@ -3,7 +3,7 @@ Exponential Distribution - + @@ -22,7 +22,7 @@
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                                                                            Exponential Distribution @@ -285,21 +285,21 @@ references
                                                                            -
                                                                              -
                                                                            • +
                                                                                +
                                                                              • Weisstein, Eric W. "Exponential Distribution." From MathWorld--A Wolfram Web Resource
                                                                              • -
                                                                              • +
                                                                              • Wolfram Mathematica calculator
                                                                              • -
                                                                              • +
                                                                              • NIST Exploratory Data Analysis
                                                                              • -
                                                                              • +
                                                                              • Wikipedia Exponential distribution
                                                                              • @@ -308,7 +308,7 @@ (See also the reference documentation for the related Extreme Distributions.)

                                                                                -
                                                                                • +
                                                                                  • Extreme Value Distributions, Theory and Applications Samuel Kotz & Saralees Nadarajah discuss the relationship of the types of extreme diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/extreme_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/extreme_dist.html index b4e1b90e8..7c26112b8 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/extreme_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/extreme_dist.html @@ -3,7 +3,7 @@ Extreme Value Distribution - + @@ -22,7 +22,7 @@
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                                                                                    Extreme Value Distribution diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html index 05a0f6a21..236493a55 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html @@ -3,7 +3,7 @@ F Distribution - + @@ -22,7 +22,7 @@
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                                                                                    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html index d4bfb8b27..25b80cce6 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html @@ -3,7 +3,7 @@ Gamma (and Erlang) Distribution - + @@ -22,7 +22,7 @@
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                                                                                    +
                                                                                    Gamma (and Erlang) Distribution diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/geometric_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/geometric_dist.html index fe09827a1..61cf4b5b5 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/geometric_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/geometric_dist.html @@ -3,7 +3,7 @@ Geometric Distribution - + @@ -22,7 +22,7 @@
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                                                                                    Geometric Distribution diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html index 5ab8ced41..ddc58adca 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html @@ -3,7 +3,7 @@ Hypergeometric Distribution - + @@ -22,7 +22,7 @@
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                                                                                    Hypergeometric Distribution diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_chi_squared_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_chi_squared_dist.html index 2436766a3..46c8b11cc 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_chi_squared_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_chi_squared_dist.html @@ -3,7 +3,7 @@ Inverse Chi Squared Distribution - + @@ -22,7 +22,7 @@
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                                                                                    Inverse Chi Squared Distribution @@ -84,23 +84,23 @@

                                                                                    See

                                                                                    -
                                                                                    -
                                                                                      -
                                                                                    1. +
                                                                                        +
                                                                                      1. Bayesian Data Analysis, Andrew Gelman, John B. Carlin, Hal S. Stern, Donald B. Rubin, ISBN-13: 978-1584883883, Chapman & Hall; 2 edition (29 July 2003).
                                                                                      2. -
                                                                                      3. +
                                                                                      4. Bayesian Computation with R, Jim Albert, ISBN-13: 978-0387922973, Springer; 2nd ed. edition (10 Jun 2009)
                                                                                      5. diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gamma_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gamma_dist.html index 0a9f625a9..0a6be5f41 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gamma_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gamma_dist.html @@ -3,7 +3,7 @@ Inverse Gamma Distribution - + @@ -22,7 +22,7 @@
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                                                                                        +
                                                                                        Inverse Gamma Distribution diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gaussian_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gaussian_dist.html index 16dc6afca..3b36b4aa1 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gaussian_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gaussian_dist.html @@ -3,7 +3,7 @@ Inverse Gaussian (or Inverse Normal) Distribution - + @@ -22,7 +22,7 @@
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                                                                                        Inverse Gaussian (or Inverse Normal) Distribution @@ -391,44 +391,44 @@ References
                                                                                        -
                                                                                          -
                                                                                        1. +
                                                                                            +
                                                                                          1. Wald, A. (1947). Sequential analysis. Wiley, NY.
                                                                                          2. -
                                                                                          3. +
                                                                                          4. The Inverse Gaussian distribution : theory, methodology, and applications, Raj S. Chhikara, J. Leroy Folks. ISBN 0824779975 (1989).
                                                                                          5. -
                                                                                          6. +
                                                                                          7. The Inverse Gaussian distribution : statistical theory and applications, Seshadri, V , ISBN - 0387986189 (pbk) (Dewey 519.2) (1998).
                                                                                          8. -
                                                                                          9. +
                                                                                          10. Numpy and Scipy Documentation.
                                                                                          11. -
                                                                                          12. +
                                                                                          13. R statmod invgauss functions.
                                                                                          14. -
                                                                                          15. +
                                                                                          16. R SuppDists invGauss functions. (Note that these R implementations names differ in case).
                                                                                          17. -
                                                                                          18. +
                                                                                          19. StatSci.org invgauss help.
                                                                                          20. -
                                                                                          21. +
                                                                                          22. invgauss R source.
                                                                                          23. -
                                                                                          24. +
                                                                                          25. pwald, qwald.
                                                                                          26. -
                                                                                          27. +
                                                                                          28. Brighton Webs wald.
                                                                                          29. diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/laplace_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/laplace_dist.html index 66a30cf10..d5450a464 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/laplace_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/laplace_dist.html @@ -3,7 +3,7 @@ Laplace Distribution - + @@ -22,7 +22,7 @@
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                                                                                            Laplace Distribution @@ -331,17 +331,17 @@ References
                                                                                            -
                                                                                              -
                                                                                            • +
                                                                                                +
                                                                                              • Weisstein, Eric W. "Laplace Distribution." From MathWorld--A Wolfram Web Resource.
                                                                                              • -
                                                                                              • +
                                                                                              • Laplace Distribution
                                                                                              • -
                                                                                              • +
                                                                                              • M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 1972, p. 930.
                                                                                              • diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/logistic_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/logistic_dist.html index e3c1e1c2e..0fc2c4523 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/logistic_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/logistic_dist.html @@ -3,7 +3,7 @@ Logistic Distribution - + @@ -22,7 +22,7 @@
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                                                                                                Logistic Distribution diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/lognormal_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/lognormal_dist.html index d1f470575..d8e588168 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/lognormal_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/lognormal_dist.html @@ -3,7 +3,7 @@ Log Normal Distribution - + @@ -22,7 +22,7 @@
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                                                                                                +
                                                                                                Log Normal Distribution diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_beta_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_beta_dist.html index a04e51808..2eaac3b59 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_beta_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_beta_dist.html @@ -3,7 +3,7 @@ Noncentral Beta Distribution - + @@ -22,7 +22,7 @@
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                                                                                                Noncentral Beta Distribution diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html index 2a8271538..499e9e1da 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html @@ -3,7 +3,7 @@ Noncentral Chi-Squared Distribution - + @@ -22,7 +22,7 @@
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                                                                                                Noncentral Chi-Squared Distribution diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_f_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_f_dist.html index 84603934b..20c11cfde 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_f_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_f_dist.html @@ -3,7 +3,7 @@ Noncentral F Distribution - + @@ -22,7 +22,7 @@
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                                                                                                Noncentral F Distribution diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_t_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_t_dist.html index db8f62d9a..ea139038d 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_t_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_t_dist.html @@ -3,7 +3,7 @@ Noncentral T Distribution - + @@ -22,7 +22,7 @@
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                                                                                                Noncentral T Distribution diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html index 66794effd..332c3dcce 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html @@ -3,7 +3,7 @@ Negative Binomial Distribution - + @@ -22,7 +22,7 @@
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                                                                                                Negative Binomial Distribution @@ -878,13 +878,13 @@

                                                                                                Implementation notes:

                                                                                                -
                                                                                                  -
                                                                                                • +
                                                                                                    +
                                                                                                  • The real concept type (that deliberately lacks the Lanczos approximation), was found to take several minutes to evaluate some extreme test values, so the test has been disabled for this type.
                                                                                                  • -
                                                                                                  • +
                                                                                                  • Much greater speed, and perhaps greater accuracy, might be achieved for extreme values by using a normal approximation. This is NOT been tested or implemented. diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html index 33143f135..28c6ecf90 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html @@ -3,7 +3,7 @@ Normal (Gaussian) Distribution - + @@ -22,7 +22,7 @@
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                                                                                                    Normal (Gaussian) Distribution diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html index 2a7331a6f..e0f9976f9 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html @@ -3,7 +3,7 @@ Pareto Distribution - + @@ -22,7 +22,7 @@
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                                                                                                    @@ -320,17 +320,17 @@ References
                                                                                                    -
                                                                                                      -
                                                                                                    • +
                                                                                                        +
                                                                                                      • Pareto Distribution
                                                                                                      • -
                                                                                                      • +
                                                                                                      • Weisstein, Eric W. "Pareto Distribution." From MathWorld--A Wolfram Web Resource.
                                                                                                      • -
                                                                                                      • +
                                                                                                      • Handbook of Statistical Distributions with Applications, K Krishnamoorthy, ISBN 1-58488-635-8, Chapter 23, pp 257 - 267. (Note the meaning of a and b is reversed in Wolfram and Krishnamoorthy). diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/poisson_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/poisson_dist.html index 5f7b4d590..5ac44182a 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/poisson_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/poisson_dist.html @@ -3,7 +3,7 @@ Poisson Distribution - + @@ -22,7 +22,7 @@
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                                                                                                        Poisson Distribution diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html index 0663b5d26..7a7390307 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html @@ -3,7 +3,7 @@ Rayleigh Distribution - + @@ -22,7 +22,7 @@
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                                                                                                        Rayleigh Distribution @@ -322,11 +322,11 @@ References
                                                                                                        -
                                                                                                        -
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                                                                                                        • + diff --git a/doc/sf_and_dist/html/math_toolkit/dist/future.html b/doc/sf_and_dist/html/math_toolkit/dist/future.html index 9d909633a..cc81b9be1 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/future.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/future.html @@ -3,7 +3,7 @@ Extras/Future Directions - + @@ -22,7 +22,7 @@
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                                                                                                          diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut.html index e9f0a041a..18cb69c3e 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut.html @@ -3,7 +3,7 @@ Statistical Distributions Tutorial - + @@ -22,7 +22,7 @@
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                                                                                                          Statistical Distributions Tutorial diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/dist_params.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/dist_params.html index 5f747760c..044e097bf 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/dist_params.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/dist_params.html @@ -3,7 +3,7 @@ Discrete Probability Distributions - + @@ -22,7 +22,7 @@
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                                                                                                          Discrete Probability Distributions diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview.html index ebe9959f2..c735e125c 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview.html @@ -3,7 +3,7 @@ Overview of Distributions - + @@ -22,7 +22,7 @@
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                                                                                                          diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/complements.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/complements.html index e3f7a3bba..35379df86 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/complements.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/complements.html @@ -3,7 +3,7 @@ Complements are supported too - and when to use them - + @@ -22,7 +22,7 @@
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                                                                                                          Complements are supported too - and when to use them diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/generic.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/generic.html index 9d20e9604..2b348fb26 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/generic.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/generic.html @@ -3,7 +3,7 @@ Generic operations common to all distributions are non-member functions - + @@ -22,7 +22,7 @@
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                                                                                                          Generic operations common to all distributions are non-member functions diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/headers.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/headers.html index e37ec40b5..d9b9fb8a1 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/headers.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/headers.html @@ -3,7 +3,7 @@ Headers and Namespaces - + @@ -22,7 +22,7 @@
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                                                                                                          Headers and Namespaces diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/objects.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/objects.html index dc772c078..8b85f9e1a 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/objects.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/objects.html @@ -3,7 +3,7 @@ Distributions are Objects - + @@ -22,7 +22,7 @@
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                                                                                                          Distributions are Objects @@ -50,13 +50,13 @@

                                                                                                          Making distributions class types does two things:

                                                                                                          -
                                                                                                            -
                                                                                                          • +
                                                                                                              +
                                                                                                            • It encapsulates the kind of distribution in the C++ type system; so, for example, Students-t distributions are always a different C++ type from Chi-Squared distributions.
                                                                                                            • -
                                                                                                            • +
                                                                                                            • The distribution objects store any parameters associated with the distribution: for example, the Students-t distribution has a degrees of freedom parameter that controls the shape of the distribution. diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/parameters.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/parameters.html index c56b7bcb0..e99532dd6 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/parameters.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/parameters.html @@ -3,7 +3,7 @@ Parameters can be calculated - + @@ -22,7 +22,7 @@
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                                                                                                              Parameters can be calculated diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/summary.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/summary.html index ee92a5a19..de7c68333 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/summary.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/summary.html @@ -3,7 +3,7 @@ Summary - + @@ -22,32 +22,32 @@
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                                                                                                              -
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                                                                                                              • +
                                                                                                                  +
                                                                                                                • Distributions are objects, which are constructed from whatever parameters the distribution may have.
                                                                                                                • -
                                                                                                                • +
                                                                                                                • Member functions allow you to retrieve the parameters of a distribution.
                                                                                                                • -
                                                                                                                • +
                                                                                                                • Generic non-member functions provide access to the properties that are common to all the distributions (PDF, CDF, quantile etc).
                                                                                                                • -
                                                                                                                • +
                                                                                                                • Complements of probabilities are calculated by wrapping the function's arguments in a call to complement(...).
                                                                                                                • -
                                                                                                                • +
                                                                                                                • Functions that accept a probability can accept a complement of the probability as well, by wrapping the function's arguments in a call to complement(...).
                                                                                                                • -
                                                                                                                • +
                                                                                                                • Static member functions allow the parameters of a distribution to be found from other information.
                                                                                                                • diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/variates.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/variates.html index 13bb6242d..5a023500c 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/variates.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/variates.html @@ -3,7 +3,7 @@ Random Variates and Distribution Parameters - + @@ -22,7 +22,7 @@
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                                                                                                                  Random Variates and Distribution Parameters diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg.html index 1ff7ff852..1ace5d9e3 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg.html @@ -3,7 +3,7 @@ Worked Examples - + @@ -22,7 +22,7 @@
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                                                                                                                  -
                                                                                                                  +
                                                                                                                  diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg.html index 39cee9096..c8385a7c2 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg.html @@ -3,7 +3,7 @@ Binomial Distribution Examples - + @@ -22,7 +22,7 @@
                                                                                                                  PrevUpHomeNext
                                                                                                                  -
                                                                                                                  +
                                                                                                                  Binomial Distribution Examples diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html index 901a98ea4..504bb9e3b 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html @@ -3,7 +3,7 @@ Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution - + @@ -22,7 +22,7 @@
                                                                                                                  PrevUpHomeNext
                                                                                                                  -
                                                                                                                  +
                                                                                                                  Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution @@ -103,13 +103,13 @@ interval. Had we calculate two single-sided intervals each with a risk that the true value is outside the interval of α, then:

                                                                                                                  -
                                                                                                                  • +
                                                                                                                    • The risk that it is less than the lower bound is α.

                                                                                                                    and

                                                                                                                    -
                                                                                                                    • +
                                                                                                                      • The risk that it is greater than the upper bound is also α.

                                                                                                                      diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_size_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_size_eg.html index 707e16e49..89e280018 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_size_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_size_eg.html @@ -3,7 +3,7 @@ Estimating Sample Sizes for a Binomial Distribution. - + @@ -22,7 +22,7 @@

                                                                                                                      PrevUpHomeNext
                                                                                                                      -
                                                                                                                      +
                                                                                                                      Estimating Sample Sizes for a Binomial Distribution. diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html index 546c83e69..062c4e21b 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html @@ -3,7 +3,7 @@ Binomial Coin-Flipping Example - + @@ -22,7 +22,7 @@
                                                                                                                      PrevUpHomeNext
                                                                                                                      -
                                                                                                                      +
                                                                                                                      Binomial Coin-Flipping Example @@ -66,8 +66,7 @@ { cout << "Using Binomial distribution to predict how many heads and tails." << endl; try - { - + {

                                                                                                                      @@ -84,8 +83,7 @@ int flips = 10; binomial flip(flips, success_fraction); -cout.precision(4); - +cout.precision(4);

                                                                                                                      @@ -105,8 +103,7 @@ // if success_fraction is exactly one half, // for example, when flipping 'fair' coins. cout << "Skewness if success_fraction is " << flip.success_fraction() - << " is " << skewness(flip) << endl << endl; // Expect zero for a 'fair' coin. - + << " is " << skewness(flip) << endl << endl; // Expect zero for a 'fair' coin.

                                                                                                                      @@ -116,8 +113,7 @@

                                                                                                                      cout << "For " << flip.trials() << " coin flips: " << endl;
                                                                                                                       cout << "Probability of getting no heads is " << pdf(flip, 0) << endl;
                                                                                                                      -cout << "Probability of getting at least one head is " << 1. - pdf(flip, 0) << endl;
                                                                                                                      -
                                                                                                                      +cout << "Probability of getting at least one head is " << 1. - pdf(flip, 0) << endl;

                                                                                                                      @@ -127,8 +123,7 @@

                                                                                                                      cout << "Probability of getting 0 or 1 heads is "
                                                                                                                      -  << pdf(flip, 0) + pdf(flip, 1) << endl; // sum of exactly == probabilities
                                                                                                                      -
                                                                                                                      + << pdf(flip, 0) + pdf(flip, 1) << endl; // sum of exactly == probabilities

                                                                                                                      @@ -137,8 +132,7 @@

                                                                                                                      cout << "Probability of getting 0 or 1 (<= 1) heads is " << cdf(flip, 1) << endl;
                                                                                                                      -cout << "Probability of getting 9 or 10 heads is " << pdf(flip, 9) + pdf(flip, 10) << endl;
                                                                                                                      -
                                                                                                                      +cout << "Probability of getting 9 or 10 heads is " << pdf(flip, 9) + pdf(flip, 10) << endl;

                                                                                                                      @@ -146,8 +140,7 @@

                                                                                                                      -
                                                                                                                      cout << "Probability of getting 9 or 10 heads is " << 1. - cdf(flip, 8) << endl;
                                                                                                                      -
                                                                                                                      +
                                                                                                                      cout << "Probability of getting 9 or 10 heads is " << 1. - cdf(flip, 8) << endl;

                                                                                                                      @@ -155,8 +148,7 @@

                                                                                                                      -
                                                                                                                      cout << "Probability of getting 9 or 10 heads is " << cdf(complement(flip, 8)) << endl;
                                                                                                                      -
                                                                                                                      +
                                                                                                                      cout << "Probability of getting 9 or 10 heads is " << cdf(complement(flip, 8)) << endl;

                                                                                                                      @@ -173,8 +165,7 @@

                                                                                                                      cout << "Probability of between 4 and 6 heads (4 or 5 or 6) is "
                                                                                                                         //  P(X == 4) + P(X == 5) + P(X == 6)
                                                                                                                      -  << pdf(flip, 4) + pdf(flip, 5) + pdf(flip, 6) << endl;
                                                                                                                      -
                                                                                                                      + << pdf(flip, 4) + pdf(flip, 5) + pdf(flip, 6) << endl;

                                                                                                                      @@ -184,8 +175,7 @@

                                                                                                                      cout << "Probability of between 4 and 6 heads (4 or 5 or 6) is "
                                                                                                                         // P(X <= 6) - P(X <= 3) == P(X < 4)
                                                                                                                      -  << cdf(flip, 6) - cdf(flip, 3) << endl;
                                                                                                                      -
                                                                                                                      + << cdf(flip, 6) - cdf(flip, 3) << endl;

                                                                                                                      @@ -196,8 +186,7 @@

                                                                                                                      cout << "Probability of between 3 and 7 heads (3, 4, 5, 6 or 7) is "
                                                                                                                         // P(X <= 7) - P(X <= 2) == P(X < 3)
                                                                                                                         << cdf(flip, 7) - cdf(flip, 2) << endl;
                                                                                                                      -cout << endl;
                                                                                                                      -
                                                                                                                      +cout << endl;

                                                                                                                      @@ -226,8 +215,7 @@ cout << setw(2) << successes << " " << setw(10) << left << probability << " or 1 in " << 1. / probability << ", or " << probability * 100. << "%"<< endl; -} // for i - +} // for i

                                                                                                                      @@ -238,8 +226,7 @@

                                                                                                                      }
                                                                                                                       catch(const std::exception& e)
                                                                                                                       {
                                                                                                                      -  //
                                                                                                                      -
                                                                                                                      + //

                                                                                                                      diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html index 2259eba73..9a5330d01 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html @@ -3,7 +3,7 @@ Binomial Quiz Example - + @@ -22,7 +22,7 @@

                                                                                                                      PrevUpHomeNext
                                                                                                                      -
                                                                                                                      +
                                                                                                                      Binomial Quiz Example @@ -55,6 +55,8 @@ using std::setw; using std::setprecision; #include <exception> using std::exception; + +

                                                                                                                      @@ -68,8 +70,7 @@
                                                                                                                      int questions = 16; // All the questions in the quiz.
                                                                                                                       int answers = 4; // Possible answers to each question.
                                                                                                                       double success_fraction = 1. / answers; // If a random guess, p = 1/4 = 0.25.
                                                                                                                      -binomial quiz(questions, success_fraction);
                                                                                                                      -
                                                                                                                      +binomial quiz(questions, success_fraction);

                                                                                                                      @@ -80,8 +81,7 @@

                                                                                                                      cout << "In a quiz with " << quiz.trials()
                                                                                                                         << " questions and with a probability of guessing right of "
                                                                                                                         << quiz.success_fraction() * 100 << " %"
                                                                                                                      -  << " or 1 in " << static_cast<int>(1. / quiz.success_fraction()) << endl;
                                                                                                                      -
                                                                                                                      + << " or 1 in " << static_cast<int>(1. / quiz.success_fraction()) << endl;

                                                                                                                      @@ -96,8 +96,7 @@ cout << "Probability of getting exactly " << pass_score << " answers right by chance is " << pdf(quiz, pass_score) << endl; cout << "Probability of getting all " << questions << " answers right by chance is " - << pdf(quiz, questions) << endl; - + << pdf(quiz, questions) << endl;

                                                                                                                      Probability of getting none right is 0.0100226
                                                                                                                      @@ -120,8 +119,7 @@ Probability of getting exactly all 16 answers right by chance is 2.32831e-010
                                                                                                                         double probability = pdf(quiz, successes);
                                                                                                                         cout << setw(2) << successes << "      " << probability << endl;
                                                                                                                       }
                                                                                                                      -cout << endl;
                                                                                                                      -
                                                                                                                      +cout << endl;

                                                                                                                      Guessed Probability
                                                                                                                      @@ -148,8 +146,7 @@ Probability of getting exactly all 16 answers right by chance is 2.32831e-010
                                                                                                                                   

                                                                                                                      -
                                                                                                                      cout << "Probability of getting none or one right is " << pdf(quiz, 0) + pdf(quiz, 1) << endl;
                                                                                                                      -
                                                                                                                      +
                                                                                                                      cout << "Probability of getting none or one right is " << pdf(quiz, 0) + pdf(quiz, 1) << endl;

                                                                                                                      Probability of getting none or one right is 0.0634764
                                                                                                                      @@ -161,8 +158,7 @@ Probability of getting exactly all 16 answers right by chance is 2.32831e-010
                                                                                                                                   

                                                                                                                      -
                                                                                                                      cout << "Probability of getting none or one right is " << cdf(quiz, 1) << endl;
                                                                                                                      -
                                                                                                                      +
                                                                                                                      cout << "Probability of getting none or one right is " << cdf(quiz, 1) << endl;

                                                                                                                      Probability of getting none or one right is 0.0634764
                                                                                                                      @@ -173,8 +169,7 @@ Probability of getting exactly all 16 answers right by chance is 2.32831e-010
                                                                                                                                   

                                                                                                                      -
                                                                                                                      cout << "Probability of getting <= 10 right (to fail) is " << cdf(quiz, 10) << endl;
                                                                                                                      -
                                                                                                                      +
                                                                                                                      cout << "Probability of getting <= 10 right (to fail) is " << cdf(quiz, 10) << endl;

                                                                                                                      Probability of getting <= 10 right (to fail) is 0.999715
                                                                                                                      @@ -189,8 +184,7 @@ Probability of getting exactly all 16 answers right by chance is 2.32831e-010
                                                                                                                                   

                                                                                                                      -
                                                                                                                      cout << "Probability of getting > 10 right (to pass) is " << 1 - cdf(quiz, 10) << endl;
                                                                                                                      -
                                                                                                                      +
                                                                                                                      cout << "Probability of getting > 10 right (to pass) is " << 1 - cdf(quiz, 10) << endl;

                                                                                                                      Probability of getting > 10 right (to pass) is 0.000285239
                                                                                                                      @@ -201,8 +195,7 @@ Probability of getting exactly all 16 answers right by chance is 2.32831e-010
                                                                                                                                   

                                                                                                                      -
                                                                                                                      cout << "Probability of getting > 10 right (to pass) is " << cdf(complement(quiz, 10)) << endl;
                                                                                                                      -
                                                                                                                      +
                                                                                                                      cout << "Probability of getting > 10 right (to pass) is " << cdf(complement(quiz, 10)) << endl;

                                                                                                                      Probability of getting > 10 right (to pass) is 0.000285239
                                                                                                                      @@ -212,8 +205,7 @@ Probability of getting exactly all 16 answers right by chance is 2.32831e-010
                                                                                                                                   

                                                                                                                      -
                                                                                                                      BOOST_ASSERT((cdf(quiz, 10) + cdf(complement(quiz, 10))) == 1.);
                                                                                                                      -
                                                                                                                      +
                                                                                                                      BOOST_ASSERT((cdf(quiz, 10) + cdf(complement(quiz, 10))) == 1.);

                                                                                                                      @@ -224,8 +216,7 @@ Probability of getting exactly all 16 answers right by chance is 2.32831e-010

                                                                                                                      cout << "Probability of getting less than " << pass_score
                                                                                                                         << " (< " << pass_score << ") answers right by guessing is "
                                                                                                                      -  << cdf(quiz, pass_score -1) << endl;
                                                                                                                      -
                                                                                                                      + << cdf(quiz, pass_score -1) << endl;

                                                                                                                      Probability of getting less than 11 (< 11) answers right by guessing is 0.999715
                                                                                                                      @@ -244,8 +235,7 @@ Probability of getting exactly all 16 answers right by chance is 2.32831e-010
                                                                                                                         << cdf(complement(quiz, pass_score-1))
                                                                                                                         << ", only 1 in " << 1/cdf(complement(quiz, pass_score-1)) << endl;
                                                                                                                       
                                                                                                                      -BOOST_ASSERT((cdf(quiz, pass_score -1) + cdf(complement(quiz, pass_score-1))) == 1);
                                                                                                                      -
                                                                                                                      +BOOST_ASSERT((cdf(quiz, pass_score -1) + cdf(complement(quiz, pass_score-1))) == 1);

                                                                                                                      Probability of getting at least 11 (>= 11) answers right by guessing is 0.000285239, only 1 in 3505.83
                                                                                                                      @@ -261,8 +251,7 @@ Probability of getting exactly all 16 answers right by chance is 2.32831e-010
                                                                                                                         cout << setw(2) << score << "           " << setprecision(10)
                                                                                                                           << cdf(quiz, score) << endl;
                                                                                                                       }
                                                                                                                      -cout << endl;
                                                                                                                      -
                                                                                                                      +cout << endl;

                                                                                                                      At most (<=)
                                                                                                                      @@ -292,8 +281,7 @@ Guessed OK   Probability
                                                                                                                       {
                                                                                                                         cout << setw(2) << score << "           "  << setprecision(10)
                                                                                                                           << cdf(complement(quiz, score)) << endl;
                                                                                                                      -}
                                                                                                                      -
                                                                                                                      +}

                                                                                                                      At least (>)
                                                                                                                      @@ -336,8 +324,7 @@ Guessed OK   Probability
                                                                                                                       cout.precision(4);
                                                                                                                       cout << "Probability of getting between "
                                                                                                                         << low << " and " << high << " answers right by guessing is "
                                                                                                                      -  << sum  << endl; // 0.61323
                                                                                                                      -
                                                                                                                      + << sum << endl; // 0.61323

                                                                                                                      Probability of getting between 3 and 5 answers right by guessing is 0.6132
                                                                                                                      @@ -348,8 +335,7 @@ Guessed OK   Probability
                                                                                                                       

                                                                                                                      cout << "Probability of getting between " << low << " and " << high << " answers right by guessing is "
                                                                                                                      -  <<  cdf(quiz, high) - cdf(quiz, low - 1) << endl; // 0.61323
                                                                                                                      -
                                                                                                                      + << cdf(quiz, high) - cdf(quiz, low - 1) << endl; // 0.61323

                                                                                                                      Probability of getting between 3 and 5 answers right by guessing is 0.6132
                                                                                                                      @@ -367,8 +353,7 @@ Guessed OK   Probability
                                                                                                                         <<  cdf(quiz, high) - cdf(quiz, low - 1) << endl; // 1 <= x 8 P = 0.9825
                                                                                                                       low = 4; high = 4;
                                                                                                                       cout << "Probability of getting between " << low << " and " << high << " answers right by guessing is "
                                                                                                                      -  <<  cdf(quiz, high) - cdf(quiz, low - 1) << endl; // 4 <= x 4 P = 0.22520
                                                                                                                      -
                                                                                                                      + << cdf(quiz, high) - cdf(quiz, low - 1) << endl; // 4 <= x 4 P = 0.22520

                                                                                                                      Probability of getting between 1 and 6 answers right by guessing is 0.9104
                                                                                                                      @@ -392,8 +377,7 @@ Probability of getting between 4 and 4 answers right by guessing is 0.2252
                                                                                                                         <<  ceil(mean(quiz) - standard_deviation(quiz))  << " and "
                                                                                                                         << floor(mean(quiz) + standard_deviation(quiz)) << " correct." << endl;
                                                                                                                       cout << "Mode (the most frequent) is " << mode(quiz) << endl;
                                                                                                                      -cout << "Skewness is " << skewness(quiz) << endl;
                                                                                                                      -
                                                                                                                      +cout << "Skewness is " << skewness(quiz) << endl;

                                                                                                                      By guessing, on average, one can expect to get 4 correct answers.
                                                                                                                      @@ -426,8 +410,7 @@ Skewness is 0.2887
                                                                                                                         << quantile(complement(quiz, 0.02)) << endl; //  2 to 98%
                                                                                                                       
                                                                                                                       cout << "If guessing then percentiles 1 to 99% will get " << quantile(quiz, 0.01)
                                                                                                                      -  << " to " << quantile(complement(quiz, 0.01)) << " right." << endl;
                                                                                                                      -
                                                                                                                      + << " to " << quantile(complement(quiz, 0.01)) << " right." << endl;

                                                                                                                      @@ -474,8 +457,7 @@ Deciles 1 to 6 using boost::math::policies::discrete_quantile; using boost::math::policies::real; using boost::math::policies::integer_round_outwards; // Default. -typedef boost::math::policies::policy<discrete_quantile<real> > real_quantile_policy; - +typedef boost::math::policies::policy<discrete_quantile<real> > real_quantile_policy;

                                                                                                                      @@ -491,8 +473,7 @@ Deciles 1 to 6

                                                                                                                      using boost::math::binomial_distribution;
                                                                                                                      -typedef binomial_distribution<double, real_quantile_policy> real_quantile_binomial;
                                                                                                                      -
                                                                                                                      +typedef binomial_distribution<double, real_quantile_policy> real_quantile_binomial;

                                                                                                                      @@ -500,8 +481,7 @@ Deciles 1 to 6

                                                                                                                      -
                                                                                                                      real_quantile_binomial quiz_real(questions, success_fraction);
                                                                                                                      -
                                                                                                                      +
                                                                                                                      real_quantile_binomial quiz_real(questions, success_fraction);

                                                                                                                      @@ -524,8 +504,7 @@ Deciles 1 to 6 << quantile(complement(quiz_real, 0.02)) << endl; // 2 to 98% 0.31311 7.7880 cout << "If guessing, then percentiles 1 to 99% will get " << quantile(quiz_real, 0.01) - << " to " << quantile(complement(quiz_real, 0.01)) << " right." << endl; - + << " to " << quantile(complement(quiz_real, 0.01)) << " right." << endl;

                                                                                                                      Real Quantiles
                                                                                                                      diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/c_sharp.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/c_sharp.html
                                                                                                                      index 51d811b54..626f75249 100644
                                                                                                                      --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/c_sharp.html
                                                                                                                      +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/c_sharp.html
                                                                                                                      @@ -3,7 +3,7 @@
                                                                                                                       
                                                                                                                       Using the Distributions from Within C#
                                                                                                                       
                                                                                                                      -
                                                                                                                      +
                                                                                                                       
                                                                                                                       
                                                                                                                       
                                                                                                                      @@ -22,7 +22,7 @@
                                                                                                                       
                                                                                                                      PrevUpHomeNext
                                                                                                                      -
                                                                                                                      +
                                                                                                                      Using the Distributions from Within C# diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg.html index 09256043b..4f3af08fe 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg.html @@ -3,7 +3,7 @@ Chi Squared Distribution Examples - + @@ -22,7 +22,7 @@
                                                                                                                      PrevUpHomeNext
                                                                                                                      -
                                                                                                                      +
                                                                                                                      Chi Squared Distribution Examples diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html index 6be1a9d28..27131bbcf 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html @@ -3,7 +3,7 @@ Confidence Intervals on the Standard Deviation - + @@ -22,7 +22,7 @@
                                                                                                                      PrevUpHomeNext
                                                                                                                      -
                                                                                                                      +
                                                                                                                      Confidence Intervals on the Standard Deviation diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html index bb2197d59..72b9579ee 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html @@ -3,7 +3,7 @@ Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation - + @@ -22,7 +22,7 @@
                                                                                                                      PrevUpHomeNext
                                                                                                                      -
                                                                                                                      +
                                                                                                                      Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_test.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_test.html index 4e154e43d..01aac83fa 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_test.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_test.html @@ -3,7 +3,7 @@ Chi-Square Test for the Standard Deviation - + @@ -22,7 +22,7 @@
                                                                                                                      PrevUpHomeNext
                                                                                                                      -
                                                                                                                      +
                                                                                                                      Chi-Square Test for the Standard Deviation diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/dist_construct_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/dist_construct_eg.html index a92b6cdf6..4c772ca7d 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/dist_construct_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/dist_construct_eg.html @@ -3,7 +3,7 @@ Distribution Construction Example - + @@ -22,7 +22,7 @@
                                                                                                                      PrevUpHomeNext
                                                                                                                      -
                                                                                                                      +
                                                                                                                      Distribution Construction Example @@ -52,8 +52,7 @@ #include <boost/math/distributions/binomial.hpp> // for binomial_distribution. #include <boost/math/distributions/beta.hpp> // for beta_distribution. #include <boost/math/distributions/gamma.hpp> // for gamma_distribution. -#include <boost/math/distributions/normal.hpp> // for normal_distribution. -
                                                                                                                      +#include <boost/math/distributions/normal.hpp> // for normal_distribution.

                                                                                                                      @@ -65,8 +64,7 @@

                                                                                                                      -
                                                                                                                      boost::math::negative_binomial_distribution<double> mydist0(8., 0.25);
                                                                                                                      -
                                                                                                                      +
                                                                                                                      boost::math::negative_binomial_distribution<double> mydist0(8., 0.25);

                                                                                                                      @@ -74,8 +72,7 @@

                                                                                                                      -
                                                                                                                      using namespace boost::math;
                                                                                                                      -
                                                                                                                      +
                                                                                                                      using namespace boost::math;

                                                                                                                      @@ -84,8 +81,7 @@

                                                                                                                      -
                                                                                                                      using boost::math::negative_binomial_distribution;
                                                                                                                      -
                                                                                                                      +
                                                                                                                      using boost::math::negative_binomial_distribution;

                                                                                                                      @@ -98,8 +94,7 @@

                                                                                                                      -
                                                                                                                      negative_binomial_distribution<> mydist9(8., 0.25); // Uses default RealType = double.
                                                                                                                      -
                                                                                                                      +
                                                                                                                      negative_binomial_distribution<> mydist9(8., 0.25); // Uses default RealType = double.

                                                                                                                      @@ -125,8 +120,7 @@

                                                                                                                      -
                                                                                                                      using boost::math::negative_binomial;
                                                                                                                      -
                                                                                                                      +
                                                                                                                      using boost::math::negative_binomial;

                                                                                                                      @@ -134,8 +128,7 @@

                                                                                                                      -
                                                                                                                      negative_binomial mydist(8., 0.25);
                                                                                                                      -
                                                                                                                      +
                                                                                                                      negative_binomial mydist(8., 0.25);

                                                                                                                      @@ -143,8 +136,7 @@

                                                                                                                      -
                                                                                                                      negative_binomial mydist10(5., 0.4); // Both arguments double.
                                                                                                                      -
                                                                                                                      +
                                                                                                                      negative_binomial mydist10(5., 0.4); // Both arguments double.

                                                                                                                      @@ -152,8 +144,7 @@

                                                                                                                      -
                                                                                                                      negative_binomial mydist11(5, 0.4); // Using provided typedef double, int and double arguments.
                                                                                                                      -
                                                                                                                      +
                                                                                                                      negative_binomial mydist11(5, 0.4); // Using provided typedef double, int and double arguments.

                                                                                                                      @@ -162,8 +153,7 @@

                                                                                                                      negative_binomial mydist12(5., 0.4F); // Double and float arguments.
                                                                                                                      -negative_binomial mydist13(5, 1); // Both arguments integer.
                                                                                                                      -
                                                                                                                      +negative_binomial mydist13(5, 1); // Both arguments integer.

                                                                                                                      @@ -172,8 +162,7 @@

                                                                                                                      binomial mybinomial(1, 0.5); // is more concise than
                                                                                                                      -binomial_distribution<> mybinomd1(1, 0.5);
                                                                                                                      -
                                                                                                                      +binomial_distribution<> mybinomd1(1, 0.5);

                                                                                                                      @@ -198,8 +187,7 @@ error C3861: 'mybetad0': identifier not found

                                                                                                                      using boost::math::beta_distribution;
                                                                                                                      -beta_distribution<> mybetad1(1, 0.5);
                                                                                                                      -
                                                                                                                      +beta_distribution<> mybetad1(1, 0.5);

                                                                                                                      @@ -207,8 +195,7 @@ error C3861: 'mybetad0': identifier not found

                                                                                                                      -
                                                                                                                      gamma_distribution<> mygammad1(1, 0.5);
                                                                                                                      -
                                                                                                                      +
                                                                                                                      gamma_distribution<> mygammad1(1, 0.5);

                                                                                                                      @@ -235,8 +222,7 @@ error C3861: 'mybetad0': identifier not found negative_binomial_distribution<double> mydist6(8., 0.25); // Explicit long double precision: -negative_binomial_distribution<long double> mydist7(8., 0.25); - +negative_binomial_distribution<long double> mydist7(8., 0.25);

                                                                                                                      @@ -279,8 +265,7 @@ error C3861: 'mybetad0': identifier not found normal norm3(2, 3); // Mean = 2, std deviation = 3. return 0; -} // int main() - +} // int main()

                                                                                                                      diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/error_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/error_eg.html index e2bfdc453..7dc6113f0 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/error_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/error_eg.html @@ -3,7 +3,7 @@ Error Handling Example - + @@ -22,7 +22,7 @@

                                                                                                                      PrevUpHomeNext
                                                                                                                      -
                                                                                                                      +
                                                                                                                      Error Handling Example @@ -80,7 +80,9 @@

                                                                                                                      -
                                                                                                                      // Boost
                                                                                                                      +
                                                                                                                         #define BOOST_MATH_DOMAIN_ERROR_POLICY ignore_error
                                                                                                                      +
                                                                                                                      +// Boost
                                                                                                                       #include <boost/math/distributions/students_t.hpp>
                                                                                                                          using boost::math::students_t;  // Probability of students_t(df, t).
                                                                                                                       
                                                                                                                      @@ -93,8 +95,7 @@
                                                                                                                          using std::exception;
                                                                                                                       
                                                                                                                       #include <cstddef>
                                                                                                                      -   // using ::errno
                                                                                                                      -
                                                                                                                      + // using ::errno

                                                                                                                      @@ -136,8 +137,7 @@ "\n""Message from thrown exception was:\n " << e.what() << std::endl; } return 0; -} // int main() - +} // int main()

                                                                                                                      diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/f_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/f_eg.html index 263781cd0..04410b317 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/f_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/f_eg.html @@ -3,7 +3,7 @@ F Distribution Examples - + @@ -22,7 +22,7 @@

                                                                                                                      PrevUpHomeNext
                                                                                                                      -
                                                                                                                      +
                                                                                                                      F Distribution Examples diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg.html index 43b01c9d6..a321584eb 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg.html @@ -3,7 +3,7 @@ Find Location and Scale Examples - + @@ -22,7 +22,7 @@
                                                                                                                      PrevUpHomeNext
                                                                                                                      -
                                                                                                                      +
                                                                                                                      Find Location and Scale Examples diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html index c24476f50..2881c4bcf 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html @@ -3,7 +3,7 @@ Find Location (Mean) Example - + @@ -22,7 +22,7 @@
                                                                                                                      PrevUpHomeNext
                                                                                                                      -
                                                                                                                      +
                                                                                                                      Find Location (Mean) Example @@ -50,6 +50,7 @@ using std::setw; using std::setprecision; #include <limits> using std::numeric_limits; +

                                                                                                                      @@ -61,8 +62,7 @@

                                                                                                                      normal N01;  // Default 'standard' normal distribution with zero mean and 
                                                                                                                      -double sd = 1.; // normal default standard deviation is 1.
                                                                                                                      -
                                                                                                                      +double sd = 1.; // normal default standard deviation is 1.

                                                                                                                      @@ -82,8 +82,7 @@ cout << "Normal distribution with mean = " << N01.location() << ", standard deviation " << N01.scale() << ", has " << "fraction > " << z - << ", p = " << cdf(complement(N01, z)) << endl; // Note: uses complement. - + << ", p = " << cdf(complement(N01, z)) << endl; // Note: uses complement.

                                                                                                                      Normal distribution with mean = 0, standard deviation 1, has fraction <= -2, p = 0.0227501
                                                                                                                      @@ -95,8 +94,7 @@ Normal distribution with mean = 0, standard deviation 1, has fraction > -2, p
                                                                                                                       

                                                                                                                      double l = find_location<normal>(z, p, sd);
                                                                                                                      -cout << "offset location (mean) = " << l << endl;
                                                                                                                      -
                                                                                                                      +cout << "offset location (mean) = " << l << endl;

                                                                                                                      @@ -114,8 +112,7 @@ Normal distribution with mean = 0, standard deviation 1, has fraction > -2, p

                                                                                                                      -
                                                                                                                      normal np001pc(l, sd); // Same standard_deviation (scale) but with mean (location) shifted.
                                                                                                                      -
                                                                                                                      +
                                                                                                                      normal np001pc(l, sd); // Same standard_deviation (scale) but with mean (location) shifted.

                                                                                                                      @@ -128,8 +125,7 @@ Normal distribution with mean = 0, standard deviation 1, has fraction > -2, p << ", p = " << cdf(np001pc, z) << endl; cout << "Normal distribution with mean = " << l << " has " << "fraction > " << z - << ", p = " << cdf(complement(np001pc, z)) << endl; - + << ", p = " << cdf(complement(np001pc, z)) << endl;

                                                                                                                      Normal distribution with mean = 1.09023 has fraction <= -2, p = 0.001
                                                                                                                      @@ -152,8 +148,7 @@ Normal distribution with mean = 1.09023 has fraction > -2, p = 0.999
                                                                                                                       

                                                                                                                      using boost::math::policies::policy;
                                                                                                                       using boost::math::policies::domain_error;
                                                                                                                      -using boost::math::policies::ignore_error;
                                                                                                                      -
                                                                                                                      +using boost::math::policies::ignore_error;

                                                                                                                      @@ -170,8 +165,7 @@ Normal distribution with mean = 1.09023 has fraction > -2, p = 0.999 // Default policy, fully specified. l = find_location<normal>(z, p, sd, boost::math::policies::policy<>()); // A new policy, ignoring domain errors, without using a typedef. -l = find_location<normal>(z, p, sd, policy<domain_error<ignore_error> >()); - +l = find_location<normal>(z, p, sd, policy<domain_error<ignore_error> >());

                                                                                                                      diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html index 39dec71bf..b0cb0289f 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html @@ -3,7 +3,7 @@ Find mean and standard deviation example - + @@ -22,7 +22,7 @@

                                                                                                                      PrevUpHomeNext
                                                                                                                      -
                                                                                                                      +
                                                                                                                      Find mean and standard deviation example @@ -77,8 +77,7 @@

                                                                                                                      double mean = 3.; // kg
                                                                                                                       double standard_deviation = 0.1; // kg
                                                                                                                      -normal packs(mean, standard_deviation);
                                                                                                                      -
                                                                                                                      +normal packs(mean, standard_deviation);

                                                                                                                      @@ -89,8 +88,7 @@

                                                                                                                      double max_weight = 3.1; // kg
                                                                                                                       cout << "Percentage of packs > " << max_weight << " is "
                                                                                                                      -<< cdf(complement(packs, max_weight)) * 100. << endl; // P(X > 3.1)
                                                                                                                      -
                                                                                                                      +<< cdf(complement(packs, max_weight)) * 100. << endl; // P(X > 3.1)

                                                                                                                      @@ -107,8 +105,7 @@

                                                                                                                      double minimum_weight = 2.9;
                                                                                                                       cout <<"Fraction of packs <= " << minimum_weight << " with a mean of " << mean
                                                                                                                         << " is " << cdf(complement(packs, minimum_weight)) << endl;
                                                                                                                      -// fraction of packs <= 2.9 with a mean of 3 is 0.841345
                                                                                                                      -
                                                                                                                      +// fraction of packs <= 2.9 with a mean of 3 is 0.841345

                                                                                                                      @@ -131,8 +128,7 @@ cout << "Fraction of packs >= " << minimum_weight << " with a mean of " << xpacks.mean() << " is " << cdf(complement(xpacks, minimum_weight)) << endl; -// fraction of packs >= 2.9 with a mean of 3.06449 is 0.950005 - +// fraction of packs >= 2.9 with a mean of 3.06449 is 0.950005

                                                                                                                      @@ -151,8 +147,7 @@ cout << "Setting the packer to " << nominal_mean << " will mean that " << "fraction of packs >= " << minimum_weight << " is " << cdf(complement(nominal_packs, minimum_weight)) << endl; -// Setting the packer to 3.06449 will mean that fraction of packs >= 2.9 is 0.95 - +// Setting the packer to 3.06449 will mean that fraction of packs >= 2.9 is 0.95

                                                                                                                      @@ -164,8 +159,7 @@

                                                                                                                      #include <boost/math/distributions/find_location.hpp>
                                                                                                                      -  using boost::math::find_location;
                                                                                                                      -
                                                                                                                      + using boost::math::find_location;

                                                                                                                      @@ -175,8 +169,7 @@

                                                                                                                      double safe_mean = find_location<normal>(minimum_weight, under_fraction, standard_deviation);
                                                                                                                      -normal good_packs(safe_mean, standard_deviation);
                                                                                                                      -
                                                                                                                      +normal good_packs(safe_mean, standard_deviation);

                                                                                                                      @@ -187,8 +180,7 @@

                                                                                                                      cout << "Setting the packer to " << nominal_mean << " will mean that "
                                                                                                                         << "fraction of packs >= " << minimum_weight
                                                                                                                         << " is " << cdf(complement(good_packs, minimum_weight)) << endl;
                                                                                                                      -// Setting the packer to 3.06449 will mean that fraction of packs >= 2.9 is 0.95
                                                                                                                      -
                                                                                                                      +// Setting the packer to 3.06449 will mean that fraction of packs >= 2.9 is 0.95

                                                                                                                      @@ -221,8 +213,7 @@ cout << "Cauchy Setting the packer to " << mean << " will mean that " << "fraction of packs >= " << minimum_weight << " is " << cdf(complement(cpacks, minimum_weight)) << endl; -// Cauchy Setting the packer to 3 will mean that fraction of packs >= 2.9 is 0.75 - +// Cauchy Setting the packer to 3 will mean that fraction of packs >= 2.9 is 0.75

                                                                                                                      @@ -234,8 +225,7 @@

                                                                                                                      double lc = find_location<cauchy>(minimum_weight, under_fraction, standard_deviation);
                                                                                                                       cout << "find_location<cauchy>(minimum_weight, over fraction, standard_deviation); " << lc << endl;
                                                                                                                      -// find_location<cauchy>(minimum_weight, over fraction, packs.standard_deviation()); 3.53138
                                                                                                                      -
                                                                                                                      +// find_location<cauchy>(minimum_weight, over fraction, packs.standard_deviation()); 3.53138

                                                                                                                      @@ -251,8 +241,7 @@ cout << "Cauchy Setting the packer to " << lc << " will mean that " << "fraction of packs >= " << minimum_weight << " is " << cdf(complement(goodcpacks, minimum_weight)) << endl; -// Cauchy Setting the packer to 3.53138 will mean that fraction of packs >= 2.9 is 0.95 - +// Cauchy Setting the packer to 3.53138 will mean that fraction of packs >= 2.9 is 0.95

                                                                                                                      @@ -265,8 +254,7 @@ << find_location<cauchy>(minimum_weight, 0.99, standard_deviation) << " will mean that " << "fraction of packs >= " << minimum_weight - << " is " << cdf(complement(goodcpacks, minimum_weight)) << endl; - + << " is " << cdf(complement(goodcpacks, minimum_weight)) << endl;

                                                                                                                      @@ -325,8 +313,7 @@

                                                                                                                      double p = 0.05; // wanted p th quantile.
                                                                                                                       cout << "Quantile of " << p << " = " << quantile(packs, p)
                                                                                                                      -  << ", mean = " << packs.mean() << ", sd = " << packs.standard_deviation() << endl;
                                                                                                                      -
                                                                                                                      + << ", mean = " << packs.mean() << ", sd = " << packs.standard_deviation() << endl;

                                                                                                                      @@ -351,8 +338,7 @@ cout <<"Fraction of packs >= " << minimum_weight << " with a mean of " << mean << " and standard deviation of " << pack05.standard_deviation() << " is " << cdf(complement(pack05, minimum_weight)) << endl; -// Fraction of packs >= 2.9 with a mean of 3 and standard deviation of 0.05 is 0.97725 - +// Fraction of packs >= 2.9 with a mean of 3 and standard deviation of 0.05 is 0.97725

                                                                                                                      @@ -371,8 +357,7 @@ cout <<"Fraction of packs >= " << minimum_weight << " with a mean of " << mean << " and standard deviation of " << pack06.standard_deviation() << " is " << cdf(complement(pack06, minimum_weight)) << endl; -// Fraction of packs >= 2.9 with a mean of 3 and standard deviation of 0.06 is 0.95221 - +// Fraction of packs >= 2.9 with a mean of 3 and standard deviation of 0.06 is 0.95221

                                                                                                                      @@ -409,8 +394,7 @@ cout << "For the "<< p << "th quantile to be located at " << minimum_weight << ", would need a standard deviation of " << sd95 << endl; -// For the 0.05th quantile to be located at 2.9, would need a standard deviation of 0.0607957 - +// For the 0.05th quantile to be located at 2.9, would need a standard deviation of 0.0607957

                                                                                                                      @@ -423,8 +407,7 @@ cout <<"Fraction of packs >= " << minimum_weight << " with a mean of " << mean << " and standard deviation of " << pack95.standard_deviation() << " is " << cdf(complement(pack95, minimum_weight)) << endl; -// Fraction of packs >= 2.9 with a mean of 3 and standard deviation of 0.0607957 is 0.95 - +// Fraction of packs >= 2.9 with a mean of 3 and standard deviation of 0.0607957 is 0.95

                                                                                                                      @@ -435,8 +418,7 @@

                                                                                                                      double ss = find_scale<normal>(minimum_weight, under_fraction, packs.mean());
                                                                                                                       cout << "find_scale<normal>(minimum_weight, under_fraction, packs.mean()); " << ss << endl;
                                                                                                                      -// find_scale<normal>(minimum_weight, under_fraction, packs.mean()); 0.0607957
                                                                                                                      -
                                                                                                                      +// find_scale<normal>(minimum_weight, under_fraction, packs.mean()); 0.0607957

                                                                                                                      @@ -444,8 +426,7 @@

                                                                                                                      -
                                                                                                                      double over_fraction = 0.95;
                                                                                                                      -
                                                                                                                      +
                                                                                                                      double over_fraction = 0.95;

                                                                                                                      @@ -469,8 +450,7 @@

                                                                                                                      double ss1o = find_scale<normal>(minimum_weight, 1 - over_fraction, packs.mean());
                                                                                                                       cout << "find_scale<normal>(minimum_weight, under_fraction, packs.mean()); " << ss1o << endl;
                                                                                                                      -// find_scale<normal>(minimum_weight, under_fraction, packs.mean()); 0.0607957
                                                                                                                      -
                                                                                                                      +// find_scale<normal>(minimum_weight, under_fraction, packs.mean()); 0.0607957

                                                                                                                      @@ -483,8 +463,7 @@

                                                                                                                      double ssc = find_scale<normal>(complement(minimum_weight, over_fraction, packs.mean()));
                                                                                                                       cout << "find_scale<normal>(complement(minimum_weight, over_fraction, packs.mean())); " << ssc << endl;
                                                                                                                      -// find_scale<normal>(complement(minimum_weight, over_fraction, packs.mean())); 0.0607957
                                                                                                                      -
                                                                                                                      +// find_scale<normal>(complement(minimum_weight, over_fraction, packs.mean())); 0.0607957

                                                                                                                      @@ -499,21 +478,20 @@ cout <<"Fraction of packs >= " << minimum_weight << " with a mean of " << mean << " and standard deviation of " << pack95c.standard_deviation() << " is " << cdf(complement(pack95c, minimum_weight)) << endl; -// Fraction of packs >= 2.9 with a mean of 3 and standard deviation of 0.0607957 is 0.95 - +// Fraction of packs >= 2.9 with a mean of 3 and standard deviation of 0.0607957 is 0.95

                                                                                                                      Notice that these two deceptively simple questions:

                                                                                                                      -
                                                                                                                      • +
                                                                                                                        • Do we over-fill to make sure we meet a minimum specification (or under-fill to avoid an overdose)?

                                                                                                                        and/or

                                                                                                                        -
                                                                                                                        • +
                                                                                                                          • Do we measure better?

                                                                                                                          diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html index 1ac81d7d4..a49aa351d 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html @@ -3,7 +3,7 @@ Find Scale (Standard Deviation) Example - + @@ -22,7 +22,7 @@

                                                                                                                          PrevUpHomeNext
                                                                                                                          -
                                                                                                                          +
                                                                                                                          Find Scale (Standard Deviation) Example @@ -59,8 +59,7 @@

                                                                                                                          normal N01;  // Default 'standard' normal distribution with zero mean
                                                                                                                          -double sd = 1.; // and standard deviation is 1.
                                                                                                                          -
                                                                                                                          +double sd = 1.; // and standard deviation is 1.

                                                                                                                          @@ -80,8 +79,7 @@ cout << "Normal distribution with mean = " << N01.location() << ", standard deviation " << N01.scale() << ", has " << "fraction > " << z - << ", p = " << cdf(complement(N01, z)) << endl; // Note: uses complement. - + << ", p = " << cdf(complement(N01, z)) << endl; // Note: uses complement.

                                                                                                                          Normal distribution with mean = 0 has fraction <= -2, p = 0.0227501
                                                                                                                          @@ -96,8 +94,7 @@ Normal distribution with mean = 0 has fraction > -2, p = 0.97725
                                                                                                                           

                                                                                                                          double l = N01.location();
                                                                                                                           double s = find_scale<normal>(z, p, l);
                                                                                                                          -cout << "scale (standard deviation) = " << s << endl;
                                                                                                                          -
                                                                                                                          +cout << "scale (standard deviation) = " << s << endl;

                                                                                                                          @@ -114,8 +111,7 @@ Normal distribution with mean = 0 has fraction > -2, p = 0.97725

                                                                                                                          -
                                                                                                                          normal np001pc(N01.location(), s);
                                                                                                                          -
                                                                                                                          +
                                                                                                                          normal np001pc(N01.location(), s);

                                                                                                                          @@ -128,8 +124,7 @@ Normal distribution with mean = 0 has fraction > -2, p = 0.97725 << ", p = " << cdf(np001pc, z) << endl; cout << "Normal distribution with mean = " << l << " has " << "fraction > " << z - << ", p = " << cdf(complement(np001pc, z)) << endl; - + << ", p = " << cdf(complement(np001pc, z)) << endl;

                                                                                                                          Normal distribution with mean = 0 has fraction <= -2, p = 0.001
                                                                                                                          @@ -152,8 +147,7 @@ Normal distribution with mean = 0 has fraction > -2, p = 0.999
                                                                                                                           

                                                                                                                          using boost::math::policies::policy;
                                                                                                                           using boost::math::policies::domain_error;
                                                                                                                          -using boost::math::policies::ignore_error;
                                                                                                                          -
                                                                                                                          +using boost::math::policies::ignore_error;

                                                                                                                          @@ -171,8 +165,7 @@ Normal distribution with mean = 0 has fraction > -2, p = 0.999 // Default policy, fully specified. l = find_scale<normal>(z, p, l, boost::math::policies::policy<>()); // New policy, without typedef. -l = find_scale<normal>(z, p, l, policy<domain_error<ignore_error> >()); - +l = find_scale<normal>(z, p, l, policy<domain_error<ignore_error> >());

                                                                                                                          @@ -192,8 +185,7 @@ Normal distribution with mean = 0 has fraction > -2, p = 0.999 cout << "Normal distribution with mean = " << l << " has " << "fraction <= " << z << " = " << cdf(np95pc, z) << endl; cout << "Normal distribution with mean = " << l << " has " - << "fraction > " << z << " = " << cdf(complement(np95pc, z)) << endl; - + << "fraction > " << z << " = " << cdf(complement(np95pc, z)) << endl;

                                                                                                                          diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/geometric_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/geometric_eg.html index 6a56334ae..d231a1014 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/geometric_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/geometric_eg.html @@ -3,7 +3,7 @@ Geometric Distribution Examples - + @@ -22,7 +22,7 @@

                                                                                                                          PrevUpHomeNext
                                                                                                                          -
                                                                                                                          +
                                                                                                                          Geometric Distribution Examples @@ -37,8 +37,7 @@

                                                                                                                          #define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
                                                                                                                          -#define BOOST_MATH_DISCRETE_QUANTILE_POLICY real
                                                                                                                          -
                                                                                                                          +#define BOOST_MATH_DISCRETE_QUANTILE_POLICY real

    @@ -110,8 +109,7 @@

    double success_fraction = 1./6; // success_fraction (p) = 0.1666
    -// (so failure_fraction is 1 - success_fraction = 5./6 = 1- 0.1666 = 0.8333)
    -
    +// (so failure_fraction is 1 - success_fraction = 5./6 = 1- 0.1666 = 0.8333)

    @@ -128,8 +126,7 @@

    -
    geometric g6(success_fraction); // type double by default.
    -
    +
    geometric g6(success_fraction); // type double by default.

    @@ -137,8 +134,7 @@

    -
    cout << "success fraction of a six-sided dice is " << g6.success_fraction() << endl;
    -
    +
    cout << "success fraction of a six-sided dice is " << g6.success_fraction() << endl;

    @@ -148,8 +144,7 @@

    cout << pdf(g6, 0) << endl; // 0.1667
    -cout << cdf(g6, 0) << endl; // 0.1667
    -
    +cout<<cdf(g6,0)<<endl;// 0.1667

    @@ -159,8 +154,7 @@

    -
    cout << pdf(g6, 1) << endl; // 0.1389
    -
    +
    cout << pdf(g6, 1) << endl; // 0.1389

    @@ -169,8 +163,7 @@

    -
    cout << "pdf(g6, 0) + pdf(g6, 1) = " << pdf(g6, 0) + pdf(g6, 1) << endl;
    -
    +
    cout << "pdf(g6, 0) + pdf(g6, 1) = " << pdf(g6, 0) + pdf(g6, 1) << endl;

    @@ -179,8 +172,7 @@

    -
    cout << "cdf(g6, 1) = " << cdf(g6, 1) << endl; // 0.3056
    -
    +
    cout << "cdf(g6, 1) = " << cdf(g6, 1) << endl; // 0.3056

    @@ -189,8 +181,7 @@

    -
    cout << "cdf(g6, 12) = " << cdf(g6, 12) << endl; // 0.9065 or 90% probability.
    -
    +
    cout << "cdf(g6, 12) = " << cdf(g6, 12) << endl; // 0.9065 or 90% probability.

    @@ -199,8 +190,7 @@

    -
    cout << "quantile(g6, 0.99) = " << quantile(g6, 0.99) << endl; // 24.26
    -
    +
    cout << "quantile(g6, 0.99) = " << quantile(g6, 0.99) << endl; // 24.26

    @@ -220,8 +210,7 @@

    negative_binomial nb(1, success_fraction);
     cout << pdf(nb, 1) << endl; // 0.1389
    -cout << cdf(nb, 1) << endl; // 0.3056
    -
    +cout<<cdf(nb,1)<<endl;// 0.3056

    @@ -230,8 +219,7 @@

    -
    cout << "quantile(complement(g6, 1 - p))  " << quantile(complement(g6, 0.01)) << endl; // 24.26
    -
    +
    cout << "quantile(complement(g6, 1 - p))  " << quantile(complement(g6, 0.01)) << endl; // 24.26

    @@ -263,8 +251,7 @@ << max_digits10 << endl; cout.precision(max_digits10); // - cout << cdf(g05, 0.0001) << endl; // returns 0.5000346561579232, not exact 0.5. - + cout << cdf(g05, 0.0001) << endl; // returns 0.5000346561579232, not exact 0.5.

    @@ -273,8 +260,7 @@

    -
    cout << cdf(g05, floor(0.0001)) << endl; // returns exactly 0.5
    -
    +
    cout << cdf(g05, floor(0.0001)) << endl; // returns exactly 0.5

    > formatC(pgeom(0.9999999,0.5, FALSE), digits=17) [1] "              0.25"
    @@ -327,8 +313,7 @@
     c = 0.80; // Only reasonably confident.
     cout << "To be " << c * 100
       << "% confident of finding we customer with a fault, need to survey "
    -  <<  ceil(quantile(g, c)) << " customers." << endl; // 79
    -
    + <<ceil(quantile(g,c))<<" customers."<<endl;// 79

    @@ -347,8 +332,7 @@

    cout.precision(2);
    -geometric gav(0.75); // Shooter averages 7.5 out of 10 in the basket.
    -
    +geometric gav(0.75); // Shooter averages 7.5 out of 10 in the basket.

    @@ -357,8 +341,7 @@

    -
    cout << "Probability of score on 1st try = " << pdf(gav, 0) << endl; // 0.75
    -
    +
    cout << "Probability of score on 1st try = " << pdf(gav, 0) << endl; // 0.75

    @@ -368,8 +351,7 @@

    -
    cout << "Probability of score on 5th try = " << pdf(gav, 4) << endl; // 0.0029
    -
    +
    cout << "Probability of score on 5th try = " << pdf(gav, 4) << endl; // 0.0029

    @@ -383,8 +365,7 @@

    geometric gbest(0.95);
     cout << "Probability of score on 5th try = " << pdf(gbest, 4) << endl; // 5.9e-6
     geometric gmediocre(0.50);
    -cout << "Probability of score on 5th try = " << pdf(gmediocre, 4) << endl; // 0.031
    -
    +cout << "Probability of score on 5th try = " << pdf(gmediocre, 4) << endl; // 0.031

    @@ -427,8 +408,7 @@ << t << endl; // 0.00025 t = geometric::find_upper_bound_on_p(k, alpha/2); cout << "geometric::find_upper_bound_on_p(" << int(k) << ", " << alpha/2 << ") = " - << t << endl; // 0.037 - + << t << endl; // 0.037

    @@ -453,8 +433,7 @@ << t << endl; // 5e-005 t = geometric::find_upper_bound_on_p(k, alpha/2); cout << "geometric::find_upper_bound_on_p(" << int(k) << ", " << alpha/2 << ") = " - << t << endl; // 0.052 - + << t << endl; // 0.052

    @@ -472,8 +451,7 @@ catch(const std::exception& e) { // Since we have set an overflow policy of ignore_error, // an overflow exception should never be thrown. - std::cout << "\nMessage from thrown exception was:\n " << e.what() << std::endl; - + std::cout << "\nMessage from thrown exception was:\n " << e.what() << std::endl;

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/inverse_chi_squared_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/inverse_chi_squared_eg.html index 96fccf19c..79dd07586 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/inverse_chi_squared_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/inverse_chi_squared_eg.html @@ -3,7 +3,7 @@ Inverse Chi-Squared Distribution Bayes Example - + @@ -22,7 +22,7 @@

    PrevUpHomeNext
    -
    +
    Inverse Chi-Squared Distribution Bayes Example @@ -46,12 +46,12 @@

    For more general information on Bayesian type of analyses, see:

    -
      -
    • +
        +
      • Andrew Gelman, John B. Carlin, Hal E. Stern, Donald B. Rubin, Bayesian Data Analysis, 2003, ISBN 978-1439840955.
      • -
      • +
      • Jim Albert, Bayesian Compution with R, Springer, 2009, ISBN 978-0387922973.
      @@ -130,6 +130,7 @@ cout << " 2.5% quantile: " << quantile(prior, 0.025) << endl; cout << " 50% quantile: " << quantile(prior, 0.5) << endl; cout << " 97.5% quantile: " << quantile(prior, 0.975) << endl << endl; +

      @@ -243,8 +244,7 @@ double posteriorScale = (priorDF * priorScale + (ballsSampleVariance * (ballsSampleSize - 1))) / posteriorDF; cout << "prior scale: " << priorScale << endl; -cout << "posterior scale: " << posteriorScale << endl; - +cout << "posterior scale: " << posteriorScale << endl;

      @@ -262,7 +262,6 @@ posterior degrees-of-freedom: 120 prior scale: 25 posterior scale: 49.5 -

      To compare the generic machinery performance with our suspect machine, @@ -285,6 +284,7 @@ cout << " probability variance <= 25: " << boost::math::cdf(posterior, 25.0) << endl; cout << " probability variance > 50: " << boost::math::cdf(boost::math::complement(posterior, 50.0)) << endl; +

      diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nag_library.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nag_library.html index 07f39002b..32215d1f6 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nag_library.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nag_library.html @@ -3,7 +3,7 @@ Comparison with C, R, FORTRAN-style Free Functions - + @@ -22,7 +22,7 @@
      PrevUpHomeNext
      -
      +
      Comparison with C, R, FORTRAN-style Free Functions diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg.html index 080f80ce2..f0aaa6bf0 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg.html @@ -3,7 +3,7 @@ Non Central Chi Squared Example - + @@ -22,7 +22,7 @@
      PrevUpHomeNext
      -
      +
      Non Central Chi Squared Example diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg/nccs_power_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg/nccs_power_eg.html index 841e8e6ff..f0e3a9ba3 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg/nccs_power_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg/nccs_power_eg.html @@ -3,7 +3,7 @@ Tables of the power function of the chi2 test. - + @@ -22,7 +22,7 @@
      PrevUpHomeNext
      -
      +
      Tables of the power function of the chi2 test. @@ -50,8 +50,7 @@ test at the 5% significance using std::setprecision; int main() -{ - +{

      @@ -65,8 +64,7 @@ test at the 5% significance { cout << "[[lambda]=" << lam << "]"; } -cout << "]\n"; - +cout << "]\n";

      @@ -82,8 +80,7 @@ test at the 5% significance { cout << "[[" << n << "]"; for(int lam = 2; lam <= 20; lam += 2) - { - + {

      @@ -91,8 +88,7 @@ test at the 5% significance

      -
      double cs = quantile(complement(chi_squared(n), 0.05));
      -
      +
      double cs = quantile(complement(chi_squared(n), 0.05));

      @@ -101,8 +97,7 @@ test at the 5% significance

      -
      double beta = cdf(complement(non_central_chi_squared(n, lam), cs));
      -
      +
      double beta = cdf(complement(non_central_chi_squared(n, lam), cs));

      @@ -115,8 +110,7 @@ test at the 5% significance cout << "]" << endl; } cout << "]" << endl; -} - +}

      diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg.html index 0ddf31ea5..5ad0dd62e 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg.html @@ -3,7 +3,7 @@ Negative Binomial Distribution Examples - + @@ -22,7 +22,7 @@

      PrevUpHomeNext
      -
      +
      Negative Binomial Distribution Examples diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html index 523eb5e66..2762a0ae3 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html @@ -3,7 +3,7 @@ Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution - + @@ -22,7 +22,7 @@
      PrevUpHomeNext
      -
      +
      Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial @@ -67,8 +67,7 @@ using std::cout; using std::endl; #include <iomanip> using std::setprecision; -using std::setw; using std::left; using std::fixed; using std::right; - +using std::setw; using std::left; using std::fixed; using std::right;

      @@ -77,8 +76,7 @@

      -
      double alpha[] = { 0.5, 0.25, 0.1, 0.05, 0.01, 0.001, 0.0001, 0.00001 };
      -
      +
      double alpha[] = { 0.5, 0.25, 0.1, 0.05, 0.01, 0.001, 0.0001, 0.00001 };

      @@ -114,8 +112,7 @@ "___________________________________________\n" "Confidence Lower Upper\n" " Value (%) Limit Limit\n" - "___________________________________________\n"; - + "___________________________________________\n";

      @@ -145,8 +142,7 @@ cout << fixed << setprecision(5) << setw(15) << right << upper << endl; } cout << endl; -} // void confidence_limits_on_frequency(unsigned trials, unsigned successes) - +} // void confidence_limits_on_frequency(unsigned trials, unsigned successes)

      @@ -163,6 +159,7 @@ return 0; } // int main() +

      diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html index 2171cbfca..93674e17d 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html @@ -3,7 +3,7 @@ Estimating Sample Sizes for the Negative Binomial. - + @@ -22,7 +22,7 @@
      -
      +
      Estimating Sample Sizes for the Negative Binomial. @@ -48,8 +48,7 @@

      -
      void find_number_of_trials(double failures, double p);
      -
      +
      void find_number_of_trials(double failures, double p);

      @@ -59,8 +58,7 @@

      -
      double alpha[] = { 0.5, 0.25, 0.1, 0.05, 0.01, 0.001, 0.0001, 0.00001 };
      -
      +
      double alpha[] = { 0.5, 0.25, 0.1, 0.05, 0.01, 0.001, 0.0001, 0.00001 };

      @@ -82,7 +80,8 @@

      -
      void find_number_of_trials(double failures, double p)
      +
      +void find_number_of_trials(double failures, double p)
       {
          // trials = number of trials
          // failures = number of failures before achieving required success(es).
      @@ -108,8 +107,7 @@
             << endl;
          }
          cout << endl;
      -} // void find_number_of_trials(double failures, double p)
      -
      +} // void find_number_of_trials(double failures, double p)

      @@ -129,6 +127,7 @@ return 0; } // int main() +

      diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html index 3380bd50d..f30f63f88 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html @@ -3,7 +3,7 @@ Negative Binomial Sales Quota Example. - + @@ -22,7 +22,7 @@
      PrevUpHomeNext
      -
      +
      Negative Binomial Sales Quota Example. @@ -73,8 +73,7 @@

      #define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
      -#define BOOST_MATH_DISCRETE_QUANTILE_POLICY real
      -
      +#define BOOST_MATH_DISCRETE_QUANTILE_POLICY real

      @@ -125,8 +124,7 @@

      try
      -{
      -
      +{

      @@ -136,8 +134,7 @@

      -
      double sales_quota = 5; // Pat's sales quota - successes (r).
      -
      +
      double sales_quota = 5; // Pat's sales quota - successes (r).

      @@ -146,8 +143,7 @@

      -
      double success_fraction = 0.4; // success_fraction (p) - so failure_fraction is 0.6.
      -
      +
      double success_fraction = 0.4; // success_fraction (p) - so failure_fraction is 0.6.

      @@ -164,8 +160,7 @@

      -
      negative_binomial nb(sales_quota, success_fraction); // type double by default.
      -
      +
      negative_binomial nb(sales_quota, success_fraction); // type double by default.

      @@ -183,8 +178,7 @@ cout << "With a success rate of " << nb.success_fraction() << ", he might expect, on average,\n" "to need to visit about " << success_fraction * all_houses - << " houses in order to sell all " << nb.successes() << " bars. " << endl; - + << " houses in order to sell all " << nb.successes() << " bars. " << endl;

      Pat has a sales per house success rate of 0.4.
      @@ -206,8 +200,7 @@ to need to visit about 12 houses in order to sell all 5 bars.
       

      cout << "Probability that Pat finishes on the " << sales_quota << "th house is "
      -  << pdf(nb, 5 - sales_quota) << endl; // == pdf(nb, 0)
      -
      + << pdf(nb, 5 - sales_quota) << endl; // == pdf(nb, 0)

      @@ -227,8 +220,7 @@ to need to visit about 12 houses in order to sell all 5 bars. cout << "Probability that Pat finishes on the 7th house is " << pdf(nb, 7 - sales_quota) << endl; cout << "Probability that Pat finishes on the 8th house is " - << pdf(nb, 8 - sales_quota) << endl; - + << pdf(nb, 8 - sales_quota) << endl;

      Probability that Pat finishes on the 6th house is 0.03072
      @@ -248,8 +240,7 @@ Probability that Pat finishes on the 8th house is 0.077414
           + pdf(nb, 6 - sales_quota) // 1 failure.
           + pdf(nb, 7 - sales_quota) // 2 failures.
           + pdf(nb, 8 - sales_quota) // 3 failures.
      -  << endl;
      -
      + << endl;

      pdf(sales_quota) + pdf(6) + pdf(7) + pdf(8) = 0.17367
      @@ -262,8 +253,7 @@ Probability that Pat finishes on the 8th house is 0.077414
       

      cout << "\nProbability of selling his quota of " << sales_quota
         << " bars\non or before the " << 8 << "th house is "
      -  << cdf(nb, 8 - sales_quota) << endl;
      -
      + << cdf(nb, 8 - sales_quota) << endl;

      Probability of selling his quota of 5 bars on or before the 8th house is 0.17367
      @@ -274,8 +264,7 @@ Probability that Pat finishes on the 8th house is 0.077414
         << pdf(nb, 10 - sales_quota) << endl;
       cout << "\nProbability of selling his quota of " << sales_quota
         << " bars\non or before the " << 10 << "th house is "
      -  << cdf(nb, 10 - sales_quota) << endl;
      -
      + << cdf(nb, 10 - sales_quota) << endl;

      Probability that Pat finishes exactly on the 10th house is 0.10033
      @@ -287,8 +276,7 @@ Probability of selling his quota of 5 bars on or before the 10th house is 0.3669
         << pdf(nb, 11 - sales_quota) << endl;
       cout << "\nProbability of selling his quota of " << sales_quota
         << " bars\non or before the " << 11 << "th house is "
      -  << cdf(nb, 11 - sales_quota) << endl;
      -
      + << cdf(nb, 11 - sales_quota) << endl;

      Probability that Pat finishes on the 11th house is 0.10033
      @@ -302,8 +290,7 @@ on or before the 11th house is 0.46723
       
       cout << "\nProbability of selling his quota of " << sales_quota
         << " bars\non or before the " << 12 << "th house is "
      -  << cdf(nb, 12 - sales_quota) << endl;
      -
      + << cdf(nb, 12 - sales_quota) << endl;

      Probability that Pat finishes on the 12th house is 0.094596
      @@ -319,8 +306,7 @@ on or before the 12th house is 0.56182
       

      cout << "Probability that Pat finishes on the " << all_houses
      -  << " house is " << pdf(nb, all_houses - sales_quota) << endl;
      -
      + << " house is " << pdf(nb, all_houses - sales_quota) << endl;

      @@ -340,8 +326,7 @@ on or before the 12th house is 0.56182

      cout << "\nProbability of selling his quota of " << sales_quota
         << " bars\non or before the " << all_houses << "th house is "
      -  << cdf(nb, all_houses - sales_quota) << endl;
      -
      + << cdf(nb, all_houses - sales_quota) << endl;

      Probability of selling his quota of 5 bars
      @@ -382,8 +367,7 @@ on or before the 30th house is 0.99849
       

      cout << "\nProbability of failing to sell his quota of " << sales_quota
         << " bars\neven after visiting all " << all_houses << " houses is "
      -  << cdf(complement(nb, all_houses - sales_quota)) << endl;
      -
      + << cdf(complement(nb, all_houses - sales_quota)) << endl;

      Probability of failing to sell his quota of 5 bars
      @@ -396,8 +380,7 @@ even after visiting all 30 houses is 0.0015101
       

      double p = cdf(nb, (8 - sales_quota));
      -cout << "Probability of meeting sales quota on or before 8th house is "<< p << endl;
      -
      +cout << "Probability of meeting sales quota on or before 8th house is "<< p << endl;

      Probability of meeting sales quota on or before 8th house is 0.174
      @@ -407,8 +390,7 @@ even after visiting all 30 houses is 0.0015101
       
      cout << "If the confidence of meeting sales quota is " << p
           << ", then the finishing house is " << quantile(nb, p) + sales_quota << endl;
       
      -cout<< " quantile(nb, p) = " << quantile(nb, p) << endl;
      -
      +cout<< " quantile(nb, p) = " << quantile(nb, p) << endl;

      If the confidence of meeting sales quota is 0.17367, then the finishing house is 8
      @@ -423,8 +405,7 @@ even after visiting all 30 houses is 0.0015101
       

      cout << "If the confidence of meeting sales quota is " << 1.
           << ", then the finishing house is " << quantile(nb, 1) + sales_quota << endl;
      -//  1.#INF == infinity.
      -
      +// 1.#INF == infinity.

      If the confidence of meeting sales quota is 1, then the finishing house is 1.#INF
      @@ -441,8 +422,7 @@ even after visiting all 30 houses is 0.0015101
           << ", then the finishing house is " << quantile(nb, 0.5) + sales_quota << endl;
       
       cout << "If the confidence of meeting sales quota is " << 1 - 0.00151 // 30 th
      -    << ", then the finishing house is " << quantile(nb, 1 - 0.00151) + sales_quota << endl;
      -
      + << ", then the finishing house is " << quantile(nb, 1 - 0.00151) + sales_quota << endl;

      If the confidence of meeting sales quota is 0, then the finishing house is 5
      @@ -461,8 +441,7 @@ If the confidence of meeting sales quota is 0.99849, then the finishing house is
       

      cout << "If confidence of meeting quota is zero\n(we assume all houses are successful sales)"
      -  ", then finishing house is " << sales_quota << endl;
      -
      + ", then finishing house is " << sales_quota << endl;

      If confidence of meeting quota is zero (we assume all houses are successful sales), then finishing house is 5
      @@ -481,8 +460,7 @@ If confidence of meeting quota is 0, then finishing house is 5
          cout << "If confidence of meeting quota is " << ps[i]
            << ", then finishing house is " << quantile(nb, ps[i]) + sales_quota
            << endl;
      -}
      -
      +}

      If confidence of meeting quota is 0, then finishing house is 5
      @@ -536,8 +514,7 @@ If confidence of meeting quota is 0.95, then finishing house is 21
       {
         cout << left << setw(3) << i << "                             " << setw(8) << cdf(nb, i - sales_quota)  << endl;
       }
      -cout << endl;
      -
      +cout << endl;

      House for 5 th (last) sale.  Probability (%)
      @@ -578,8 +555,7 @@ If confidence of meeting quota is 0.95, then finishing house is 21
       catch(const std::exception& e)
       { // Since we have set an overflow policy of ignore_error,
         // an overflow exception should never be thrown.
      -   std::cout << "\nMessage from thrown exception was:\n " << e.what() << std::endl;
      -
      + std::cout << "\nMessage from thrown exception was:\n " << e.what() << std::endl;

      diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html index a0d451a75..af3dfa805 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html @@ -3,7 +3,7 @@ Negative Binomial Table Printing Example. - + @@ -22,7 +22,7 @@

      PrevUpHomeNext
      -
      +
      Negative Binomial Table Printing Example. diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example.html index 447cc2737..845fbc943 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example.html @@ -3,7 +3,7 @@ Normal Distribution Examples - + @@ -22,7 +22,7 @@
      PrevUpHomeNext
      -
      +
      Normal Distribution Examples diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html index 6ac4cc272..07541a86e 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html @@ -3,7 +3,7 @@ Some Miscellaneous Examples of the Normal (Gaussian) Distribution - + @@ -22,7 +22,7 @@
      PrevUpHomeNext
      -
      +
      Some Miscellaneous Examples of the Normal (Gaussian) Distribution @@ -58,8 +58,7 @@ try { - { // Traditional tables and values. - + { // Traditional tables and values.

      @@ -78,8 +77,7 @@ // Construct a standard normal distribution s normal s; // (default mean = zero, and standard deviation = unity) cout << "Standard normal distribution, mean = "<< s.mean() - << ", standard deviation = " << s.standard_deviation() << endl; - + << ", standard deviation = " << s.standard_deviation() << endl;

      @@ -95,8 +93,7 @@ cout << left << setprecision(3) << setw(6) << z << " " << setprecision(precision) << setw(12) << pdf(s, z) << endl; } -cout.precision(6); // default - +cout.precision(6); // default

      @@ -115,8 +112,7 @@ cout << left << setprecision(3) << setw(6) << z << " " << setprecision(precision) << setw(12) << cdf(s, z) << endl; } -cout.precision(6); // default - +cout.precision(6); // default

      @@ -138,8 +134,7 @@

      double z = 2.;
      -cout << "Area for z = " << z << " is " << cdf(s, z) << endl; // to get the area for z.
      -
      +cout << "Area for z = " << z << " is " << cdf(s, z) << endl; // to get the area for z.

      @@ -151,8 +146,7 @@

        cout << "95% of area has a z below " << quantile(s, 0.95) << endl;
      -// 95% of area has a z below 1.64485
      -
      +// 95% of area has a z below 1.64485

      @@ -163,8 +157,7 @@

        cout << "95% of area has a z between " << quantile(s, 0.975)
           << " and " << -quantile(s, 0.975) << endl;
      -// 95% of area has a z between 1.95996 and -1.95996
      -
      +// 95% of area has a z between 1.95996 and -1.95996

      @@ -179,8 +172,7 @@

      double alpha1 = cdf(s, -1) * 2; // 0.3173105078629142
      -cout << setprecision(17) << "Significance level for z == 1 is " << alpha1 << endl;
      -
      +cout << setprecision(17) << "Significance level for z == 1 is " << alpha1 << endl;

      @@ -189,8 +181,7 @@

      double alpha[] = {0.3173105078629142, // z for 1 standard deviation.
      -  0.20, 0.1, 0.05, 0.01, 0.001, 0.0001, 0.00001 };
      -
      + 0.20, 0.1, 0.05, 0.01, 0.001, 0.0001, 0.00001 };

      @@ -207,8 +198,7 @@ cout << setw(15) << alpha[i] << setw(15) << alpha[i] /2 << setw(10) << quantile(complement(s, alpha[i]/2)) << endl; // Use quantile(complement(s, alpha[i]/2)) to avoid potential loss of accuracy from quantile(s, 1 - alpha[i]/2) } -cout << endl; - +cout << endl;

      @@ -251,8 +241,7 @@ cout << "Fraction 2 standard deviations within either side of mean is " << 1 - cdf(complement(s, 2 * s.standard_deviation())) * 2 << endl; cout << "Fraction 3 standard deviations within either side of mean is " - << 1 - cdf(complement(s, 3 * s.standard_deviation())) * 2 << endl; - + << 1 - cdf(complement(s, 3 * s.standard_deviation())) * 2 << endl;

      @@ -300,8 +289,7 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740

      // K. Krishnamoorthy, Handbook of Statistical Distributions with Applications,
      - // ISBN 1 58488 635 8, page 125, example 10.3.5
      -
      + // ISBN 1 58488 635 8, page 125, example 10.3.5

      @@ -315,8 +303,7 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740

      double mean_life = 1100.;
       double life_standard_deviation = 100.;
       normal bulbs(mean_life, life_standard_deviation);
      -double expected_life = 1000.;
      -
      +double expected_life = 1000.;

      @@ -334,8 +321,7 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740 cout << "Fraction of bulbs that will last between " << min_life << " and " << max_life << " is " << cdf(bulbs, max_life) // P(X <= 1200) - - cdf(bulbs, min_life) << endl; // P(X <= 900) - + - cdf(bulbs, min_life) << endl; // P(X <= 900)

    @@ -368,8 +354,7 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740 doublestock=160.;// per week.cout<<"Percentage of weeks overstocked "<<cdf(sacks,stock)*100.<<endl;// P(X <=160) -// Percentage of weeks overstocked 97.7 - +// Percentage of weeks overstocked 97.7

    @@ -379,8 +364,7 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740

    double stock_95 = quantile(sacks, 0.95);
    -cout << "Store should stock " << int(stock_95) << " sacks to meet 95% of demands." << endl;
    -
    +cout<<"Store should stock "<<int(stock_95)<<" sacks to meet 95% of demands."<<endl;

    @@ -437,8 +421,7 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740 normal nominal_packs(nominal_mean, standard_deviation); cout << "Setting the packer to " << nominal_mean << " will mean that " << "fraction of packs >= " << under_weight - << " is " << cdf(complement(nominal_packs, under_weight)) << endl; - + << " is " << cdf(complement(nominal_packs, under_weight)) << endl;

    @@ -463,8 +446,7 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740

    double p = 0.05; // wanted p th quantile.
     cout << "Quantile of " << p << " = " << quantile(packs, p)
    -  << ", mean = " << packs.mean() << ", sd = " << packs.standard_deviation() << endl; //
    -
    + <<", mean = "<<packs.mean()<<", sd = "<<packs.standard_deviation()<<endl;//

    @@ -488,8 +470,7 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740 cout <<"Fraction of packs >= " << under_weight << " with a mean of " << mean << " and standard deviation of " << pack05.standard_deviation() << " is " << cdf(complement(pack05, under_weight)) << endl; -// - +//

    @@ -509,8 +490,7 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740 cout <<"Fraction of packs >= " << under_weight << " with a mean of " << mean << " and standard deviation of " << pack06.standard_deviation() - << " is " << cdf(complement(pack06, under_weight)) << endl; - + << " is " << cdf(complement(pack06, under_weight)) << endl;

    @@ -551,8 +531,7 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740 << " and standard deviation of " << pack95.standard_deviation() << " is " << cdf(complement(pack95, under_weight)) << endl; -// Fraction of packs >= 2.9 with a mean of 3 and standard deviation of 0.0608 is 0.95 - +// Fraction of packs >= 2.9 with a mean of 3 and standard deviation of 0.0608 is 0.95

    @@ -591,6 +570,7 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740 << cdf(complement(bolts, top)) << endl; cout << "95% of bolts are shorter than " << quantile(bolts, 0.95) << endl; +

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg.html index c888c5f48..3619b9509 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg.html @@ -3,7 +3,7 @@ Student's t Distribution Examples - + @@ -22,7 +22,7 @@
    PrevUpHomeNext
    -
    +
    Student's t Distribution Examples diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/paired_st.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/paired_st.html index 9e0bf08fa..14b0fb82e 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/paired_st.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/paired_st.html @@ -3,7 +3,7 @@ Comparing two paired samples with the Student's t distribution - + @@ -22,7 +22,7 @@
    PrevUpHomeNext
    -
    +
    Comparing two paired samples with the Student's t distribution @@ -42,20 +42,20 @@

    That means we can:

    -
      -
    • +
        +
      • Calculate confidence intervals of the mean. If the endpoints of the interval differ in sign then we are unable to reject the null-hypothesis that there is no change.
      • -
      • +
      • Test whether the true mean is zero. If the result is consistent with a true mean of zero, then we are unable to reject the null-hypothesis that there is no change.
      • -
      • +
      • Calculate how many pairs of readings we would need in order to obtain a significant result. diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_intervals.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_intervals.html index 30c04a1ba..391b5e54e 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_intervals.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_intervals.html @@ -3,7 +3,7 @@ Calculating confidence intervals on the mean with the Students-t distribution - + @@ -22,7 +22,7 @@
        PrevUpHomeNext
        -
        +
        Calculating confidence intervals on the mean with the Students-t distribution @@ -84,19 +84,19 @@

        From the formula, it should be clear that:

        -
          -
        • +
            +
          • The width of the confidence interval decreases as the sample size increases.
          • -
          • +
          • The width increases as the standard deviation increases.
          • -
          • +
          • The width increases as the confidence level increases (0.5 towards 0.99999 - stronger).
          • -
          • +
          • The width increases as the significance level decreases (0.5 towards 0.00000...01 - stronger).
          • diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_size.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_size.html index a05fa0da1..c05d0cd17 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_size.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_size.html @@ -3,7 +3,7 @@ Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test - + @@ -22,7 +22,7 @@
            PrevUpHomeNext
            -
            +
            Estimating how large a sample size would have to become in order to give a significant diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_test.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_test.html index 51bad107c..c417f5660 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_test.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_test.html @@ -3,7 +3,7 @@ Testing a sample mean for difference from a "true" mean - + @@ -22,7 +22,7 @@ -
            +
            Testing a sample mean for difference from a "true" mean diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/two_sample_students_t.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/two_sample_students_t.html index 2789de4bb..660fbb04e 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/two_sample_students_t.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/two_sample_students_t.html @@ -3,7 +3,7 @@ Comparing the means of two samples with the Students-t test - + @@ -22,7 +22,7 @@
            PrevUpHomeNext
            -
            +
            Comparing the means of two samples with the Students-t test diff --git a/doc/sf_and_dist/html/math_toolkit/extern_c.html b/doc/sf_and_dist/html/math_toolkit/extern_c.html index a530bb2e9..f84c960d9 100644 --- a/doc/sf_and_dist/html/math_toolkit/extern_c.html +++ b/doc/sf_and_dist/html/math_toolkit/extern_c.html @@ -3,7 +3,7 @@ TR1 and C99 external "C" Functions - + @@ -22,7 +22,7 @@
            PrevUpHomeNext
            -
            +

            TR1 and C99 external "C" Functions diff --git a/doc/sf_and_dist/html/math_toolkit/extern_c/c99.html b/doc/sf_and_dist/html/math_toolkit/extern_c/c99.html index 77cd4d152..aeed4f50d 100644 --- a/doc/sf_and_dist/html/math_toolkit/extern_c/c99.html +++ b/doc/sf_and_dist/html/math_toolkit/extern_c/c99.html @@ -3,7 +3,7 @@ C99 C Functions - + @@ -22,7 +22,7 @@
            PrevUpHomeNext
            -
            +
            diff --git a/doc/sf_and_dist/html/math_toolkit/extern_c/tr1.html b/doc/sf_and_dist/html/math_toolkit/extern_c/tr1.html index a503b2915..e381cc3b9 100644 --- a/doc/sf_and_dist/html/math_toolkit/extern_c/tr1.html +++ b/doc/sf_and_dist/html/math_toolkit/extern_c/tr1.html @@ -3,7 +3,7 @@ C99 and TR1 C Functions Overview - + @@ -22,7 +22,7 @@
            PrevUpHomeNext
            -
            +
            @@ -40,30 +40,30 @@

            Pros:

            -
              -
            • +
                +
              • The header to include is lightweight (i.e. fast to compile).
              • -
              • +
              • The functions have extern "C" linkage, and so are usable from other languages (not just C and C++).
              • -
              • +
              • C99 and C++ TR1 Standard compatibility.

              Cons:

              -
                -
              • +
                  +
                • You will need to compile and link to the external Boost.Math libraries.
                • -
                • +
                • Limited to support for the types, float, double and long double.
                • -
                • +
                • Error handling is handled via setting ::errno and returning NaN's and infinities: this may be less flexible than an C++ exception based approach.
                • @@ -265,12 +265,12 @@

                  This library now presents the user with a choice:

                  -
                    -
                  • +
                      +
                    • To include the header only versions of the functions and have an easier time linking, but a longer compile time.
                    • -
                    • +
                    • To include the TR1 headers and link against an external library.
                    diff --git a/doc/sf_and_dist/html/math_toolkit/extern_c/tr1_ref.html b/doc/sf_and_dist/html/math_toolkit/extern_c/tr1_ref.html index 322e382bb..35cf64682 100644 --- a/doc/sf_and_dist/html/math_toolkit/extern_c/tr1_ref.html +++ b/doc/sf_and_dist/html/math_toolkit/extern_c/tr1_ref.html @@ -3,7 +3,7 @@ TR1 C Functions Quick Reference - + @@ -22,7 +22,7 @@
                    PrevUpHomeNext
                    -
                    +

                    TR1 C Functions Quick Reference diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview.html b/doc/sf_and_dist/html/math_toolkit/main_overview.html index fb3a92ee7..5098226b9 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview.html @@ -3,7 +3,7 @@ Overview - + @@ -22,7 +22,7 @@
                    PrevUpHomeNext
                    -
                    +
                    diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/building.html b/doc/sf_and_dist/html/math_toolkit/main_overview/building.html index e9aa84d6e..1f1a8af5b 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/building.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/building.html @@ -3,7 +3,7 @@ If and How to Build a Boost.Math Library, and its Examples and Tests - + @@ -22,7 +22,7 @@
                    PrevUpHomeNext
                    -
                    +

                    If and How to Build a Boost.Math Library, and its Examples and Tests diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/compilers_overview.html b/doc/sf_and_dist/html/math_toolkit/main_overview/compilers_overview.html index bdb6ab8b6..13070b190 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/compilers_overview.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/compilers_overview.html @@ -3,7 +3,7 @@ Compilers - + @@ -22,7 +22,7 @@
                    PrevUpHomeNext
                    -
                    +
                    diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/config_macros.html b/doc/sf_and_dist/html/math_toolkit/main_overview/config_macros.html index cefc0a7f8..f5755bb94 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/config_macros.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/config_macros.html @@ -3,7 +3,7 @@ Configuration Macros - + @@ -22,7 +22,7 @@
                    PrevUpHomeNext
                    -
                    +

                    Configuration Macros diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/contact.html b/doc/sf_and_dist/html/math_toolkit/main_overview/contact.html index 8b1526759..484a2e037 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/contact.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/contact.html @@ -3,7 +3,7 @@ Contact Info and Support - + @@ -22,7 +22,7 @@
                    PrevUpHomeNext
                    -
                    +

                    Contact Info and Support @@ -30,12 +30,12 @@

                    The main support for this library is via the Boost mailing lists:

                    -
                      -
                    • +
                        +
                      • Use the boost-user list for general support questions.
                      • -
                      • +
                      • Use the boost-developer list for discussion about implementation and or submission of extensions. diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html b/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html index ea4cac308..0b079dff3 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html @@ -3,7 +3,7 @@ Document Conventions - + @@ -22,46 +22,46 @@
                        PrevUpHomeNext
                        -
                        +

                        - +

                        This documentation aims to use of the following naming and formatting conventions.

                        -
                          -
                        • +
                            +
                          • C++ Code is in fixed width font and is syntax-highlighted in color, for example double.
                          • -
                          • +
                          • Other code is in block teletype fixed-width font.
                          • -
                          • +
                          • Replaceable text that you will need to supply is in italics.
                          • -
                          • +
                          • If a name refers to a free function, it is specified like this: free_function(); that is, it is in code font and its name is followed by () to indicate that it is a free function.
                          • -
                          • +
                          • If a name refers to a class template, it is specified like this: class_template<>; that is, it is in code font and its name is followed by <> to indicate that it is a class template.
                          • -
                          • +
                          • If a name refers to a function-like macro, it is specified like this: MACRO(); that is, it is uppercase in code font and its name is followed by () to indicate that it is a function-like macro. Object-like macros appear without the trailing ().
                          • -
                          • +
                          • Names that refer to concepts in the generic programming sense (like template parameter names) are specified in CamelCase.
                          • diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/directories.html b/doc/sf_and_dist/html/math_toolkit/main_overview/directories.html index f11c459cb..2ec7edcf9 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/directories.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/directories.html @@ -3,7 +3,7 @@ Directory and File Structure - + @@ -22,7 +22,7 @@
                            PrevUpHomeNext
                            -
                            +

                            Directory and File Structure diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/error_handling.html b/doc/sf_and_dist/html/math_toolkit/main_overview/error_handling.html index 745d53842..16dd51c81 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/error_handling.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/error_handling.html @@ -3,7 +3,7 @@ Error Handling - + @@ -22,7 +22,7 @@
                            PrevUpHomeNext
                            -
                            +
                            @@ -34,11 +34,11 @@

                            Handling of errors by this library is split into two orthogonal parts:

                            -
                              -
                            • +
                                +
                              • What kind of error has been raised?
                              • -
                              • +
                              • What should be done when the error is raised?
                              @@ -766,16 +766,16 @@ the default behaviours were chosen based on feedback during the formal review of this library. It was felt that:

                              -
                                -
                              • +
                                  +
                                • Genuine errors should be flagged with exceptions rather than following C-compatible behaviour and setting ::errno.
                                • -
                                • +
                                • Numeric underflow and denormalised results were not considered to be fatal errors in most cases, so it was felt that these should be ignored.
                                • -
                                • +
                                • If there is more than one error, only the first detected will be reported in the throw message.
                                • diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/faq.html b/doc/sf_and_dist/html/math_toolkit/main_overview/faq.html index aee1d0c02..697e39a76 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/faq.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/faq.html @@ -3,7 +3,7 @@ Frequently Asked Questions FAQ - + @@ -22,13 +22,13 @@
                                  PrevUpHomeNext
                                  -
                                  +
                                  -
                                    -
                                  1. +
                                      +
                                    1. I'm a FORTRAN/NAG/SPSS/SAS/Cephes/MathCad/R user and I don't see where the functions like dnorm(mean, sd) are in Boost.Math?
                                      Nearly all are provided, and many more like mean, skewness, quantiles, @@ -42,7 +42,7 @@ my_norm(0, 1); pdf(my_norm, 2.0);
                                    2. -
                                    3. +
                                    4. I'm a user of New SAS Functions for Computing Probabilities.
                                      You will find the interface more familar, but to be able to select a distribution (perhaps @@ -51,7 +51,7 @@ find useful): see Statistical Distribution Explorer
                                      .
                                    5. -
                                    6. +
                                    7. I'm allegic to reading manuals and prefer to learn from examples.
                                      Fear not - you are not alone! Many examples are available for functions and distributions. Some are referenced directly from the text. Others @@ -60,7 +60,7 @@ these, making sure that the Boost library is in the include directories list.
                                    8. -
                                    9. +
                                    10. How do I make sure that the Boost library is in the Visual Studio include directories list?
                                      You can add an include path, for example, your Boost place /boost-latest_release, for example @@ -72,7 +72,7 @@ sheets to assist. You may find it convenient to create a new one adding \boost-latest_release; to the existing include items in $(IncludePath).
                                    11. -
                                    12. +
                                    13. I'm a FORTRAN/NAG/SPSS/SAS/Cephes/MathCad/R user and I don't see where the properties like mean, median, mode, variance, skewness of distributions are in Boost.Math?
                                      They are all available @@ -86,13 +86,13 @@ kurtosis, kurtosis_excess, range and support.
                                    14. -
                                    15. +
                                    16. I am a C programmer. Can I user Boost.Math with C?
                                      Yes you can, including all the special functions, and TR1 functions like isnan. They appear as C functions, by being declared as "extern C".
                                    17. -
                                    18. +
                                    19. I am a C# (Basic? F# FORTRAN? Other CLI?) programmer. Can I use Boost.Math with C#?
                                      Yes you can, including all the special functions, and TR1 functions like isnan. But you must build the Boost.Math as a dynamic library (.dll) and @@ -101,7 +101,7 @@ app with a GUI. See Statistical Distribution Explorer
                                    20. -
                                    21. +
                                    22. What these "policies" things for?
                                      Policies are a powerful (if necessarily complex) fine-grain mechanism that allow you to customise the behaviour of the Boost.Math library according @@ -109,21 +109,21 @@ But if, very probably, the default behaviour suits you, you don't need to know more.
                                    23. -
                                    24. +
                                    25. I am a C user and expect to see global C-style::errno set for overflow/errors etc?
                                      You can achieve what you want - see error handling policies and user error handling and many examples.
                                    26. -
                                    27. +
                                    28. I am a C user and expect to silently return a max value for overflow?
                                      You (and C++ users too) can return whatever you want on overflow - see overflow_error and error handling policies and several examples.
                                    29. -
                                    30. +
                                    31. I don't want any error message for overflow etc?
                                      You can control exactly what happens for all the abnormal conditions, including the values returned. See domain_error, @@ -131,14 +131,14 @@ handling policies user error handling etc and examples.
                                    32. -
                                    33. +
                                    34. My environment doesn't allow and/or I don't want exceptions. Can I still user Boost.Math?
                                      Yes but you must customise the error handling: see user error handling and changing policies defaults .
                                    35. -
                                    36. +
                                    37. The docs are several hundreds of pages long! Can I read the docs off-line or on paper?
                                      Yes - you can download the Boost current release of most documentation as a zip of pdfs (including @@ -149,7 +149,7 @@ Reader, Edit, Find ... This can often find what you seek, a partial substitute for a full index.
                                    38. -
                                    39. +
                                    40. I want a compact version for an embedded application. Can I use float precision?
                                      Yes - by selecting RealType template parameter as float: for example normal_distribution<float> your_normal(mean, @@ -157,7 +157,7 @@ less that you hope for). You can also change the promotion policy, but accuracy might be much reduced.
                                    41. -
                                    42. +
                                    43. I seem to get somewhat different results compared to other programs. Why? We hope Boost.Math to be more accurate: our priority is accuracy (over speed). See the section on accuracy. But for @@ -165,7 +165,7 @@ the required accuracy. You might be able to squeeze a little more accuracy at the cost of runtime.
                                    44. -
                                    45. +
                                    46. Will my program run more slowly compared to other math functions and statistical libraries? Probably, thought not always, and not by too much: our priority is accuracy. For most functions, making @@ -174,18 +174,18 @@ be able to gain a little more speed at the expense of accuracy. See detailed suggestions and results on performance.
                                    47. -
                                    48. +
                                    49. How do I handle infinity and NaNs portably?
                                      See nonfinite fp_facets for Facets for Floating-Point Infinities and NaNs.
                                    50. -
                                    51. +
                                    52. Where are the pre-built libraries?
                                      Good news - you probably don't need any! - just #include <boost/math/distribution_you_want>. But in the unlikely event that you do, see building libraries.
                                    53. -
                                    54. +
                                    55. I don't see the function or distribution that I want.
                                      You could try an email to ask the authors - but no promises!
                                    56. diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/hints.html b/doc/sf_and_dist/html/math_toolkit/main_overview/hints.html index 53a2dae49..0ccb9275c 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/hints.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/hints.html @@ -3,7 +3,7 @@ Other Hints and tips - + @@ -22,28 +22,28 @@
                                      PrevUpHomeNext
                                      -
                                      +
                                      -
                                        -
                                      • +
                                          +
                                        • If you have a feature request, or if it appears that the implementation is in error, please search first in the Boost Trac.
                                        • -
                                        • +
                                        • Trac entries may indicate that updates or corrections that solve your problem are in Boost-trunk where changes are being assembled and tested ready for the next release. You may, at your own risk, download new versions from there.
                                        • -
                                        • +
                                        • If you do not understand why things work the way they do, see the rationale section.
                                        • -
                                        • +
                                        • If you do not find your idea/feature/complaint, please reach the author preferably through the Boost development list, or email the author(s) direct. diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html b/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html index 595bc2293..54d2c50b9 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html @@ -3,7 +3,7 @@ History and What's New - + @@ -22,7 +22,7 @@
                                          PrevUpHomeNext
                                          -
                                          +

                                          History and What's New @@ -37,23 +37,23 @@ Boost-1.51

                                          -
                                            -
                                          • +
                                              +
                                            • Added Airy functions and Jacobi Elliptic functions.
                                            • -
                                            • +
                                            • Corrected failure to detect bad parameters in many distributions #6934 (reported by Florian Schoppmann) by adding a function check_out_of_range to test many possible bad parameters. This test revealed several distributions where the checks for bad parameters were ineffective, and these have been rectified.
                                            • -
                                            • +
                                            • Fixed issue in Hankel functions that causes incorrect values to be returned for x < 0 and ν odd, see #7135.
                                            • -
                                            • +
                                            • Fixed issues #6517, #6362, #7053, @@ -66,29 +66,29 @@ Boost-1.50

                            -
                              -
                            • +
                                +
                              • Promoted math constants to be 1st class citizens, including convenient access to the most widely used built-in float, double, long double via three namespaces.
                              • -
                              • +
                              • Added the Owen's T function and Skew Normal distribution written by Benjamin Sobotta: see Owens T and skew_normal_distrib.
                              • -
                              • +
                              • Added Hankel functions cyl_hankel_1, cyl_hankel_2, sph_hankel_1 and sph_hankel_2.
                              • -
                              • +
                              • Corrected issue #6627 nonfinite_num_put formatting of 0.0 is incorrect based on a patch submitted by K R Walker.
                              • -
                              • +
                              • Changed constant initialization mechanism so that it is thread safe even for user-defined types, also so that user defined types get the full precision of the constant, even when long @@ -96,7 +96,7 @@ 128-bit rational approximations will work with UDT's and do the right thing, even though long double may be only 64 or 80 bits.
                              • -
                              • +
                              • Fixed issue in bessel_jy which causes Y8.5(4π) to yield a NaN.
                              • @@ -105,37 +105,37 @@ Boost-1.49

                    -
                      -
                    • +
                        +
                      • Deprecated wrongly named twothirds math constant in favour of two_thirds (with underscore separator). (issue #6199).
                      • -
                      • +
                      • Refactored test data and some special function code to improve support for arbitary precision and/or expression-template-enabled types.
                      • -
                      • +
                      • Added new faster zeta function evaluation method.

                      Fixed issues:

                      -
                        -
                      • +
                          +
                        • Corrected CDF complement for Laplace distribution (issue #6151).
                        • -
                        • +
                        • Corrected branch cuts on the complex inverse trig functions, to handle signed zeros (issue #6171).
                        • -
                        • +
                        • Fixed bug in bessel_yn which caused incorrect overflow errors to be raised for negative n (issue #6367).
                        • -
                        • +
                        • Also fixed minor/cosmetic/configuration issues #6120, #6191, #5982, @@ -149,50 +149,50 @@ Boost-1.48

                    -
                      -
                    • +
                        +
                      • Added new series evaluation methods to the cyclic Bessel I, J, K and Y functions. Also taken great care to avoid spurious over and underflow of these functions. Fixes issue #5560
                      • -
                      • +
                      • Added an example of using Inverse Chi-Squared distribution for Bayesian statistics, provided by Thomas Mang.
                      • -
                      • +
                      • Added tests to use improved version of lexical_cast which handles C99 nonfinites without using globale facets.
                      • -
                      • +
                      • Corrected wrong out-of-bound uniform distribution CDF complement values #5733.
                      • -
                      • +
                      • Enabled long double support on OpenBSD (issue #6014).
                      • -
                      • +
                      • Changed nextafter and related functions to behave in the same way as other implementations - so that nextafter(+INF, 0) is a finite value (issue #5832).
                      • -
                      • +
                      • Changed tuple include configuration to fix issue when using in conjunction with Boost.Tr1 (issue #5934).
                      • -
                      • +
                      • Changed class eps_tolerance to behave correctly when both ends of the range are zero (issue #6001).
                      • -
                      • +
                      • Fixed missing include guards on prime.hpp (issue #5927).
                      • -
                      • +
                      • Removed unused/undocumented constants from constants.hpp (issue #5982).
                      • -
                      • +
                      • Fixed missing std:: prefix in nonfinite_num_facets.hpp (issue #5914).
                      • -
                      • +
                      • Minor patches for Cray compiler compatibility.
                      @@ -200,16 +200,16 @@ Boost-1.47

                    -
                      -
                    • +
                        +
                      • Added changesign function to sign.hpp to facilitate addition of nonfinite facets.
                      • -
                      • +
                      • Addition of nonfinite facets from Johan Rade, with tests, examples of use for C99 format infinity and NaN, and documentation.
                      • -
                      • +
                      • Added tests and documentation of changesign from Johan Rade.
                      @@ -217,7 +217,7 @@ Boost-1.46.1

                    -

            -
              -
            • +
                +
              • Added Wald, Inverse Gaussian and geometric distributions.
              • -
              • +
              • Added information about configuration macros.
              • -
              • +
              • Added support for mpreal as a real-numbered type.
              @@ -240,16 +240,16 @@ Boost-1.45.0
            -
              -
            • +
                +
              • Added warnings about potential ambiguity with std random library in distribution and function names.
              • -
              • +
              • Added inverse gamma distribution and inverse chi_square and scaled inverse chi_square.
              • -
              • +
              • Editorial revision of documentation, and added FAQ.
              @@ -257,11 +257,11 @@ Boost-1.44.0
            -
              -
            • +
                +
              • Fixed incorrect range and support for Rayleigh distribution.
              • -
              • +
              • Fixed numerical error in the quantile of the Student's T distribution: the function was returning garbage values for non-integer degrees of freedom between 2 and 3. @@ -271,7 +271,7 @@ Boost-1.41.0
            -
            • +
              • Significantly improved performance for the incomplete gamma function and its inverse.
              @@ -279,36 +279,36 @@ Boost-1.40.0
        -
          -
        • +
            +
          • Added support for MPFR as a bignum type.
          • -
          • +
          • Added some full specializations of the policy classes to reduce compile times.
          • -
          • +
          • Added logistic and hypergeometric distributions, from Gautam Sewani's Google Summer of Code project.
          • -
          • +
          • Added Laplace distribution submitted by Thijs van den Berg.
          • -
          • +
          • Updated performance test code to include new distributions, and improved the performance of the non-central distributions.
          • -
          • +
          • Added SSE2 optimised Lanczos approximation code, from Gautam Sewani's Google Summer of Code project.
          • -
          • +
          • Fixed bug in cyl_bessel_i that used an incorrect approximation for ν = 0.5, also effects the non-central Chi Square Distribution when ν = 3, see bug report #2877.
          • -
          • +
          • Fixed minor bugs #2873.
          @@ -316,11 +316,11 @@ Boost-1.38.0
    -
      -
    • +
        +
      • Added Johan Råde's optimised floating point classification routines.
      • -
      • +
      • Fixed code so that it compiles in GCC's -pedantic mode (bug report #1451).
      @@ -328,39 +328,39 @@ Boost-1.37.0
    -
    • +
      • Improved accuracy and testing of the inverse hypergeometric functions.
      Boost-1.36.0
      -
        -
      • +
          +
        • Added Noncentral Chi Squared Distribution.
        • -
        • +
        • Added Noncentral Beta Distribution.
        • -
        • +
        • Added Noncentral F Distribution.
        • -
        • +
        • Added Noncentral T Distribution.
        • -
        • +
        • Added Exponential Integral Functions.
        • -
        • +
        • Added Zeta Function.
        • -
        • +
        • Added Rounding and Truncation functions.
        • -
        • +
        • Added Compile time powers of runtime bases.
        • -
        • +
        • Added SSE2 optimizations for Lanczos evaluation.
        @@ -369,30 +369,30 @@ Boost-1.35.0: Post Review First Official Release -
          -
        • +
            +
          • Added Policy based framework that allows fine grained control over function behaviour.
          • -
          • +
          • Breaking change: Changed default behaviour for domain, pole and overflow errors to throw an exception (based on review feedback), this behaviour can be customised using Policy's.
          • -
          • +
          • Breaking change: Changed exception thrown when an internal evaluation error occurs to boost::math::evaluation_error.
          • -
          • +
          • Breaking change: Changed discrete quantiles to return an integer result: this is anything up to 20 times faster than finding the true root, this behaviour can be customised using Policy's.
          • -
          • +
          • Polynomial/rational function evaluation is now customisable and hopefully faster than before.
          • -
          • +
          • Added performance test program.
          @@ -401,12 +401,12 @@ Milestone 4: Second Review Candidate (1st March 2007) -
            -
          • +
              +
            • Moved Xiaogang Zhang's Bessel Functions code into the library, and brought them into line with the rest of the code.
            • -
            • +
            • Added C# "Distribution Explorer" demo application.
            @@ -415,25 +415,25 @@ Milestone 3: First Review Candidate (31st Dec 2006) -
              -
            • +
                +
              • Implemented the main probability distribution and density functions.
              • -
              • +
              • Implemented digamma.
              • -
              • +
              • Added more factorial functions.
              • -
              • +
              • Implemented the Hermite, Legendre and Laguerre polynomials plus the spherical harmonic functions from TR1.
              • -
              • +
              • Moved Xiaogang Zhang's elliptic integral code into the library, and brought them into line with the rest of the code.
              • -
              • +
              • Moved Hubert Holin's existing Boost.Math special functions into this library and brought them into line with the rest of the code.
              • @@ -443,34 +443,34 @@ Milestone 2: Released September 10th 2006 -
                  -
                • +
                    +
                  • Implement preview release of the statistical distributions.
                  • -
                  • +
                  • Added statistical distributions tutorial.
                  • -
                  • +
                  • Implemented root finding algorithms.
                  • -
                  • +
                  • Implemented the inverses of the incomplete gamma and beta functions.
                  • -
                  • +
                  • Rewrite erf/erfc as rational approximations (valid to 128-bit precision).
                  • -
                  • +
                  • Integrated the statistical results generated from the test data with Boost.Test: uses a database of expected results, indexed by test, floating point type, platform, and compiler.
                  • -
                  • +
                  • Improved lgamma near 1 and 2 (rational approximations).
                  • -
                  • +
                  • Improved erf/erfc inverses (rational approximations).
                  • -
                  • +
                  • Implemented Rational function generation (the Remez method).
                  @@ -479,23 +479,23 @@ Milestone 1: Released March 31st 2006 -
                    -
                  • +
                      +
                    • Implement gamma/beta/erf functions along with their incomplete counterparts.
                    • -
                    • +
                    • Generate high quality test data, against which future improvements can be judged.
                    • -
                    • +
                    • Provide tools for the evaluation of infinite series, continued fractions, and rational functions.
                    • -
                    • +
                    • Provide tools for testing against tabulated test data, and collecting statistics on error rates.
                    • -
                    • +
                    • Provide sufficient docs for people to be able to find their way around the library.
                    • diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/intro.html b/doc/sf_and_dist/html/math_toolkit/main_overview/intro.html index 25b5f635f..b6e272042 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/intro.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/intro.html @@ -3,7 +3,7 @@ About the Math Toolkit - + @@ -22,7 +22,7 @@
                      PrevUpHomeNext
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                      +
                      diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/namespaces.html b/doc/sf_and_dist/html/math_toolkit/main_overview/namespaces.html index c1e51f122..9d687619c 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/namespaces.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/namespaces.html @@ -3,7 +3,7 @@ Namespaces - + @@ -22,7 +22,7 @@
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                      +
                      diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html index 920f1721b..8056c760c 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html @@ -3,7 +3,7 @@ Navigation - + @@ -22,30 +22,30 @@
                      PrevUpHomeNext
                      -
                      +

                      - +

                      Boost.Math documentation is provided in both HTML and PDF formats.

                      -
                        -
                      • +
                          +
                        • Tutorials are listed in the Table of Contents and include many examples that should help you get started quickly.
                        • -
                        • +
                        • Source code of the many Examples will often be your quickest starting point.
                        • -
                        • +
                        • Index (general) includes all entries.
                        • -
                        • +
                        • Specific Indexes list only functions, class signatures, macros and typedefs.
                        • diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/perf_over.html b/doc/sf_and_dist/html/math_toolkit/main_overview/perf_over.html index a30695657..746f8f66b 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/perf_over.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/perf_over.html @@ -3,7 +3,7 @@ Performance - + @@ -22,7 +22,7 @@
                          PrevUpHomeNext
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                          +
                          @@ -46,13 +46,13 @@ The two most important things you can do to ensure the best performance from this library are:

                          -
                            -
                          1. +
                              +
                            1. Turn on your compilers optimisations: the difference between "release" and "debug" builds can easily be a factor of 20.
                            2. -
                            3. +
                            4. Pick your compiler carefully: performance differences of up to 8 fold have been found between some Windows compilers for example. diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/pol_overview.html b/doc/sf_and_dist/html/math_toolkit/main_overview/pol_overview.html index c52c2c652..48537d4ef 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/pol_overview.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/pol_overview.html @@ -3,7 +3,7 @@ Policies - + @@ -22,7 +22,7 @@
                              PrevUpHomeNext
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                              +
                              @@ -49,31 +49,31 @@

                              Using policies you can control:

                              -
                                -
                              • +
                                  +
                                • How results from 'bad' arguments are handled, including those that cannot be fully evaluated.
                                • -
                                • +
                                • How accuracy is controlled by internal promotion to use more precise types.
                                • -
                                • +
                                • What working precision should be used to calculate results.
                                • -
                                • +
                                • What to do when a mathematically undefined function is used: Should this raise a run-time or compile-time error?
                                • -
                                • +
                                • Whether discrete functions, like the binomial, should return real or only integral values, and how they are rounded.
                                • -
                                • +
                                • How many iterations a special function is permitted to perform in a series evaluation or root finding algorithm before it gives up and raises an evaluation_error. @@ -82,18 +82,18 @@

                                  You can control policies:

                                  -
                                    -
                                  • +
                                      +
                                    • Using macros to change any default policy: the is the prefered method for installation wide policies.
                                    • -
                                    • +
                                    • At your chosen namespace scope for distributions and/or functions: this is the prefered method for project, namespace, or translation unit scope policies.
                                    • -
                                    • +
                                    • In an ad-hoc manner by passing a specific policy to a special function, or to a statistical distribution. diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/result_type.html b/doc/sf_and_dist/html/math_toolkit/main_overview/result_type.html index 8490bf68f..5055de925 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/result_type.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/result_type.html @@ -3,7 +3,7 @@ Calculation of the Type of the Result - + @@ -22,7 +22,7 @@
                                      PrevUpHomeNext
                                      -
                                      +

                                      Calculation of the Type of the Result @@ -40,7 +40,7 @@ two floating-point arguments. But that leaves the question:

    -

    [1] +

    [1] Cephes gets stuck in an infinite loop while trying to execute our test cases.

    -

    [2] +

    [2] The performance here is dominated by a few cases where the parameters grow very large: faster asymptotic expansions are available, but are of limited (or even frankly terrible) precision. The @@ -1811,28 +1811,28 @@

    -

    [1] +

    [1] There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result.

    -

    [2] +

    [2] This result is somewhat misleading: for small values of the parameters there is virtually no difference between the two libraries, but for large values the Boost implementation is much slower, albeit with much improved precision.

    -

    [3] +

    [3] The R library appears to use a linear-search strategy, that can perform very badly in a small number of pathological cases, but may or may not be more efficient in "typical" cases

    -

    [4] +

    [4] There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result.

    -

    [5] +

    [5] There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result. @@ -3088,28 +3088,28 @@

    -

    [1] +

    [1] There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result.

    -

    [2] +

    [2] This result is somewhat misleading: for small values of the parameters there is virtually no difference between the two libraries, but for large values the Boost implementation is much slower, albeit with much improved precision.

    -

    [3] +

    [3] The R library appears to use a linear-search strategy, that can perform very badly in a small number of pathological cases, but may or may not be more efficient in "typical" cases

    -

    [4] +

    [4] There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result.

    -

    [5] +

    [5] There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result. diff --git a/doc/sf_and_dist/html/math_toolkit/perf/getting_best.html b/doc/sf_and_dist/html/math_toolkit/perf/getting_best.html index 00838c3b5..e5324c20e 100644 --- a/doc/sf_and_dist/html/math_toolkit/perf/getting_best.html +++ b/doc/sf_and_dist/html/math_toolkit/perf/getting_best.html @@ -3,7 +3,7 @@ Getting the Best Performance from this Library - + @@ -22,7 +22,7 @@

    PrevUpHomeNext
    -
    +

    Getting the Best Performance from this Library diff --git a/doc/sf_and_dist/html/math_toolkit/perf/interp.html b/doc/sf_and_dist/html/math_toolkit/perf/interp.html index 9f2f2174c..2d7c61fa9 100644 --- a/doc/sf_and_dist/html/math_toolkit/perf/interp.html +++ b/doc/sf_and_dist/html/math_toolkit/perf/interp.html @@ -3,7 +3,7 @@ Interpreting these Results - + @@ -22,7 +22,7 @@
    PrevUpHomeNext
    -
    +
    diff --git a/doc/sf_and_dist/html/math_toolkit/perf/perf_over.html b/doc/sf_and_dist/html/math_toolkit/perf/perf_over.html index 6da85de64..d72678c3b 100644 --- a/doc/sf_and_dist/html/math_toolkit/perf/perf_over.html +++ b/doc/sf_and_dist/html/math_toolkit/perf/perf_over.html @@ -3,7 +3,7 @@ Performance Overview - + @@ -22,7 +22,7 @@
    PrevUpHomeNext
    -
    +
    @@ -46,13 +46,13 @@ The two most important things you can do to ensure the best performance from this library are:

    -
      -
    1. +
        +
      1. Turn on your compilers optimisations: the difference between "release" and "debug" builds can easily be a factor of 20.
      2. -
      3. +
      4. Pick your compiler carefully: performance differences of up to 8 fold have been found between some Windows compilers for example. diff --git a/doc/sf_and_dist/html/math_toolkit/perf/perf_test_app.html b/doc/sf_and_dist/html/math_toolkit/perf/perf_test_app.html index 68cbbd24c..69ea11452 100644 --- a/doc/sf_and_dist/html/math_toolkit/perf/perf_test_app.html +++ b/doc/sf_and_dist/html/math_toolkit/perf/perf_test_app.html @@ -3,7 +3,7 @@ The Performance Test Application - + @@ -22,7 +22,7 @@
        PrevUpHomeNext
        -
        +

        The Performance Test Application diff --git a/doc/sf_and_dist/html/math_toolkit/perf/tuning.html b/doc/sf_and_dist/html/math_toolkit/perf/tuning.html index e82a9a20d..3213c2bda 100644 --- a/doc/sf_and_dist/html/math_toolkit/perf/tuning.html +++ b/doc/sf_and_dist/html/math_toolkit/perf/tuning.html @@ -3,7 +3,7 @@ Performance Tuning Macros - + @@ -22,7 +22,7 @@
        PrevUpHomeNext
        -
        +
        diff --git a/doc/sf_and_dist/html/math_toolkit/policy.html b/doc/sf_and_dist/html/math_toolkit/policy.html index 04f720d5a..6cb913905 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy.html +++ b/doc/sf_and_dist/html/math_toolkit/policy.html @@ -3,7 +3,7 @@ Policies - + @@ -22,7 +22,7 @@
        PrevUpHomeNext
        -
        +
        diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_overview.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_overview.html index 839e71e63..da0f123d4 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_overview.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_overview.html @@ -3,7 +3,7 @@ Policy Overview - + @@ -22,7 +22,7 @@
        PrevUpHomeNext
        -
        +
        @@ -49,31 +49,31 @@

        Using policies you can control:

        -
          -
        • +
            +
          • How results from 'bad' arguments are handled, including those that cannot be fully evaluated.
          • -
          • +
          • How accuracy is controlled by internal promotion to use more precise types.
          • -
          • +
          • What working precision should be used to calculate results.
          • -
          • +
          • What to do when a mathematically undefined function is used: Should this raise a run-time or compile-time error?
          • -
          • +
          • Whether discrete functions, like the binomial, should return real or only integral values, and how they are rounded.
          • -
          • +
          • How many iterations a special function is permitted to perform in a series evaluation or root finding algorithm before it gives up and raises an evaluation_error. @@ -82,18 +82,18 @@

            You can control policies:

            -
              -
            • +
                +
              • Using macros to change any default policy: the is the prefered method for installation wide policies.
              • -
              • +
              • At your chosen namespace scope for distributions and/or functions: this is the prefered method for project, namespace, or translation unit scope policies.
              • -
              • +
              • In an ad-hoc manner by passing a specific policy to a special function, or to a statistical distribution. diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref.html index f204c9165..1c02b07be 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref.html @@ -3,7 +3,7 @@ Policy Reference - + @@ -22,7 +22,7 @@
                PrevUpHomeNext
                -
                +
                diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/assert_undefined.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/assert_undefined.html index fdc82f522..61255c378 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/assert_undefined.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/assert_undefined.html @@ -3,7 +3,7 @@ Mathematically Undefined Function Policies - + @@ -22,7 +22,7 @@
                PrevUpHomeNext
                -
                +

                Mathematically Undefined Function Policies diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/discrete_quant_ref.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/discrete_quant_ref.html index 95cb6d4bb..0c4565c18 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/discrete_quant_ref.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/discrete_quant_ref.html @@ -3,7 +3,7 @@ Discrete Quantile Policies - + @@ -22,7 +22,7 @@
                PrevUpHomeNext
                -
                +

                Discrete Quantile Policies @@ -78,6 +78,7 @@ double x = quantile(dist_type(20, 0.3), 0.05); // Upper 95% quantile: double y = quantile(complement(dist_type(20, 0.3), 0.05)); +

                @@ -93,12 +94,12 @@

                This is the default policy: an integer value is returned so that:

                -
                  -
                • +
                    +
                  • Lower quantiles (where the probability is less than 0.5) are rounded down.
                  • -
                  • +
                  • Upper quantiles (where the probability is greater than 0.5) are rounded up.
                  • @@ -118,6 +119,7 @@ double x = quantile(negative_binomial(20, 0.3), 0.05); // rounded up 27 from 27.3898 // Upper quantile rounded up: double y = quantile(complement(negative_binomial(20, 0.3), 0.05)); // rounded down to 69 from 68.1584 +

                    @@ -146,12 +148,12 @@ This is the opposite of integer_round_outwards: an integer value is returned so that:

                    -
                      -
                    • +
                        +
                      • Lower quantiles (where the probability is less than 0.5) are rounded up.
                      • -
                      • +
                      • Upper quantiles (where the probability is greater than 0.5) are rounded down.
                      • @@ -175,6 +177,7 @@ double x = quantile(dist_type(20, 0.3), 0.05); // 28 rounded up from 27.3898 // Upper quantile rounded down: double y = quantile(complement(dist_type(20, 0.3), 0.05)); // 68 rounded down from 68.1584 +

                        @@ -241,6 +244,7 @@ double x = quantile(dist_type(20, 0.3), 0.05); // 27 // Upper quantile rounded (down) to nearest: double y = quantile(complement(dist_type(20, 0.3), 0.05)); // 68 +

                        diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/error_handling_policies.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/error_handling_policies.html index 7bf1bb9b1..06749dbc1 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/error_handling_policies.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/error_handling_policies.html @@ -3,7 +3,7 @@ Error Handling Policies - + @@ -22,7 +22,7 @@
                        PrevUpHomeNext
                        -
                        +

                        Error Handling Policies @@ -30,11 +30,11 @@

                        There are two orthogonal aspects to error handling:

                        -
                          -
                        • +
                            +
                          • What to do (if anything) with the error.
                          • -
                          • +
                          • What kind of error is being raised.
                          @@ -760,6 +760,7 @@ // Construct a my_norm distribution, using default mean and standard deviation, // and get a 0.05 or 5% quantile: double q = quantile(my_norm(), 0.05); // = -1.64485 +

                          diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/internal_promotion.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/internal_promotion.html index e8aee2905..3965fa54a 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/internal_promotion.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/internal_promotion.html @@ -3,7 +3,7 @@ Internal Floating-point Promotion Policies - + @@ -22,7 +22,7 @@
                          PrevUpHomeNext
                          -
                          +

                          Internal Floating-point Promotion Policies @@ -111,6 +111,7 @@ // Alternatively we could use helper function make_policy, // and concisely define everything at the call site: double t2 = tgamma(some_value, make_policy(promote_double<false>())); +

                          @@ -135,6 +136,7 @@ // Get a quantile: float q = quantile(my_norm(), 0.05f); +

                          diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/iteration_pol.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/iteration_pol.html index 8219eb7d2..740cecc43 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/iteration_pol.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/iteration_pol.html @@ -3,7 +3,7 @@ Iteration Limits Policies - + @@ -22,7 +22,7 @@
                          PrevUpHomeNext
                          -
                          +

                          Iteration Limits Policies diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/namespace_pol.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/namespace_pol.html index c66cc6e63..09e511026 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/namespace_pol.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/namespace_pol.html @@ -3,7 +3,7 @@ Setting Polices at Namespace Scope - + @@ -22,7 +22,7 @@
                          PrevUpHomeNext
                          -
                          +

                          Setting Polices at Namespace Scope @@ -68,6 +68,7 @@ double t = myspace::tgamma(30.0); // Will *not* throw on overflow, // despite the large value of factorial 30 = 265252859812191058636308480000000 // unlike default policy boost::math::tgamma; +

                          @@ -132,6 +133,7 @@ cout << e.what() << endl; } } +

                          diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/pol_ref_ref.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/pol_ref_ref.html index 5735006e4..1c795737c 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/pol_ref_ref.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/pol_ref_ref.html @@ -3,7 +3,7 @@ Policy Class Reference - + @@ -22,7 +22,7 @@
                          PrevUpHomeNext
                          -
                          +

                          Policy Class Reference diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/policy_defaults.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/policy_defaults.html index 7c0c1dd16..901387d61 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/policy_defaults.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/policy_defaults.html @@ -3,7 +3,7 @@ Using Macros to Change the Policy Defaults - + @@ -22,7 +22,7 @@
                          PrevUpHomeNext
                          -
                          +

                          Using Macros to Change the Policy Defaults diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/precision_pol.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/precision_pol.html index d893131e7..18e2fe4d5 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/precision_pol.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/precision_pol.html @@ -3,7 +3,7 @@ Precision Policies - + @@ -22,7 +22,7 @@
                          PrevUpHomeNext
                          -
                          +

                          Precision Policies @@ -82,6 +82,7 @@ using namespace boost::math::policies; double t = tgamma(12, policy<digits10<5> >()); // Concise make_policy. +

                          @@ -100,6 +101,7 @@ double q = quantile( normal_distribution<double, policy<digits2<bits> > >(), 0.05); // 5% quantile. +

                          diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial.html index b098878e7..84c2943be 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial.html @@ -3,7 +3,7 @@ Policy Tutorial - + @@ -22,7 +22,7 @@
                          PrevUpHomeNext
                          -
                          +
                          diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html index 0ed804df9..965afc00f 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html @@ -3,7 +3,7 @@ Setting Policies for Distributions on an Ad Hoc Basis - + @@ -22,7 +22,7 @@
                          PrevUpHomeNext
                          -
                          +

                          Setting Policies for Distributions on an Ad Hoc Basis @@ -83,6 +83,7 @@ cout << "quantile(mybinom(200, 0.25), 0.05) is: " << quantile(mybinom(200, 0.25), 0.05) << endl; } +

                          diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html index 142629ce8..fa210421b 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html @@ -3,7 +3,7 @@ Changing the Policy on an Ad Hoc Basis for the Special Functions - + @@ -22,7 +22,7 @@
                          PrevUpHomeNext
                          -
                          +

                          Changing the Policy on an Ad Hoc Basis for the Special Functions @@ -101,6 +101,7 @@ << boost::math::tgamma(-10, c_policy()) << endl; // Negative parameter. cout << "errno = " << errno << endl; // error 33 Numerical argument out of domain. } // int main() +

                          @@ -159,6 +160,7 @@ errno = 33 // Check errno was set: std::cout << "errno = " << errno << std::endl; } +

                          diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/changing_policy_defaults.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/changing_policy_defaults.html index 76ac9a9c0..808ccb493 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/changing_policy_defaults.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/changing_policy_defaults.html @@ -3,7 +3,7 @@ Changing the Policy Defaults - + @@ -22,7 +22,7 @@
                          PrevUpHomeNext
                          -
                          +

                          Changing the Policy Defaults @@ -99,14 +99,14 @@

                          That means there are only two safe ways to use these macros:

                          -
                            -
                          • +
                              +
                            • Edit them in boost/math/tools/user.hpp, so that the defaults are set on an installation-wide basis. Unfortunately this may not be convenient if you are using a pre-installed Boost distribution (on Linux for example).
                            • -
                            • +
                            • Set the defines in your project's Makefile or build environment, so that they are set uniformly across all translation units.
                            • @@ -114,7 +114,7 @@

                              What you should not do is:

                              -
                              • +
                                • Set the defines in the source file using #define as doing so almost certainly will break your program, unless you're absolutely certain that the program is restricted to a single translation @@ -162,7 +162,9 @@

                                  -
                                  // Boost
                                  +
                                     #define BOOST_MATH_DOMAIN_ERROR_POLICY ignore_error
                                  +
                                  +// Boost
                                   #include <boost/math/distributions/students_t.hpp>
                                      using boost::math::students_t;  // Probability of students_t(df, t).
                                   
                                  @@ -175,8 +177,7 @@
                                      using std::exception;
                                   
                                   #include <cstddef>
                                  -   // using ::errno
                                  -
                                  + // using ::errno

                                  @@ -218,8 +219,7 @@ "\n""Message from thrown exception was:\n " << e.what() << std::endl; } return 0; -} // int main() - +} // int main()

                                  diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/namespace_policies.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/namespace_policies.html index b75c334c5..a58fe562d 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/namespace_policies.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/namespace_policies.html @@ -3,7 +3,7 @@ Setting Policies at Namespace or Translation Unit Scope - + @@ -22,7 +22,7 @@

                                  PrevUpHomeNext
                                  -
                                  +

                                  Setting Policies at Namespace or Translation Unit Scope @@ -53,8 +53,7 @@

                                  #include <boost/math/special_functions.hpp>
                                  -//using boost::math::tgamma; // Not needed because using C::tgamma.
                                  -
                                  +//using boost::math::tgamma; // Not needed because using C::tgamma.

                                  @@ -83,8 +82,7 @@ pole_error<errno_on_error>, overflow_error<errno_on_error>, evaluation_error<errno_on_error> - > c_policy; - + > c_policy;

                                  @@ -95,8 +93,7 @@

                                  BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS(c_policy)
                                   
                                  -} // close namespace C
                                  -
                                  +} // close namespace C

                                  @@ -130,8 +127,7 @@ cout << "Result of tgamma(-10) is: " << C::tgamma(-10) << endl; cout << "errno = " << errno << endl; // errno = 33, overwriting previous value of 34. -} - +}

                                  @@ -171,8 +167,7 @@ errno = 33 evaluation_error<errno_on_error> > c_policy; -BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS(c_policy) - +BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS(c_policy)

                                  @@ -196,6 +191,7 @@ errno = 33 cout << "errno = " << errno << endl; // Default tgamma policy would throw an exception, and abort. } +

                                  @@ -218,14 +214,14 @@ errno = 33

                                  Suppose we want a set of distributions to behave as follows:

                                  -
                                    -
                                  • +
                                      +
                                    • Return infinity on overflow, rather than throwing an exception.
                                    • -
                                    • +
                                    • Don't perform any promotion from double to long double internally.
                                    • -
                                    • +
                                    • Return the closest integer result from the quantiles of discrete distributions.
                                    @@ -234,8 +230,7 @@ errno = 33

                                    -
                                    #include <boost/math/distributions.hpp>
                                    -
                                    +
                                    #include <boost/math/distributions.hpp>

                                    @@ -257,8 +252,7 @@ errno = 33 promote_double<false>, // Return the closest integer result for discrete quantiles: discrete_quantile<integer_round_nearest> - > my_policy; - + > my_policy;

                                    @@ -271,8 +265,7 @@ errno = 33

                                    BOOST_MATH_DECLARE_DISTRIBUTIONS(double, my_policy)
                                     
                                    -} // close namespace my_namespace
                                    -
                                    +} // close namespace my_namespace

                                    @@ -314,8 +307,7 @@ errno = 33 << quantile(binom, 0.05) << endl; // To check we get integer results. cout << "Result of quantile(complement(binom, 0.05)) is: " << quantile(complement(binom, 0.05)) << endl; -} - +}

                                    @@ -395,6 +387,7 @@ Result of quantile(complement(binom, 0.05)) is: 8 cout << "Result of quantile(complement(binom, 0.05)) is: " << quantile(complement(binom, 0.05)) << endl; } +

                                    diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_tut_defaults.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_tut_defaults.html index ff8c95913..836d7ac91 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_tut_defaults.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_tut_defaults.html @@ -3,7 +3,7 @@ Policies Have Sensible Defaults - + @@ -22,7 +22,7 @@
                                    PrevUpHomeNext
                                    -
                                    +

                                    Policies Have Sensible Defaults diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_usage.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_usage.html index bb66b9990..3441e843d 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_usage.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_usage.html @@ -3,7 +3,7 @@ So How are Policies Used Anyway? - + @@ -22,7 +22,7 @@
                                    PrevUpHomeNext
                                    -
                                    +

                                    So How are Policies Used Anyway? @@ -30,20 +30,20 @@

                                    The details follow later, but basically policies can be set by either:

                                    -
                                      -
                                    • +
                                        +
                                      • Defining some macros that change the default behaviour: this is the recommended method for setting installation-wide policies.
                                      • -
                                      • +
                                      • By instantiating a distribution object with an explicit policy: this is mainly reserved for ad hoc policy changes.
                                      • -
                                      • +
                                      • By passing a policy to a special function as an optional final argument: this is mainly reserved for ad hoc policy changes.
                                      • -
                                      • +
                                      • By using some helper macros to define a set of functions or distributions in the current namespace that use a specific policy: this is the recommended method for setting policies on a project- or translation-unit-wide diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/understand_dis_quant.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/understand_dis_quant.html index b251aae7b..109619d03 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/understand_dis_quant.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/understand_dis_quant.html @@ -3,7 +3,7 @@ Understanding Quantiles of Discrete Distributions - + @@ -22,7 +22,7 @@
                                        PrevUpHomeNext
                                        -
                                        +

                                        Understanding Quantiles of Discrete Distributions @@ -53,11 +53,11 @@ As can be seen there is no random variable that corresponds to a probability of exactly 0.05, so we're left with two choices as shown in the figure:

                                        -
                                          -
                                        • +
                                            +
                                          • We could round the result down to 18.
                                          • -
                                          • +
                                          • We could round the result up to 19.
                                          @@ -77,12 +77,12 @@

                                          In coming to an answer we should realise that:

                                          -
                                            -
                                          • +
                                              +
                                            • Calculating an integer result is often much faster than calculating a real-valued result: in fact in our tests it was up to 20 times faster.
                                            • -
                                            • +
                                            • Normally people calculate quantiles so that they can perform a test of some kind: "If the random variable is less than N then we can reject our null-hypothesis with 90% confidence." @@ -256,8 +256,7 @@ using std::setw; using std::setprecision; -#include <boost/math/distributions/binomial.hpp> - +#include <boost/math/distributions/binomial.hpp>

                                              @@ -314,8 +313,7 @@ typedef binomial_distribution< double, policy<discrete_quantile<real> > > - binom_real_quantile; - + binom_real_quantile;

                                              @@ -389,8 +387,7 @@ << setw(18) << right << quantile(binom_real_quantile(50, 0.5), 0.95) << endl; -} // int main() - +} // int main()

                                              diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/user_def_err_pol.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/user_def_err_pol.html index b1cac051c..23ba349e6 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/user_def_err_pol.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/user_def_err_pol.html @@ -3,7 +3,7 @@ Calling User Defined Error Handlers - + @@ -22,7 +22,7 @@

                                              PrevUpHomeNext
                                              -
                                              +

                                              Calling User Defined Error Handlers @@ -84,8 +84,7 @@ return std::numeric_limits<T>::quiet_NaN(); } } // namespace policies -}} // namespace boost{ namespace math - +}} // namespace boost{ namespace math

                                              @@ -105,8 +104,7 @@ BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS(user_error_policy) -} // close unnamed namespace - +} // close unnamed namespace

                                              @@ -138,8 +136,7 @@ << erf_inv(-10) << endl; cout << "Result of tgamma(-10) is: " << tgamma(-10) << endl; -} - +}

                                              @@ -199,8 +196,7 @@

                                              -
                                              #include <boost/math/special_functions.hpp>
                                              -
                                              +
                                              #include <boost/math/special_functions.hpp>

                                              @@ -215,8 +211,7 @@ template <class T> T user_domain_error(const char* function, const char* message, const T& val) -{ - +{

                                              @@ -228,8 +223,7 @@

                                              if(function == 0)
                                                   function = "Unknown function with arguments of type %1%";
                                               if(message == 0)
                                              -    message = "Cause unknown with bad argument %1%";
                                              -
                                              + message = "Cause unknown with bad argument %1%";

                                              @@ -239,8 +233,7 @@

                                              std::string msg("Error in function ");
                                              -msg += (boost::format(function) % typeid(T).name()).str();
                                              -
                                              +msg += (boost::format(function) % typeid(T).name()).str();

                                              @@ -252,8 +245,7 @@

                                              msg += ": \n";
                                               int prec = 2 + (std::numeric_limits<T>::digits * 30103UL) / 100000UL;
                                               // int prec = std::numeric_limits<T>::max_digits10; //  For C++0X Standard Library
                                              -msg += (boost::format(message) % boost::io::group(std::setprecision(prec), val)).str();
                                              -
                                              +msg += (boost::format(message) % boost::io::group(std::setprecision(prec), val)).str();

                                              @@ -262,8 +254,7 @@

                                              -
                                              std::cerr << msg << std::endl;
                                              -
                                              +
                                              std::cerr << msg << std::endl;

                                              @@ -273,8 +264,7 @@

                                                 return std::numeric_limits<T>::quiet_NaN();
                                              -}
                                              -
                                              +}

                                              @@ -287,8 +277,7 @@ T user_pole_error(const char* function, const char* message, const T& val) { return user_domain_error(function, message, val); -} - +}

                                              @@ -315,8 +304,7 @@ // Value passed to the function is an infinity, just return it: return val; -} - +}

                                              @@ -342,8 +330,7 @@ // Value passed to the function is zero, just return it: return val; -} - +}

                                              @@ -369,8 +356,7 @@ // Value passed to the function is denormalised, just return it: return val; -} - +}

                                              @@ -406,8 +392,7 @@ } } // policies -}} // boost::math - +}} // boost::math

                                              @@ -432,8 +417,7 @@ BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS(user_error_policy) -} // unnamed namespace - +} // unnamed namespace

                                              @@ -476,8 +460,7 @@ // Unfortunately we can't predicably raise a denormalised // result, nor can we raise an evaluation error in this example // since these should never really occur! -} // int main() - +} // int main()

                                              diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/what_is_a_policy.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/what_is_a_policy.html index b211664e1..00c2d4dee 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/what_is_a_policy.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/what_is_a_policy.html @@ -3,7 +3,7 @@ So Just What is a Policy Anyway? - + @@ -22,7 +22,7 @@

                                              PrevUpHomeNext
                                              -
                                              +

                                              So Just What is a Policy Anyway? @@ -32,23 +32,23 @@ special function, or a statistical distribution. With Policies you can control:

                                              -
                                                -
                                              • +
                                                  +
                                                • What action to take when an error occurs.
                                                • -
                                                • +
                                                • What happens when you call a function that is mathematically undefined (for example, if you ask for the mean of a Cauchy distribution).
                                                • -
                                                • +
                                                • What happens when you ask for a quantile of a discrete distribution.
                                                • -
                                                • +
                                                • Whether the library is allowed to internally promote float to double and double to long double in order to improve precision.
                                                • -
                                                • +
                                                • What precision to use when calculating the result.
                                                diff --git a/doc/sf_and_dist/html/math_toolkit/special.html b/doc/sf_and_dist/html/math_toolkit/special.html index 370b4ce1b..1ea84a1ff 100644 --- a/doc/sf_and_dist/html/math_toolkit/special.html +++ b/doc/sf_and_dist/html/math_toolkit/special.html @@ -3,7 +3,7 @@ Special Functions - + @@ -22,7 +22,7 @@
                                                PrevUpHomeNext
                                                -
                                                +
                                                diff --git a/doc/sf_and_dist/html/math_toolkit/special/airy.html b/doc/sf_and_dist/html/math_toolkit/special/airy.html index 9b8a2cb4b..62b7fb203 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/airy.html +++ b/doc/sf_and_dist/html/math_toolkit/special/airy.html @@ -3,7 +3,7 @@ Airy Functions - + @@ -22,7 +22,7 @@
                                                PrevUpHomeNext
                                                -
                                                +
                                                diff --git a/doc/sf_and_dist/html/math_toolkit/special/airy/ai.html b/doc/sf_and_dist/html/math_toolkit/special/airy/ai.html index 8e3d83055..dcce1334b 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/airy/ai.html +++ b/doc/sf_and_dist/html/math_toolkit/special/airy/ai.html @@ -3,7 +3,7 @@ Airy Ai Function - + @@ -22,7 +22,7 @@
                                                PrevUpHomeNext
                                                -
                                                +
                                                @@ -92,7 +92,7 @@

                                              Since this function is implemented in terms of other special functions, - there are only a few basic sanity checks, using test values from functions.wolfram.com. + there are only a few basic sanity checks, using test values from Wolfram Airy Functions.

                                              diff --git a/doc/sf_and_dist/html/math_toolkit/special/airy/aip.html b/doc/sf_and_dist/html/math_toolkit/special/airy/aip.html index a0180d0e3..0beaf8259 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/airy/aip.html +++ b/doc/sf_and_dist/html/math_toolkit/special/airy/aip.html @@ -3,7 +3,7 @@ Airy Ai' Function - + @@ -22,7 +22,7 @@
                                              PrevUpHomeNext
                                              -
                                              +
                                              diff --git a/doc/sf_and_dist/html/math_toolkit/special/airy/bi.html b/doc/sf_and_dist/html/math_toolkit/special/airy/bi.html index aef1cfde6..3e9193c51 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/airy/bi.html +++ b/doc/sf_and_dist/html/math_toolkit/special/airy/bi.html @@ -3,7 +3,7 @@ Airy Bi Function - + @@ -22,7 +22,7 @@
                                              PrevUpHomeNext
                                              -
                                              +
                                              diff --git a/doc/sf_and_dist/html/math_toolkit/special/airy/bip.html b/doc/sf_and_dist/html/math_toolkit/special/airy/bip.html index 50143b930..a24f05af6 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/airy/bip.html +++ b/doc/sf_and_dist/html/math_toolkit/special/airy/bip.html @@ -3,7 +3,7 @@ Airy Bi' Function - + @@ -22,7 +22,7 @@
                                              PrevUpHomeNext
                                              -
                                              +
                                              diff --git a/doc/sf_and_dist/html/math_toolkit/special/bessel.html b/doc/sf_and_dist/html/math_toolkit/special/bessel.html index 1e92928ad..62e1a20e8 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/bessel.html +++ b/doc/sf_and_dist/html/math_toolkit/special/bessel.html @@ -3,7 +3,7 @@ Bessel Functions - + @@ -22,7 +22,7 @@
                                              PrevUpHomeNext
                                              -
                                              +
                                              diff --git a/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel.html b/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel.html index fc23e89f1..3f11f4018 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel.html +++ b/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel.html @@ -3,7 +3,7 @@ Bessel Functions of the First and Second Kinds - + @@ -22,7 +22,7 @@
                                              PrevUpHomeNext
                                              -
                                              +

                                              Bessel Functions of the First and Second Kinds diff --git a/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel_over.html b/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel_over.html index 5ead6c678..d074a0ecb 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel_over.html +++ b/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel_over.html @@ -3,7 +3,7 @@ Bessel Function Overview - + @@ -22,7 +22,7 @@
                                              PrevUpHomeNext
                                              -
                                              +

                                              Bessel Function Overview diff --git a/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html b/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html index 5d6adc8a1..64fb69d03 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html +++ b/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html @@ -3,7 +3,7 @@ Modified Bessel Functions of the First and Second Kinds - + @@ -22,7 +22,7 @@
                                              PrevUpHomeNext
                                              -
                                              +

                                              Modified Bessel Functions of the First and Second Kinds @@ -339,13 +339,13 @@ The 0 and 1 cases use minimax rational approximations on finite and infinite intervals. The coefficients are from:

                                              -
                                                -
                                              • +
                                                  +
                                                • J.M. Blair and C.A. Edwards, Stable rational minimax approximations to the modified Bessel functions I_0(x) and I_1(x), Atomic Energy of Canada Limited Report 4928, Chalk River, 1974.
                                                • -
                                                • +
                                                • S. Moshier, Methods and Programs for Mathematical Functions, Ellis Horwood Ltd, Chichester, 1989.
                                                • diff --git a/doc/sf_and_dist/html/math_toolkit/special/bessel/sph_bessel.html b/doc/sf_and_dist/html/math_toolkit/special/bessel/sph_bessel.html index 8bd007acc..3340fcb45 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/bessel/sph_bessel.html +++ b/doc/sf_and_dist/html/math_toolkit/special/bessel/sph_bessel.html @@ -3,7 +3,7 @@ Spherical Bessel Functions of the First and Second Kinds - + @@ -22,7 +22,7 @@
                                                  PrevUpHomeNext
                                                  -
                                                  +

                                                  Spherical Bessel Functions of the First and Second Kinds diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint.html b/doc/sf_and_dist/html/math_toolkit/special/ellint.html index f27885254..35cd1efca 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/ellint.html +++ b/doc/sf_and_dist/html/math_toolkit/special/ellint.html @@ -3,7 +3,7 @@ Elliptic Integrals - + @@ -22,7 +22,7 @@
                                                  PrevUpHomeNext
                                                  -
                                                  +
                                                  diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_1.html b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_1.html index c096ca02e..92dac8e30 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_1.html +++ b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_1.html @@ -3,7 +3,7 @@ Elliptic Integrals of the First Kind - Legendre Form - + @@ -22,7 +22,7 @@
                                                  PrevUpHomeNext
                                                  -
                                                  +

                                                  Elliptic Integrals of the First Kind - Legendre Form diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_2.html b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_2.html index e124a8fc5..78e46a1e6 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_2.html +++ b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_2.html @@ -3,7 +3,7 @@ Elliptic Integrals of the Second Kind - Legendre Form - + @@ -22,7 +22,7 @@
                                                  PrevUpHomeNext
                                                  -
                                                  +

                                                  Elliptic Integrals of the Second Kind - Legendre Form diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html index 34c7a0039..c9c2d5acc 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html +++ b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html @@ -3,7 +3,7 @@ Elliptic Integrals of the Third Kind - Legendre Form - + @@ -22,7 +22,7 @@
                                                  PrevUpHomeNext
                                                  -
                                                  +

                                                  Elliptic Integrals of the Third Kind - Legendre Form @@ -297,7 +297,7 @@



                                                  -

                                                  [1] +

                                                  [1] I haven't been able to find a literature reference for this relation, but it appears to be the convention used by Mathematica. Intuitively the first 2 * m * Π(n, k) terms cancel out as the diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_carlson.html b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_carlson.html index dbc8d5ad3..c6533e398 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_carlson.html +++ b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_carlson.html @@ -3,7 +3,7 @@ Elliptic Integrals - Carlson Form - + @@ -22,7 +22,7 @@

                                                  PrevUpHomeNext
                                                  -
                                                  +

                                                  Elliptic Integrals - Carlson Form diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_intro.html b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_intro.html index b65ccd86a..1b836c2ae 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_intro.html +++ b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_intro.html @@ -3,7 +3,7 @@ Elliptic Integral Overview - + @@ -22,7 +22,7 @@
                                                  PrevUpHomeNext
                                                  -
                                                  +

                                                  Elliptic Integral Overview @@ -300,65 +300,65 @@

                                                  However the main references are:

                                                  -
                                                    -
                                                  1. +
                                                      +
                                                    1. M. Abramowitz and I. A. Stegun (Eds.) (1964) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards Applied Mathematics Series, U.S. Government Printing Office, Washington, D.C.
                                                    2. -
                                                    3. +
                                                    4. B.C. Carlson, Computing elliptic integrals by duplication, Numerische Mathematik, vol 33, 1 (1979).
                                                    5. -
                                                    6. +
                                                    7. B.C. Carlson, Elliptic Integrals of the First Kind, SIAM Journal on Mathematical Analysis, vol 8, 231 (1977).
                                                    8. -
                                                    9. +
                                                    10. B.C. Carlson, Short Proofs of Three Theorems on Elliptic Integrals, SIAM Journal on Mathematical Analysis, vol 9, 524 (1978).
                                                    11. -
                                                    12. +
                                                    13. B.C. Carlson and E.M. Notis, ALGORITHM 577: Algorithms for Incomplete Elliptic Integrals, ACM Transactions on Mathematmal Software, vol 7, 398 (1981).
                                                    14. -
                                                    15. +
                                                    16. B. C. Carlson, On computing elliptic integrals and functions. J. Math. and Phys., 44 (1965), pp. 36-51.
                                                    17. -
                                                    18. +
                                                    19. B. C. Carlson, A table of elliptic integrals of the second kind. Math. Comp., 49 (1987), pp. 595-606. (Supplement, ibid., pp. S13-S17.)
                                                    20. -
                                                    21. +
                                                    22. B. C. Carlson, A table of elliptic integrals of the third kind. Math. Comp., 51 (1988), pp. 267-280. (Supplement, ibid., pp. S1-S5.)
                                                    23. -
                                                    24. +
                                                    25. B. C. Carlson, A table of elliptic integrals: cubic cases. Math. Comp., 53 (1989), pp. 327-333.
                                                    26. -
                                                    27. +
                                                    28. B. C. Carlson, A table of elliptic integrals: one quadratic factor. Math. Comp., 56 (1991), pp. 267-280.
                                                    29. -
                                                    30. +
                                                    31. B. C. Carlson, A table of elliptic integrals: two quadratic factors. Math. Comp., 59 (1992), pp. 165-180.
                                                    32. -
                                                    33. +
                                                    34. B. C. Carlson, Numerical computation of real or complex elliptic integrals. Numerical Algorithms, Volume 10, Number 1 / March, 1995, p13-26.
                                                    35. -
                                                    36. +
                                                    37. B. C. Carlson and John L. Gustafson, Asymptotic Approximations for Symmetric Elliptic Integrals, SIAM Journal on Mathematical Analysis, Volume 25, Issue 2 (March 1994), @@ -369,21 +369,21 @@ The following references, while not directly relevent to our implementation, may also be of interest:

                                                      -
                                                        -
                                                      1. +
                                                          +
                                                        1. R. Burlisch, Numerical Compuation of Elliptic Integrals and Elliptic Functions. Numerical Mathematik 7, 78-90.
                                                        2. -
                                                        3. +
                                                        4. R. Burlisch, An extension of the Bartky Transformation to Incomplete Elliptic Integrals of the Third Kind. Numerical Mathematik 13, 266-284.
                                                        5. -
                                                        6. +
                                                        7. R. Burlisch, Numerical Compuation of Elliptic Integrals and Elliptic Functions. III. Numerical Mathematik 13, 305-315.
                                                        8. -
                                                        9. +
                                                        10. T. Fukushima and H. Ishizaki, Numerical Computation of Incomplete Elliptic Integrals of a General Form. Celestial Mechanics and Dynamical Astronomy, Volume 59, Number 3 / diff --git a/doc/sf_and_dist/html/math_toolkit/special/expint.html b/doc/sf_and_dist/html/math_toolkit/special/expint.html index 7297239be..9430aaf9e 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/expint.html +++ b/doc/sf_and_dist/html/math_toolkit/special/expint.html @@ -3,7 +3,7 @@ Exponential Integrals - + @@ -22,7 +22,7 @@
                                                          PrevUpHomeNext
                                                          -
                                                          +
                                                          diff --git a/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html b/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html index 6ae3a731f..57014962c 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html +++ b/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html @@ -3,7 +3,7 @@ Exponential Integral Ei - + @@ -22,7 +22,7 @@
                                                          PrevUpHomeNext
                                                          -
                                                          +

                                                          Exponential Integral Ei @@ -276,7 +276,7 @@



                                                          -

                                                          [5] +

                                                          [5] W. J. Cody and H. C. Thacher, Jr., Rational Chebyshev approximations for the exponential integral E1(x), Math. Comp. 22 (1968), 641-649, and W. J. Cody and H. C. Thacher, Jr., Chebyshev approximations for the exponential diff --git a/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html b/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html index 69a8e91c1..860fe2198 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html +++ b/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html @@ -3,7 +3,7 @@ Exponential Integral En - + @@ -22,7 +22,7 @@

                                                          PrevUpHomeNext
                                                          -
                                                          +

                                                          Exponential Integral En diff --git a/doc/sf_and_dist/html/math_toolkit/special/factorials.html b/doc/sf_and_dist/html/math_toolkit/special/factorials.html index 976b1c5b0..afbfe939c 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/factorials.html +++ b/doc/sf_and_dist/html/math_toolkit/special/factorials.html @@ -3,7 +3,7 @@ Factorials and Binomial Coefficients - + @@ -22,7 +22,7 @@
                                                          PrevUpHomeNext
                                                          -
                                                          +

                                                          Factorials and Binomial Coefficients diff --git a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_binomial.html b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_binomial.html index c525b11db..ab2e86828 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_binomial.html +++ b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_binomial.html @@ -3,7 +3,7 @@ Binomial Coefficients - + @@ -22,7 +22,7 @@
                                                          PrevUpHomeNext
                                                          -
                                                          +

                                                          Binomial Coefficients diff --git a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_double_factorial.html b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_double_factorial.html index 779003b06..4bca14404 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_double_factorial.html +++ b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_double_factorial.html @@ -3,7 +3,7 @@ Double Factorial - + @@ -22,7 +22,7 @@
                                                          PrevUpHomeNext
                                                          -
                                                          +

                                                          Double Factorial diff --git a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_factorial.html b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_factorial.html index d4731e140..6423810a7 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_factorial.html +++ b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_factorial.html @@ -3,7 +3,7 @@ Factorial - + @@ -22,7 +22,7 @@
                                                          PrevUpHomeNext
                                                          -
                                                          +
                                                          diff --git a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_falling_factorial.html b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_falling_factorial.html index 3dcb4d48a..ea18b8163 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_falling_factorial.html +++ b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_falling_factorial.html @@ -3,7 +3,7 @@ Falling Factorial - + @@ -22,7 +22,7 @@
                                                          PrevUpHomeNext
                                                          -
                                                          +

                                                          Falling Factorial diff --git a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_rising_factorial.html b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_rising_factorial.html index 809abcd4d..e0eac8547 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_rising_factorial.html +++ b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_rising_factorial.html @@ -3,7 +3,7 @@ Rising Factorial - + @@ -22,7 +22,7 @@
                                                          PrevUpHomeNext
                                                          -
                                                          +

                                                          Rising Factorial diff --git a/doc/sf_and_dist/html/math_toolkit/special/hankel.html b/doc/sf_and_dist/html/math_toolkit/special/hankel.html index c37dc139a..d58d2ef64 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/hankel.html +++ b/doc/sf_and_dist/html/math_toolkit/special/hankel.html @@ -3,7 +3,7 @@ Hankel Functions - + @@ -22,7 +22,7 @@
                                                          PrevUpHomeNext
                                                          -
                                                          +
                                                          diff --git a/doc/sf_and_dist/html/math_toolkit/special/hankel/cyl_hankel.html b/doc/sf_and_dist/html/math_toolkit/special/hankel/cyl_hankel.html index b4e890ea8..af879f979 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/hankel/cyl_hankel.html +++ b/doc/sf_and_dist/html/math_toolkit/special/hankel/cyl_hankel.html @@ -3,7 +3,7 @@ Cyclic Hankel Functions - + @@ -22,7 +22,7 @@
                                                          PrevUpHomeNext
                                                          -
                                                          +

                                                          Cyclic Hankel Functions diff --git a/doc/sf_and_dist/html/math_toolkit/special/hankel/sph_hankel.html b/doc/sf_and_dist/html/math_toolkit/special/hankel/sph_hankel.html index 7c0d69afa..4a7397aa0 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/hankel/sph_hankel.html +++ b/doc/sf_and_dist/html/math_toolkit/special/hankel/sph_hankel.html @@ -3,7 +3,7 @@ Spherical Hankel Functions - + @@ -22,7 +22,7 @@
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                                                          -
                                                          +

                                                          Spherical Hankel Functions diff --git a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper.html b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper.html index af3e29f01..e221ad879 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper.html +++ b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper.html @@ -3,7 +3,7 @@ Inverse Hyperbolic Functions - + @@ -22,7 +22,7 @@
                                                          PrevUpHomeNext
                                                          -
                                                          +
                                                          diff --git a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/acosh.html b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/acosh.html index 2140a9e04..0d3e0ef0e 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/acosh.html +++ b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/acosh.html @@ -3,7 +3,7 @@ acosh - + @@ -22,7 +22,7 @@
                                                          PrevUpHomeNext
                                                          -
                                                          +
                                                          diff --git a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/asinh.html b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/asinh.html index a1d386ffc..cba70a3d3 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/asinh.html +++ b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/asinh.html @@ -3,7 +3,7 @@ asinh - + @@ -22,7 +22,7 @@
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                                                          diff --git a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/atanh.html b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/atanh.html index 6df001bed..7825f4585 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/atanh.html +++ b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/atanh.html @@ -3,7 +3,7 @@ atanh - + @@ -22,7 +22,7 @@
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                                                          diff --git a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/inv_hyper_over.html b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/inv_hyper_over.html index d6579df64..58876d95f 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/inv_hyper_over.html +++ b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/inv_hyper_over.html @@ -3,7 +3,7 @@ Inverse Hyperbolic Functions Overview - + @@ -22,7 +22,7 @@
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                                                          Inverse Hyperbolic Functions Overview diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi.html index 3f7129dd1..d59b20c8f 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi.html @@ -3,7 +3,7 @@ Jacobi Elliptic Functions - + @@ -22,7 +22,7 @@
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                                                          diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jac_over.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jac_over.html index c89461767..3ccc76b4d 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jac_over.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jac_over.html @@ -3,7 +3,7 @@ Overvew of the Jacobi Elliptic Functions - + @@ -22,7 +22,7 @@
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                                                          Overvew of the Jacobi Elliptic Functions @@ -40,15 +40,15 @@

                                                          Like all elliptic functions these can be parameterised in a number of ways:

                                                          -
                                                            -
                                                          • +
                                                              +
                                                            • In terms of a parameter m.
                                                            • -
                                                            • +
                                                            • In terms of the elliptic modulus k where m = k2.
                                                            • -
                                                            • +
                                                            • In terms of the modular angle α, where m = sin2α.
                                                            @@ -94,16 +94,16 @@



                                                            -

                                                            [2] +

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                                                            [3] +

                                                            -

                                                            [4] +

                                                            diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cd.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cd.html index a8ff7ac01..57226b5d1 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cd.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cd.html @@ -3,7 +3,7 @@ Jacobi Elliptic Function cd - + @@ -22,7 +22,7 @@
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                                                            Jacobi Elliptic Function cd diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cn.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cn.html index d2ead927a..34dfe4d3e 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cn.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cn.html @@ -3,7 +3,7 @@ Jacobi Elliptic Function cn - + @@ -22,7 +22,7 @@
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                                                            Jacobi Elliptic Function cn diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cs.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cs.html index 890854164..13efdf21c 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cs.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cs.html @@ -3,7 +3,7 @@ Jacobi Elliptic Function cs - + @@ -22,7 +22,7 @@
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                                                            Jacobi Elliptic Function cs diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_dc.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_dc.html index ba4d98855..d480f38e0 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_dc.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_dc.html @@ -3,7 +3,7 @@ Jacobi Elliptic Function dc - + @@ -22,7 +22,7 @@
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                                                            Jacobi Elliptic Function dc diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_dn.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_dn.html index 0afcd41c3..e31f43c6b 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_dn.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_dn.html @@ -3,7 +3,7 @@ Jacobi Elliptic Function dn - + @@ -22,7 +22,7 @@
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                                                            Jacobi Elliptic Function dn diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_ds.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_ds.html index 81fa28194..bee68eecc 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_ds.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_ds.html @@ -3,7 +3,7 @@ Jacobi Elliptic Function ds - + @@ -22,7 +22,7 @@
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                                                            Jacobi Elliptic Function ds diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_elliptic.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_elliptic.html index fdf945765..ad43f6938 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_elliptic.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_elliptic.html @@ -3,7 +3,7 @@ Jacobi Elliptic SN, CN and DN - + @@ -22,7 +22,7 @@
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                                                            Jacobi Elliptic SN, CN and DN diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_nc.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_nc.html index 4d0137f48..9ac08efea 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_nc.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_nc.html @@ -3,7 +3,7 @@ Jacobi Elliptic Function nc - + @@ -22,7 +22,7 @@
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                                                            Jacobi Elliptic Function nc diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_nd.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_nd.html index c094ae4e1..9c2dfea8a 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_nd.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_nd.html @@ -3,7 +3,7 @@ Jacobi Elliptic Function nd - + @@ -22,7 +22,7 @@
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                                                            Jacobi Elliptic Function nd diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_ns.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_ns.html index 4ff7a5024..0a9e5ccfd 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_ns.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_ns.html @@ -3,7 +3,7 @@ Jacobi Elliptic Function ns - + @@ -22,7 +22,7 @@
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                                                            Jacobi Elliptic Function ns diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sc.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sc.html index 2c4a68220..3f54eca54 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sc.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sc.html @@ -3,7 +3,7 @@ Jacobi Elliptic Function sc - + @@ -22,7 +22,7 @@
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                                                            Jacobi Elliptic Function sc diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sd.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sd.html index 54233b2cc..0a849d476 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sd.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sd.html @@ -3,7 +3,7 @@ Jacobi Elliptic Function sd - + @@ -22,7 +22,7 @@
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                                                            Jacobi Elliptic Function sd diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sn.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sn.html index 9ed44383d..59fc551e1 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sn.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sn.html @@ -3,7 +3,7 @@ Jacobi Elliptic Function sn - + @@ -22,7 +22,7 @@
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                                                            Jacobi Elliptic Function sn diff --git a/doc/sf_and_dist/html/math_toolkit/special/owens_t.html b/doc/sf_and_dist/html/math_toolkit/special/owens_t.html index a80c5feba..7feb0183b 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/owens_t.html +++ b/doc/sf_and_dist/html/math_toolkit/special/owens_t.html @@ -3,7 +3,7 @@ Owen's T function - + @@ -22,7 +22,7 @@
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                                                            @@ -131,15 +131,15 @@ Test data was generated by Patefield and Tandy algorithms T1 and T4, and also the suggested reference routine T7.

                                                            -
                                                              -
                                                            • +
                                                                +
                                                              • T1 was rejected if the result was too small compared to atan(a) (ie cancellation),
                                                              • -
                                                              • +
                                                              • T4 was rejected if there was no convergence,
                                                              • -
                                                              • +
                                                              • Both were rejected if they didn't agree.
                                                              @@ -181,8 +181,8 @@ The Patefield-Tandy algorithm is accurate to approximately 20 decimal places, so for types with greater precision we use:

                                                              -
                                                                -
                                                              • +
                                                                  +
                                                                • A modified version of T1 which folds the calculation of atan(h) into the T1 series (to avoid subtracting two values similar in magnitude), and then accelerates the resulting alternating series using method 1 @@ -191,15 +191,15 @@ but doesn't always converge, or may become too divergent in the first few terms to sum accurately. This is used for ah < 1.
                                                                • -
                                                                • +
                                                                • A modified version of T2 which is accelerated in the same manner as T1. This is used for h > 1.
                                                                • -
                                                                • +
                                                                • A version of T4 only when both T1 and T2 have failed to produce an accurate answer.
                                                                • -
                                                                • +
                                                                • Fallback to the Patefiled Tandy algorithm when all the above methods fail: this happens not at all for our test data at 100 decimal digits precision. However, there is a difficult area when a diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers.html b/doc/sf_and_dist/html/math_toolkit/special/powers.html index 19307c012..d8846168e 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/powers.html +++ b/doc/sf_and_dist/html/math_toolkit/special/powers.html @@ -3,7 +3,7 @@ Logs, Powers, Roots and Exponentials - + @@ -22,7 +22,7 @@
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                                                                  Logs, Powers, Roots and Exponentials diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/cbrt.html b/doc/sf_and_dist/html/math_toolkit/special/powers/cbrt.html index 15be4ffa1..ec7e83fb0 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/powers/cbrt.html +++ b/doc/sf_and_dist/html/math_toolkit/special/powers/cbrt.html @@ -3,7 +3,7 @@ cbrt - + @@ -22,7 +22,7 @@
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                                                                  diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/ct_pow.html b/doc/sf_and_dist/html/math_toolkit/special/powers/ct_pow.html index af3573014..d0ba301ee 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/powers/ct_pow.html +++ b/doc/sf_and_dist/html/math_toolkit/special/powers/ct_pow.html @@ -3,7 +3,7 @@ Compile Time Power of a Runtime Base - + @@ -22,7 +22,7 @@
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                                                                  Compile Time Power of a Runtime Base @@ -99,16 +99,16 @@ The return type of these functions is computed using the result type calculation rules. For example:

                                                                  -
                                                                    -
                                                                  • +
                                                                      +
                                                                    • If T is a float, the return type is a float.
                                                                    • -
                                                                    • +
                                                                    • If T is a long double, the return type is a long double.
                                                                    • -
                                                                    • +
                                                                    • Otherwise, the return type is a double.
                                                                    @@ -129,12 +129,12 @@

                                                                    Two cases of errors can occur when using pow:

                                                                    -
                                                                      -
                                                                    • +
                                                                        +
                                                                      • In case of null base and negative exponent, an overflow_error occurs since this operation is a division by 0 (it equals to 1/0).
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                                                                      • +
                                                                      • In case of null base and null exponent, an indeterminate_result_error occurs since the result of this operation is indeterminate. Those errors follow the general @@ -147,18 +147,18 @@ exception. As shown in the link given above, other error handling policies can be used:

                                                                        -
                                                                          -
                                                                        • +
                                                                            +
                                                                          • errno_on_error: Sets ::errno to ERANGE and returns std::numeric_limits<T>::infinity().
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                                                                          • +
                                                                          • ignore_error: Returns std::numeric_limits<T>::infinity().
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                                                                          • +
                                                                          • user_error: Returns the result of boost::math::policies::user_overflow_error: this function must be defined by the user. @@ -169,18 +169,18 @@ which for this function returns 1 since it's the most commonly chosen result for a power of 0. Here again, other error handling policies can be used:

                                                                            -
                                                                              -
                                                                            • +
                                                                                +
                                                                              • throw_on_error: Throws std::domain_error
                                                                              • -
                                                                              • +
                                                                              • errno_on_error: Sets ::errno to EDOM and returns 1.
                                                                              • -
                                                                              • +
                                                                              • user_error: Returns the result of boost::math::policies::user_indeterminate_result_error: this function must be defined by the user. diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/expm1.html b/doc/sf_and_dist/html/math_toolkit/special/powers/expm1.html index 414973e33..bf40bd584 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/powers/expm1.html +++ b/doc/sf_and_dist/html/math_toolkit/special/powers/expm1.html @@ -3,7 +3,7 @@ expm1 - + @@ -22,7 +22,7 @@ -
                                                                                +
                                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/hypot.html b/doc/sf_and_dist/html/math_toolkit/special/powers/hypot.html index 56a162888..b68021b90 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/powers/hypot.html +++ b/doc/sf_and_dist/html/math_toolkit/special/powers/hypot.html @@ -3,7 +3,7 @@ hypot - + @@ -22,7 +22,7 @@
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                                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/log1p.html b/doc/sf_and_dist/html/math_toolkit/special/powers/log1p.html index 3ed0735f8..42ef6f4b8 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/powers/log1p.html +++ b/doc/sf_and_dist/html/math_toolkit/special/powers/log1p.html @@ -3,7 +3,7 @@ log1p - + @@ -22,7 +22,7 @@
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                                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/powm1.html b/doc/sf_and_dist/html/math_toolkit/special/powers/powm1.html index 04cb2a344..7db13eb64 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/powers/powm1.html +++ b/doc/sf_and_dist/html/math_toolkit/special/powers/powm1.html @@ -3,7 +3,7 @@ powm1 - + @@ -22,7 +22,7 @@
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                                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/sqrt1pm1.html b/doc/sf_and_dist/html/math_toolkit/special/powers/sqrt1pm1.html index bd73cda14..a29ebc16e 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/powers/sqrt1pm1.html +++ b/doc/sf_and_dist/html/math_toolkit/special/powers/sqrt1pm1.html @@ -3,7 +3,7 @@ sqrt1pm1 - + @@ -22,7 +22,7 @@
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                                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_beta.html b/doc/sf_and_dist/html/math_toolkit/special/sf_beta.html index d97dbc9ca..bdcc39c44 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_beta.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_beta.html @@ -3,7 +3,7 @@ Beta Functions - + @@ -22,7 +22,7 @@
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                                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_derivative.html b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_derivative.html index 4afd714dc..fd509f234 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_derivative.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_derivative.html @@ -3,7 +3,7 @@ Derivative of the Incomplete Beta Function - + @@ -22,7 +22,7 @@
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                                                                                Derivative of the Incomplete Beta Function diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_function.html b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_function.html index 2e6166c58..07e9d8de5 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_function.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_function.html @@ -3,7 +3,7 @@ Beta - + @@ -22,7 +22,7 @@
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                                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_function.html b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_function.html index d96fb135a..f0efafef7 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_function.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_function.html @@ -3,7 +3,7 @@ Incomplete Beta Functions - + @@ -22,7 +22,7 @@
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                                                                                Incomplete Beta Functions diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_inv_function.html b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_inv_function.html index a0d993c6e..99772503c 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_inv_function.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_inv_function.html @@ -3,7 +3,7 @@ The Incomplete Beta Function Inverses - + @@ -22,7 +22,7 @@
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                                                                                The Incomplete Beta Function Inverses @@ -305,8 +305,8 @@

                                                                                There are two sets of tests:

                                                                                -
                                                                                  -
                                                                                • +
                                                                                    +
                                                                                  • Basic sanity checks attempt to "round-trip" from a, b and x to p or q and back again. These tests have quite generous @@ -317,7 +317,7 @@ enough "information content" in the input to the inverse function to get back where you started.
                                                                                  • -
                                                                                  • +
                                                                                  • Accuracy checks using high precision test values. These measure the accuracy of the result, given exact input values.
                                                                                  • diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_erf.html b/doc/sf_and_dist/html/math_toolkit/special/sf_erf.html index 289fa9540..a1b4df768 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_erf.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_erf.html @@ -3,7 +3,7 @@ Error Functions - + @@ -22,7 +22,7 @@
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                                                                                    diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_function.html b/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_function.html index 906c9b065..61e930364 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_function.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_function.html @@ -3,7 +3,7 @@ Error Functions - + @@ -22,7 +22,7 @@
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                                                                                    diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_inv.html b/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_inv.html index 43f849fa3..51855afb9 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_inv.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_inv.html @@ -3,7 +3,7 @@ Error Function Inverses - + @@ -22,7 +22,7 @@
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                                                                                    Error Function Inverses @@ -113,8 +113,8 @@

                                                                                    There are two sets of tests:

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                                                                                      • Basic sanity checks attempt to "round-trip" from x to p and back again. These tests have quite generous tolerances: in general both the error functions and their inverses @@ -124,7 +124,7 @@ enough "information content" in the input to the inverse function to get back where you started.
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                                                                                      • Accuracy checks using high-precision test values. These measure the accuracy of the result, given exact input values.
                                                                                      • diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma.html index 68016cd66..9c8a970b4 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma.html @@ -3,7 +3,7 @@ Gamma Functions - + @@ -22,7 +22,7 @@
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                                                                                        diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/digamma.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/digamma.html index f46620983..11dfc5ae1 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/digamma.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/digamma.html @@ -3,7 +3,7 @@ Digamma - + @@ -22,7 +22,7 @@
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                                                                                        Derivative of the Incomplete Gamma Function diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_ratios.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_ratios.html index 04181110e..4f9bc5445 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_ratios.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_ratios.html @@ -3,7 +3,7 @@ Ratios of Gamma Functions - + @@ -22,7 +22,7 @@
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                                                                                        Ratios of Gamma Functions diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html index a7f1dbce7..7f5b6de56 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html @@ -3,7 +3,7 @@ Incomplete Gamma Functions - + @@ -22,7 +22,7 @@
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                                                                                        Incomplete Gamma Functions @@ -1010,21 +1010,21 @@ References

                                                                                        -
                                                                                          -
                                                                                        • +
                                                                                            +
                                                                                          • N. M. Temme, A Set of Algorithms for the Incomplete Gamma Functions, Probability in the Engineering and Informational Sciences, 8, 1994.
                                                                                          • -
                                                                                          • +
                                                                                          • N. M. Temme, The Asymptotic Expansion of the Incomplete Gamma Functions, Siam J. Math Anal. Vol 10 No 4, July 1979, p757.
                                                                                          • -
                                                                                          • +
                                                                                          • A. R. Didonato and A. H. Morris, Computation of the Incomplete Gamma Function Ratios and their Inverse. ACM TOMS, Vol 12, No 4, Dec 1986, p377.
                                                                                          • -
                                                                                          • +
                                                                                          • W. Gautschi, The Incomplete Gamma Functions Since Tricomi, In Tricomi's Ideas and Contemporary Applied Mathematics, Atti dei Convegni Lincei, n. 147, Accademia Nazionale dei Lincei, Roma, 1998, pp. 203--237. diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma_inv.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma_inv.html index d72923af9..0bb16cfd5 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma_inv.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma_inv.html @@ -3,7 +3,7 @@ Incomplete Gamma Function Inverses - + @@ -22,7 +22,7 @@
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                                                                                            Incomplete Gamma Function Inverses @@ -187,8 +187,8 @@

                                                                                            There are two sets of tests:

                                                                                            -
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                                                                                            • +
                                                                                                +
                                                                                              • Basic sanity checks attempt to "round-trip" from a and x to p or q and back again. These tests have quite generous tolerances: in general @@ -199,7 +199,7 @@ content" in the input to the inverse function to get back where you started.
                                                                                              • -
                                                                                              • +
                                                                                              • Accuracy checks using high precision test values. These measure the accuracy of the result, given exact input values.
                                                                                              • diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/lgamma.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/lgamma.html index 5786ff3e8..ca010d54b 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/lgamma.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/lgamma.html @@ -3,7 +3,7 @@ Log Gamma - + @@ -22,7 +22,7 @@
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                                                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/tgamma.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/tgamma.html index d0c7d6766..59b9fb046 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/tgamma.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/tgamma.html @@ -3,7 +3,7 @@ Gamma - + @@ -22,7 +22,7 @@
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                                                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_poly.html b/doc/sf_and_dist/html/math_toolkit/special/sf_poly.html index 7be55ec5c..c00562719 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_poly.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_poly.html @@ -3,7 +3,7 @@ Polynomials - + @@ -22,7 +22,7 @@
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                                                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/hermite.html b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/hermite.html index 422966d08..8dcf9f62e 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/hermite.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/hermite.html @@ -3,7 +3,7 @@ Hermite Polynomials - + @@ -22,7 +22,7 @@
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                                                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/laguerre.html b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/laguerre.html index 290de0bc9..8a03a812e 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/laguerre.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/laguerre.html @@ -3,7 +3,7 @@ Laguerre (and Associated) Polynomials - + @@ -22,7 +22,7 @@
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                                                                                                Laguerre (and Associated) Polynomials diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/legendre.html b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/legendre.html index fc14a2831..03dbd1685 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/legendre.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/legendre.html @@ -3,7 +3,7 @@ Legendre (and Associated) Polynomials - + @@ -22,7 +22,7 @@
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                                                                                                Legendre (and Associated) Polynomials diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/sph_harm.html b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/sph_harm.html index 0d2432d31..d4b546cdb 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/sph_harm.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/sph_harm.html @@ -3,7 +3,7 @@ Spherical Harmonics - + @@ -22,7 +22,7 @@
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                                                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/special/sinc.html b/doc/sf_and_dist/html/math_toolkit/special/sinc.html index 5b4a51d63..e25f029e0 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sinc.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sinc.html @@ -3,7 +3,7 @@ Sinus Cardinal and Hyperbolic Sinus Cardinal Functions - + @@ -22,7 +22,7 @@
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                                                                                                Sinus Cardinal and Hyperbolic Sinus Cardinal Functions diff --git a/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_overview.html b/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_overview.html index 02932e9a6..4fcf71107 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_overview.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_overview.html @@ -3,7 +3,7 @@ Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview - + @@ -22,7 +22,7 @@
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                                                                                                Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview diff --git a/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_pi.html b/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_pi.html index 5985d4f96..41f4533f4 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_pi.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_pi.html @@ -3,7 +3,7 @@ sinc_pi - + @@ -22,7 +22,7 @@
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                                                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/special/sinc/sinhc_pi.html b/doc/sf_and_dist/html/math_toolkit/special/sinc/sinhc_pi.html index 150c1decd..692e9cf9e 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sinc/sinhc_pi.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sinc/sinhc_pi.html @@ -3,7 +3,7 @@ sinhc_pi - + @@ -22,7 +22,7 @@
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                                                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/special/zetas.html b/doc/sf_and_dist/html/math_toolkit/special/zetas.html index b50621460..27e872e53 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/zetas.html +++ b/doc/sf_and_dist/html/math_toolkit/special/zetas.html @@ -3,7 +3,7 @@ Zeta Functions - + @@ -22,7 +22,7 @@
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                                                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html b/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html index 572d5742b..60facf14f 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html +++ b/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html @@ -3,7 +3,7 @@ Riemann Zeta Function - + @@ -22,7 +22,7 @@
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                                                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/status.html b/doc/sf_and_dist/html/math_toolkit/status.html index 9bb9ff048..b495e4b7f 100644 --- a/doc/sf_and_dist/html/math_toolkit/status.html +++ b/doc/sf_and_dist/html/math_toolkit/status.html @@ -3,7 +3,7 @@ Library Status - + @@ -22,7 +22,7 @@
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                                                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/status/credits.html b/doc/sf_and_dist/html/math_toolkit/status/credits.html index 04dd3d92b..3501fde05 100644 --- a/doc/sf_and_dist/html/math_toolkit/status/credits.html +++ b/doc/sf_and_dist/html/math_toolkit/status/credits.html @@ -3,7 +3,7 @@ Credits and Acknowledgements - + @@ -22,7 +22,7 @@
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                                                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/status/history1.html b/doc/sf_and_dist/html/math_toolkit/status/history1.html index 5f68e3c8e..78c12f142 100644 --- a/doc/sf_and_dist/html/math_toolkit/status/history1.html +++ b/doc/sf_and_dist/html/math_toolkit/status/history1.html @@ -3,7 +3,7 @@ History and What's New - + @@ -22,7 +22,7 @@
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                                                                                                @@ -36,23 +36,23 @@ Boost-1.51

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                                                                                                  • Added Airy functions and Jacobi Elliptic functions.
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                                                                                                  • Corrected failure to detect bad parameters in many distributions #6934 (reported by Florian Schoppmann) by adding a function check_out_of_range to test many possible bad parameters. This test revealed several distributions where the checks for bad parameters were ineffective, and these have been rectified.
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                                                                                                  • Fixed issue in Hankel functions that causes incorrect values to be returned for x < 0 and ν odd, see #7135.
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                                                                                                  • Fixed issues #6517, #6362, #7053, @@ -65,29 +65,29 @@ Boost-1.50

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                                                                                                  • Promoted math constants to be 1st class citizens, including convenient access to the most widely used built-in float, double, long double via three namespaces.
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                                                                                                  • Added the Owen's T function and Skew Normal distribution written by Benjamin Sobotta: see Owens T and skew_normal_distrib.
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                                                                                                  • Added Hankel functions cyl_hankel_1, cyl_hankel_2, sph_hankel_1 and sph_hankel_2.
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                                                                                                  • Corrected issue #6627 nonfinite_num_put formatting of 0.0 is incorrect based on a patch submitted by K R Walker.
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                                                                                                  • Changed constant initialization mechanism so that it is thread safe even for user-defined types, also so that user defined types get the full precision of the constant, even when long @@ -95,7 +95,7 @@ 128-bit rational approximations will work with UDT's and do the right thing, even though long double may be only 64 or 80 bits.
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                                                                                                  • Fixed issue in bessel_jy which causes Y8.5(4π) to yield a NaN.
                                                                                                  • @@ -104,37 +104,37 @@ Boost-1.49

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                                                                                                  • Deprecated wrongly named twothirds math constant in favour of two_thirds (with underscore separator). (issue #6199).
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                                                                                                  • Added new faster zeta function evaluation method.

                                                                                                  Fixed issues:

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                                                                                                    • Corrected CDF complement for Laplace distribution (issue #6151).
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                                                                                                    • Corrected branch cuts on the complex inverse trig functions, to handle signed zeros (issue #6171).
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                                                                                                    • Fixed bug in bessel_yn which caused incorrect overflow errors to be raised for negative n (issue #6367).
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                                                                                                  • Added new series evaluation methods to the cyclic Bessel I, J, K and Y functions. Also taken great care to avoid spurious over and underflow of these functions. Fixes issue #5560
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                                                                                                  • Added an example of using Inverse Chi-Squared distribution for Bayesian statistics, provided by Thomas Mang.
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                                                                                                  • Corrected wrong out-of-bound uniform distribution CDF complement values #5733.
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                                                                                                  @@ -199,16 +199,16 @@ Boost-1.47

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                                                                                              • Addition of nonfinite facets from Johan Rade, with tests, examples of use for C99 format infinity and NaN, and documentation.
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                                                                                              @@ -216,7 +216,7 @@ Boost-1.46.1

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                                                                                          @@ -239,16 +239,16 @@ Boost-1.45.0

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                                                                                      • Editorial revision of documentation, and added FAQ.
                                                                                      @@ -256,11 +256,11 @@ Boost-1.44.0

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                                                                                  • Fixed incorrect range and support for Rayleigh distribution.
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                                                                                  • Fixed numerical error in the quantile of the Student's T distribution: the function was returning garbage values for non-integer degrees of freedom between 2 and 3. @@ -270,7 +270,7 @@ Boost-1.41.0

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                                                                                  • Significantly improved performance for the incomplete gamma function and its inverse.
                                                                                  @@ -278,36 +278,36 @@ Boost-1.40.0

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                                                                                  • Added logistic and hypergeometric distributions, from Gautam Sewani's Google Summer of Code project.
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                                                                                  • Added Laplace distribution submitted by Thijs van den Berg.
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                                                                                  • Updated performance test code to include new distributions, and improved the performance of the non-central distributions.
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                                                                                  • Fixed bug in cyl_bessel_i that used an incorrect approximation for ν = 0.5, also effects the non-central Chi Square Distribution when ν = 3, see bug report #2877.
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                                                                                  • Fixed minor bugs #2873.
                                                                                  @@ -315,11 +315,11 @@ Boost-1.38.0

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                                                                    • Added Johan Råde's optimised floating point classification routines.
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                                                                    @@ -327,39 +327,39 @@ Boost-1.37.0

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                                                                    • Improved accuracy and testing of the inverse hypergeometric functions.
                                                                    Boost-1.36.0
                                                                    -
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                                                                      • Added Noncentral Chi Squared Distribution.
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                                                                      • Added Noncentral Beta Distribution.
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                                                                      • Added Noncentral F Distribution.
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                                                                      • Added Noncentral T Distribution.
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                                                                      • Added Exponential Integral Functions.
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                                                                      • Added Zeta Function.
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                                                                      • Added Rounding and Truncation functions.
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                                                                      • Added SSE2 optimizations for Lanczos evaluation.
                                                                      @@ -368,30 +368,30 @@ Boost-1.35.0: Post Review First Official Release

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                                                              • Added Policy based framework that allows fine grained control over function behaviour.
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                                                              • Breaking change: Changed default behaviour for domain, pole and overflow errors to throw an exception (based on review feedback), this behaviour can be customised using Policy's.
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                                                              • Breaking change: Changed exception thrown when an internal evaluation error occurs to boost::math::evaluation_error.
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                                                              • Breaking change: Changed discrete quantiles to return an integer result: this is anything up to 20 times faster than finding the true root, this behaviour can be customised using Policy's.
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                                                              • Polynomial/rational function evaluation is now customisable and hopefully faster than before.
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                                                              • Added performance test program.
                                                              @@ -400,12 +400,12 @@ Milestone 4: Second Review Candidate (1st March 2007)

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                                                              • Implemented the main probability distribution and density functions.
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                                                              • Implemented digamma.
                                                              • -
                                                              • +
                                                              • Added more factorial functions.
                                                              • -
                                                              • +
                                                              • Implemented the Hermite, Legendre and Laguerre polynomials plus the spherical harmonic functions from TR1.
                                                              • -
                                                              • +
                                                              • Moved Xiaogang Zhang's elliptic integral code into the library, and brought them into line with the rest of the code.
                                                              • -
                                                              • +
                                                              • Moved Hubert Holin's existing Boost.Math special functions into this library and brought them into line with the rest of the code.
                                                              • @@ -442,34 +442,34 @@ Milestone 2: Released September 10th 2006

                                                            -
                                                              -
                                                            • +
                                                                +
                                                              • Implement preview release of the statistical distributions.
                                                              • -
                                                              • +
                                                              • Added statistical distributions tutorial.
                                                              • -
                                                              • +
                                                              • Implemented root finding algorithms.
                                                              • -
                                                              • +
                                                              • Implemented the inverses of the incomplete gamma and beta functions.
                                                              • -
                                                              • +
                                                              • Rewrite erf/erfc as rational approximations (valid to 128-bit precision).
                                                              • -
                                                              • +
                                                              • Integrated the statistical results generated from the test data with Boost.Test: uses a database of expected results, indexed by test, floating point type, platform, and compiler.
                                                              • -
                                                              • +
                                                              • Improved lgamma near 1 and 2 (rational approximations).
                                                              • -
                                                              • +
                                                              • Improved erf/erfc inverses (rational approximations).
                                                              • -
                                                              • +
                                                              • Implemented Rational function generation (the Remez method).
                                                              @@ -478,23 +478,23 @@ Milestone 1: Released March 31st 2006

                                                            -
                                                              -
                                                            • +
                                                                +
                                                              • Implement gamma/beta/erf functions along with their incomplete counterparts.
                                                              • -
                                                              • +
                                                              • Generate high quality test data, against which future improvements can be judged.
                                                              • -
                                                              • +
                                                              • Provide tools for the evaluation of infinite series, continued fractions, and rational functions.
                                                              • -
                                                              • +
                                                              • Provide tools for testing against tabulated test data, and collecting statistics on error rates.
                                                              • -
                                                              • +
                                                              • Provide sufficient docs for people to be able to find their way around the library.
                                                              • diff --git a/doc/sf_and_dist/html/math_toolkit/status/issues.html b/doc/sf_and_dist/html/math_toolkit/status/issues.html index 89453779a..8db1f4aa5 100644 --- a/doc/sf_and_dist/html/math_toolkit/status/issues.html +++ b/doc/sf_and_dist/html/math_toolkit/status/issues.html @@ -3,7 +3,7 @@ Known Issues, and TODO List - + @@ -22,7 +22,7 @@
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                                                            -

                                                            -
                                                            • +
                                                              • Investigate Didonato and Morris' asymptotic expansion for large a and b (medium priority).
                                                              @@ -61,7 +61,7 @@ Inverse Gamma

                                                            -
                                                            • +
                                                              • Investigate whether we can skip iteration altogether if the first approximation is good enough (Medium Priority).
                                                              @@ -69,7 +69,7 @@ Polynomials

                                                            -
                                                            • +
                                                              • The Legendre and Laguerre Polynomials have surprisingly different error rates on different platforms, considering they are evaluated with only basic arithmetic operations. Maybe this is telling us something, or maybe @@ -80,8 +80,8 @@ Elliptic Integrals

                                                            -
                                                              -
                                                            • +
                                                                +
                                                              • Carlson's algorithms are essentially unchanged from Xiaogang Zhang's Google Summer of Code student project, and are based on Carlson's original papers. However, Carlson has revised his algorithms since then (refer @@ -89,7 +89,7 @@ performance and accuracy, we may be able to take advantage of these improvements too (Low Priority).
                                                              • -
                                                              • +
                                                              • Carlson's algorithms (mainly RJ) are somewhat prone to internal overflow/underflow when the arguments are very large or small. The homogeneity relations:

                                                                RF(ka, @@ -100,27 +100,27 @@ be used to sidestep trouble here: provided the problem domains can be accurately identified. (Medium Priority).

                                                              • -
                                                              • +
                                                              • Carlson's RC can be reduced to elementary funtions (asin and log), would it be more efficient evaluated this way, rather than by Carlson's algorithms? (Low Priority).
                                                              • -
                                                              • +
                                                              • Should we add an implementation of Carlson's RG? It's not required for the Legendre form integrals, but some people may find it useful (Low Priority).
                                                              • -
                                                              • +
                                                              • There are a several other integrals: D(φ, k), Z(β, k), Λ0(β, k) and Bulirsch's el functions that could be implemented using Carlson's integrals (Low Priority).
                                                              • -
                                                              • +
                                                              • The integrals K(k) and E(k) could be implemented using rational approximations (both for efficiency and accuracy), assuming we can find them. (Medium Priority).
                                                              • -
                                                              • +
                                                              • There is a sub-domain of ellint_3 that is unimplemented (see the docs for details), currently it's not clear how to solve this issue, or if it's ever likely to be an real problem @@ -158,7 +158,7 @@ Statistical distributions

                                                            -
                                                            • +
                                                              • Student's t Perhaps switch to normal distribution as a better approximation for very large degrees of freedom?
                                                              @@ -1211,16 +1211,16 @@

                                                              Also asked for more than once:

                                                              -
                                                                -
                                                              • +
                                                                  +
                                                                • Add support for interpolated distributions, possibly combine with numeric integration and differentiation.
                                                                • -
                                                                • +
                                                                • Add support for bivariate and multivariate distributions: most especially the normal.
                                                                • -
                                                                • +
                                                                • Add support for the log of the cdf and pdf: this is mainly a performance optimisation since we can avoid some special function calls for some distributions by returning the log of the result. diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit.html b/doc/sf_and_dist/html/math_toolkit/toolkit.html index 96082d2bd..1c4e25aad 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit.html @@ -3,7 +3,7 @@ Tools and Internal Details - + @@ -22,7 +22,7 @@
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                                                                  diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1.html index 60873ae56..fd6e571c9 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1.html @@ -3,7 +3,7 @@ Utilities & Tools - + @@ -22,7 +22,7 @@
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                                                                  diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/cf.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/cf.html index 0168e4770..a279c0e20 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/cf.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/cf.html @@ -3,7 +3,7 @@ Continued Fraction Evaluation - + @@ -22,7 +22,7 @@
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                                                                  Continued Fraction Evaluation diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/minima.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/minima.html index befe42724..34dda3ffe 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/minima.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/minima.html @@ -3,7 +3,7 @@ Locating Function Minima: Brent's algorithm - + @@ -22,7 +22,7 @@
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                                                                  Locating Function Minima: Brent's algorithm diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/rational.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/rational.html index c2d8ad689..972f42f95 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/rational.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/rational.html @@ -3,7 +3,7 @@ Polynomial and Rational Function Evaluation - + @@ -22,7 +22,7 @@
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                                                                  Polynomial and Rational Function Evaluation diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots.html index e0293aac3..a184684a3 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots.html @@ -3,7 +3,7 @@ Root Finding With Derivatives: Newton-Raphson, Halley & Schroeder - + @@ -22,7 +22,7 @@
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                                                                  +

                                                                  Root Finding With Derivatives: Newton-Raphson, Halley & Schroeder @@ -67,12 +67,12 @@

                                                                  These functions all perform iterative root finding using derivatives:

                                                                  -
                                                                    -
                                                                  • +
                                                                      +
                                                                    • newton_raphson_iterateperforms second order Newton-Raphson iteration,
                                                                    • -
                                                                    • +
                                                                    • halley_iterate andschroeder_iterate perform third order Halley and Schroeder iteration. @@ -130,48 +130,48 @@

                                                                      When using these functions you should note that:

                                                                      -
                                                                        -
                                                                      • +
                                                                          +
                                                                        • Default max_iter = (std::numeric_limits<boost::uintmax_t>::max)() is effectively 'iterate for ever'!.
                                                                        • -
                                                                        • +
                                                                        • They may be very sensitive to the initial guess, typically they converge very rapidly if the initial guess has two or three decimal digits correct. However convergence can be no better than bisection, or in some rare cases, even worse than bisection if the initial guess is a long way from the correct value and the derivatives are close to zero.
                                                                        • -
                                                                        • +
                                                                        • These functions include special cases to handle zero first (and second where appropriate) derivatives, and fall back to bisection in this case. However, it is helpful if functor F is defined to return an arbitrarily small value of the correct sign rather than zero.
                                                                        • -
                                                                        • +
                                                                        • If the derivative at the current best guess for the result is infinite (or very close to being infinite) then these functions may terminate prematurely. A large first derivative leads to a very small next step, triggering the termination condition. Derivative based iteration may not be appropriate in such cases.
                                                                        • -
                                                                        • +
                                                                        • If the function is 'Really Well Behaved' (monotonic and has only one root) the bracket bounds min and max may as well be set to the widest limits like zero and numeric_limits<T>::max().
                                                                        • -
                                                                        • +
                                                                        • But if the function more complex and may have more than one root or a pole, the choice of bounds is protection against jumping out to seek the 'wrong' root.
                                                                        • -
                                                                        • +
                                                                        • These functions fall back to bisection if the next computed step would take the next value out of bounds. The bounds are updated after each step to ensure this leads to convergence. However, a good initial guess backed up by asymptotically-tight bounds will improve performance no end - rather than relying on bisection.
                                                                        • -
                                                                        • +
                                                                        • The value of digits is crucial to good performance of these functions, if it is set too high then at best you will get one extra (unnecessary) iteration, and at worst the last few steps @@ -186,17 +186,17 @@ final iteration just takes the next value into the zone where f(x) becomes inaccurate.
                                                                        • -
                                                                        • +
                                                                        • To get the binary digits of accuracy, use policies::get_max_root_iterations<Policy>()).
                                                                        • -
                                                                        • +
                                                                        • If you need some diagnostic output to see what is going on, you can #define BOOST_MATH_INSTRUMENT before the #include <boost/math/tools/roots.hpp>, and also ensure that display of all the possibly significant digits with cout.precision(std::numeric_limits<double>::max_digits10): but be warned, this may produce copious output!
                                                                        • -
                                                                        • +
                                                                        • Finally: you may well be able to do better than these functions by hand-coding the heuristics used so that they are tailored to a specific function. You may also be able to compute the ratio of derivatives diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots2.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots2.html index cfb6db2e0..879879c5f 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots2.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots2.html @@ -3,7 +3,7 @@ Root Finding Without Derivatives: Bisection, Bracket and TOMS748 - + @@ -22,7 +22,7 @@
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                                                                          Root Finding Without Derivatives: Bisection, Bracket and TOMS748 diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/series_evaluation.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/series_evaluation.html index d0e25f72d..2c460c339 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/series_evaluation.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/series_evaluation.html @@ -3,7 +3,7 @@ Series Evaluation - + @@ -22,7 +22,7 @@
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                                                                          Series Evaluation @@ -99,14 +99,14 @@ value of the sum to which the terms of the series should be added. This is useful in two situations:

                                                                          -
                                                                            -
                                                                          • +
                                                                              +
                                                                            • Where the first value of the series has a different formula to successive terms. In this case the first value in the series can be passed as the last argument and the logic of the function object can then be simplified to return subsequent terms.
                                                                            • -
                                                                            • +
                                                                            • Where the series is being added (or subtracted) from some other value: termination of the series will likely occur much more rapidly if that other value is passed as the last argument. For example, there are diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/tuples.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/tuples.html index 5e6a6f348..6abafa641 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/tuples.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/tuples.html @@ -3,7 +3,7 @@ Tuples - + @@ -22,7 +22,7 @@
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                                                                              @@ -50,17 +50,17 @@

                                                                              These types and functions are aliases for:

                                                                              -
                                                                                -
                                                                              • +
                                                                                  +
                                                                                • std::tuple etc when available, otherwise:
                                                                                • -
                                                                                • +
                                                                                • std::tr1::tuple etc when available, otherwise:
                                                                                • -
                                                                                • +
                                                                                • boost::fusion::tuple etc if the compiler supports it, otherwise:
                                                                                • -
                                                                                • +
                                                                                • boost::tuple.
                                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2.html index 8e9cf4cf7..5631caf84 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2.html @@ -3,7 +3,7 @@ Testing and Development - + @@ -22,7 +22,7 @@
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                                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/error_test.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/error_test.html index b611e43cd..12ed5329f 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/error_test.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/error_test.html @@ -3,7 +3,7 @@ Relative Error and Testing - + @@ -22,7 +22,7 @@
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                                                                                Relative Error and Testing @@ -60,11 +60,11 @@

                                                                                In addition the value returned is zero if:

                                                                                -
                                                                                  -
                                                                                • +
                                                                                    +
                                                                                  • Both a and v are infinite.
                                                                                  • -
                                                                                  • +
                                                                                  • Both a and v are denormalised numbers or zero.
                                                                                  • diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html index f718e22a9..6f3af82aa 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html @@ -3,7 +3,7 @@ Minimax Approximations and the Remez Algorithm - + @@ -22,7 +22,7 @@
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                                                                                    Minimax Approximations and the Remez Algorithm diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/polynomials.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/polynomials.html index 8f78f3de8..9e8c4af1e 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/polynomials.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/polynomials.html @@ -3,7 +3,7 @@ Polynomials - + @@ -22,7 +22,7 @@
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                                                                                    diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/test_data.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/test_data.html index a74246b25..c386da4c8 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/test_data.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/test_data.html @@ -3,7 +3,7 @@ Graphing, Profiling, and Generating Test Data for Special Functions - + @@ -22,7 +22,7 @@
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                                                                                    Graphing, Profiling, and Generating Test Data for Special Functions @@ -32,16 +32,16 @@ associated helper functions are designed so that in just a few lines of code you should be able to:

                                                                                    -
                                                                                      -
                                                                                    • +
                                                                                        +
                                                                                      • Profile a continued fraction, or infinite series for convergence and accuracy.
                                                                                      • -
                                                                                      • +
                                                                                      • Generate csv data from a special function that can be imported into your favorite graphing program (or spreadsheet) for further analysis.
                                                                                      • -
                                                                                      • +
                                                                                      • Generate high precision test data.
                                                                                      @@ -156,22 +156,22 @@

                                                                                      The functionality of test_data is split into the following parts:

                                                                                      -
                                                                                        -
                                                                                      • +
                                                                                          +
                                                                                        • A functor that implements the function for which data is being generated: this is the bit you have to write.
                                                                                        • -
                                                                                        • +
                                                                                        • One of more parameters that are to be passed to the functor, these are described in fairly abstract terms: give me N points distributed like this etc.
                                                                                        • -
                                                                                        • +
                                                                                        • The class test_data, that takes the functor and descriptions of the parameters and computes how ever many output points have been requested, these are stored in a sorted container.
                                                                                        • -
                                                                                        • +
                                                                                        • Routines to iterate over the test_data container and output the data in either csv format, or as C++ source code (as a table using Boost.Array).
                                                                                        • @@ -354,14 +354,14 @@

                                                                                          The first #define serves two purposes:

                                                                                          -
                                                                                            -
                                                                                          • +
                                                                                              +
                                                                                            • It reduces the file sizes considerably: all those static_cast's add up to a lot of bytes otherwise (they are needed to suppress compiler warnings when T is narrower than a long double).
                                                                                            • -
                                                                                            • +
                                                                                            • It provides a useful customisation point: for example if we were testing a user-defined type that has more precision than a long double we could change it to: diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals_overview.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals_overview.html index 6c3055ed0..a6902f02b 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals_overview.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals_overview.html @@ -3,7 +3,7 @@ Overview - + @@ -22,7 +22,7 @@
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                                                                                              diff --git a/doc/sf_and_dist/html/math_toolkit/using_udt.html b/doc/sf_and_dist/html/math_toolkit/using_udt.html index 8d0659f94..b88cd1eb9 100644 --- a/doc/sf_and_dist/html/math_toolkit/using_udt.html +++ b/doc/sf_and_dist/html/math_toolkit/using_udt.html @@ -3,7 +3,7 @@ Use with User-Defined Floating-Point Types - + @@ -22,7 +22,7 @@
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                                                                                              Use with User-Defined Floating-Point Types diff --git a/doc/sf_and_dist/html/math_toolkit/using_udt/archetypes.html b/doc/sf_and_dist/html/math_toolkit/using_udt/archetypes.html index c0daf12e0..177f6c448 100644 --- a/doc/sf_and_dist/html/math_toolkit/using_udt/archetypes.html +++ b/doc/sf_and_dist/html/math_toolkit/using_udt/archetypes.html @@ -3,7 +3,7 @@ Conceptual Archetypes for Reals and Distributions - + @@ -22,7 +22,7 @@
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                                                                                              Conceptual Archetypes for Reals and Distributions @@ -30,11 +30,11 @@

                                                                                              There are a few concept archetypes available:

                                                                                              -
                                                                                                -
                                                                                              • +
                                                                                                  +
                                                                                                • Real concept for floating-point types.
                                                                                                • -
                                                                                                • +
                                                                                                • distribution Concept for statistical distributions.
                                                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/using_udt/concepts.html b/doc/sf_and_dist/html/math_toolkit/using_udt/concepts.html index 04199be35..43024b5e3 100644 --- a/doc/sf_and_dist/html/math_toolkit/using_udt/concepts.html +++ b/doc/sf_and_dist/html/math_toolkit/using_udt/concepts.html @@ -3,7 +3,7 @@ Conceptual Requirements for Real Number Types - + @@ -22,7 +22,7 @@
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                                                                                                Conceptual Requirements for Real Number Types @@ -977,21 +977,21 @@

                                                                                                Note that:

                                                                                                -
                                                                                                  -
                                                                                                1. +
                                                                                                    +
                                                                                                  1. The functions log_max_value and log_min_value can be synthesised from the others, and so no explicit specialisation is required.
                                                                                                  2. -
                                                                                                  3. +
                                                                                                  4. The function epsilon can be synthesised from the others, so no explicit specialisation is required provided the precision of RealType does not vary at runtime (see the header boost/math/bindings/rr.hpp for an example where the precision does vary at runtime).
                                                                                                  5. -
                                                                                                  6. +
                                                                                                  7. The functions digits, max_value and min_value, all get synthesised automatically from std::numeric_limits. However, if numeric_limits is not specialised for diff --git a/doc/sf_and_dist/html/math_toolkit/using_udt/dist_concept.html b/doc/sf_and_dist/html/math_toolkit/using_udt/dist_concept.html index f06d86e76..7c3c4e5f1 100644 --- a/doc/sf_and_dist/html/math_toolkit/using_udt/dist_concept.html +++ b/doc/sf_and_dist/html/math_toolkit/using_udt/dist_concept.html @@ -3,7 +3,7 @@ Conceptual Requirements for Distribution Types - + @@ -22,7 +22,7 @@
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                                                                                                    Conceptual Requirements for Distribution Types diff --git a/doc/sf_and_dist/html/math_toolkit/using_udt/e_float.html b/doc/sf_and_dist/html/math_toolkit/using_udt/e_float.html index dbef5e7be..907d017ae 100644 --- a/doc/sf_and_dist/html/math_toolkit/using_udt/e_float.html +++ b/doc/sf_and_dist/html/math_toolkit/using_udt/e_float.html @@ -3,7 +3,7 @@ e_float Support - + @@ -22,7 +22,7 @@
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                                                                                                    diff --git a/doc/sf_and_dist/html/math_toolkit/using_udt/use_mpfr.html b/doc/sf_and_dist/html/math_toolkit/using_udt/use_mpfr.html index 89927f5a8..1e6c37b7a 100644 --- a/doc/sf_and_dist/html/math_toolkit/using_udt/use_mpfr.html +++ b/doc/sf_and_dist/html/math_toolkit/using_udt/use_mpfr.html @@ -3,7 +3,7 @@ Using With MPFR / GMP - a High-Precision Floating-Point Library - + @@ -22,7 +22,7 @@
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                                                                                                    -
                                                                                                    +

                                                                                                    Using With MPFR / GMP - a High-Precision Floating-Point Library diff --git a/doc/sf_and_dist/html/math_toolkit/using_udt/use_ntl.html b/doc/sf_and_dist/html/math_toolkit/using_udt/use_ntl.html index 0aa490474..a681ef2ca 100644 --- a/doc/sf_and_dist/html/math_toolkit/using_udt/use_ntl.html +++ b/doc/sf_and_dist/html/math_toolkit/using_udt/use_ntl.html @@ -3,7 +3,7 @@ Using With NTL - a High-Precision Floating-Point Library - + @@ -22,7 +22,7 @@
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                                                                                                    +

                                                                                                    Using With NTL - a High-Precision Floating-Point Library diff --git a/doc/sf_and_dist/html/math_toolkit/utils.html b/doc/sf_and_dist/html/math_toolkit/utils.html index 286a21a80..4611ee2fc 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils.html +++ b/doc/sf_and_dist/html/math_toolkit/utils.html @@ -3,7 +3,7 @@ Floating Point Utilities - + @@ -22,7 +22,7 @@
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                                                                                                    diff --git a/doc/sf_and_dist/html/math_toolkit/utils/fp_facets.html b/doc/sf_and_dist/html/math_toolkit/utils/fp_facets.html index 57eb7aa7b..345bf8dc3 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/fp_facets.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/fp_facets.html @@ -3,7 +3,7 @@ Facets for Floating-Point Infinities and NaNs - + @@ -22,7 +22,7 @@
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                                                                                                    +

                                                                                                    Facets for Floating-Point Infinities and NaNs diff --git a/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/examples.html b/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/examples.html index 5f80192ea..3dc34039a 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/examples.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/examples.html @@ -3,7 +3,7 @@ Examples - + @@ -22,7 +22,7 @@
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                                                                                                    @@ -57,6 +57,7 @@ // with the new locale containing the nonfinite_numput facet. // So the cout output will be "1.#INF on MS platforms // and may be "inf" or other string representation on other platforms. +

                                                                                                    diff --git a/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/intro.html b/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/intro.html index f06505e43..f2e13dfa3 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/intro.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/intro.html @@ -3,7 +3,7 @@ Introduction - + @@ -22,7 +22,7 @@
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                                                                                                    +
                                                                                                    @@ -124,6 +124,7 @@ // with the new locale containing the nonfinite_numput facet. // So the cout output will be "1.#INF on MS platforms // and may be "inf" or other string representation on other platforms. +

                                                                                                    @@ -339,23 +340,23 @@ NaN fprintf. That implementation specifies for Binary Floating Point NANs:

                                                                                                    -
                                                                                                      -
                                                                                                    • +
                                                                                                        +
                                                                                                      • A NaN ordinal sequence is a left-parenthesis character '(', followed by a digit sequence representing an integer n, where 1 <= n <= INT_MAX-1, followed by a right-parenthesis character ')'.
                                                                                                      • -
                                                                                                      • +
                                                                                                      • The integer value, n, is determined by the fraction bits of the NaN argument value as follows:
                                                                                                      • -
                                                                                                      • +
                                                                                                      • For a signalling NaN value, NaN fraction bits are reversed (left to right) to produce bits (right to left) of an even integer value, 2*n. Then formatted output functions produce a (signalling) NaN ordinal sequence corresponding to the integer value n.
                                                                                                      • -
                                                                                                      • +
                                                                                                      • For a quiet NaN value, NaN fraction bits are reversed (left to right) to produce bits (right to left) of an odd integer value, 2*n-1. Then formatted output functions produce a (quiet) NaN ordinal sequence corresponding diff --git a/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/portability.html b/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/portability.html index 76c457042..dc1df4357 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/portability.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/portability.html @@ -3,7 +3,7 @@ Portability - + @@ -22,7 +22,7 @@
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                                                                                                        diff --git a/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/rationale.html b/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/rationale.html index ac9360cf9..a9df3e892 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/rationale.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/rationale.html @@ -3,7 +3,7 @@ Design Rationale - + @@ -22,12 +22,12 @@
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                                                                                                        -
                                                                                                          -
                                                                                                        • +
                                                                                                            +
                                                                                                          • The flags are implemented as a const data member of the facet. Facets are reference counted, and locales can share facets. Therefore changing the flags of a facet would have effects that are hard to predict. An @@ -38,7 +38,7 @@ file would have to be added to the library. It was judged be more desirable to have a headers only library, than to have mutable flags and manipulators.
                                                                                                          • -
                                                                                                          • +
                                                                                                          • The facet nonfinite_num_put throws an exception when the trap_infinity or trap_nan flag is diff --git a/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/reference.html b/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/reference.html index aae5801ac..b2866fb00 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/reference.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/reference.html @@ -3,7 +3,7 @@ Reference - + @@ -22,7 +22,7 @@
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                                                                                                            @@ -262,17 +262,17 @@ and nonfinite_num_get take an optional bit flags argument. There are four different bit flags:

                                                                                                            -
                                                                                                              -
                                                                                                            • +
                                                                                                                +
                                                                                                              • legacy
                                                                                                              • -
                                                                                                              • +
                                                                                                              • signed_zero
                                                                                                              • -
                                                                                                              • +
                                                                                                              • trap_infinity
                                                                                                              • -
                                                                                                              • +
                                                                                                              • trap_nan
                                                                                                              @@ -364,23 +364,23 @@

    -
      -
    • +
        +
      • The numbers can be of type float, double and long double.
      • -
      • +
      • The facet is case-insensitive.
      • -
      • +
      • An optional + sign can be used with the positive values.
      • -
      • +
      • The dots in nan(...) stand for an arbitrary string.
      • -
      • +
      • one stands for any string that std::num_get parses as the number 1, typically "1.#INF", "1.QNAN" but also "000001.#INF"... diff --git a/doc/sf_and_dist/html/math_toolkit/utils/fpclass.html b/doc/sf_and_dist/html/math_toolkit/utils/fpclass.html index 3c1ad40cc..4d8a266b5 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/fpclass.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/fpclass.html @@ -3,7 +3,7 @@ Floating-Point Classification: Infinities and NaNs - + @@ -22,7 +22,7 @@
        PrevUpHomeNext
        -
        +

        Floating-Point Classification: Infinities and NaNs diff --git a/doc/sf_and_dist/html/math_toolkit/utils/next_float.html b/doc/sf_and_dist/html/math_toolkit/utils/next_float.html index 97ebdcdf4..ddf22def3 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/next_float.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/next_float.html @@ -3,7 +3,7 @@ Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values - + @@ -22,7 +22,7 @@
        PrevUpHomeNext
        -
        +

        Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values diff --git a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_advance.html b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_advance.html index 28bcf19b4..f84c015d4 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_advance.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_advance.html @@ -3,7 +3,7 @@ Advancing a Floating Point Value by a Specific Representation Distance (ULP) float_advance - + @@ -22,7 +22,7 @@
        PrevUpHomeNext
        -
        +

        Advancing a Floating Point Value by a Specific Representation Distance (ULP) float_advance diff --git a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_distance.html b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_distance.html index 23f75e1d8..031477850 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_distance.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_distance.html @@ -3,7 +3,7 @@ Calculating the Representation Distance Between Two Floating Point Values (ULP) float_distance - + @@ -22,7 +22,7 @@
        PrevUpHomeNext
        -
        +

        Calculating the Representation Distance Between Two Floating Point Values (ULP) float_distance @@ -64,16 +64,16 @@

        Note that

        -
          -
        • +
            +
          • float_distance(a, a) always returns 0.
          • -
          • +
          • float_distance(float_next(a), a) always returns 1.
          • -
          • +
          • float_distance(float_prior(a), a) always returns -1.
          • diff --git a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_next.html b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_next.html index 61139d7dd..1170346bb 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_next.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_next.html @@ -3,7 +3,7 @@ Finding the Next Greater Representable Value (float_next) - + @@ -22,7 +22,7 @@
            PrevUpHomeNext
            -
            +

            Finding the Next Greater Representable Value (float_next) @@ -57,7 +57,7 @@

            Has the same effect as

            -
            nextafter(val, std::numeric_limits<FPT>::max());
            +
            nextafter(val, (std::numeric_limits<FPT>::max)());
             

            diff --git a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_prior.html b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_prior.html index 594b70bfa..8ca93ac9a 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_prior.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_prior.html @@ -3,7 +3,7 @@ Finding the Next Smaller Representable Value (float_prior) - + @@ -22,7 +22,7 @@
            PrevUpHomeNext
            -
            +

            Finding the Next Smaller Representable Value (float_prior) @@ -57,7 +57,7 @@

            Has the same effect as

            -
            nextafter(val, -std::numeric_limits<FPT>::max());  // Note most negative value -max.
            +
            nextafter(val, -(std::numeric_limits<FPT>::max)());  // Note most negative value -max.
             

            diff --git a/doc/sf_and_dist/html/math_toolkit/utils/next_float/nextafter.html b/doc/sf_and_dist/html/math_toolkit/utils/next_float/nextafter.html index dd6c8d67f..e0c60c4c4 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/next_float/nextafter.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/next_float/nextafter.html @@ -3,7 +3,7 @@ Finding the Next Representable Value in a Specific Direction (nextafter) - + @@ -22,7 +22,7 @@
            PrevUpHomeNext
            -
            +

            Finding the Next Representable Value in a Specific Direction (nextafter) @@ -74,6 +74,27 @@ If there is no such value in the direction of y then returns an overflow_error.

            +

            + + + + + +
            [Warning]Warning

            + The template parameter FTP must be a floating-point type. An integer + type, for example, will produce an unhelpful error message. +

            +
            + + + + + +
            [Tip]Tip

            + Nearly always, you just want the next or prior representable value, so + instead use float_next + or float_prior below. +

            Examples diff --git a/doc/sf_and_dist/html/math_toolkit/utils/rounding.html b/doc/sf_and_dist/html/math_toolkit/utils/rounding.html index 1e5520248..4aaee28cd 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/rounding.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/rounding.html @@ -3,7 +3,7 @@ Rounding Truncation and Integer Conversion - + @@ -22,7 +22,7 @@ -
            +

            Rounding Truncation and Integer Conversion diff --git a/doc/sf_and_dist/html/math_toolkit/utils/rounding/modf.html b/doc/sf_and_dist/html/math_toolkit/utils/rounding/modf.html index c57c43ac3..4d2d3734e 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/rounding/modf.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/rounding/modf.html @@ -3,7 +3,7 @@ Integer and Fractional Part Splitting (modf) - + @@ -22,7 +22,7 @@
            PrevUpHomeNext
            -
            +

            Integer and Fractional Part Splitting (modf) diff --git a/doc/sf_and_dist/html/math_toolkit/utils/rounding/round.html b/doc/sf_and_dist/html/math_toolkit/utils/rounding/round.html index 92510699b..0b63fda6e 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/rounding/round.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/rounding/round.html @@ -3,7 +3,7 @@ Rounding Functions - + @@ -22,7 +22,7 @@
            PrevUpHomeNext
            -
            +
            diff --git a/doc/sf_and_dist/html/math_toolkit/utils/rounding/trunc.html b/doc/sf_and_dist/html/math_toolkit/utils/rounding/trunc.html index bf2a6425b..10f9317c4 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/rounding/trunc.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/rounding/trunc.html @@ -3,7 +3,7 @@ Truncation Functions - + @@ -22,7 +22,7 @@
            PrevUpHomeNext
            -
            +
            diff --git a/doc/sf_and_dist/html/math_toolkit/utils/sign_functions.html b/doc/sf_and_dist/html/math_toolkit/utils/sign_functions.html index 3a75c1853..c228b9aa7 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/sign_functions.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/sign_functions.html @@ -3,7 +3,7 @@ Sign Manipulation Functions - + @@ -22,7 +22,7 @@
            PrevUpHomeNext
            -
            +

            Sign Manipulation Functions @@ -159,23 +159,23 @@

            The library supports the following binary floating-point formats:

            -
              -
            • +
                +
              • IEEE 754 single precision
              • -
              • +
              • IEEE 754 double precision
              • -
              • +
              • IEEE 754 extended double precision with 15 exponent bits
              • -
              • +
              • Intel extended double precision
              • -
              • +
              • PowerPC extended double precision
              • -
              • +
              • Motorola 68K extended double precision
              @@ -186,14 +186,14 @@

              The main portability issues are:

              -
                -
              • +
                  +
                • Unsupported floating point formats
                • -
                • +
                • The library depends on the header boost/detail/endian.hpp
                • -
                • +
                • Code such as #if defined(__ia64) || defined(__ia64__) || defined(_M_IA64) is used to determine the processor type.
                • @@ -201,38 +201,38 @@

                  The library has passed all tests on the following platforms:

                  -
                    -
                  • +
                      +
                    • Win32 / MSVC 7.1 / 10.0 / x86
                    • -
                    • +
                    • Win32 / Intel C++ 7.1, 8.1, 9.1 / x86
                    • -
                    • +
                    • Mac OS X / GCC 3.3, 4.0 / ppc
                    • -
                    • +
                    • Linux / Intel C++ 9.1 / x86, ia64
                    • -
                    • +
                    • Linux / GCC 3.3 / x86, x64, ia64, ppc, hppa, mips, m68k
                    • -
                    • +
                    • Linux / GCC 3.4 / x64
                    • -
                    • +
                    • HP-UX / aCC, GCC 4.1 / ia64
                    • -
                    • +
                    • HP-UX / aCC / hppa
                    • -
                    • +
                    • Tru64 / Compaq C++ 7.1 / alpha
                    • -
                    • +
                    • VMS / HP C++ 7.1 / alpha (in IEEE floating point mode)
                    • -
                    • +
                    • VMS / HP C++ 7.2 / ia64 (in IEEE floating point mode)
                    From 69ba66929d983d68d6acf8a8f27fd0c35e3eeb8e Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Wed, 1 Aug 2012 16:32:48 +0000 Subject: [PATCH 074/115] Rebuilt after edits to quiet nags. [SVN r79834] --- test/jacobi_elliptic.ipp | 805 ++++---- test/jacobi_elliptic_small.ipp | 3367 ++++++++++++++++---------------- test/jacobi_large_phi.ipp | 605 +++--- test/jacobi_near_1.ipp | 685 +++---- test/owens_t_T7.hpp | 14 +- test/owens_t_large_data.ipp | 1313 ++++++------- test/table_type.hpp | 6 + test/test_constants.cpp | 540 ++--- 8 files changed, 3686 insertions(+), 3649 deletions(-) diff --git a/test/jacobi_elliptic.ipp b/test/jacobi_elliptic.ipp index dcaae4f5b..a8138804c 100644 --- a/test/jacobi_elliptic.ipp +++ b/test/jacobi_elliptic.ipp @@ -1,406 +1,413 @@ +// Copyright John Maddock 2012. + +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt +// or copy at http://www.boost.org/LICENSE_1_0.txt) + #ifndef SC_ # define SC_(x) static_cast(BOOST_JOIN(x, L)) #endif static const boost::array, 400> jacobi_elliptic = {{ - {{ SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.7384321813508780300050309993112921610348339609531096226291156957843807163438391463300771570266454611e-02), SC_(9.9524685071841496279438927849850673342525676921414792528840427410727111940782381944976305408868157855e-01), SC_(9.9995488439733316729114394585903874689886199946693440341361736436672692239264636048488084336908171547e-01) }}, - {{ SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7383306026428126815811673852101862643417212675894886262329096942831342806175591481538515201116435095e-02), SC_(9.9524695011206291426731901545274769005867525867705503210833924341584688692109569818882782443312019870e-01), SC_(9.9992353321916073154296514614318371763529995049379965142148455053362169878708374701587696243287582131e-01) }}, - {{ SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(1.3547700643539428710937500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7382963663268679354766311462039914384149178492941126840831062817834448292082576674044335924290112792e-02), SC_(9.9524698361168545268757042933526662768772514619668023376490370653166168736869277815425438301697322693e-01), SC_(9.9991296657753407444565165371686075323189094367991128619066744668429579140503359966446931860569605749e-01) }}, - {{ SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(1.8838196992874145507812500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7380331287488173017819681812505333548000401340832607031998520409371778408842832201970632399407455377e-02), SC_(9.9524724118097360944629737689090579536626111956092105184429209919209960381948277540779135011872980164e-01), SC_(9.9983172185713251267253025953154802657840786163407200767760200375372426265381549093953869220602182213e-01) }}, - {{ SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(2.2103404998779296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7378277454797060918439287025630752988524259325176347053163180340804501139998370882347991305783292950e-02), SC_(9.9524744213684697238369251137951559191374873239697065458847170083807556278595809556474002748294261664e-01), 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SC_(5.4722046852111816406250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.1699261272360843718094896717933608151745983515066309372984104102996139405622722607210355081833891513e-01), SC_(5.7664813426824850966137934301882037328247242522271394061105905414771445854256739255757146117096354987e-01), SC_(8.9449643518753563454611035039011276118628076201799942256582642209492573307351767556846756787034337047e-01) }}, + {{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(6.3235926628112792968750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.0917470232222200804623180098129133036872476212345687946408231027401224355414186080302191412417315445e-01), SC_(5.8756812466448807626035048020623505899237385118588318521559957175811892777170782847243623726402163039e-01), SC_(8.5917067186634159636297999262881680727474209461119658335870527906879501356002165645327808755884914641e-01) }}, + {{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.1472349166870117187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.8807119444979816800923969304385287292785209340565035630430040254664427368175755115143127657804319275e-01), SC_(6.1558410674616056493571795007635947841655775384258519636348871522168706473724532307349806008226940840e-01), SC_(7.6665429525726110361447413684552291171054174846338591438308890401356527577849589856356276150225732188e-01) }}, + {{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.3500838279724121093750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.8533974060861189062248546305583049909685081062975650698710874051826667020351572955065423608667621888e-01), SC_(6.1906501421159166628343674250361648671913040974698965825105617076167069374238270072189557585460007272e-01), SC_(7.5496484350046113300800020039074081961933680785286101512645919124096025389484980045855949751906931482e-01) }}, + {{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.0579175949096679687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.7518052347000925314010007943527768455040920946345973339627012081381376695222757183254277030896944957e-01), SC_(6.3173978506404235602086192410695037495356623570300207001965408561482576560706910009779017218552967902e-01), SC_(7.1202695591348996943901212719172676293237917080282599202090818283760895203386224684127468737115722039e-01) }}, + {{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.1337585449218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.7403326959640178723563496098403563126044877288657909026716436291016997542128873110698916026557616324e-01), SC_(6.3314492618823376986676740088221455887438346847232176226658849048417517890369368618344349029048271542e-01), SC_(7.0723024179015572507350410631921738029759560477969903360400060435126461530726016656465837852310688792e-01) }}, + {{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.5750665664672851562500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.6712800823285619471798123561258913583803638220534736201364708009370629428320353958750416444955694982e-01), SC_(6.4149405218185064504992339458407016741795699167416304441730489787216690117110750201301703730190120252e-01), SC_(6.7857602589593721337697403304549699145452424462317392210364305668406670401778150852638680470506706518e-01) }}, + {{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.6488833427429199218750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.6593441813020686107904272195284976164911143038148978940760933715399917785398101606027733051459971132e-01), SC_(6.4291870957652293482277601636810697919275457997668849096935959115861162055784408260876292546568984644e-01), SC_(6.7366024601538257589655742562219072544530334312218911862590121331700593411003613779831508617892420325e-01) }}, + {{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.6769475936889648437500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.6547770865632652104311857431350648982519639693036504351701283181609474922881977308885338563907679349e-01), SC_(6.4346241347126103408603307544875846579869659656475523368458255827578551435308991733382243465986469958e-01), SC_(6.7178215521760534606784911003038819524570089099102635584446923804691272196126068898352982615576142014e-01) }}, + {{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.6886777877807617187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.6528633729797841460176785222203390514942625072618331938529597075420681577693034777030027274670865291e-01), SC_(6.4369000454026378494764961458275300252507916799112249356864558832261907901572939091058344628185994802e-01), SC_(6.7099566282750678306967995163385198199449520575839393027024329721293501791261343629006364525136879702e-01) }}, + {{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.9288129806518554687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.6130656170513378346158650596006841065509926127276492299715158864622868192915634720105938405478654273e-01), SC_(6.4839210290125166440291833468322114687478245067783826919074500661090573579759551799996853065323027448e-01), SC_(6.5470204815482800802602415811048971704607358039770120289884409108362609917793951796905679822441221683e-01) }}, {{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.6070308834386404159049681239553434730978977615881969147142722819631969635063229458010769940901615571e-01), SC_(6.4910000106617422443762696869434170692368988825415526998433303308325407487195203453870690819261137407e-01), SC_(6.5224167903128336698276201258993391810194122946207851950380395682119994293224476046299862066823494348e-01) }} }}; //#undef SC_ diff --git a/test/jacobi_elliptic_small.ipp b/test/jacobi_elliptic_small.ipp index 13549a684..1b0ca996e 100644 --- a/test/jacobi_elliptic_small.ipp +++ b/test/jacobi_elliptic_small.ipp @@ -1,1687 +1,1694 @@ +// Copyright John Maddock 2012. + +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt +// or copy at http://www.boost.org/LICENSE_1_0.txt) + #ifndef SC_ # define SC_(x) static_cast(BOOST_JOIN(x, L)) #endif static const boost::array, 1681> jacobi_elliptic_small = {{ - {{ SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.6504814008555523940913182524024344909690304914367592725655712600281923768045401283620998764707764693e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973696151635920379696565170086974190992e-01), SC_(9.9999999999999999999999999999999999999999999999628966995620346223342181461431515637620350243665215080e-01) }}, - {{ SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(2.0654207510961697380480472929775714874267578125000000000000000000000000000000000000000000000000000000e-12), SC_(1.6504814008555523940913182524024344909690304914356038800613310054830865914687618301634103078917338168e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973696151826615763590211178195021758793e-01), SC_(9.9999999999999999999999999999999999999999999999418956903357324218784742231100976423667721244640328945e-01) }}, - {{ SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(6.9332300317581641024844429921358823776245117187500000000000000000000000000000000000000000000000000000e-12), SC_(1.6504814008555523940913182524024344909690304914027798723391089616386590188266692256822553895004737691e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973696157244157188296862020758148130289e-01), SC_(9.9999999999999999999999999999999999999999999993452696204168490870911613561919090434443527881778962629e-01) }}, - {{ SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.3351444949627477853937307372689247131347656250000000000000000000000000000000000000000000000000000000e-11), SC_(1.6504814008555523940913182524024344909690304913052218556582079673621348947108779104417637686162896722e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973696173345926391915144123663683144195e-01), SC_(9.9999999999999999999999999999999999999999999975720048632921041975214334983463922773663246301371558079e-01) }}, - {{ SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.6399812063916385795891983434557914733886718750000000000000000000000000000000000000000000000000000000e-11), SC_(1.6504814008555523940913182524024344909690304912372618758507282714946015960583626600059283156291032012e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973696184562594659391558357034445701976e-01), SC_(9.9999999999999999999999999999999999999999999963367292684459290855251530901083881607676209352596350232e-01) }}, - {{ SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(5.7301594025283009159466018900275230407714843750000000000000000000000000000000000000000000000000000000e-11), SC_(1.6504814008555523940913182524024344909690304889783532888043627371778016267672955616082803704829236507e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973696557391255574683748524224459833699e-01), SC_(9.9999999999999999999999999999999999999999999552776433700754495454636367587944076648284400103707184302e-01) }}, - {{ SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.1137313293829720350913703441619873046875000000000000000000000000000000000000000000000000000000000000e-10), SC_(1.6504814008555523940913182524024344909690304821439689287767962044790479566381944530155678406625631702e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973697685393682827041343608589118700995e-01), SC_(9.9999999999999999999999999999999999999999998310523532852882161708648652005740665368880880910156584491e-01) }}, - {{ SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.4214707189097453010617755353450775146484375000000000000000000000000000000000000000000000000000000000e-10), SC_(1.6504814008555523940913182524024344909690304762977332560523723670737117904598123506030905571007525820e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973698650304007112032323166148527367075e-01), SC_(9.9999999999999999999999999999999999999999997247881626734957219094542687145216261006406307420236809325e-01) }}, - {{ SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(3.8006320313144215106149204075336456298828125000000000000000000000000000000000000000000000000000000000e-10), SC_(1.6504814008555523940913182524024344909690303831976744007277642905699914309078508034857277902993981434e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973714016295563039085806793646480974079e-01), SC_(9.9999999999999999999999999999999999999999980325535429971135087765023210979692154823009643251966522036e-01) }}, - {{ SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(6.0916272026645401638234034180641174316406250000000000000000000000000000000000000000000000000000000000e-10), SC_(1.6504814008555523940913182524024344909690302133731854710685114641012066105734375850645869948919458138e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973742045511601859311127502555051080985e-01), SC_(9.9999999999999999999999999999999999999999949457361664130189602800079536313829981986427076949318817789e-01) }}, - {{ SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.0221641311147777742007747292518615722656250000000000000000000000000000000000000000000000000000000000e-09), SC_(1.6504814008555523940913182524024344909690297085106157246959147019549187034633366860135865373130072792e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133973825372139737312017993425357327472681e-01), SC_(9.9999999999999999999999999999999999999999857690940760870814533399831245189911999724717703220387897201e-01) }}, - {{ SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(2.8819222563924995483830571174621582031250000000000000000000000000000000000000000000000000000000000000e-09), SC_(1.6504814008555523940913182524024344909690242677885948711088664385488861032724509329344622403207481410e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133974723353190001720047690056131101093059e-01), SC_(9.9999999999999999999999999999999999999998868757284550027385876551628249984105649518984138605236580531e-01) }}, - {{ SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(4.7627768395841485471464693546295166015625000000000000000000000000000000000000000000000000000000000000e-09), SC_(1.6504814008555523940913182524024344909690134933098417362621376030351507143097515536131758800073666674e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133976501660868597958778702500430601729980e-01), SC_(9.9999999999999999999999999999999999999996910332533889451002177040231472679603830330500099612602677035e-01) }}, - {{ SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(8.8541334264391480246558785438537597656250000000000000000000000000000000000000000000000000000000000000e-09), SC_(1.6504814008555523940913182524024344909689717461858586327957602950267806604551468156898254148882224748e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244133983391946035930262518846860865434979203e-01), SC_(9.9999999999999999999999999999999999999989322160265823321349052149682027615133455037665915804501555188e-01) }}, - {{ SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(2.3050326092288742074742913246154785156250000000000000000000000000000000000000000000000000000000000000e-08), SC_(1.6504814008555523940913182524024344909686323523656956557466573268843129097061735969718419269903756412e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244134039408264810361040874003831061763988570e-01), SC_(9.9999999999999999999999999999999999999927632191511183545177421364285740672490570631107123629541620207e-01) }}, - {{ SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(5.9392490925347374286502599716186523437500000000000000000000000000000000000000000000000000000000000000e-08), SC_(1.6504814008555523940913182524024344909663872080081406338583759571333756176566943414887198590991250826e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244134409965165248396214212813572057652287157e-01), SC_(9.9999999999999999999999999999999999999519543189770621643635884806523323694404582563651057704462697028e-01) }}, - {{ SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.1667648891489079687744379043579101562500000000000000000000000000000000000000000000000000000000000000e-07), SC_(1.6504814008555523940913182524024344909588293831710191198186747356949388380517396812042654193369934302e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244135657370097707716573801601901386768273769e-01), SC_(9.9999999999999999999999999999999999998145794021824142620974495770659414222168637044587970657748003597e-01) }}, - {{ SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(2.3799674409019644372165203094482421875000000000000000000000000000000000000000000000000000000000000000e-07), SC_(1.6504814008555523940913182524024344909265858679866731016390766452234122292419645132917080994605064614e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244140979102308704385651739160793286510212057e-01), SC_(9.9999999999999999999999999999999999992285046636067702713907942013032905297195860994461375719475855459e-01) }}, - {{ SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(4.6846594159433152526617050170898437500000000000000000000000000000000000000000000000000000000000000000e-07), SC_(1.6504814008555523940913182524024344908045794234673931872034147213497000375265822385091582975735928436e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244161116039055063020239008290949554874460617e-01), SC_(9.9999999999999999999999999999999999970108526902606423004774330258537078837146430522090471722713952519e-01) }}, - {{ SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(9.3826997726864647120237350463867187500000000000000000000000000000000000000000000000000000000000000000e-07), SC_(1.6504814008555523940913182524024344903093459707187946270419675021577786501184313307591933565375527000e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244242853399339366916813650688688000362016475e-01), SC_(9.9999999999999999999999999999999999880092343898322941123574529398516994582299038041465074714265274086e-01) }}, - {{ SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.1039855962735600769519805908203125000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(1.6504814008555523940913182524024344900557430873575286480834184767300136835270193965664311004583807788e-12), SC_(9.9999999999999999999999863795557271494668646082344582907244284710083558477870086857644172480108004954e-01), 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SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.1667648891489079687744379043579101562500000000000000000000000000000000000000000000000000000000000000e-07), SC_(9.9639439232989442634500045409108731549010046464738105516502928086111610280466324094451263332286349668e-01), SC_(-8.4842294485359265104059019529370046157498710478206515609612241056089073719873849031215963836157014509e-02), SC_(9.9999999999999324229456786787708285791330553826966224546894562447049868987754673200814836010122411685e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(2.3799674409019644372165203094482421875000000000000000000000000000000000000000000000000000000000000000e-07), SC_(9.9639439232989601464506713603381888542259911240503341675783382339161277310613605184904978207815355032e-01), SC_(-8.4842294485340611986655972919139731689757639273427541000107716774717614400759544871959901034018042843e-02), SC_(9.9999999999997188263716667439324205731591559804198846266833701690218952604787767494000497709598522931e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(4.6846594159433152526617050170898437500000000000000000000000000000000000000000000000000000000000000000e-07), SC_(9.9639439232990202462390652698782609254008348156336889962480221504612347767144033019437727795000288797e-01), SC_(-8.4842294485270030335724459320249478221757594901193169180860648559415124811781045436362107593672631223e-02), SC_(9.9999999999989105969212577782282360468512833476252007017681875725911844408283469933768767175294955914e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(9.3826997726864647120237350463867187500000000000000000000000000000000000000000000000000000000000000000e-07), SC_(9.9639439232992641958585545262463099799848333149274561871563771543583526269224291176910216375332908961e-01), SC_(-8.4842294484983534037686783527835454992921912092660968995212001703740264338631718205138843401870012274e-02), SC_(9.9999999999956299320111678065381414005117728640827006034551068145838423608076432341954064670386808729e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.1039855962735600769519805908203125000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(9.9639439232993891194204703088677522512244399512487298590549937155560273073731965241606747269890480607e-01), SC_(-8.4842294484836822851575585886567413907326892374168197022264779245842189375666044735899310645141599057e-02), SC_(9.9999999999939499443691302955871808429687868700747141390968336493895645754611108621555597704991416291e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(3.2917760108830407261848449707031250000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(9.9639439233029389748956932327129091158075264859718512367948708207416066779749862612144734336172739459e-01), SC_(-8.4842294480667845443953102163404296318391883798145226147266545577967646060269205478578768927922719434e-02), SC_(9.9999999999462110451726763223295498660227375746905159152874896311796553700194885004383959875991323374e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(7.5172138167545199394226074218750000000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(9.9639439233197978132686693916203190106576896483533805609341298516578495517691112332138923484292414188e-01), SC_(-8.4842294460868696775433694073450150907679394654211248232058407564229451823414329968769544117088087361e-02), SC_(9.9999999997194912839320992947154918460071662296190735712959073259087663139642400252423085776091530486e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.5114666894078254699707031250000000000000000000000000000000000000000000000000000000000000000000000000e-05), SC_(9.9639439233832664977629705536669831435426827137573865519655076721199119234036829353543026053815720129e-01), SC_(-8.4842294386330588454991996610694144597747353486819290842374731164755639767707663806305724394100907510e-02), SC_(9.9999999988659564978929333754573013725483609109446164465889782429126367311703263380098309270395970454e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(2.9863993404433131217956542968750000000000000000000000000000000000000000000000000000000000000000000000e-05), SC_(9.9639439236281443624753158687038454096577564270991214083469840809539610364509563625849219075623699280e-01), SC_(-8.4842294098744151302953238350800256832596089936119182803734993418583767146069333200039628065940693344e-02), SC_(9.9999999955728084199715672255718504172741717470542761906819535951864276950458540373205623386616537109e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(3.3870281185954809188842773437500000000000000000000000000000000000000000000000000000000000000000000000e-05), SC_(9.9639439237223953724581982941629132748498983887981035908604585745857826395065250770878869942510011341e-01), SC_(-8.4842293988055044082583610914447143938044232971226932593724715633534115772196868151866529219226744951e-02), SC_(9.9999999943053090748253932656368900765792555269780716890189615989575800344105114676634210224581246448e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(9.0660119894891977310180664062500000000000000000000000000000000000000000000000000000000000000000000000e-05), SC_(9.9639439263328541366719031725241577314079198743209947847909476415592779981710088614620793535022214474e-01), SC_(-8.4842290922312241463028290901886236468697679576893295365022598381737118235652753487965129582714048961e-02), SC_(9.9999999591995330997524068647525151887288634403876011421441510310561160493295521892857438617062912841e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(2.1949532674625515937805175781250000000000000000000000000000000000000000000000000000000000000000000000e-04), SC_(9.9639439410826067431307822604787492127597668642195114647761391647693455985378034591691491702705577906e-01), SC_(-8.4842273600087509888806940837110422629864742105524848164093163940289071489404486929406333024041952399e-02), SC_(9.9999997608429891075272698981098375011760545789757386788033103243299232149774232751941797398008621709e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(4.3952150736004114151000976562500000000000000000000000000000000000000000000000000000000000000000000000e-04), SC_(9.9639439946057283654855935236752624035880191284049054750658244297828725656065644035418378639820004094e-01), SC_(-8.4842210742085271589035996870541465107472441820952998743617829037111050036348887366217833042583183538e-02), SC_(9.9999990410568885432730450661406780382747893720931957290008095471902273911676718477882188550504429360e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(6.3331518322229385375976562500000000000000000000000000000000000000000000000000000000000000000000000000e-04), SC_(9.9639440713495471434923143724675451317717484796503726041028796498492176802332554253832509916871965935e-01), SC_(-8.4842120613419993829653470484176332143015609165075405322937128639532532687627013454703366335136057687e-02), SC_(9.9999980089947286502621224734144392936772145074199619421807467791812848947570762271107897628498946539e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.1151232756674289703369140625000000000000000000000000000000000000000000000000000000000000000000000000e-03), SC_(9.9639443823016524654104629623362614491579693467989253808727772715845343535280963682357379812867245026e-01), SC_(-8.4841755427344930663007460100028833354954911466256337396719760700291713295727386906732582556927571057e-02), SC_(9.9999938272528249391312307608807398374816383372852435374472406644589615977465186408873728224171642189e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.9624670967459678649902343750000000000000000000000000000000000000000000000000000000000000000000000000e-03), SC_(9.9639453448794504753671533455904797532119598152365059838083231543209853813817276459987896643847885629e-01), SC_(-8.4840624953799622786068044598030741055063642230082296390150800205369862431346329264619378174286838014e-02), SC_(9.9999808822023431586330507223399599331299259546946802809286583619824066393501989056548364182611503082e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(5.5537540465593338012695312500000000000000000000000000000000000000000000000000000000000000000000000000e-03), SC_(9.9639553077217003511353530043413808033920247930882092573188708783469515876938649937674371540560702420e-01), SC_(-8.4828923470981032069634272050225777540758810269842969047296062581637761984301166734820582381456553004e-02), SC_(9.9998468876732348097939012173864087757227234405891503826150435694363062945422284532826470182539791518e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(8.6911283433437347412109375000000000000000000000000000000000000000000000000000000000000000000000000000e-03), SC_(9.9639718000461594989260420944042571499940208837940453162707360749418854616064045702840166901838974039e-01), SC_(-8.4809549455523940355185466702194582862099119856342307034787941990006897379697771484768623427437519652e-02), SC_(9.9996250309238530117640656410289279207641184807525627009919430951232501378233250614276839898342947194e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(2.9933363199234008789062500000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.9642739273361037624425236003709998424423669985681772457419514437854858892669295864838396904074334791e-01), SC_(-8.4453839522542653735176696295242418341771308961936320935099661751459635173562095780038126996050284763e-02), SC_(9.9955509327307226870482882280431162855249849172060889261100838598526189994716425561466757382237089590e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(5.1242604851722717285156250000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.9649068766424200577985721184356752955601723188930074293915835068113130632428255591007970917819025182e-01), SC_(-8.3703700028410244770061826214701529976799484885620218724844567694731485856500558608813841851268272143e-02), SC_(9.9869544539219827767678663556107790796001205357457841120474538750514167458555525624218345986227679244e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.1201295256614685058593750000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.9684313604934398930539235390129770939609825850290918420113575774717084081891501166979587762444196098e-01), SC_(-7.9396234868594807401272204725688142828934281134460946403103848657930854463427457876250364818746217174e-02), SC_(9.9374654270592187744997687020550454797638290050151265651320047733411371840069209832488090292039717367e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(2.3480379581451416015625000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.9814934866490320978806688580871390672680066453416779059422743215014552518552147816785137038565167474e-01), SC_(-6.0810178094045119247364122651955570809342076623943187762098707626057061856818089052462136539473338148e-02), SC_(9.7214764923305873458032862854350162073206678556449933567459172269681798829001261625830288160524321418e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(4.8987305164337158203125000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.9976967292952005755481095245256024937692734652402590999991494952154282866789560889911025306718779168e-01), SC_(2.1461619006973565646536174052546379410807514047370718515791347175325100002601713407336650423975813432e-02), SC_(8.7185717081396898541065289390703478456116878515433892820948672390341209634334005744800539221410270970e-01) }}, + {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(7.5183129310607910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.8539034324839560936682949899637621959818856082648192169501428326661400191997487509531927187367953439e-01), SC_(1.7031110190709553832350904690514019306839852576492774590778059270526592192267334810770243087477878657e-01), SC_(6.7167349511579774208520897966660216379314520347464078477957664271219777907511857160535742769433089892e-01) }}, {{ SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.6557407379150390625000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(4.0815375315288640577475196367102453532926947422123146010409415723479279392954356853433706994064428463e-01), SC_(9.1291320167210457006284950226993895289063450955873095160130726593569036267152905012436288527918734100e-01), SC_(-7.3708797978087103688004545584461400336979146221355035197387826317949437602283858594803646637152865976e-01) }} }}; //#undef SC_ diff --git a/test/jacobi_large_phi.ipp b/test/jacobi_large_phi.ipp index a2fc15964..a9a716fa1 100644 --- a/test/jacobi_large_phi.ipp +++ b/test/jacobi_large_phi.ipp @@ -1,306 +1,313 @@ +// Copyright John Maddock 2012. + +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt +// or copy at http://www.boost.org/LICENSE_1_0.txt) + #ifndef SC_ # define SC_(x) static_cast(BOOST_JOIN(x, L)) #endif static const boost::array, 300> jacobi_large_phi = {{ - {{ SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.1058797357690320086682997888107252211628291495151688601393407863373061954395848396257429511756176811e-01), SC_(-9.9386633915238026812869743952282655015178929533806734450981604274006648191113417152643248132020074274e-01), SC_(9.9990138922139577345821742312959843927086669798900631576940452344894647029651168866543336495621319962e-01) }}, - {{ SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(1.3547700643539428710937500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.9796027195728077189442848498661232305049387865637023002287165495702857395230146075769449539819678763e-02), SC_(-9.9980403945336507845151345500450800737097833473134761034812701539547907788852267602747381881654129683e-01), SC_(9.9999640368228571150326548705630160155372276544820513372782759452847671460675392468118278515564642670e-01) }}, - {{ SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(2.2103404998779296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-9.4524463054363015830543554229266024611315133648646726829860103132985305860006657410579310878453671719e-01), SC_(-3.2636266396209619739852328880763978392918068940083223909131243802010656037702645968281828914985898722e-01), SC_(9.7793033147839850499560648584765033296353170435094191917820984988398156187728059208365609303718763468e-01) }}, - {{ SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(3.0816698074340820312500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(3.8467092829206275416395221453254971947309775360749050985209931262282264520459122402381792953068010283e-02), SC_(9.9925986748656589242807594841179280186636858779886436718703277243900358292074844422479042190466225049e-01), SC_(9.9992973546117087872258976240789404601766963067622683679015332787486976781350082685530756477017893531e-01) }}, - {{ SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(6.3235926628112792968750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.1828487869642382837142082205368890409594444563859603885036504087100530651689815737374300479572152806e-01), SC_(-5.7481288894454945115324043802657481607935129579981996144467071525751961910351319915758240211691782206e-01), SC_(8.5571342814553735162229894739444873282853333740663537333659164564589208017713251914590680386027272809e-01) }}, - {{ SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(8.1472349166870117187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.0342555778181684908553725700040860110642531214149151205515131896190048290879021057059409802362096946e-01), SC_(5.9540521756445540531188114127706021212880690887199697020660799772318324844598317460087416642725615927e-01), SC_(7.5600167963587697285196939810169457229824831904454088987922148028116675585554507425145383067593756070e-01) }}, - {{ SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(8.3500838279724121093750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-5.2923808769191278344096906576129452977508979277324972114028585485897292732749175191104387817153243622e-01), SC_(-8.4847336230208620189522999730668948980498026956351676759653713074643763505826560196595716137493813219e-01), SC_(8.9705533240946393665356057247371866574922627996248245980741140274917656623741748929349898927165638735e-01) }}, - {{ SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.0579175949096679687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-4.3588329433998778344118299461470119260462800471832395414994779852496041561445544177910644873466410470e-01), SC_(-9.0000319650283441310099684480078605946721143546738341042331933310537915309970277408204072796535470377e-01), 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SC_(5.5702897854142442809611654478963959324261775797147550071864942887044712808658131231637010349995702522e-01) }}, + {{ SC_(1.9244384765625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.0579175949096679687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-8.8270115775193423620255579638055734154142840720846053962016385963039891369058232571134438249971299782e-01), SC_(4.6993474664403664402801695571076121740057255160045194624946246537172391662751582864322860663846755794e-01), SC_(6.0060827158178863368404500172080102632076625684813771196020909629280641279574615153270312721676292993e-01) }}, + {{ SC_(1.9244384765625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.1337585449218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-3.0499633309357216160837947685508809398255521078686485810289070559124369255099465411452008206591216497e-01), SC_(-9.5235352511526662520363937890584200804697113358196926071621691184261145069006498967839187367230278540e-01), SC_(9.6041410479017780647642546421853134094118233510049076119516206412560578636505769948373386720382050372e-01) }}, + {{ SC_(1.9244384765625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.6886777877807617187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.7703562086186605707652810260085804979481250950420318258041728072494841225884138094911078872313703606e-01), SC_(4.8042535293158825529589641475682597199231357338121232115205565947900759506420661006157314061468657855e-01), SC_(5.2721559756651726382324256487897356272038238081316030704213375897027127034023294653929546320025247369e-01) }}, + {{ SC_(1.9715252685546875000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.9999149217579438025155419990378050503774435663431440953044152660042130222829826356772642068616800226e-01), SC_(-4.1249940640159451218905143653088260520196509809885200974912119735128876297229127837040396959124726935e-03), SC_(9.9190454510523192870151020257793218111789942952070638913195077330681594450955229828271818098523095175e-01) }}, + {{ SC_(1.9715252685546875000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(1.3547700643539428710937500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.9434482768426277476649034779467733059368058898480629473319245010863119376582776653994755154495576583e-01), SC_(1.0619964057167881835341514888736790094923878910656293614977154420369967365183882337460116321223340636e-01), SC_(9.9088494994688427220084094311943729183292306647285928784964966773416757025282807085924859312912955955e-01) }}, + {{ SC_(1.9715252685546875000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(2.2103404998779296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-7.2863923780197472375944729124012739432330206691625337430224005433942015077316427862679405956591677094e-02), SC_(9.9734189153537192292701855468804208804195911507161872562581122221034533964836167194345541261731262046e-01), SC_(9.9987029950271100759091086168773309508042475821354228254985342328629376377136953466595469759241932790e-01) }}, + {{ SC_(1.9715252685546875000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(3.0816698074340820312500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-6.4438953143877535562212080854310540201100159071875241724085078651193139555040088765595284332588609031e-01), SC_(-7.6469741190363365029329825419758457032026733632510013400465585566734752595369338949010268046961883438e-01), SC_(9.8008476769416633442530577739220493732979907125425643755174397779481355690658870638758907227004465396e-01) }}, + {{ SC_(1.9715252685546875000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(6.3235926628112792968750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-9.9387502689389878225183349526237932217471297287328121519769701617770894461916996339991668619614720106e-01), SC_(-1.1050986796052184360390211918956482356707307302792124668112446870634519675064841811303841609817046435e-01), SC_(7.7782083010783148384110038999967915981917233380252884615756446459464833713263012454253928377642176473e-01) }}, + {{ SC_(1.9715252685546875000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(8.1472349166870117187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.0692896438948333078582609551292864727528807834406627454741719659705582459890889300047150852328383914e-01), SC_(-4.2128357854468915494007141925104755456992245674324379641374290838680438635975287956170633686988273788e-01), SC_(6.7381912240981059330307389773430099004172998609294423672920782115012163917779546323448667567467913871e-01) }}, + {{ SC_(1.9715252685546875000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(8.3500838279724121093750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-9.7776321201636010382337424408562096668543234507605495641318225337144791625772419859562530121151790673e-01), SC_(2.0971194822291466346030421849595858014680805590559492690127261632363629066019576649612096090094549878e-01), SC_(5.7742960193439094700348356947016724682361321289632632659151235741183259429995820997477679950807256189e-01) }}, + {{ SC_(1.9715252685546875000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.0579175949096679687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.5335552637509468619177212910424271793500604536736315130170091868994872898355573407901286288639274304e-01), SC_(-5.2132940220659440319333211591248886524580006933686352224178661371782672213885596221974167956318085725e-01), SC_(6.3445182831800375269300932933670770833130898600306348885566817247186267453097547880914732346671069865e-01) }}, + {{ SC_(1.9715252685546875000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.1337585449218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(3.2552432416186685026934526193128921379766826802420069334155189741447969109871574924231483351424206599e-01), SC_(9.4553366644396106872879025738016398857917167142462917144519103981246913164050418116860896385695109638e-01), SC_(9.5477600273005629053462961893870689852992588659840987337775533495567475431257098929765560217201525781e-01) }}, + {{ SC_(1.9715252685546875000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.6886777877807617187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-3.9412307228568629478091636297546153976117178431143042104414325984436672903094560979335786919432390159e-01), SC_(-9.1905767168991723490423535241594951632963991958559280799910799985557761425472976757206816773545655546e-01), SC_(9.2422301160881704148508838860716761915357124551323944774087944758929470657071593948190980722116431319e-01) }}, + {{ SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.4054705213152072851451664130651061216499217259757217431721599006205998223273563720851776196554659711e-01), SC_(-9.9007400033388392914671454535086242072251869165129442669867317682364702240378428827847175171458794744e-01), SC_(9.9984071853366842614471458726841084906264079357521344888761890568442619129819452826610841761945249390e-01) }}, + {{ SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(1.3547700643539428710937500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(2.5070640492058129942565255217740163494695763216559037381456171424195061110398681756028914124819463101e-01), SC_(-9.6806316866813889172199931228900862951312842168003652810485498962347027876607999917857526043808893858e-01), SC_(9.9942302452559713852269084116030636732630369591763149069010267256421389522467628458268739532812633610e-01) }}, + {{ SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(2.2103404998779296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7460959847396629023213294151850600468186754526453359707119955774767291431614264354511495305616871082e-01), SC_(2.2391098803411637082502445867797619686052486034294717623183478584718412642662476193997851593899862294e-01), SC_(9.7652107100176220018304071389988193041833109679443427832086050938061220329457600374867819614433504174e-01) }}, + {{ SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(3.0816698074340820312500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-8.7591137819560965793227178075846254493991687812511266984816459225474516690755277726181572540400781692e-01), SC_(4.8247202773577212421607049007306835524095045191215664111886203507494519542708812099117851390243407605e-01), SC_(9.6288079930202121551356736451843753542939778244370285463921850847493493915725115345472885123365413983e-01) }}, + {{ SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(6.3235926628112792968750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-4.6250242396649649980482066020190351615612321919279456557494609907194412689120822625415608757186732226e-01), SC_(8.8661801686245645800217768700725799498166537819118235942894900353237994345457404176820430584219016246e-01), SC_(9.5627540398922768507958728734673192109735702301637317713655951281056100713965361590625156345008848052e-01) }}, + {{ SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(8.1472349166870117187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-1.1735531008826291520919245508896005477690524195845718339880048475212741686661323687535843820697763115e-01), SC_(-9.9308999148822744363057759901009520225182513004952136286524553869898571573704761432739426689545184600e-01), SC_(9.9541866617977664359846799474228301142404409511589411389238630589212796142638172458066619231854538725e-01) }}, + {{ SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(8.3500838279724121093750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-2.5661560264047896550977697577574285271994983541443544067356972715404806414952219948705677776708497000e-01), SC_(9.6651354490325887257750254185816231220218423716636053686841904330333698328423906111679391851744157820e-01), SC_(9.7677311539491902219065627087092296908401907255979252384756489646051968319678552175412452558572875080e-01) }}, + {{ SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.0579175949096679687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-2.3043688031022365976100265167863985776533246242764453911544714145699594137367180026912374835735577553e-01), SC_(-9.7308727470504497158374043000785726585723147362213332885195842776034698222933783780401814107209214425e-01), SC_(9.7797376965032175821022437157898388837314600109117623736975241337618528076029566654878957935590182792e-01) }}, + {{ SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.1337585449218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7024515945744297738657357466434755079331657796883714801833862664891641843430559561966177382852691399e-01), SC_(2.4212461780950951071551165255952297503000013061390990430320407464582844014750946659296356182356525586e-01), SC_(4.6330574762904332411829744686422163790342838342235753322328220006082956185458756739898418452935999869e-01) }}, {{ SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.6886777877807617187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-9.6271921666412527706611162998623278828344436746037642935689292731054871089839252562699168099269047894e-01), SC_(-2.7050269844423550857864806232371501929916695397580524032916105445727409203649388936347088607548210605e-01), SC_(3.6052997174588038100329734639411992177585754440288098151836194079410246809516008674605501002506176314e-01) }} }}; //#undef SC_ diff --git a/test/jacobi_near_1.ipp b/test/jacobi_near_1.ipp index 9b1eea7a4..3784aee17 100644 --- a/test/jacobi_near_1.ipp +++ b/test/jacobi_near_1.ipp @@ -1,346 +1,353 @@ +// Copyright John Maddock 2012. + +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. +// (See accompanying file LICENSE_1_0.txt +// or copy at http://www.boost.org/LICENSE_1_0.txt) + #ifndef SC_ # define SC_(x) static_cast(BOOST_JOIN(x, L)) #endif static const boost::array, 340> jacobi_near_1 = {{ - {{ SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000004768371582031250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9936124862178929657881621645181864085183918423681860187396785862520605717123413406685399380582107113e-01), SC_(3.5736462515171262671173658796361885282655550407797367368767246967565775142270960241294075546367351927e-02), SC_(3.5723133911895480121899640922445600550831965573961005650871698226561870552026541364948342613336582806e-02) }}, - {{ SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000014305114746093750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9936077436182305740265762942505880070947367818181132794898773596144577761932318153752214737153329561e-01), SC_(3.5749722613432715628553169307272741195011102329188833383668050964850356815583084732679478209132508739e-02), SC_(3.5709736745792682671599404581373263526701044801333523535341814550620045496488948203712498732057017070e-02) }}, - {{ SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000033378601074218750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9935982531025601614500364655259025282505814635665229090640399025716517540590131557526316221367105587e-01), SC_(3.5776242897411389640336798137070232128793830106896650516594399176561812055650730083125160534386857905e-02), SC_(3.5682942269816429157188838670831408020383121223997457406594651516016868258020580067207389880661065297e-02) }}, - {{ SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), 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SC_(5.8686103182775385959094432164210470495146664187835729337215293512993909532328740626483958923893141231e-02), SC_(-3.0893124798500284820335880409303644182778189826173654652430374404846006649343381743921738919251947699e-02) }}, + {{ SC_(4.9646129608154296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0023207664489746093750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(9.9526992589997827420306117917427182178979741082729092965897483434868497193943333068777040666157481100e-01), SC_(9.7148209448510965618814190119451117927847310257093339481999337817751394945307795550093447421264799168e-02), SC_(-6.9532095588469802480589239010157975152091841708321990467488846359840797625840328044562828776517609113e-02) }}, + {{ SC_(4.9646129608154296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0060424804687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(9.7327357090730138720367359153239323902247504897821653720406237386695349159240208217001492967466592893e-01), SC_(2.2964876697546228888931649787788742930944361620108470728002449961617243383843764035729632038084809597e-01), SC_(-2.0311659859397708228829612914540972881961033272228812487026550233039579579564016302202736438925829861e-01) }}, + {{ SC_(4.9646129608154296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0155692100524902343750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(8.4069051112564740388498305703743050846741943876819566564676351892344788777074732833738047977587592836e-01), SC_(5.4151589496828042658602571182616923878595213758699386834940240440502083614232854508648303249637786229e-01), SC_(-5.2063493838617445779646407770009371209785483807741597530330738738065076402146210854614754006055477215e-01) }}, + {{ SC_(4.9646129608154296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0305857658386230468750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(4.8671357579638665629126370168770921319757407213502466576345439294626879685237098285286502834996393092e-01), SC_(8.7356161496227327149253838986791328231133879539230423927448398220130445285498224963240552394450600870e-01), SC_(-8.6509962228485538958789361261824061503929655387763193064181839580439422746694246738587153880942281811e-01) }}, {{ SC_(4.9646129608154296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0623893737792968750000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-2.2293187234404279005404405123453640992362355261738577610576210777344443465871289033909805344032394449e-01), SC_(9.7483402704931233304677248889105249284034868811789307005518001217555908178599047906139783223849231970e-01), SC_(-9.7154855780636670580019454689623684007923466283994781397066875280116362115119765459157832338091463773e-01) }} }}; //#undef SC_ diff --git a/test/owens_t_T7.hpp b/test/owens_t_T7.hpp index d2d201a30..b3ad30dd6 100644 --- a/test/owens_t_T7.hpp +++ b/test/owens_t_T7.hpp @@ -1,4 +1,4 @@ -// (C) Benjamin Sobotta 2012 +// Copyright (C) Benjamin Sobotta 2012 // Use, modification and distribution are subject to the // Boost Software License, Version 1.0. (See accompanying file @@ -145,10 +145,10 @@ namespace boost val *= exp(-half()*hs*as); val *= exp(-half()*hs); val *= one_div_two_pi() * a; - + return val; } // RealType compute_owens_t_T7(const RealType h, const RealType a) - + // compute Owen's T function, T(h,a), for arbitrary values of h and a template inline RealType owens_t_T7(RealType h, RealType a, const Policy&) @@ -170,7 +170,7 @@ namespace boost { val = compute_owens_t_T7(h, fabs_a); } // if(fabs_a <= 1.0) - else + else { if( h <= 0.67 ) { @@ -196,9 +196,9 @@ namespace boost return val; } // RealType owens_t(RealType h, RealType a) - + } // namespace detail - + template inline typename tools::promote_args::type owens_t_T7(T1 h, T2 a, const Policy& pol) { @@ -212,7 +212,7 @@ namespace boost { return owens_t_T7(h, a, policies::policy<>()); } - + } // namespace math } // namespace boost diff --git a/test/owens_t_large_data.ipp b/test/owens_t_large_data.ipp index 07ac3f258..27c4c4878 100644 --- a/test/owens_t_large_data.ipp +++ b/test/owens_t_large_data.ipp @@ -2,666 +2,667 @@ // Use, modification and distribution are subject to the // Boost Software License, Version 1.0. (See accompanying file // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + #ifndef SC_ #define SC_(x) static_cast(BOOST_JOIN(x, L)) #endif static const boost::array, 657> owens_t_large_data = {{ - {{ SC_(1.7306551853835117071866989135742187500000000000000000000000000000000000000000000000000000000000000000e-06), SC_(1.7306551853835117071866989135742187500000000000000000000000000000000000000000000000000000000000000000e-06), SC_(2.7544232754071888169814325928268239884486372691874342956812521082730648643186974640936808405777870468e-07) }}, - {{ SC_(1.7306551853835117071866989135742187500000000000000000000000000000000000000000000000000000000000000000e-06), SC_(2.1657506295014172792434692382812500000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(3.4468991818847944488358292096162674677254240401591803431829935684111943192188266678541525762196399584e-07) }}, - {{ SC_(1.7306551853835117071866989135742187500000000000000000000000000000000000000000000000000000000000000000e-06), SC_(7.2700186137808486819267272949218750000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(1.1570593987311932421290676513166688187937163430741211292434026295198499510842189554839176055050374544e-06) }}, - {{ SC_(1.7306551853835117071866989135742187500000000000000000000000000000000000000000000000000000000000000000e-06), SC_(1.4000004739500582218170166015625000000000000000000000000000000000000000000000000000000000000000000000e-05), SC_(2.2281699574525694076153268820857826830055812284202546456173259636892591278545272175070257347473957471e-06) }}, - {{ SC_(1.7306551853835117071866989135742187500000000000000000000000000000000000000000000000000000000000000000e-06), SC_(1.7196449334733188152313232421875000000000000000000000000000000000000000000000000000000000000000000000e-05), SC_(2.7368999149782398254303511225955773937565838792307860324522944171713046852204658446919929065792444550e-06) }}, - {{ SC_(1.7306551853835117071866989135742187500000000000000000000000000000000000000000000000000000000000000000e-06), SC_(6.0085076256655156612396240234375000000000000000000000000000000000000000000000000000000000000000000000e-05), SC_(9.5628368807778517977859121445879678015097215977830989982024716756760879493692438419837710322114090046e-06) }}, - {{ SC_(1.7306551853835117071866989135742187500000000000000000000000000000000000000000000000000000000000000000e-06), SC_(1.1678319424390792846679687500000000000000000000000000000000000000000000000000000000000000000000000000e-04), SC_(1.8586622549454356237914810697873043993635206365954012730510556735989900392568584658824015899162236906e-05) }}, - {{ SC_(1.7306551853835117071866989135742187500000000000000000000000000000000000000000000000000000000000000000e-06), SC_(1.4905200805515050888061523437500000000000000000000000000000000000000000000000000000000000000000000000e-04), SC_(2.3722363684038706237945294842381666580083784201001212579385105433029945599357139440208530502011634474e-05) }}, - {{ SC_(1.7306551853835117071866989135742187500000000000000000000000000000000000000000000000000000000000000000e-06), SC_(3.9852515328675508499145507812500000000000000000000000000000000000000000000000000000000000000000000000e-04), SC_(6.3427244734060608269367960782024063961865409580776331380624911803749846156793249487878248545601531213e-05) }}, - {{ SC_(1.7306551853835117071866989135742187500000000000000000000000000000000000000000000000000000000000000000e-06), SC_(6.3875340856611728668212890625000000000000000000000000000000000000000000000000000000000000000000000000e-04), SC_(1.0166074856388151418367878313779849987420034318618585018302377265757651137097414111936620111406427125e-04) }}, - {{ SC_(1.7306551853835117071866989135742187500000000000000000000000000000000000000000000000000000000000000000e-06), SC_(1.0718167759478092193603515625000000000000000000000000000000000000000000000000000000000000000000000000e-03), SC_(1.7058487265854326602682518279285919877142362926912968296718492493077609349871988400610440167118741999e-04) }}, - {{ SC_(1.7306551853835117071866989135742187500000000000000000000000000000000000000000000000000000000000000000e-06), SC_(3.0219145119190216064453125000000000000000000000000000000000000000000000000000000000000000000000000000e-03), SC_(4.8095116816577310187698736588393620680459824561821356129805868982439168323299871013712685313280875065e-04) }}, - {{ SC_(1.7306551853835117071866989135742187500000000000000000000000000000000000000000000000000000000000000000e-06), SC_(4.9941334873437881469726562500000000000000000000000000000000000000000000000000000000000000000000000000e-03), SC_(7.9483442292800033761621353006620921283539059944892037051546280947997409804311231554324236901282463379e-04) }}, - {{ SC_(1.7306551853835117071866989135742187500000000000000000000000000000000000000000000000000000000000000000e-06), SC_(9.2842318117618560791015625000000000000000000000000000000000000000000000000000000000000000000000000000e-03), SC_(1.4775889320683304881597520708559050400479343071447923717275214173990753020524212319899235756498695064e-03) }}, - {{ SC_(1.7306551853835117071866989135742187500000000000000000000000000000000000000000000000000000000000000000e-06), SC_(2.4170018732547760009765625000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(3.8460291355353431423529489109702508499010549722887836494454489720400429148478458034710749752701465677e-03) }}, - {{ SC_(1.7306551853835117071866989135742187500000000000000000000000000000000000000000000000000000000000000000e-06), SC_(6.2277540564537048339843750000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.8989939107544875264882926761541078102873613724757945283132599714888310624832442855939190526870888106e-03) }}, - {{ SC_(1.7306551853835117071866989135742187500000000000000000000000000000000000000000000000000000000000000000e-06), SC_(1.2234416604042053222656250000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.9375390752352412863732016249824209087483013904103071613680871378667263275228741402793087929136772709e-02) }}, - {{ SC_(1.7306551853835117071866989135742187500000000000000000000000000000000000000000000000000000000000000000e-06), SC_(2.4955767393112182617187500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(3.8923300996768761237101143353675181372107282287973902962217761551716451429685664617055964579169309354e-02) }}, - {{ SC_(1.7306551853835117071866989135742187500000000000000000000000000000000000000000000000000000000000000000e-06), SC_(4.9122214317321777343750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.2670257957136651636798532116450898262892417529230686056739100208577508554316612972269210305616970946e-02) }}, - {{ SC_(1.7306551853835117071866989135742187500000000000000000000000000000000000000000000000000000000000000000e-06), SC_(9.8384737968444824218750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.2370417826092910200386273146083632151611832692409321149229531049480606468601722775882411690476638119e-01) }}, - {{ SC_(2.1657506295014172792434692382812500000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(1.7306551853835117071866989135742187500000000000000000000000000000000000000000000000000000000000000000e-06), SC_(2.7544232754048540184979886423303512409939672743833798663433829739102689479214640901302773560786450597e-07) }}, - {{ SC_(2.1657506295014172792434692382812500000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(2.1657506295014172792434692382812500000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(3.4468991818818726702354564531690723357532551557300734742264029632431947434763801755115481126836150164e-07) }}, - {{ SC_(2.1657506295014172792434692382812500000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(7.2700186137808486819267272949218750000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(1.1570593987302124558593692546020629805959765227389520550879373735687364514529604494412561248689031244e-06) }}, - {{ SC_(2.1657506295014172792434692382812500000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(1.4000004739500582218170166015625000000000000000000000000000000000000000000000000000000000000000000000e-05), SC_(2.2281699574506806899718553071679341970529778880781898560131185186504643782830396693831168591175317233e-06) }}, - {{ SC_(2.1657506295014172792434692382812500000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(1.7196449334733188152313232421875000000000000000000000000000000000000000000000000000000000000000000000e-05), SC_(2.7368999149759198806969085379899977063455512108168391599269041505755685202919317411782479480658359390e-06) }}, - {{ SC_(2.1657506295014172792434692382812500000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(6.0085076256655156612396240234375000000000000000000000000000000000000000000000000000000000000000000000e-05), SC_(9.5628368807697458188418415959815698326243194118159875339484284948616094231925906127588538838433407846e-06) }}, - {{ 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SC_(6.3427244734006843895541987411824601508866273939725635132871459415441302569003612239640240135652238511e-05) }}, - {{ SC_(2.1657506295014172792434692382812500000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(6.3875340856611728668212890625000000000000000000000000000000000000000000000000000000000000000000000000e-04), SC_(1.0166074856379534101052388108080041159566288098802777073456413189509642688626957361938611868090525234e-04) }}, - {{ SC_(2.1657506295014172792434692382812500000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(1.0718167759478092193603515625000000000000000000000000000000000000000000000000000000000000000000000000e-03), SC_(1.7058487265839866898611206218003624386577188607420424467256510051225964682626675059165902904726536266e-04) }}, - {{ SC_(2.1657506295014172792434692382812500000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(3.0219145119190216064453125000000000000000000000000000000000000000000000000000000000000000000000000000e-03), SC_(4.8095116816536542035387897782551349754503722699222550802682229939411184087904507617088832412137594247e-04) }}, - {{ SC_(2.1657506295014172792434692382812500000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(4.9941334873437881469726562500000000000000000000000000000000000000000000000000000000000000000000000000e-03), SC_(7.9483442292732658727063079559057199747577619995930466481453551807299540252428863673307976975997241977e-04) }}, - {{ SC_(2.1657506295014172792434692382812500000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(9.2842318117618560791015625000000000000000000000000000000000000000000000000000000000000000000000000000e-03), SC_(1.4775889320670779676959925554881559875838142182748325192066640457568157543761698088553286307933916194e-03) }}, - {{ SC_(2.1657506295014172792434692382812500000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(2.4170018732547760009765625000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(3.8460291355320824048265964820002189626866633910862265609732098857609729932960566516839012681872216101e-03) }}, - {{ SC_(2.1657506295014172792434692382812500000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(6.2277540564537048339843750000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.8989939107460857657857135478909664526215873923996728419537423322775481650208621214536117255227072021e-03) }}, - {{ SC_(2.1657506295014172792434692382812500000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(1.2234416604042053222656250000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.9375390752335907613249893988001654834371634310017323014293971978142943221787504294985709749768735994e-02) }}, - {{ SC_(2.1657506295014172792434692382812500000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(2.4955767393112182617187500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(3.8923300996735093821226094771034107315488077427230676960904037558371557927002597098083501223910964697e-02) }}, - {{ SC_(2.1657506295014172792434692382812500000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(4.9122214317321777343750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.2670257957070381664327927833317792293914559191891429927005082327551091953751101182443853636138564427e-02) }}, - {{ SC_(2.1657506295014172792434692382812500000000000000000000000000000000000000000000000000000000000000000000e-06), 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BOOST_MATH_TEST_TABLE_TYPE_HPP #define BOOST_MATH_TEST_TABLE_TYPE_HPP diff --git a/test/test_constants.cpp b/test/test_constants.cpp index 47cbe3550..76ac714c0 100644 --- a/test/test_constants.cpp +++ b/test/test_constants.cpp @@ -24,7 +24,7 @@ #include #include -#include +#include #include #include @@ -91,7 +91,7 @@ void test_spots(RealType) // it can never really have precision greater than a long double. typedef typename boost::math::constants::construction_traits >::type construction_type; - RealType tolerance = std::max(static_cast(boost::math::tools::epsilon()), boost::math::tools::epsilon()) * 2; // double + RealType tolerance = (std::max)(static_cast(boost::math::tools::epsilon()), boost::math::tools::epsilon()) * 2; // double if((construction_type::value == 0) && (boost::math::tools::digits() > boost::math::constants::max_string_digits)) tolerance *= 30; // Allow a little extra tolerance // for calculated (perhaps using a series representation) constants. @@ -104,61 +104,63 @@ void test_spots(RealType) using namespace boost::math::constants; BOOST_MATH_STD_USING - BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L, pi(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L), root_pi(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L/2), root_half_pi(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L * 2), root_two_pi(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(sqrt(log(4.0L)), root_ln_four(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(2.71828182845904523536028747135266249775724709369995L, e(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(0.5L, half(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(0.57721566490153286060651209008240243104259335L, euler(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(sqrt(2.0L), root_two(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(log(2.0L), ln_two(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(log(log(2.0L)), ln_ln_two(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(1)/3, third(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(2)/3, twothirds(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(0.14159265358979323846264338327950288419716939937510L, pi_minus_three(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(4.L - 3.14159265358979323846264338327950288419716939937510L, four_minus_pi(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L, pi(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L), root_pi(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L/2), root_half_pi(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L * 2), root_two_pi(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(sqrt(log(4.0L)), root_ln_four(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(2.71828182845904523536028747135266249775724709369995L, e(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(0.5L, half(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(0.57721566490153286060651209008240243104259335L, euler(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(sqrt(2.0L), root_two(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(log(2.0L), ln_two(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(log(10.0L), ln_ten(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(log(log(2.0L)), ln_ln_two(), tolerance); + + BOOST_CHECK_CLOSE_FRACTION(static_cast(1)/3, third(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(2)/3, twothirds(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(0.14159265358979323846264338327950288419716939937510L, pi_minus_three(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(4.L - 3.14159265358979323846264338327950288419716939937510L, four_minus_pi(), tolerance); #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS - BOOST_CHECK_CLOSE_FRACTION(pow((4 - 3.14159265358979323846264338327950288419716939937510L), 1.5L), pow23_four_minus_pi(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510L), 2.71828182845904523536028747135266249775724709369995L), pi_pow_e(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510L), 0.33333333333333333333333333333333333333333333333333L), cbrt_pi(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(exp(-0.5L), exp_minus_half(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(pow(2.71828182845904523536028747135266249775724709369995L, 3.14159265358979323846264338327950288419716939937510L), e_pow_pi(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(pow((4 - 3.14159265358979323846264338327950288419716939937510L), 1.5L), pow23_four_minus_pi(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510L), 2.71828182845904523536028747135266249775724709369995L), pi_pow_e(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510L), 0.33333333333333333333333333333333333333333333333333L), cbrt_pi(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(exp(-0.5L), exp_minus_half(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(pow(2.71828182845904523536028747135266249775724709369995L, 3.14159265358979323846264338327950288419716939937510L), e_pow_pi(), tolerance); #else // Only double, so no suffix L. - BOOST_CHECK_CLOSE_FRACTION(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5), pow23_four_minus_pi(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995), pi_pow_e(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333), cbrt_pi(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(exp(-0.5), exp_minus_half(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5), pow23_four_minus_pi(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995), pi_pow_e(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333), cbrt_pi(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(exp(-0.5), exp_minus_half(), tolerance); #endif // Rational fractions. - BOOST_CHECK_CLOSE_FRACTION(0.333333333333333333333333333333333333333L, third(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(0.666666666666666666666666666666666666667L, two_thirds(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(0.75L, three_quarters(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(0.333333333333333333333333333333333333333L, third(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(0.666666666666666666666666666666666666667L, two_thirds(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(0.75L, three_quarters(), tolerance); // Two and related. - BOOST_CHECK_CLOSE_FRACTION(sqrt(2.L), root_two(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(sqrt(3.L), root_three(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(sqrt(2.L)/2, half_root_two(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(log(2.L), ln_two(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(log(log(2.0L)), ln_ln_two(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(sqrt(log(4.0L)), root_ln_four(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(1/sqrt(2.0L), one_div_root_two(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(sqrt(2.L), root_two(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(sqrt(3.L), root_three(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(sqrt(2.L)/2, half_root_two(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(log(2.L), ln_two(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(log(log(2.0L)), ln_ln_two(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(sqrt(log(4.0L)), root_ln_four(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(1/sqrt(2.0L), one_div_root_two(), tolerance); // pi. - BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L, pi(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L/2, half_pi(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L/3, third_pi(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L/6, sixth_pi(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(2 * 3.14159265358979323846264338327950288419716939937510L, two_pi(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(3 * 3.14159265358979323846264338327950288419716939937510L / 4, three_quarters_pi(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(4 * 3.14159265358979323846264338327950288419716939937510L / 3, four_thirds_pi(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(1 / (2 * 3.14159265358979323846264338327950288419716939937510L), one_div_two_pi(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L), root_pi(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L / 2), root_half_pi(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(sqrt(2 * 3.14159265358979323846264338327950288419716939937510L), root_two_pi(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(1 / sqrt(3.14159265358979323846264338327950288419716939937510L), one_div_root_pi(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L, pi(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L/2, half_pi(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L/3, third_pi(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L/6, sixth_pi(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(2 * 3.14159265358979323846264338327950288419716939937510L, two_pi(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(3 * 3.14159265358979323846264338327950288419716939937510L / 4, three_quarters_pi(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(4 * 3.14159265358979323846264338327950288419716939937510L / 3, four_thirds_pi(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(1 / (2 * 3.14159265358979323846264338327950288419716939937510L), one_div_two_pi(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L), root_pi(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L / 2), root_half_pi(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(sqrt(2 * 3.14159265358979323846264338327950288419716939937510L), root_two_pi(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(1 / sqrt(3.14159265358979323846264338327950288419716939937510L), one_div_root_pi(), tolerance); BOOST_CHECK_CLOSE_FRACTION(1 / sqrt(2 * 3.14159265358979323846264338327950288419716939937510L), one_div_root_two_pi(), tolerance); BOOST_CHECK_CLOSE_FRACTION(sqrt(1. / 3.14159265358979323846264338327950288419716939937510L), root_one_div_pi(), tolerance); BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L - 3.L, pi_minus_three(), tolerance * 2 ); // tolerance * 2 because of cancellation loss. @@ -171,11 +173,11 @@ void test_spots(RealType) BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L, pi_cubed(), tolerance); // See above. // BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L, cbrt_pi(), tolerance); // See above. - BOOST_CHECK_CLOSE_FRACTION(cbrt_pi() * cbrt_pi() * cbrt_pi(), pi(), tolerance); - BOOST_CHECK_CLOSE_FRACTION((1)/cbrt_pi(), one_div_cbrt_pi(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(cbrt_pi() * cbrt_pi() * cbrt_pi(), pi(), tolerance); + BOOST_CHECK_CLOSE_FRACTION((1)/cbrt_pi(), one_div_cbrt_pi(), tolerance); // Euler - BOOST_CHECK_CLOSE_FRACTION(2.71828182845904523536028747135266249775724709369995L, e(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(2.71828182845904523536028747135266249775724709369995L, e(), tolerance); //BOOST_CHECK_CLOSE_FRACTION(exp(-0.5L), exp_minus_half(), tolerance); // See above. BOOST_CHECK_CLOSE_FRACTION(pow(e(), pi()), e_pow_pi(), tolerance); // See also above. @@ -207,7 +209,7 @@ void test_spots(RealType) BOOST_CHECK_CLOSE_FRACTION(.91596559417721901505460351493238411077414937428167213L, catalan(), tolerance); // A006752 as a constant in OEIS. BOOST_CHECK_CLOSE_FRACTION(1.1395470994046486574927930193898461120875997958365518247216557100852480077060706857071875468869385150L, extreme_value_skewness(), tolerance); // Mathematica: N[12 Sqrt[6] Zeta[3]/Pi^3, 1101] BOOST_CHECK_CLOSE_FRACTION(0.6311106578189371381918993515442277798440422031347194976580945856929268196174737254599050270325373067L, rayleigh_skewness(), tolerance); // Mathematica: N[2 Sqrt[Pi] (Pi - 3)/((4 - Pi)^(3/2)), 1100] - BOOST_CHECK_CLOSE_FRACTION(2.450893006876380628486604106197544154e-01L, rayleigh_kurtosis_excess(), tolerance * 2); + BOOST_CHECK_CLOSE_FRACTION(2.450893006876380628486604106197544154e-01L, rayleigh_kurtosis_excess(), tolerance * 2); BOOST_CHECK_CLOSE_FRACTION(2.68545200106530644530971483548179569382038229399446295305115234555721885953715200280114117493184769799515L, khinchin(), tolerance ); // A002210 as a constant https://oeis.org/A002210/constant BOOST_CHECK_CLOSE_FRACTION(1.2824271291006226368753425688697917277676889273250011L, glaisher(), tolerance ); // https://oeis.org/A074962/constant @@ -217,20 +219,20 @@ void test_spots(RealType) if(boost::math::tools::digits() > boost::math::constants::max_string_digits) { // This suffers from cancellation error, so increased tolerance: - BOOST_CHECK_CLOSE_FRACTION(static_cast(4. - 3.14159265358979323846264338327950288419716939937510L), four_minus_pi(), tolerance * 3); - BOOST_CHECK_CLOSE_FRACTION(static_cast(0.14159265358979323846264338327950288419716939937510L), pi_minus_three(), tolerance * 3); + BOOST_CHECK_CLOSE_FRACTION(static_cast(4. - 3.14159265358979323846264338327950288419716939937510L), four_minus_pi(), tolerance * 3); + BOOST_CHECK_CLOSE_FRACTION(static_cast(0.14159265358979323846264338327950288419716939937510L), pi_minus_three(), tolerance * 3); } else { - BOOST_CHECK_CLOSE_FRACTION(static_cast(4. - 3.14159265358979323846264338327950288419716939937510L), four_minus_pi(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(0.14159265358979323846264338327950288419716939937510L), pi_minus_three(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(4. - 3.14159265358979323846264338327950288419716939937510L), four_minus_pi(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(0.14159265358979323846264338327950288419716939937510L), pi_minus_three(), tolerance); } } // template void test_spots(RealType) void test_float_spots() { - // Basic sanity checks for constants in boost::math::float_constants:: - // for example: boost::math::float_constants::pi + // Basic sanity checks for constants in boost::math::float_constants:: + // for example: boost::math::float_constants::pi // (rather than boost::math::constants::pi() ). float tolerance = boost::math::tools::epsilon() * 2; @@ -238,61 +240,61 @@ void test_float_spots() using namespace boost::math::float_constants; BOOST_MATH_STD_USING - BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510F), pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.14159265358979323846264338327950288419716939937510F)), root_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.14159265358979323846264338327950288419716939937510F/2)), root_half_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.14159265358979323846264338327950288419716939937510F * 2)), root_two_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(log(4.0F))), root_ln_four, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(2.71828182845904523536028747135266249775724709369995F), e, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(0.5), half, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(0.57721566490153286060651209008240243104259335F), euler, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(2.0F)), root_two, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(log(2.0F)), ln_two, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(log(log(2.0F))), ln_ln_two, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(1)/3, third, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(2)/3, twothirds, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(0.14159265358979323846264338327950288419716939937510F), pi_minus_three, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(4.F - 3.14159265358979323846264338327950288419716939937510F), four_minus_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510F), pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.14159265358979323846264338327950288419716939937510F)), root_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.14159265358979323846264338327950288419716939937510F/2)), root_half_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.14159265358979323846264338327950288419716939937510F * 2)), root_two_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(log(4.0F))), root_ln_four, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(2.71828182845904523536028747135266249775724709369995F), e, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(0.5), half, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(0.57721566490153286060651209008240243104259335F), euler, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(2.0F)), root_two, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(log(2.0F)), ln_two, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(log(log(2.0F))), ln_ln_two, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(1)/3, third, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(2)/3, twothirds, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(0.14159265358979323846264338327950288419716939937510F), pi_minus_three, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(4.F - 3.14159265358979323846264338327950288419716939937510F), four_minus_pi, tolerance); #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS - BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((4 - 3.14159265358979323846264338327950288419716939937510F), 1.5F)), pow23_four_minus_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((3.14159265358979323846264338327950288419716939937510F), 2.71828182845904523536028747135266249775724709369995F)), pi_pow_e, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((3.14159265358979323846264338327950288419716939937510F), 0.33333333333333333333333333333333333333333333333333F)), cbrt_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(exp(-0.5F)), exp_minus_half, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(pow(2.71828182845904523536028747135266249775724709369995F, 3.14159265358979323846264338327950288419716939937510F)), e_pow_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((4 - 3.14159265358979323846264338327950288419716939937510F), 1.5F)), pow23_four_minus_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((3.14159265358979323846264338327950288419716939937510F), 2.71828182845904523536028747135266249775724709369995F)), pi_pow_e, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((3.14159265358979323846264338327950288419716939937510F), 0.33333333333333333333333333333333333333333333333333F)), cbrt_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(exp(-0.5F)), exp_minus_half, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(pow(2.71828182845904523536028747135266249775724709369995F, 3.14159265358979323846264338327950288419716939937510F)), e_pow_pi, tolerance); #else // Only double, so no suffix F. - BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5)), pow23_four_minus_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995)), pi_pow_e, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333)), cbrt_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(exp(-0.5)), exp_minus_half, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5)), pow23_four_minus_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995)), pi_pow_e, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333)), cbrt_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(exp(-0.5)), exp_minus_half, tolerance); #endif // Rational fractions. - BOOST_CHECK_CLOSE_FRACTION(static_cast(0.333333333333333333333333333333333333333F), third, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(0.666666666666666666666666666666666666667F), two_thirds, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(0.75F), three_quarters, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(0.333333333333333333333333333333333333333F), third, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(0.666666666666666666666666666666666666667F), two_thirds, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(0.75F), three_quarters, tolerance); // Two and related. - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(2.F)), root_two, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.F)), root_three, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(2.F)/2), half_root_two, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(log(2.F)), ln_two, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(log(log(2.0F))), ln_ln_two, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(log(4.0F))), root_ln_four, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(1/sqrt(2.0F)), one_div_root_two, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(2.F)), root_two, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.F)), root_three, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(2.F)/2), half_root_two, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(log(2.F)), ln_two, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(log(log(2.0F))), ln_ln_two, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(log(4.0F))), root_ln_four, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(1/sqrt(2.0F)), one_div_root_two, tolerance); // pi. - BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510F), pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510F/2), half_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510F/3), third_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510F/6), sixth_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(2 * 3.14159265358979323846264338327950288419716939937510F), two_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(3 * 3.14159265358979323846264338327950288419716939937510F / 4), three_quarters_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(4 * 3.14159265358979323846264338327950288419716939937510F / 3), four_thirds_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(1 / (2 * 3.14159265358979323846264338327950288419716939937510F)), one_div_two_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.14159265358979323846264338327950288419716939937510F)), root_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.14159265358979323846264338327950288419716939937510F / 2)), root_half_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(2 * 3.14159265358979323846264338327950288419716939937510F)), root_two_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(1 / sqrt(3.14159265358979323846264338327950288419716939937510F)), one_div_root_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510F), pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510F/2), half_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510F/3), third_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510F/6), sixth_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(2 * 3.14159265358979323846264338327950288419716939937510F), two_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(3 * 3.14159265358979323846264338327950288419716939937510F / 4), three_quarters_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(4 * 3.14159265358979323846264338327950288419716939937510F / 3), four_thirds_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(1 / (2 * 3.14159265358979323846264338327950288419716939937510F)), one_div_two_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.14159265358979323846264338327950288419716939937510F)), root_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.14159265358979323846264338327950288419716939937510F / 2)), root_half_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(2 * 3.14159265358979323846264338327950288419716939937510F)), root_two_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(1 / sqrt(3.14159265358979323846264338327950288419716939937510F)), one_div_root_pi, tolerance); BOOST_CHECK_CLOSE_FRACTION(static_cast(1 / sqrt(2 * 3.14159265358979323846264338327950288419716939937510F)), one_div_root_two_pi, tolerance); BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(1. / 3.14159265358979323846264338327950288419716939937510F)), root_one_div_pi, tolerance); BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510L - 3.L), pi_minus_three, tolerance * 2 ); // tolerance * 2 because of cancellation loss. @@ -305,11 +307,11 @@ void test_float_spots() BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510F * 3.14159265358979323846264338327950288419716939937510F * 3.14159265358979323846264338327950288419716939937510F), pi_cubed, tolerance); // See above. // BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510F * 3.14159265358979323846264338327950288419716939937510F), cbrt_pi, tolerance); // See above. - BOOST_CHECK_CLOSE_FRACTION(cbrt_pi * cbrt_pi * cbrt_pi, pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION((static_cast(1)/cbrt_pi), one_div_cbrt_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(cbrt_pi * cbrt_pi * cbrt_pi, pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION((static_cast(1)/cbrt_pi), one_div_cbrt_pi, tolerance); // Euler - BOOST_CHECK_CLOSE_FRACTION(static_cast(2.71828182845904523536028747135266249775724709369995F), e, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(2.71828182845904523536028747135266249775724709369995F), e, tolerance); //BOOST_CHECK_CLOSE_FRACTION(static_cast(exp(-0.5F)), exp_minus_half, tolerance); // See above. BOOST_CHECK_CLOSE_FRACTION(pow(e, pi), e_pow_pi, tolerance); // See also above. @@ -341,7 +343,7 @@ void test_float_spots() BOOST_CHECK_CLOSE_FRACTION(.91596559417721901505460351493238411077414937428167213F, catalan, tolerance); // A006752 as a constant in OEIS. BOOST_CHECK_CLOSE_FRACTION(1.1395470994046486574927930193898461120875997958365518247216557100852480077060706857071875468869385150F, extreme_value_skewness, tolerance); // Mathematica: N[12 Sqrt[6] Zeta[3]/Pi^3, 1101] BOOST_CHECK_CLOSE_FRACTION(0.6311106578189371381918993515442277798440422031347194976580945856929268196174737254599050270325373067F, rayleigh_skewness, tolerance); // Mathematica: N[2 Sqrt[Pi] (Pi - 3)/((4 - Pi)^(3/2)), 1100] - BOOST_CHECK_CLOSE_FRACTION(2.450893006876380628486604106197544154e-01F, rayleigh_kurtosis_excess, tolerance); + BOOST_CHECK_CLOSE_FRACTION(2.450893006876380628486604106197544154e-01F, rayleigh_kurtosis_excess, tolerance); BOOST_CHECK_CLOSE_FRACTION(2.68545200106530644530971483548179569382038229399446295305115234555721885953715200280114117493184769799515F, khinchin, tolerance ); // A002210 as a constant https://oeis.org/A002210/constant BOOST_CHECK_CLOSE_FRACTION(1.2824271291006226368753425688697917277676889273250011F, glaisher, tolerance ); // https://oeis.org/A074962/constant @@ -350,7 +352,7 @@ void test_float_spots() void test_double_spots() { // Basic sanity checks for constants in boost::math::double_constants:: - // for example: boost::math::double_constants::pi + // for example: boost::math::double_constants::pi // (rather than boost::math::constants::pi() ). double tolerance = boost::math::tools::epsilon() * 2; @@ -358,61 +360,61 @@ void test_double_spots() using namespace boost::math::double_constants; BOOST_MATH_STD_USING - BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510), pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.14159265358979323846264338327950288419716939937510)), root_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.14159265358979323846264338327950288419716939937510/2)), root_half_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.14159265358979323846264338327950288419716939937510 * 2)), root_two_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(log(4.0))), root_ln_four, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(2.71828182845904523536028747135266249775724709369995), e, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(0.5), half, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(0.57721566490153286060651209008240243104259335), euler, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(2.0)), root_two, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(log(2.0)), ln_two, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(log(log(2.0))), ln_ln_two, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(1)/3, third, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(2)/3, twothirds, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(0.14159265358979323846264338327950288419716939937510), pi_minus_three, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(4. - 3.14159265358979323846264338327950288419716939937510), four_minus_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510), pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.14159265358979323846264338327950288419716939937510)), root_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.14159265358979323846264338327950288419716939937510/2)), root_half_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.14159265358979323846264338327950288419716939937510 * 2)), root_two_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(log(4.0))), root_ln_four, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(2.71828182845904523536028747135266249775724709369995), e, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(0.5), half, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(0.57721566490153286060651209008240243104259335), euler, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(2.0)), root_two, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(log(2.0)), ln_two, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(log(log(2.0))), ln_ln_two, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(1)/3, third, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(2)/3, twothirds, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(0.14159265358979323846264338327950288419716939937510), pi_minus_three, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(4. - 3.14159265358979323846264338327950288419716939937510), four_minus_pi, tolerance); #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS - BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5)), pow23_four_minus_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995)), pi_pow_e, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333)), cbrt_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(exp(-0.5)), exp_minus_half, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(pow(2.71828182845904523536028747135266249775724709369995, 3.14159265358979323846264338327950288419716939937510)), e_pow_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5)), pow23_four_minus_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995)), pi_pow_e, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333)), cbrt_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(exp(-0.5)), exp_minus_half, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(pow(2.71828182845904523536028747135266249775724709369995, 3.14159265358979323846264338327950288419716939937510)), e_pow_pi, tolerance); #else // Only double, so no suffix . - BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5)), pow23_four_minus_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995)), pi_pow_e, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333)), cbrt_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(exp(-0.5)), exp_minus_half, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5)), pow23_four_minus_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995)), pi_pow_e, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333)), cbrt_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(exp(-0.5)), exp_minus_half, tolerance); #endif // Rational fractions. - BOOST_CHECK_CLOSE_FRACTION(static_cast(0.333333333333333333333333333333333333333), third, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(0.666666666666666666666666666666666666667), two_thirds, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(0.75), three_quarters, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(0.333333333333333333333333333333333333333), third, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(0.666666666666666666666666666666666666667), two_thirds, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(0.75), three_quarters, tolerance); // Two and related. - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(2.)), root_two, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.)), root_three, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(2.)/2), half_root_two, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(log(2.)), ln_two, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(log(log(2.0))), ln_ln_two, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(log(4.0))), root_ln_four, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(1/sqrt(2.0)), one_div_root_two, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(2.)), root_two, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.)), root_three, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(2.)/2), half_root_two, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(log(2.)), ln_two, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(log(log(2.0))), ln_ln_two, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(log(4.0))), root_ln_four, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(1/sqrt(2.0)), one_div_root_two, tolerance); // pi. - BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510), pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510/2), half_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510/3), third_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510/6), sixth_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(2 * 3.14159265358979323846264338327950288419716939937510), two_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(3 * 3.14159265358979323846264338327950288419716939937510 / 4), three_quarters_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(4 * 3.14159265358979323846264338327950288419716939937510 / 3), four_thirds_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(1 / (2 * 3.14159265358979323846264338327950288419716939937510)), one_div_two_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.14159265358979323846264338327950288419716939937510)), root_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.14159265358979323846264338327950288419716939937510 / 2)), root_half_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(2 * 3.14159265358979323846264338327950288419716939937510)), root_two_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(1 / sqrt(3.14159265358979323846264338327950288419716939937510)), one_div_root_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510), pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510/2), half_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510/3), third_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510/6), sixth_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(2 * 3.14159265358979323846264338327950288419716939937510), two_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(3 * 3.14159265358979323846264338327950288419716939937510 / 4), three_quarters_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(4 * 3.14159265358979323846264338327950288419716939937510 / 3), four_thirds_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(1 / (2 * 3.14159265358979323846264338327950288419716939937510)), one_div_two_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.14159265358979323846264338327950288419716939937510)), root_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.14159265358979323846264338327950288419716939937510 / 2)), root_half_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(2 * 3.14159265358979323846264338327950288419716939937510)), root_two_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(1 / sqrt(3.14159265358979323846264338327950288419716939937510)), one_div_root_pi, tolerance); BOOST_CHECK_CLOSE_FRACTION(static_cast(1 / sqrt(2 * 3.14159265358979323846264338327950288419716939937510)), one_div_root_two_pi, tolerance); BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(1. / 3.14159265358979323846264338327950288419716939937510)), root_one_div_pi, tolerance); BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510 - 3.), pi_minus_three, tolerance * 2 ); // tolerance * 2 because of cancellation loss. @@ -425,11 +427,11 @@ void test_double_spots() BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510 * 3.14159265358979323846264338327950288419716939937510 * 3.14159265358979323846264338327950288419716939937510), pi_cubed, tolerance); // See above. // BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510 * 3.14159265358979323846264338327950288419716939937510), cbrt_pi, tolerance); // See above. - BOOST_CHECK_CLOSE_FRACTION(cbrt_pi * cbrt_pi * cbrt_pi, pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION((static_cast(1)/cbrt_pi), one_div_cbrt_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(cbrt_pi * cbrt_pi * cbrt_pi, pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION((static_cast(1)/cbrt_pi), one_div_cbrt_pi, tolerance); // Euler - BOOST_CHECK_CLOSE_FRACTION(static_cast(2.71828182845904523536028747135266249775724709369995), e, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(2.71828182845904523536028747135266249775724709369995), e, tolerance); //BOOST_CHECK_CLOSE_FRACTION(static_cast(exp(-0.5)), exp_minus_half, tolerance); // See above. BOOST_CHECK_CLOSE_FRACTION(pow(e, pi), e_pow_pi, tolerance); // See also above. @@ -461,7 +463,7 @@ void test_double_spots() BOOST_CHECK_CLOSE_FRACTION(.91596559417721901505460351493238411077414937428167213, catalan, tolerance); // A006752 as a constant in OEIS. BOOST_CHECK_CLOSE_FRACTION(1.1395470994046486574927930193898461120875997958365518247216557100852480077060706857071875468869385150, extreme_value_skewness, tolerance); // Mathematica: N[12 Sqrt[6] Zeta[3]/Pi^3, 1101] BOOST_CHECK_CLOSE_FRACTION(0.6311106578189371381918993515442277798440422031347194976580945856929268196174737254599050270325373067, rayleigh_skewness, tolerance); // Mathematica: N[2 Sqrt[Pi] (Pi - 3)/((4 - Pi)^(3/2)), 1100] - BOOST_CHECK_CLOSE_FRACTION(2.450893006876380628486604106197544154e-01, rayleigh_kurtosis_excess, tolerance); + BOOST_CHECK_CLOSE_FRACTION(2.450893006876380628486604106197544154e-01, rayleigh_kurtosis_excess, tolerance); BOOST_CHECK_CLOSE_FRACTION(2.68545200106530644530971483548179569382038229399446295305115234555721885953715200280114117493184769799515, khinchin, tolerance ); // A002210 as a constant https://oeis.org/A002210/constant BOOST_CHECK_CLOSE_FRACTION(1.2824271291006226368753425688697917277676889273250011, glaisher, tolerance ); // https://oeis.org/A074962/constant @@ -470,7 +472,7 @@ void test_double_spots() void test_long_double_spots() { // Basic sanity checks for constants in boost::math::long double_constants:: - // for example: boost::math::long_double_constants::pi + // for example: boost::math::long_double_constants::pi // (rather than boost::math::constants::pi() ). // All constants are tested here using at least long double precision @@ -482,61 +484,61 @@ void test_long_double_spots() using namespace boost::math::long_double_constants; BOOST_MATH_STD_USING - BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510L), pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.14159265358979323846264338327950288419716939937510L)), root_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.14159265358979323846264338327950288419716939937510L/2)), root_half_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.14159265358979323846264338327950288419716939937510L * 2)), root_two_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(log(4.0L))), root_ln_four, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(2.71828182845904523536028747135266249775724709369995L), e, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(0.5), half, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(0.57721566490153286060651209008240243104259335L), euler, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(2.0L)), root_two, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(log(2.0L)), ln_two, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(log(log(2.0L))), ln_ln_two, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(1)/3, third, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(2)/3, twothirds, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(0.14159265358979323846264338327950288419716939937510L), pi_minus_three, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(4.L - 3.14159265358979323846264338327950288419716939937510L), four_minus_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510L), pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.14159265358979323846264338327950288419716939937510L)), root_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.14159265358979323846264338327950288419716939937510L/2)), root_half_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.14159265358979323846264338327950288419716939937510L * 2)), root_two_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(log(4.0L))), root_ln_four, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(2.71828182845904523536028747135266249775724709369995L), e, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(0.5), half, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(0.57721566490153286060651209008240243104259335L), euler, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(2.0L)), root_two, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(log(2.0L)), ln_two, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(log(log(2.0L))), ln_ln_two, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(1)/3, third, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(2)/3, twothirds, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(0.14159265358979323846264338327950288419716939937510L), pi_minus_three, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(4.L - 3.14159265358979323846264338327950288419716939937510L), four_minus_pi, tolerance); #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS - BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((4 - 3.14159265358979323846264338327950288419716939937510L), 1.5L)), pow23_four_minus_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((3.14159265358979323846264338327950288419716939937510L), 2.71828182845904523536028747135266249775724709369995L)), pi_pow_e, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((3.14159265358979323846264338327950288419716939937510L), 0.33333333333333333333333333333333333333333333333333L)), cbrt_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(exp(-0.5L)), exp_minus_half, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(pow(2.71828182845904523536028747135266249775724709369995L, 3.14159265358979323846264338327950288419716939937510L)), e_pow_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((4 - 3.14159265358979323846264338327950288419716939937510L), 1.5L)), pow23_four_minus_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((3.14159265358979323846264338327950288419716939937510L), 2.71828182845904523536028747135266249775724709369995L)), pi_pow_e, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((3.14159265358979323846264338327950288419716939937510L), 0.33333333333333333333333333333333333333333333333333L)), cbrt_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(exp(-0.5L)), exp_minus_half, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(pow(2.71828182845904523536028747135266249775724709369995L, 3.14159265358979323846264338327950288419716939937510L)), e_pow_pi, tolerance); #else // Only double, so no suffix L. - BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5)), pow23_four_minus_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995)), pi_pow_e, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333)), cbrt_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(exp(-0.5)), exp_minus_half, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5)), pow23_four_minus_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995)), pi_pow_e, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333)), cbrt_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(exp(-0.5)), exp_minus_half, tolerance); #endif // Rational fractions. - BOOST_CHECK_CLOSE_FRACTION(static_cast(0.333333333333333333333333333333333333333L), third, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(0.666666666666666666666666666666666666667L), two_thirds, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(0.75L), three_quarters, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(0.333333333333333333333333333333333333333L), third, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(0.666666666666666666666666666666666666667L), two_thirds, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(0.75L), three_quarters, tolerance); // Two and related. - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(2.L)), root_two, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.L)), root_three, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(2.L)/2), half_root_two, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(log(2.L)), ln_two, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(log(log(2.0L))), ln_ln_two, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(log(4.0L))), root_ln_four, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(1/sqrt(2.0L)), one_div_root_two, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(2.L)), root_two, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.L)), root_three, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(2.L)/2), half_root_two, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(log(2.L)), ln_two, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(log(log(2.0L))), ln_ln_two, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(log(4.0L))), root_ln_four, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(1/sqrt(2.0L)), one_div_root_two, tolerance); // pi. - BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510L), pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510L/2), half_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510L/3), third_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510L/6), sixth_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(2 * 3.14159265358979323846264338327950288419716939937510L), two_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(3 * 3.14159265358979323846264338327950288419716939937510L / 4), three_quarters_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(4 * 3.14159265358979323846264338327950288419716939937510L / 3), four_thirds_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(1 / (2 * 3.14159265358979323846264338327950288419716939937510L)), one_div_two_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.14159265358979323846264338327950288419716939937510L)), root_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.14159265358979323846264338327950288419716939937510L / 2)), root_half_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(2 * 3.14159265358979323846264338327950288419716939937510L)), root_two_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(1 / sqrt(3.14159265358979323846264338327950288419716939937510L)), one_div_root_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510L), pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510L/2), half_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510L/3), third_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510L/6), sixth_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(2 * 3.14159265358979323846264338327950288419716939937510L), two_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(3 * 3.14159265358979323846264338327950288419716939937510L / 4), three_quarters_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(4 * 3.14159265358979323846264338327950288419716939937510L / 3), four_thirds_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(1 / (2 * 3.14159265358979323846264338327950288419716939937510L)), one_div_two_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.14159265358979323846264338327950288419716939937510L)), root_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(3.14159265358979323846264338327950288419716939937510L / 2)), root_half_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(2 * 3.14159265358979323846264338327950288419716939937510L)), root_two_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(1 / sqrt(3.14159265358979323846264338327950288419716939937510L)), one_div_root_pi, tolerance); BOOST_CHECK_CLOSE_FRACTION(static_cast(1 / sqrt(2 * 3.14159265358979323846264338327950288419716939937510L)), one_div_root_two_pi, tolerance); BOOST_CHECK_CLOSE_FRACTION(static_cast(sqrt(1. / 3.14159265358979323846264338327950288419716939937510L)), root_one_div_pi, tolerance); BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510L - 3.L), pi_minus_three, tolerance * 2 ); // tolerance * 2 because of cancellation loss. @@ -549,14 +551,14 @@ void test_long_double_spots() BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L), pi_cubed, tolerance); // See above. // BOOST_CHECK_CLOSE_FRACTION(static_cast(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L), cbrt_pi, tolerance); // See above. - BOOST_CHECK_CLOSE_FRACTION(cbrt_pi * cbrt_pi * cbrt_pi, pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION((static_cast(1)/cbrt_pi), one_div_cbrt_pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION(cbrt_pi * cbrt_pi * cbrt_pi, pi, tolerance); + BOOST_CHECK_CLOSE_FRACTION((static_cast(1)/cbrt_pi), one_div_cbrt_pi, tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(6.366197723675813430755350534900574481378385829618257E-1L), two_div_pi, tolerance * 3); // 2/pi + BOOST_CHECK_CLOSE_FRACTION(static_cast(6.366197723675813430755350534900574481378385829618257E-1L), two_div_pi, tolerance * 3); // 2/pi BOOST_CHECK_CLOSE_FRACTION(static_cast(7.97884560802865355879892119868763736951717262329869E-1L), root_two_div_pi, tolerance * 3); // sqrt(2/pi) // Euler - BOOST_CHECK_CLOSE_FRACTION(static_cast(2.71828182845904523536028747135266249775724709369995L), e, tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(2.71828182845904523536028747135266249775724709369995L), e, tolerance); //BOOST_CHECK_CLOSE_FRACTION(static_cast(exp(-0.5L)), exp_minus_half, tolerance); // See above. BOOST_CHECK_CLOSE_FRACTION(pow(e, pi), e_pow_pi, tolerance); // See also above. @@ -588,7 +590,7 @@ void test_long_double_spots() BOOST_CHECK_CLOSE_FRACTION(.91596559417721901505460351493238411077414937428167213L, catalan, tolerance); // A006752 as a constant in OEIS. BOOST_CHECK_CLOSE_FRACTION(1.1395470994046486574927930193898461120875997958365518247216557100852480077060706857071875468869385150L, extreme_value_skewness, tolerance); // Mathematica: N[12 Sqrt[6] Zeta[3]/Pi^3, 1101] BOOST_CHECK_CLOSE_FRACTION(0.6311106578189371381918993515442277798440422031347194976580945856929268196174737254599050270325373067L, rayleigh_skewness, tolerance); // Mathematica: N[2 Sqrt[Pi] (Pi - 3)/((4 - Pi)^(3/2)), 1100] - BOOST_CHECK_CLOSE_FRACTION(2.450893006876380628486604106197544154e-01L, rayleigh_kurtosis_excess, tolerance); + BOOST_CHECK_CLOSE_FRACTION(2.450893006876380628486604106197544154e-01L, rayleigh_kurtosis_excess, tolerance); BOOST_CHECK_CLOSE_FRACTION(2.68545200106530644530971483548179569382038229399446295305115234555721885953715200280114117493184769799515L, khinchin, tolerance ); // A002210 as a constant https://oeis.org/A002210/constant BOOST_CHECK_CLOSE_FRACTION(1.2824271291006226368753425688697917277676889273250011L, glaisher, tolerance ); // https://oeis.org/A074962/constant @@ -598,7 +600,7 @@ template void test_real_concept_policy(const Policy&) { // Basic sanity checks for constants using real_concept. - // Parameter Policy is used to control precision. + // Parameter Policy is used to control precision. using boost::math::concepts::real_concept; @@ -612,61 +614,61 @@ void test_real_concept_policy(const Policy&) using namespace boost::math::constants; BOOST_MATH_STD_USING - BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L, (pi)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L), (root_pi)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L/2), (root_half_pi)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L * 2), (root_two_pi)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(sqrt(log(4.0L)), (root_ln_four)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(2.71828182845904523536028747135266249775724709369995L, (e)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(0.5, (half)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(0.57721566490153286060651209008240243104259335L, (euler)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(sqrt(2.0L), (root_two)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(log(2.0L), (ln_two)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(log(log(2.0L)), (ln_ln_two)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(1)/3, (third)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(static_cast(2)/3, (twothirds)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(0.14159265358979323846264338327950288419716939937510L, (pi_minus_three)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(4.L - 3.14159265358979323846264338327950288419716939937510L, (four_minus_pi)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L, (pi)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L), (root_pi)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L/2), (root_half_pi)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L * 2), (root_two_pi)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(sqrt(log(4.0L)), (root_ln_four)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(2.71828182845904523536028747135266249775724709369995L, (e)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(0.5, (half)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(0.57721566490153286060651209008240243104259335L, (euler)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(sqrt(2.0L), (root_two)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(log(2.0L), (ln_two)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(log(log(2.0L)), (ln_ln_two)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(1)/3, (third)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(static_cast(2)/3, (twothirds)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(0.14159265358979323846264338327950288419716939937510L, (pi_minus_three)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(4.L - 3.14159265358979323846264338327950288419716939937510L, (four_minus_pi)(), tolerance); #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS - BOOST_CHECK_CLOSE_FRACTION(pow((4 - 3.14159265358979323846264338327950288419716939937510L), 1.5L), (pow23_four_minus_pi)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510L), 2.71828182845904523536028747135266249775724709369995L), (pi_pow_e)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510L), 0.33333333333333333333333333333333333333333333333333L), (cbrt_pi)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(exp(-0.5L), (exp_minus_half)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(pow(2.71828182845904523536028747135266249775724709369995L, 3.14159265358979323846264338327950288419716939937510L), (e_pow_pi)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(pow((4 - 3.14159265358979323846264338327950288419716939937510L), 1.5L), (pow23_four_minus_pi)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510L), 2.71828182845904523536028747135266249775724709369995L), (pi_pow_e)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510L), 0.33333333333333333333333333333333333333333333333333L), (cbrt_pi)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(exp(-0.5L), (exp_minus_half)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(pow(2.71828182845904523536028747135266249775724709369995L, 3.14159265358979323846264338327950288419716939937510L), (e_pow_pi)(), tolerance); #else // Only double, so no suffix L. - BOOST_CHECK_CLOSE_FRACTION(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5), (pow23_four_minus_pi)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995), (pi_pow_e)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333), (cbrt_pi)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(exp(-0.5), (exp_minus_half)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5), (pow23_four_minus_pi)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995), (pi_pow_e)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333), (cbrt_pi)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(exp(-0.5), (exp_minus_half)(), tolerance); #endif // Rational fractions. - BOOST_CHECK_CLOSE_FRACTION(0.333333333333333333333333333333333333333L, (third)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(0.666666666666666666666666666666666666667L, (two_thirds)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(0.75L, (three_quarters)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(0.333333333333333333333333333333333333333L, (third)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(0.666666666666666666666666666666666666667L, (two_thirds)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(0.75L, (three_quarters)(), tolerance); // Two and related. - BOOST_CHECK_CLOSE_FRACTION(sqrt(2.L), (root_two)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(sqrt(3.L), (root_three)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(sqrt(2.L)/2, (half_root_two)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(log(2.L), (ln_two)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(log(log(2.0L)), (ln_ln_two)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(sqrt(log(4.0L)), (root_ln_four)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(1/sqrt(2.0L), (one_div_root_two)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(sqrt(2.L), (root_two)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(sqrt(3.L), (root_three)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(sqrt(2.L)/2, (half_root_two)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(log(2.L), (ln_two)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(log(log(2.0L)), (ln_ln_two)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(sqrt(log(4.0L)), (root_ln_four)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(1/sqrt(2.0L), (one_div_root_two)(), tolerance); // pi. - BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L, (pi)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L/2, (half_pi)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L/3, (third_pi)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L/6, (sixth_pi)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(2 * 3.14159265358979323846264338327950288419716939937510L, (two_pi)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(3 * 3.14159265358979323846264338327950288419716939937510L / 4, (three_quarters_pi)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(4 * 3.14159265358979323846264338327950288419716939937510L / 3, (four_thirds_pi)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(1 / (2 * 3.14159265358979323846264338327950288419716939937510L), (one_div_two_pi)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L), (root_pi)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L / 2), (root_half_pi)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(sqrt(2 * 3.14159265358979323846264338327950288419716939937510L), (root_two_pi)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION(1 / sqrt(3.14159265358979323846264338327950288419716939937510L), (one_div_root_pi)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L, (pi)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L/2, (half_pi)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L/3, (third_pi)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L/6, (sixth_pi)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(2 * 3.14159265358979323846264338327950288419716939937510L, (two_pi)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(3 * 3.14159265358979323846264338327950288419716939937510L / 4, (three_quarters_pi)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(4 * 3.14159265358979323846264338327950288419716939937510L / 3, (four_thirds_pi)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(1 / (2 * 3.14159265358979323846264338327950288419716939937510L), (one_div_two_pi)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L), (root_pi)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L / 2), (root_half_pi)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(sqrt(2 * 3.14159265358979323846264338327950288419716939937510L), (root_two_pi)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(1 / sqrt(3.14159265358979323846264338327950288419716939937510L), (one_div_root_pi)(), tolerance); BOOST_CHECK_CLOSE_FRACTION(1 / sqrt(2 * 3.14159265358979323846264338327950288419716939937510L), (one_div_root_two_pi)(), tolerance); BOOST_CHECK_CLOSE_FRACTION(sqrt(1. / 3.14159265358979323846264338327950288419716939937510L), (root_one_div_pi)(), tolerance); BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L - 3.L, (pi_minus_three)(), tolerance * 2 ); // tolerance * 2 because of cancellation loss. @@ -679,11 +681,11 @@ void test_real_concept_policy(const Policy&) BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L, (pi_cubed)(), tolerance); // See above. // BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L, (cbrt_pi)(), tolerance); // See above. - BOOST_CHECK_CLOSE_FRACTION((cbrt_pi)() * (cbrt_pi)() * (cbrt_pi)(), (pi)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION((1)/(cbrt_pi)(), (one_div_cbrt_pi)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION((cbrt_pi)() * (cbrt_pi)() * (cbrt_pi)(), (pi)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION((1)/(cbrt_pi)(), (one_div_cbrt_pi)(), tolerance); // Euler - BOOST_CHECK_CLOSE_FRACTION(2.71828182845904523536028747135266249775724709369995L, (e)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(2.71828182845904523536028747135266249775724709369995L, (e)(), tolerance); //BOOST_CHECK_CLOSE_FRACTION(exp(-0.5L), (exp_minus_half)(), tolerance); // See above. BOOST_CHECK_CLOSE_FRACTION(pow(e(), (pi)()), (e_pow_pi)(), tolerance); // See also above. @@ -715,7 +717,7 @@ void test_real_concept_policy(const Policy&) BOOST_CHECK_CLOSE_FRACTION(.91596559417721901505460351493238411077414937428167213L, (catalan)(), tolerance); // A006752 as a constant in OEIS. BOOST_CHECK_CLOSE_FRACTION(1.1395470994046486574927930193898461120875997958365518247216557100852480077060706857071875468869385150L, (extreme_value_skewness)(), tolerance); // Mathematica: N[12 Sqrt[6] Zeta[3]/Pi^3, 1101] BOOST_CHECK_CLOSE_FRACTION(0.6311106578189371381918993515442277798440422031347194976580945856929268196174737254599050270325373067L, (rayleigh_skewness)(), tolerance); // Mathematica: N[2 Sqrt[Pi] (Pi - 3)/((4 - Pi)^(3/2)), 1100] - BOOST_CHECK_CLOSE_FRACTION(2.450893006876380628486604106197544154e-01L, (rayleigh_kurtosis_excess)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION(2.450893006876380628486604106197544154e-01L, (rayleigh_kurtosis_excess)(), tolerance); BOOST_CHECK_CLOSE_FRACTION(2.68545200106530644530971483548179569382038229399446295305115234555721885953715200280114117493184769799515L, (khinchin)(), tolerance ); // A002210 as a constant https://oeis.org/A002210/constant BOOST_CHECK_CLOSE_FRACTION(1.2824271291006226368753425688697917277676889273250011L, (glaisher)(), tolerance ); // https://oeis.org/A074962/constant @@ -725,13 +727,13 @@ void test_real_concept_policy(const Policy&) if(boost::math::tools::digits() > boost::math::constants::max_string_digits) { // This suffers from cancellation error, so increased tolerance: - BOOST_CHECK_CLOSE_FRACTION((static_cast(4. - 3.14159265358979323846264338327950288419716939937510L)), (four_minus_pi)(), tolerance * 3); - BOOST_CHECK_CLOSE_FRACTION((static_cast(0.14159265358979323846264338327950288419716939937510L)), (pi_minus_three)(), tolerance * 3); + BOOST_CHECK_CLOSE_FRACTION((static_cast(4. - 3.14159265358979323846264338327950288419716939937510L)), (four_minus_pi)(), tolerance * 3); + BOOST_CHECK_CLOSE_FRACTION((static_cast(0.14159265358979323846264338327950288419716939937510L)), (pi_minus_three)(), tolerance * 3); } else { - BOOST_CHECK_CLOSE_FRACTION((static_cast(4. - 3.14159265358979323846264338327950288419716939937510L)), (four_minus_pi)(), tolerance); - BOOST_CHECK_CLOSE_FRACTION((static_cast(0.14159265358979323846264338327950288419716939937510L)), (pi_minus_three)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION((static_cast(4. - 3.14159265358979323846264338327950288419716939937510L)), (four_minus_pi)(), tolerance); + BOOST_CHECK_CLOSE_FRACTION((static_cast(0.14159265358979323846264338327950288419716939937510L)), (pi_minus_three)(), tolerance); } } // template void test_spots(boost::math::concepts::real_concept) @@ -750,7 +752,7 @@ int test_main(int, char* []) // (Parameter value, arbitrarily zero, only communicates the floating-point type). test_spots(0.0F); // Test float. - test_spots(0.0); // Test double. + test_spots(0.0); // Test double. #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS test_spots(0.0L); // Test long double. #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x0582)) @@ -771,7 +773,7 @@ int test_main(int, char* []) Output: - 1 Feb 2012 + 1 Feb 2012 test_constants.cpp test_constants.vcxproj -> J:\Cpp\MathToolkit\test\Math_test\Debug\test_constants.exe @@ -784,7 +786,7 @@ test_constants.cpp Tolerance for type long double is 4.44089e-016. Tolerance for type class boost::math::concepts::real_concept is 4.44089e-016. Tolerance for type class boost::math::concepts::big_real_concept is 1.33227e-014. - + *** No errors detected */ From a2fc557d7901b4101011dbcaed6f9b3afdceb97e Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Wed, 1 Aug 2012 16:37:01 +0000 Subject: [PATCH 075/115] Added comments [SVN r79835] --- test/s_.ipp | 14 +++++++++----- test/test_nonfinite_io.cpp | 16 +++++++++++----- 2 files changed, 20 insertions(+), 10 deletions(-) diff --git a/test/s_.ipp b/test/s_.ipp index 6df30043f..a9cc74689 100644 --- a/test/s_.ipp +++ b/test/s_.ipp @@ -2,6 +2,7 @@ #define BOOST_MATH_S__HPP // Copyright (c) 2006 Johan Rade +// Copyright (c) 2012 Paul A. Bristow // Distributed under the Boost Software License, Version 1.0. // (See accompanying file LICENSE_1_0.txt @@ -10,17 +11,19 @@ // The macro S_ lets you write // // basic_string s = S_("foo"); +// and // CharType c = S_('a'); // -// provided that CharType is char or wchar_t - -#include +// provided that CharType is either char or wchar_t. +// Used by tests of output of signed zero and others. #ifdef _MSC_VER # pragma warning(push) -# pragma warning(disable : 4512) +# pragma warning(disable : 4512) // conditional expression is constant. #endif +#include + //------------------------------------------------------------------------------ #define S_(a) make_literal_helper(a, L##a) @@ -61,4 +64,5 @@ inline string_literal_helper make_literal_helper(const char* s, const wchar_t* w # pragma warning(pop) #endif -#endif +#endif // BOOST_MATH_S__HPP + diff --git a/test/test_nonfinite_io.cpp b/test/test_nonfinite_io.cpp index a5f6eb202..7ee913707 100644 --- a/test/test_nonfinite_io.cpp +++ b/test/test_nonfinite_io.cpp @@ -8,9 +8,7 @@ // test_nonfinite_trap.cpp #ifdef _MSC_VER -# pragma warning(disable : 4702) // Unreachable code. # pragma warning(disable : 4127) // Expression is constant. - #endif #define BOOST_TEST_MAIN @@ -35,6 +33,11 @@ using boost::math::changesign; using boost::math::isnan; //------------------------------------------------------------------------------ +// Test nonfinite_num_put and nonfinite_num_get facets by checking +// loopback (output and re-input) of a few values, +// but using all the built-in char and floating-point types. +// Only the default output is used but various ostream options are tested seperately below. +// Finite, infinite and NaN values (positive and negative) are used for the test. void trap_test_finite(); void trap_test_inf(); @@ -52,7 +55,7 @@ BOOST_AUTO_TEST_CASE(trap_test) template void trap_test_finite_impl(); void trap_test_finite() -{ +{ // Test finite using all the built-in char and floating-point types. trap_test_finite_impl(); trap_test_finite_impl(); trap_test_finite_impl(); @@ -105,7 +108,7 @@ template void trap_test_put_inf_impl(); template void trap_test_get_inf_impl(); void trap_test_inf() -{ +{ // Test infinity using all the built-in char and floating-point types. trap_test_inf_impl(); trap_test_inf_impl(); trap_test_inf_impl(); @@ -174,7 +177,7 @@ template void trap_test_put_nan_impl(); template void trap_test_get_nan_impl(); void trap_test_nan() -{ +{ // Test NaN using all the built-in char and floating-point types. trap_test_nan_impl(); trap_test_nan_impl(); trap_test_nan_impl(); @@ -238,6 +241,9 @@ template void trap_test_get_nan_impl() //------------------------------------------------------------------------------ +// Test a selection of stream output options comparing result with expected string. +// Only uses CharType = char and ValType = double. +// Other types have already been tested above. #define CHECKOUT(manips, expected)\ {\ From 139a12844ef15684bf3df90eb9bec0730cd67494 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Wed, 1 Aug 2012 17:11:31 +0000 Subject: [PATCH 076/115] Back to plan A! not defined for v <= k - no infinity from moments. (TODO use normal for df = infinity?) [SVN r79836] --- .../boost/math/distributions/students_t.hpp | 73 ++++--------------- 1 file changed, 15 insertions(+), 58 deletions(-) diff --git a/include/boost/math/distributions/students_t.hpp b/include/boost/math/distributions/students_t.hpp index 5ada2d099..dfd5ae0ab 100644 --- a/include/boost/math/distributions/students_t.hpp +++ b/include/boost/math/distributions/students_t.hpp @@ -325,34 +325,16 @@ inline RealType variance(const students_t_distribution& dist) { // http://en.wikipedia.org/wiki/Student%27s_t-distribution // Revised for https://svn.boost.org/trac/boost/ticket/7177 RealType df = dist.degrees_of_freedom(); - if (!(boost::math::isfinite)(df)) + if (!(boost::math::isfinite)(df) || (df <= 2)) { // Infinity or NaN - policies::raise_domain_error( - "boost::math::variance(students_t_distribution<%1%> const&, %1%)", - "variance is undefined for nonfinite degrees of freedom, but got %1%.", - df, Policy()); - return std::numeric_limits::quiet_NaN(); // Undefined. - } - if (df > 2) - { // normal case. - return df / (df - 2); - } - if ((df > 1) && (df <= 2)) - { // - policies::raise_overflow_error( - "boost::math::variance(students_t_distribution<%1%> const&, %1%)", - "variance is infinity for 1 < degrees of freedom <= 2.", - Policy()); - return std::numeric_limits::infinity(); // Infinity. - } - else - { + policies::raise_domain_error( "boost::math::variance(students_t_distribution<%1%> const&, %1%)", - "variance is undefined for degrees of freedom <= 1, but got %1%.", + "variance is undefined for degrees of freedom <= 2, but got %1%.", df, Policy()); return std::numeric_limits::quiet_NaN(); // Undefined. } + return df / (df - 2); } // variance template @@ -376,26 +358,14 @@ inline RealType kurtosis(const students_t_distribution& dist) RealType df = dist.degrees_of_freedom(); if((!(boost::math::isfinite)(df)) || (df <= 4)) { // Undefined or infinity for moment k = 4. - RealType result; - if ((df > 2) && (df <= 4)) - { - policies::raise_overflow_error( - "boost::math::kurtosis(students_t_distribution<%1%> const&, %1%)", - "Kurtosis is infinity for 2 < degrees of freedom <= 4.", - Policy()); - return std::numeric_limits::infinity(); // Infinity. - } - else - { - policies::raise_domain_error( - "boost::math::kurtosis(students_t_distribution<%1%> const&, %1%)", - "Kurtosis is undefined for degrees of freedom <= 2, but got %1%.", - df, Policy()); + policies::raise_domain_error( + "boost::math::kurtosis(students_t_distribution<%1%> const&, %1%)", + "Kurtosis is undefined for degrees of freedom <= 4, but got %1%.", + df, Policy()); return std::numeric_limits::quiet_NaN(); // Undefined. - } - return result; } - return 3 * (df - 2) / (df - 4); + //return 3 * (df - 2) / (df - 4); + return 6 / (df - 4) + 3; } template @@ -406,24 +376,11 @@ inline RealType kurtosis_excess(const students_t_distribution& RealType df = dist.degrees_of_freedom(); if((!(boost::math::isfinite)(df)) || (df <= 4)) { // Undefined or infinity for moment k = 4. - RealType result; - if ((df > 2) && (df <= 4)) - { - policies::raise_overflow_error( - "boost::math::kurtosis_excess(students_t_distribution<%1%> const&, %1%)", - "Kurtosis_excess is infinity for 2 < degrees of freedom <= 4.", - Policy()); - return std::numeric_limits::infinity(); // Infinity. - } - else - { - policies::raise_domain_error( - "boost::math::kurtosis_excess(students_t_distribution<%1%> const&, %1%)", - "Kurtosis_excess is undefined for degrees of freedom <= 2, but got %1%.", - df, Policy()); - return std::numeric_limits::quiet_NaN(); // Undefined. - } - return result; + policies::raise_domain_error( + "boost::math::kurtosis_excess(students_t_distribution<%1%> const&, %1%)", + "Kurtosis_excess is undefined for degrees of freedom <= 4, but got %1%.", + df, Policy()); + return std::numeric_limits::quiet_NaN(); // Undefined. } return 6 / (df - 4); } From c9fde3be322be4f9027c04de242675e24f4f9593 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Wed, 1 Aug 2012 17:12:00 +0000 Subject: [PATCH 077/115] Back to plan A! not defined for v <= k - no infinity from moments. (TODO use normal for df = infinity?) [SVN r79837] --- test/test_students_t.cpp | 95 ++++++++++++++++++---------------------- 1 file changed, 43 insertions(+), 52 deletions(-) diff --git a/test/test_students_t.cpp b/test/test_students_t.cpp index d7a7d989a..13a471ec2 100644 --- a/test/test_students_t.cpp +++ b/test/test_students_t.cpp @@ -472,7 +472,7 @@ void test_spots(RealType) 9); - // Checks added for Trac #7717 report by Thomas Mang + // Checks added for Trac #7717 report by Thomas Mang. RealType inf = std::numeric_limits::infinity(); RealType nan = std::numeric_limits::quiet_NaN(); @@ -480,7 +480,6 @@ void test_spots(RealType) BOOST_CHECK_THROW(quantile(dist, 2), std::domain_error); BOOST_CHECK_THROW(pdf(students_t_distribution(0), 0), std::domain_error); BOOST_CHECK_THROW(pdf(students_t_distribution(-1), 0), std::domain_error); - // Check on df for mean (moment k = 1) BOOST_CHECK_THROW(mean(students_t_distribution(-1)), std::domain_error); @@ -495,9 +494,9 @@ void test_spots(RealType) BOOST_CHECK_THROW(variance(students_t_distribution(-1)), std::domain_error); BOOST_CHECK_THROW(variance(students_t_distribution(0)), std::domain_error); BOOST_CHECK_THROW(variance(students_t_distribution(1)), std::domain_error); - BOOST_CHECK_THROW(variance(students_t_distribution(static_cast(1.99999L))), std::overflow_error); - BOOST_CHECK_THROW(variance(students_t_distribution(static_cast(1.99999L))), std::overflow_error); - BOOST_CHECK_THROW(variance(students_t_distribution(2)), std::overflow_error); // df == + BOOST_CHECK_THROW(variance(students_t_distribution(static_cast(1.99999L))), std::domain_error); + BOOST_CHECK_THROW(variance(students_t_distribution(static_cast(1.99999L))), std::domain_error); + BOOST_CHECK_THROW(variance(students_t_distribution(2)), std::domain_error); // df == BOOST_CHECK_EQUAL(variance(students_t_distribution(2.5)), 5); // OK. BOOST_CHECK_EQUAL(variance(students_t_distribution(3)), 3); // OK. @@ -517,9 +516,9 @@ void test_spots(RealType) BOOST_CHECK_THROW(kurtosis_excess(students_t_distribution(1)), std::domain_error); BOOST_CHECK_THROW(kurtosis_excess(students_t_distribution(1.5L)), std::domain_error); BOOST_CHECK_THROW(kurtosis_excess(students_t_distribution(2)), std::domain_error); - BOOST_CHECK_THROW(kurtosis(students_t_distribution(static_cast(2.1))), std::overflow_error); - BOOST_CHECK_THROW(kurtosis_excess(students_t_distribution(3)), std::overflow_error); - BOOST_CHECK_THROW(kurtosis_excess(students_t_distribution(4)), std::overflow_error); // df == k + BOOST_CHECK_THROW(kurtosis(students_t_distribution(static_cast(2.1))), std::domain_error); + BOOST_CHECK_THROW(kurtosis_excess(students_t_distribution(3)), std::domain_error); + BOOST_CHECK_THROW(kurtosis_excess(students_t_distribution(4)), std::domain_error); // df == k BOOST_CHECK_EQUAL(kurtosis_excess(students_t_distribution(5)), 6); // OK. // Check on df for kurtosis (moment 4) @@ -527,9 +526,9 @@ void test_spots(RealType) BOOST_CHECK_THROW(kurtosis(students_t_distribution(0)), std::domain_error); BOOST_CHECK_THROW(kurtosis(students_t_distribution(1)), std::domain_error); BOOST_CHECK_THROW(kurtosis(students_t_distribution(2)), std::domain_error); - BOOST_CHECK_THROW(kurtosis(students_t_distribution(static_cast(2.0001L))), std::overflow_error); - BOOST_CHECK_THROW(kurtosis(students_t_distribution(3)), std::overflow_error); - BOOST_CHECK_THROW(kurtosis(students_t_distribution(4)), std::overflow_error); // df == k + BOOST_CHECK_THROW(kurtosis(students_t_distribution(static_cast(2.0001L))), std::domain_error); + BOOST_CHECK_THROW(kurtosis(students_t_distribution(3)), std::domain_error); + BOOST_CHECK_THROW(kurtosis(students_t_distribution(4)), std::domain_error); // df == k BOOST_CHECK_EQUAL(kurtosis(students_t_distribution(5)), 9); // OK. // Use a new distribution ignore_error_students_t with a custom policy to ignore all errors, @@ -577,70 +576,62 @@ void test_spots(RealType) typedef students_t_distribution ignore_error_students_t; // Only test NaN and infinity if type has these features (realconcept returns zero). - // Integers are always converted to RealType, others requires static cast. + // Integers are always converted to RealType, + // others requires static cast to RealType from long double. - // Mean if(std::numeric_limits::has_quiet_NaN) { + // Mean BOOST_CHECK(boost::math::isnan(mean(ignore_error_students_t(-1)))); BOOST_CHECK(boost::math::isnan(mean(ignore_error_students_t(0)))); BOOST_CHECK(boost::math::isnan(mean(ignore_error_students_t(1)))); - BOOST_CHECK(boost::math::isfinite(mean(ignore_error_students_t(1 + std::numeric_limits::epsilon())))); // Variance BOOST_CHECK(boost::math::isnan(variance(ignore_error_students_t(std::numeric_limits::quiet_NaN())))); - - if(!std::numeric_limits::has_infinity) - { - BOOST_CHECK(boost::math::isnan(variance(ignore_error_students_t(std::numeric_limits::infinity())))); - } - BOOST_CHECK(boost::math::isnan(variance(ignore_error_students_t(-1)))); BOOST_CHECK(boost::math::isnan(variance(ignore_error_students_t(0)))); BOOST_CHECK(boost::math::isnan(variance(ignore_error_students_t(1)))); - } - if(std::numeric_limits::has_infinity) - { - BOOST_CHECK(boost::math::isinf(variance(ignore_error_students_t(static_cast(1.7L))))); - BOOST_CHECK(boost::math::isinf(variance(ignore_error_students_t(2)))); - } - BOOST_CHECK(boost::math::isfinite(variance(ignore_error_students_t(2 + 2 * std::numeric_limits::epsilon())))); - BOOST_CHECK(boost::math::isfinite(variance(ignore_error_students_t(static_cast(2.0001L))))); + BOOST_CHECK(boost::math::isnan(variance(ignore_error_students_t(static_cast(1.7L))))); + BOOST_CHECK(boost::math::isnan(variance(ignore_error_students_t(2)))); // Skewness - if(std::numeric_limits::has_quiet_NaN) - { BOOST_CHECK(boost::math::isnan(skewness(ignore_error_students_t(std::numeric_limits::quiet_NaN())))); - if(!std::numeric_limits::has_infinity) - { - BOOST_CHECK(boost::math::isnan(skewness(ignore_error_students_t(std::numeric_limits::infinity())))); - } + BOOST_CHECK(boost::math::isnan(skewness(ignore_error_students_t(std::numeric_limits::quiet_NaN())))); BOOST_CHECK(boost::math::isnan(skewness(ignore_error_students_t(-1)))); BOOST_CHECK(boost::math::isnan(skewness(ignore_error_students_t(0)))); BOOST_CHECK(boost::math::isnan(skewness(ignore_error_students_t(1)))); BOOST_CHECK(boost::math::isnan(skewness(ignore_error_students_t(2)))); BOOST_CHECK(boost::math::isnan(skewness(ignore_error_students_t(3)))); - BOOST_CHECK(boost::math::isfinite(skewness(ignore_error_students_t(3 + 3 * std::numeric_limits::epsilon())))); - // Kurtosis (and assume this tests kurtosis excess too?). + // Kurtosis BOOST_CHECK(boost::math::isnan(kurtosis(ignore_error_students_t(std::numeric_limits::quiet_NaN())))); - if(std::numeric_limits::has_infinity) - { - BOOST_CHECK(boost::math::isnan(kurtosis(ignore_error_students_t(std::numeric_limits::infinity())))); - BOOST_CHECK(boost::math::isnan(kurtosis(ignore_error_students_t(-1)))); - BOOST_CHECK(boost::math::isnan(kurtosis(ignore_error_students_t(0)))); - BOOST_CHECK(boost::math::isnan(kurtosis(ignore_error_students_t(1)))); - BOOST_CHECK(boost::math::isnan(kurtosis(ignore_error_students_t(2)))); - } - } + BOOST_CHECK(boost::math::isnan(kurtosis(ignore_error_students_t(std::numeric_limits::infinity())))); + BOOST_CHECK(boost::math::isnan(kurtosis(ignore_error_students_t(-1)))); + BOOST_CHECK(boost::math::isnan(kurtosis(ignore_error_students_t(0)))); + BOOST_CHECK(boost::math::isnan(kurtosis(ignore_error_students_t(1)))); + BOOST_CHECK(boost::math::isnan(kurtosis(ignore_error_students_t(2)))); + BOOST_CHECK(boost::math::isnan(kurtosis(ignore_error_students_t(static_cast(2.0001L))))); + BOOST_CHECK(boost::math::isnan(kurtosis(ignore_error_students_t(3)))); + BOOST_CHECK(boost::math::isnan(kurtosis(ignore_error_students_t(4)))); + + // Kurtosis excess + BOOST_CHECK(boost::math::isnan(kurtosis_excess(ignore_error_students_t(std::numeric_limits::quiet_NaN())))); + BOOST_CHECK(boost::math::isnan(kurtosis_excess(ignore_error_students_t(std::numeric_limits::infinity())))); + BOOST_CHECK(boost::math::isnan(kurtosis_excess(ignore_error_students_t(-1)))); + BOOST_CHECK(boost::math::isnan(kurtosis_excess(ignore_error_students_t(0)))); + BOOST_CHECK(boost::math::isnan(kurtosis_excess(ignore_error_students_t(1)))); + BOOST_CHECK(boost::math::isnan(kurtosis_excess(ignore_error_students_t(2)))); + BOOST_CHECK(boost::math::isnan(kurtosis_excess(ignore_error_students_t(static_cast(2.0001L))))); + BOOST_CHECK(boost::math::isnan(kurtosis_excess(ignore_error_students_t(3)))); + BOOST_CHECK(boost::math::isnan(kurtosis_excess(ignore_error_students_t(4)))); + } // has_quiet_NaN + + BOOST_CHECK(boost::math::isfinite(mean(ignore_error_students_t(1 + std::numeric_limits::epsilon())))); BOOST_CHECK(boost::math::isfinite(variance(ignore_error_students_t(2 + 2 * std::numeric_limits::epsilon())))); - if(std::numeric_limits::has_infinity) - { - BOOST_CHECK(boost::math::isinf(kurtosis(ignore_error_students_t(static_cast(2.0001L))))); - BOOST_CHECK(boost::math::isinf(kurtosis(ignore_error_students_t(3)))); - BOOST_CHECK(boost::math::isinf(kurtosis(ignore_error_students_t(4)))); - } - BOOST_CHECK(boost::math::isfinite(variance(ignore_error_students_t(4 + 4 * std::numeric_limits::epsilon())))); + BOOST_CHECK(boost::math::isfinite(variance(ignore_error_students_t(static_cast(2.0001L))))); + BOOST_CHECK(boost::math::isfinite(variance(ignore_error_students_t(2 + 2 * std::numeric_limits::epsilon())))); + BOOST_CHECK(boost::math::isfinite(skewness(ignore_error_students_t(3 + 3 * std::numeric_limits::epsilon())))); + BOOST_CHECK(boost::math::isfinite(kurtosis(ignore_error_students_t(4 + 4 * std::numeric_limits::epsilon())))); BOOST_CHECK(boost::math::isfinite(kurtosis(ignore_error_students_t(static_cast(4.0001L))))); check_out_of_range >(1); From 3e816a2cd759aebda88ee957b025f0fac58bfbca Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Thu, 2 Aug 2012 09:23:18 +0000 Subject: [PATCH 078/115] Added Trac #7177 [SVN r79843] --- doc/sf_and_dist/roadmap.qbk | 3 +++ 1 file changed, 3 insertions(+) diff --git a/doc/sf_and_dist/roadmap.qbk b/doc/sf_and_dist/roadmap.qbk index f3ea7bade..ff0c4176b 100644 --- a/doc/sf_and_dist/roadmap.qbk +++ b/doc/sf_and_dist/roadmap.qbk @@ -6,6 +6,9 @@ Currently open bug reports can be viewed All bug reports including closed ones can be viewed [@https://svn.boost.org/trac/boost/query?status=assigned&status=closed&status=new&status=reopened&component=math&col=id&col=summary&col=status&col=type&col=milestone&col=component&order=priority here]. +[h4 Boost-1.52] +* Corrected moments for small degrees of freedom [@https://svn.boost.org/trac/boost/ticket/7177 #7177] (reported by Thomas Mang). + [h4 Boost-1.51] * Added [link math_toolkit.special.airy Airy functions] and [link math_toolkit.special.jacobi Jacobi Elliptic functions]. From dc8b7e0af2a300087c8e75766e35a5f4cbbcb947 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Thu, 2 Aug 2012 09:24:31 +0000 Subject: [PATCH 079/115] Changed back to always returning NaN for moments k <= v and Added Trac #7177 [SVN r79844] --- doc/sf_and_dist/distributions/students_t.qbk | 25 +++++++++++++------- 1 file changed, 17 insertions(+), 8 deletions(-) diff --git a/doc/sf_and_dist/distributions/students_t.qbk b/doc/sf_and_dist/distributions/students_t.qbk index 80dce1a70..ea7877e92 100644 --- a/doc/sf_and_dist/distributions/students_t.qbk +++ b/doc/sf_and_dist/distributions/students_t.qbk @@ -35,7 +35,8 @@ A statistical distribution published by William Gosset in 1908. His employer, Guinness Breweries, required him to publish under a -pseudonym, so he chose "Student". Given N independent measurements, let +pseudonym (possibly to hide that they were using statistics), +so he chose "Student". Given N independent measurements, let [equation students_t_dist] @@ -152,18 +153,26 @@ y = 1 - x The quantities /x/ and /y/ are both returned by __ibeta_inv without the subtraction implied above.]] [[quantile from the complement][Using the relation: t = -quantile(q)]] -[[mean][0]] -[[variance][v \/ (v - 2)]] [[mode][0]] -[[skewness][0]] -[[kurtosis][3 * (v - 2) \/ (v - 4)]] -[[kurtosis excess][6 \/ (df - 4)]] +[[mean][0]] +[[variance][if (v > 2) v \/ (v - 2) else NaN]] +[[skewness][if (v > 3) 0 else NaN ]] +[[kurtosis][if (v > 4) 3 * (v - 2) \/ (v - 4) else NaN]] +[[kurtosis excess][if (v > 4) 6 \/ (df - 4) else NaN]] ] -[endsect][/section:students_t_dist Students t] +If the moment index k is less than v, then the moment is undefined. +Evaluating the moment will throw a 'domain_error' unless ignored by a policy, +when it will return 'std::numeric_limits<>::quiet_NaN();' + +(For simplicity, we have not implemented the return of infinity in some cases +as suggested by [@http://en.wikipedia.org/wiki/Student%27s_t-distribution Wikipedia Student's t]. +See also [@https://svn.boost.org/trac/boost/ticket/7177].) + +[endsect] [/section:students_t_dist Students t] [/ students_t.qbk - Copyright 2006 John Maddock and Paul A. Bristow. + Copyright 2006, 2012 John Maddock and Paul A. Bristow. Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt). From fd81001d153f64374c16c899eed65b293ed1f4cf Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Thu, 2 Aug 2012 13:52:49 +0000 Subject: [PATCH 080/115] Corrected wolfram links to functions and added a link to mathworld airy site. [SVN r79849] --- doc/sf_and_dist/airy.qbk | 15 ++++++++++----- 1 file changed, 10 insertions(+), 5 deletions(-) diff --git a/doc/sf_and_dist/airy.qbk b/doc/sf_and_dist/airy.qbk index 9b7419161..dd898d561 100644 --- a/doc/sf_and_dist/airy.qbk +++ b/doc/sf_and_dist/airy.qbk @@ -27,10 +27,15 @@ LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) [heading Description] -The function __airy_ai calculates the Airy function Ai which is the first solution to the differential equation: +The function __airy_ai calculates the Airy function Ai which is the first solution +to the differential equation: [equation airy] +See Weisstein, Eric W. "Airy Functions." From MathWorld--A Wolfram Web Resource. +[*http://mathworld.wolfram.com/AiryFunctions.html]; + + [optional_policy] The following graph illustrates how this function changes as /x/ changes: for negative /x/ @@ -49,7 +54,7 @@ only the absolute error is low for /x < 0/. [heading Testing] Since this function is implemented in terms of other special functions, there are only a few -basic sanity checks, using test values from [@http://mathworld.wolfram.com/AiryFunctions.html Wolfram Airy Functions]. +basic sanity checks, using test values from [@http://functions.wolfram.com/ Wolfram Airy Functions]. [heading Implementation] @@ -101,7 +106,7 @@ only the absolute error is low for /x < 0/. [heading Testing] Since this function is implemented in terms of other special functions, there are only a few -basic sanity checks, using test values from [@http:functions.wolfram.com functions.wolfram.com]. +basic sanity checks, using test values from [@http://functions.wolfram.com functions.wolfram.com]. [heading Implementation] @@ -153,7 +158,7 @@ only the absolute error is low for /x < 0/. [heading Testing] Since this function is implemented in terms of other special functions, there are only a few -basic sanity checks, using test values from [@http:functions.wolfram.com functions.wolfram.com]. +basic sanity checks, using test values from [@http://functions.wolfram.com functions.wolfram.com]. [heading Implementation] @@ -205,7 +210,7 @@ only the absolute error is low for /x < 0/. [heading Testing] Since this function is implemented in terms of other special functions, there are only a few -basic sanity checks, using test values from [@http:functions.wolfram.com functions.wolfram.com]. +basic sanity checks, using test values from [@http://functions.wolfram.com functions.wolfram.com]. [heading Implementation] From 5ed9615fb5bdfe4fa6cdfe8afdf2341052853490 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 2 Aug 2012 15:16:21 +0000 Subject: [PATCH 081/115] Fixes for multiprecision and expression template enabled types. [SVN r79851] --- include/boost/math/special_functions/next.hpp | 6 +++--- include/boost/math/tools/big_constant.hpp | 2 +- 2 files changed, 4 insertions(+), 4 deletions(-) diff --git a/include/boost/math/special_functions/next.hpp b/include/boost/math/special_functions/next.hpp index b3d2651bc..b8a5d2ad0 100644 --- a/include/boost/math/special_functions/next.hpp +++ b/include/boost/math/special_functions/next.hpp @@ -127,7 +127,7 @@ T float_next(const T& val, const Policy& pol) // would not be a denorm, then shift the input, increment, and shift back. // This avoids issues with the Intel SSE2 registers when the FTZ or DAZ flags are set. // - return ldexp(float_next(ldexp(val, 2 * tools::digits()), pol), -2 * tools::digits()); + return ldexp(float_next(T(ldexp(val, 2 * tools::digits())), pol), -2 * tools::digits()); } if(-0.5f == frexp(val, &expon)) @@ -198,7 +198,7 @@ T float_prior(const T& val, const Policy& pol) // would not be a denorm, then shift the input, increment, and shift back. // This avoids issues with the Intel SSE2 registers when the FTZ or DAZ flags are set. // - return ldexp(float_prior(ldexp(val, 2 * tools::digits()), pol), -2 * tools::digits()); + return ldexp(float_prior(T(ldexp(val, 2 * tools::digits())), pol), -2 * tools::digits()); } T remain = frexp(val, &expon); @@ -323,7 +323,7 @@ T float_distance(const T& a, const T& b, const Policy& pol) // T a2 = ldexp(a, tools::digits()); T b2 = ldexp(b, tools::digits()); - mb = -(std::min)(ldexp(upper, tools::digits()), b2); + mb = -(std::min)(T(ldexp(upper, tools::digits())), b2); x = a2 + mb; z = x - a2; y = (a2 - (x - z)) + (mb - z); diff --git a/include/boost/math/tools/big_constant.hpp b/include/boost/math/tools/big_constant.hpp index be397a93e..495f89c13 100644 --- a/include/boost/math/tools/big_constant.hpp +++ b/include/boost/math/tools/big_constant.hpp @@ -53,7 +53,7 @@ inline BOOST_CONSTEXPR const char* make_big_value(long double, const char* s, mp // For constants too huge for any conceivable long double (and which generate compiler errors if we try and declare them as such): // #define BOOST_MATH_HUGE_CONSTANT(T, D, x)\ - boost::math::tools::make_big_value(0.0L, BOOST_STRINGIZE(x), is_floating_point(), boost::is_convertible()) + boost::math::tools::make_big_value(0.0L, BOOST_STRINGIZE(x), mpl::bool_::value || (std::numeric_limits::is_specialized && std::numeric_limits::max_exponent <= std::numeric_limits::max_exponent)>(), boost::is_convertible()) }}} // namespaces From 80f48336383d85fd1e9d3087023cd7bb52e0415b Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Thu, 2 Aug 2012 15:48:22 +0000 Subject: [PATCH 082/115] correctes wolfram function links in airy [SVN r79853] --- doc/sf_and_dist/airy.qbk | 2 +- doc/sf_and_dist/html/index.html | 4 +- doc/sf_and_dist/html/index/s13.html | 4 +- doc/sf_and_dist/html/index/s14.html | 4 +- doc/sf_and_dist/html/index/s15.html | 4 +- doc/sf_and_dist/html/index/s16.html | 4 +- doc/sf_and_dist/html/index/s17.html | 4 +- .../dist/dist_ref/dists/students_t_dist.html | 47 ++++++++++++------- .../main_overview/conventions.html | 2 +- .../math_toolkit/main_overview/history1.html | 44 ++++++++++------- .../main_overview/navigation.html | 2 +- .../html/math_toolkit/special/airy/ai.html | 6 ++- .../html/math_toolkit/special/airy/aip.html | 2 +- .../html/math_toolkit/special/airy/bi.html | 2 +- .../html/math_toolkit/special/airy/bip.html | 2 +- .../html/math_toolkit/status/history1.html | 44 ++++++++++------- 16 files changed, 105 insertions(+), 72 deletions(-) diff --git a/doc/sf_and_dist/airy.qbk b/doc/sf_and_dist/airy.qbk index dd898d561..c08c16c11 100644 --- a/doc/sf_and_dist/airy.qbk +++ b/doc/sf_and_dist/airy.qbk @@ -33,7 +33,7 @@ to the differential equation: [equation airy] See Weisstein, Eric W. "Airy Functions." From MathWorld--A Wolfram Web Resource. -[*http://mathworld.wolfram.com/AiryFunctions.html]; +[@http://mathworld.wolfram.com/AiryFunctions.html]; [optional_policy] diff --git a/doc/sf_and_dist/html/index.html b/doc/sf_and_dist/html/index.html index b40a88cc6..93f657e4a 100644 --- a/doc/sf_and_dist/html/index.html +++ b/doc/sf_and_dist/html/index.html @@ -316,6 +316,8 @@

    Jacobi Elliptic Functions
    +
    Overvew of the + Jacobi Elliptic Functions
    Jacobi Elliptic SN, CN and DN
    Jacobi Elliptic @@ -577,7 +579,7 @@

    - +

    Last revised: June 06, 2012 at 11:22:49 GMT

    Last revised: August 02, 2012 at 14:37:58 GMT


    diff --git a/doc/sf_and_dist/html/index/s13.html b/doc/sf_and_dist/html/index/s13.html index 46f89e843..e11b3ddc2 100644 --- a/doc/sf_and_dist/html/index/s13.html +++ b/doc/sf_and_dist/html/index/s13.html @@ -22,9 +22,9 @@
    -
    +

    -Function Index

    +Function Index

    A B C D E F G H I J K L M N O P Q R S T U V W Z

    diff --git a/doc/sf_and_dist/html/index/s14.html b/doc/sf_and_dist/html/index/s14.html index 4c65acaeb..14ffec64a 100644 --- a/doc/sf_and_dist/html/index/s14.html +++ b/doc/sf_and_dist/html/index/s14.html @@ -22,9 +22,9 @@
    PrevUpHomeNext
    -
    +

    -Class Index

    +Class Index

    B C D E F G H I L M N P R S T U W

    diff --git a/doc/sf_and_dist/html/index/s15.html b/doc/sf_and_dist/html/index/s15.html index bb8efc3aa..31ddb715c 100644 --- a/doc/sf_and_dist/html/index/s15.html +++ b/doc/sf_and_dist/html/index/s15.html @@ -22,9 +22,9 @@
    PrevUpHomeNext
    -
    +

    -Typedef Index

    +Typedef Index

    A B C D E F G H I L N O P R S T U V W

    diff --git a/doc/sf_and_dist/html/index/s16.html b/doc/sf_and_dist/html/index/s16.html index 40236e492..06856a35b 100644 --- a/doc/sf_and_dist/html/index/s16.html +++ b/doc/sf_and_dist/html/index/s16.html @@ -22,9 +22,9 @@
    PrevUpHomeNext
    -
    +

    -Macro Index

    +Macro Index

    B F

    diff --git a/doc/sf_and_dist/html/index/s17.html b/doc/sf_and_dist/html/index/s17.html index db4343dd2..4ff6d32c4 100644 --- a/doc/sf_and_dist/html/index/s17.html +++ b/doc/sf_and_dist/html/index/s17.html @@ -21,9 +21,9 @@
    PrevUpHome
    -
    +

    -Index

    +Index

    A B C D E F G H I J K L M N O P Q R S T U V W Z

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/students_t_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/students_t_dist.html index 03d40e7e8..00372bbd1 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/students_t_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/students_t_dist.html @@ -65,8 +65,9 @@

    A statistical distribution published by William Gosset in 1908. His employer, - Guinness Breweries, required him to publish under a pseudonym, so he - chose "Student". Given N independent measurements, let + Guinness Breweries, required him to publish under a pseudonym (possibly + to hide that they were using statistics), so he chose "Student". + Given N independent measurements, let

    @@ -331,6 +332,18 @@ + +

    + mode +

    + + +

    + 0 +

    + + +

    mean @@ -350,19 +363,7 @@

    - v / (v - 2) -

    - - - - -

    - mode -

    - - -

    - 0 + if (v > 2) v / (v - 2) else NaN

    @@ -374,7 +375,7 @@

    - 0 + if (v > 3) 0 else NaN

    @@ -386,7 +387,7 @@

    - 3 * (v - 2) / (v - 4) + if (v > 4) 3 * (v - 2) / (v - 4) else NaN

    @@ -398,12 +399,22 @@

    - 6 / (df - 4) + if (v > 4) 6 / (df - 4) else NaN

    +

    + If the moment index k is less than v, then the moment is undefined. Evaluating + the moment will throw a 'domain_error' unless ignored by a policy, when + it will return 'std::numeric_limits<>::quiet_NaN();' +

    +

    + (For simplicity, we have not implemented the return of infinity in some + cases as suggested by Wikipedia + Student's t. See also https://svn.boost.org/trac/boost/ticket/7177.) +

    diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html b/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html index 0b079dff3..c2edc3872 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html @@ -27,7 +27,7 @@ Document Conventions

    - +

    This documentation aims to use of the following naming and formatting conventions. diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html b/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html index 54d2c50b9..7c2f86b2b 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html @@ -35,6 +35,14 @@

    + Boost-1.52 +
    +
    • + Corrected moments for small degrees of freedom #7177 + (reported by Thomas Mang). +
    +
    + Boost-1.51
      @@ -63,7 +71,7 @@
    - + Boost-1.50
      @@ -102,7 +110,7 @@
    - + Boost-1.49
      @@ -146,7 +154,7 @@
    - + Boost-1.48
      @@ -197,7 +205,7 @@
    - + Boost-1.47
      @@ -214,7 +222,7 @@
    - + Boost-1.46.1
    • @@ -222,7 +230,7 @@ #5113.
    - + Boost-1.46.0
      @@ -237,7 +245,7 @@
    - + Boost-1.45.0
      @@ -254,7 +262,7 @@
    - + Boost-1.44.0
      @@ -268,7 +276,7 @@
    - + Boost-1.41.0
    • @@ -276,7 +284,7 @@ and its inverse.
    - + Boost-1.40.0
      @@ -313,7 +321,7 @@
    - + Boost-1.38.0
      @@ -325,14 +333,14 @@
    - + Boost-1.37.0
    • Improved accuracy and testing of the inverse hypergeometric functions.
    - + Boost-1.36.0
      @@ -365,7 +373,7 @@
    - + Boost-1.35.0: Post Review First Official Release
    @@ -397,7 +405,7 @@
    - + Milestone 4: Second Review Candidate (1st March 2007)
    @@ -411,7 +419,7 @@
    - + Milestone 3: First Review Candidate (31st Dec 2006)
    @@ -439,7 +447,7 @@
    - + Milestone 2: Released September 10th 2006
    @@ -475,7 +483,7 @@
    - + Milestone 1: Released March 31st 2006
    diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html index 8056c760c..1af20cbf7 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html @@ -27,7 +27,7 @@ Navigation

    - +

    Boost.Math documentation is provided in both HTML and PDF formats. diff --git a/doc/sf_and_dist/html/math_toolkit/special/airy/ai.html b/doc/sf_and_dist/html/math_toolkit/special/airy/ai.html index dcce1334b..35c3a6eb7 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/airy/ai.html +++ b/doc/sf_and_dist/html/math_toolkit/special/airy/ai.html @@ -58,6 +58,10 @@

    +

    + See Weisstein, Eric W. "Airy Functions." From MathWorld--A Wolfram + Web Resource. http://mathworld.wolfram.com/AiryFunctions.html; +

    The final Policy argument is optional and can be used to control the behaviour of the function: how @@ -92,7 +96,7 @@

    Since this function is implemented in terms of other special functions, - there are only a few basic sanity checks, using test values from Wolfram Airy Functions. + there are only a few basic sanity checks, using test values from Wolfram Airy Functions.

    diff --git a/doc/sf_and_dist/html/math_toolkit/special/airy/aip.html b/doc/sf_and_dist/html/math_toolkit/special/airy/aip.html index 0beaf8259..92c2b288e 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/airy/aip.html +++ b/doc/sf_and_dist/html/math_toolkit/special/airy/aip.html @@ -92,7 +92,7 @@

    Since this function is implemented in terms of other special functions, - there are only a few basic sanity checks, using test values from functions.wolfram.com. + there are only a few basic sanity checks, using test values from functions.wolfram.com.

    diff --git a/doc/sf_and_dist/html/math_toolkit/special/airy/bi.html b/doc/sf_and_dist/html/math_toolkit/special/airy/bi.html index 3e9193c51..a1ea19c47 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/airy/bi.html +++ b/doc/sf_and_dist/html/math_toolkit/special/airy/bi.html @@ -92,7 +92,7 @@

    Since this function is implemented in terms of other special functions, - there are only a few basic sanity checks, using test values from functions.wolfram.com. + there are only a few basic sanity checks, using test values from functions.wolfram.com.

    diff --git a/doc/sf_and_dist/html/math_toolkit/special/airy/bip.html b/doc/sf_and_dist/html/math_toolkit/special/airy/bip.html index a24f05af6..e5b7e8ea8 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/airy/bip.html +++ b/doc/sf_and_dist/html/math_toolkit/special/airy/bip.html @@ -92,7 +92,7 @@

    Since this function is implemented in terms of other special functions, - there are only a few basic sanity checks, using test values from functions.wolfram.com. + there are only a few basic sanity checks, using test values from functions.wolfram.com.

    diff --git a/doc/sf_and_dist/html/math_toolkit/status/history1.html b/doc/sf_and_dist/html/math_toolkit/status/history1.html index 78c12f142..0882530c4 100644 --- a/doc/sf_and_dist/html/math_toolkit/status/history1.html +++ b/doc/sf_and_dist/html/math_toolkit/status/history1.html @@ -34,6 +34,14 @@

    + Boost-1.52 +
    +
    • + Corrected moments for small degrees of freedom #7177 + (reported by Thomas Mang). +
    +
    + Boost-1.51
      @@ -62,7 +70,7 @@
    - + Boost-1.50
      @@ -101,7 +109,7 @@
    - + Boost-1.49
      @@ -145,7 +153,7 @@
    - + Boost-1.48
      @@ -196,7 +204,7 @@
    - + Boost-1.47
      @@ -213,7 +221,7 @@
    - + Boost-1.46.1
    • @@ -221,7 +229,7 @@ #5113.
    - + Boost-1.46.0
      @@ -236,7 +244,7 @@
    - + Boost-1.45.0
      @@ -253,7 +261,7 @@
    - + Boost-1.44.0
      @@ -267,7 +275,7 @@
    - + Boost-1.41.0
    • @@ -275,7 +283,7 @@ and its inverse.
    - + Boost-1.40.0
      @@ -312,7 +320,7 @@
    - + Boost-1.38.0
      @@ -324,14 +332,14 @@
    - + Boost-1.37.0
    • Improved accuracy and testing of the inverse hypergeometric functions.
    - + Boost-1.36.0
      @@ -364,7 +372,7 @@
    - + Boost-1.35.0: Post Review First Official Release
    @@ -396,7 +404,7 @@
    - + Milestone 4: Second Review Candidate (1st March 2007)
    @@ -410,7 +418,7 @@
    - + Milestone 3: First Review Candidate (31st Dec 2006)
    @@ -438,7 +446,7 @@
    - + Milestone 2: Released September 10th 2006
    @@ -474,7 +482,7 @@
    - + Milestone 1: Released March 31st 2006
    From a261d44d3ed8c64aa12b204bdd9d5900243a61fd Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Mon, 6 Aug 2012 16:29:38 +0000 Subject: [PATCH 083/115] Test of using the 1/eps to switch to normal distribution. [SVN r79891] --- test/test_students_t.cpp | 23 +++++++++++++++++++++++ 1 file changed, 23 insertions(+) diff --git a/test/test_students_t.cpp b/test/test_students_t.cpp index 13a471ec2..6b15cdcb1 100644 --- a/test/test_students_t.cpp +++ b/test/test_students_t.cpp @@ -471,6 +471,29 @@ void test_spots(RealType) static_cast(1.0))), 9); + // Test for large degrees of freedom when should be same as normal. + + std::string type = typeid(RealType).name(); + if (type != "class boost::math::concepts::real_concept") + { + RealType limit = 1/ boost::math::tools::epsilon(); + // Default policy to get full accuracy. + // std::cout << "Switch over to normal if df > " << limit << std::endl; + // float Switch over to normal if df > 8.38861e+006 + // double Switch over to normal if df > 4.5036e+015 + // Can't test real_concept - doesn't converge. + + boost::math::normal_distribution n(0, 1); // + students_t_distribution st(boost::math::tools::max_value()); // Well over the switchover point, + // PDF + BOOST_CHECK_EQUAL(pdf(st, 0), pdf(n, 0.)); // should be exactly equal. + students_t_distribution st2(limit /5 ); // Just below the switchover point, + BOOST_CHECK_CLOSE_FRACTION(pdf(st2, 0), pdf(n, 0.), tolerance); // should be very close to normal. + // CDF + BOOST_CHECK_EQUAL(cdf(st, 0), cdf(n, 0.)); // should be exactly equal. + BOOST_CHECK_CLOSE_FRACTION(cdf(st2, 0), cdf(n, 0.), tolerance); // should be very close to normal. + } + // Checks added for Trac #7717 report by Thomas Mang. RealType inf = std::numeric_limits::infinity(); From 5d887432cdfb2ea78cbdc9e803e65c464111cd31 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Mon, 6 Aug 2012 16:30:12 +0000 Subject: [PATCH 084/115] Using the 1/eps to switch to normal distribution. [SVN r79892] --- .../boost/math/distributions/students_t.hpp | 127 +++++++++++------- 1 file changed, 80 insertions(+), 47 deletions(-) diff --git a/include/boost/math/distributions/students_t.hpp b/include/boost/math/distributions/students_t.hpp index dfd5ae0ab..5dfce88c9 100644 --- a/include/boost/math/distributions/students_t.hpp +++ b/include/boost/math/distributions/students_t.hpp @@ -14,6 +14,7 @@ #include // for ibeta(a, b, x). #include #include +#include #include @@ -53,9 +54,9 @@ public: private: // - // Data members: + // Data member: // - RealType m_df; // degrees of freedom are a real number. + RealType m_df; // degrees of freedom is a real number. }; typedef students_t_distribution students_t; @@ -63,6 +64,7 @@ typedef students_t_distribution students_t; template inline const std::pair range(const students_t_distribution& /*dist*/) { // Range of permissible values for random variable x. + // No including infinity. using boost::math::tools::max_value; return std::pair(-max_value(), max_value()); } @@ -76,32 +78,48 @@ inline const std::pair support(const students_t_distribution } template -inline RealType pdf(const students_t_distribution& dist, const RealType& t) +inline RealType pdf(const students_t_distribution& dist, const RealType& x) { BOOST_FPU_EXCEPTION_GUARD BOOST_MATH_STD_USING // for ADL of std functions RealType degrees_of_freedom = dist.degrees_of_freedom(); - // Error check: + // common handling Error check is for finite and > 0: + // Might conceivably permit df = +infinity too? RealType error_result; if(false == detail::check_df( "boost::math::pdf(const students_t_distribution<%1%>&, %1%)", degrees_of_freedom, &error_result, Policy())) return error_result; if(false == detail::check_x( - "boost::math::pdf(const students_t_distribution<%1%>&, %1%)", t, &error_result, Policy())) + "boost::math::pdf(const students_t_distribution<%1%>&, %1%)", x, &error_result, Policy())) return error_result; - // Might conceivably permit df = +infinity and use normal distribution. + RealType result; - RealType basem1 = t * t / degrees_of_freedom; - if(basem1 < 0.125) - { - result = exp(-boost::math::log1p(basem1, Policy()) * (1+degrees_of_freedom) / 2); + + RealType limit = policies::get_epsilon(); + // Use policies so that if policy requests lower precision, + // then get the normal distribution approximation earlier. + limit = static_cast(1) / limit; // 1/eps + // for 64-bit double 1/eps = 4503599627370496 + if (degrees_of_freedom > limit) + { // Special case for really big degrees_of_freedom > 1 / eps (perhaps infinite?) + // - use normal distribution which is much faster and more accurate. + normal_distribution n(0, 1); + result = pdf(n, x); } else - { - result = pow(1 / (1 + basem1), (degrees_of_freedom + 1) / 2); + { // + RealType basem1 = x * x / degrees_of_freedom; + if(basem1 < 0.125) + { + result = exp(-boost::math::log1p(basem1, Policy()) * (1+degrees_of_freedom) / 2); + } + else + { + result = pow(1 / (1 + basem1), (degrees_of_freedom + 1) / 2); + } + result /= sqrt(degrees_of_freedom) * boost::math::beta(degrees_of_freedom / 2, RealType(0.5f), Policy()); } - result /= sqrt(degrees_of_freedom) * boost::math::beta(degrees_of_freedom / 2, RealType(0.5f), Policy()); return result; } // pdf @@ -122,37 +140,54 @@ inline RealType cdf(const students_t_distribution& dist, const { return 0.5; } - // - // Calculate probability of Student's t using the incomplete beta function. - // probability = ibeta(degrees_of_freedom / 2, 1/2, degrees_of_freedom / (degrees_of_freedom + t*t)) - // - // However when t is small compared to the degrees of freedom, that formula - // suffers from rounding error, use the identity formula to work around - // the problem: - // - // I[x](a,b) = 1 - I[1-x](b,a) - // - // and: - // - // x = df / (df + t^2) - // - // so: - // - // 1 - x = t^2 / (df + t^2) - // - RealType t2 = t * t; - RealType probability; - if(degrees_of_freedom > 2 * t2) - { - RealType z = t2 / (degrees_of_freedom + t2); - probability = ibetac(static_cast(0.5), degrees_of_freedom / 2, z, Policy()) / 2; + + RealType limit = policies::get_epsilon(); + // Use policies so that if policy requests lower precision, + // then get the normal distribution approximation earlier. + limit = static_cast(1) / limit; // 1/eps + // for 64-bit double 1/eps = 4503599627370496 + if (degrees_of_freedom > limit) + { // Special case for really big degrees_of_freedom > 1 / eps (perhaps infinite?) + // - use normal distribution which is much faster and more accurate. + normal_distribution n(0, 1); + RealType result = cdf(n, t); + return result; } else - { - RealType z = degrees_of_freedom / (degrees_of_freedom + t2); - probability = ibeta(degrees_of_freedom / 2, static_cast(0.5), z, Policy()) / 2; - } - return (t > 0 ? 1 - probability : probability); + { // normal case. + + // + // Calculate probability of Student's t using the incomplete beta function. + // probability = ibeta(degrees_of_freedom / 2, 1/2, degrees_of_freedom / (degrees_of_freedom + t*t)) + // + // However when t is small compared to the degrees of freedom, that formula + // suffers from rounding error, use the identity formula to work around + // the problem: + // + // I[x](a,b) = 1 - I[1-x](b,a) + // + // and: + // + // x = df / (df + t^2) + // + // so: + // + // 1 - x = t^2 / (df + t^2) + // + RealType t2 = t * t; + RealType probability; + if(degrees_of_freedom > 2 * t2) + { + RealType z = t2 / (degrees_of_freedom + t2); + probability = ibetac(static_cast(0.5), degrees_of_freedom / 2, z, Policy()) / 2; + } + else + { + RealType z = degrees_of_freedom / (degrees_of_freedom + t2); + probability = ibeta(degrees_of_freedom / 2, static_cast(0.5), z, Policy()) / 2; + } + return (t > 0 ? 1 - probability : probability); + } } // cdf template @@ -182,10 +217,9 @@ inline RealType quantile(const students_t_distribution& dist, if (probability == static_cast(0.5)) return 0; // - // This next block is disabled in favour of a faster method than - // incomplete beta inverse, code retained for future reference: - // #if 0 + // This next block is disabled in favour of a faster method than + // incomplete beta inverse, but code retained for future reference: // // Calculate quantile of Student's t using the incomplete beta function inverse: // @@ -326,8 +360,7 @@ inline RealType variance(const students_t_distribution& dist) // Revised for https://svn.boost.org/trac/boost/ticket/7177 RealType df = dist.degrees_of_freedom(); if (!(boost::math::isfinite)(df) || (df <= 2)) - { // Infinity or NaN - + { // Infinity or NaN. policies::raise_domain_error( "boost::math::variance(students_t_distribution<%1%> const&, %1%)", "variance is undefined for degrees of freedom <= 2, but got %1%.", From cf1d644c4e397a13099705e0a2e1ad424166a3a0 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Tue, 7 Aug 2012 15:53:54 +0000 Subject: [PATCH 085/115] Major update to allow df == +infinity. [SVN r79911] --- .../detail/common_error_handling.hpp | 1 + .../boost/math/distributions/students_t.hpp | 215 ++++++++++++------ 2 files changed, 144 insertions(+), 72 deletions(-) diff --git a/include/boost/math/distributions/detail/common_error_handling.hpp b/include/boost/math/distributions/detail/common_error_handling.hpp index 46ded33cd..931747485 100644 --- a/include/boost/math/distributions/detail/common_error_handling.hpp +++ b/include/boost/math/distributions/detail/common_error_handling.hpp @@ -13,6 +13,7 @@ #include // using boost::math::isfinite; + namespace boost{ namespace math{ namespace detail { diff --git a/include/boost/math/distributions/students_t.hpp b/include/boost/math/distributions/students_t.hpp index 5dfce88c9..5ed4c9877 100644 --- a/include/boost/math/distributions/students_t.hpp +++ b/include/boost/math/distributions/students_t.hpp @@ -1,5 +1,7 @@ // Copyright John Maddock 2006. -// Copyright Paul A. Bristow 2006. +// Copyright Paul A. Bristow 2006, 2012. +// Copyright Thomas Mang 2012. + // Use, modification and distribution are subject to the // Boost Software License, Version 1.0. (See accompanying file // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) @@ -25,6 +27,20 @@ namespace boost{ namespace math{ +template +inline bool check_df(const char* function, RealType const& df, RealType* result, const Policy& pol) +{ // df > 0 or +infinity are allowed. + // if((df <= 0) || (boost::math::isnan)(df)) // but use signbit to ensure catch -inf and -NaN. + if(((boost::math::signbit)(df) != 0) || (boost::math::isnan)(df)) + { // is bad df <= 0 or NaN or -infinity. + *result = policies::raise_domain_error( + function, + "Degrees of freedom argument is %1%, but must be > 0 !", df, pol); + return false; + } + return true; +} // check_df + template > class students_t_distribution { @@ -32,16 +48,16 @@ public: typedef RealType value_type; typedef Policy policy_type; - students_t_distribution(RealType i) : m_df(i) + students_t_distribution(RealType df) : df_(df) { // Constructor. RealType result; - detail::check_df( - "boost::math::students_t_distribution<%1%>::students_t_distribution", m_df, &result, Policy()); + check_df( // Checks that df > 0 or df == inf. + "boost::math::students_t_distribution<%1%>::students_t_distribution", df_, &result, Policy()); } // students_t_distribution RealType degrees_of_freedom()const { - return m_df; + return df_; } // Parameter estimation: @@ -53,18 +69,16 @@ public: RealType hint = 100); private: - // // Data member: - // - RealType m_df; // degrees of freedom is a real number. + RealType df_; // degrees of freedom is a real number or +infinity. }; -typedef students_t_distribution students_t; +typedef students_t_distribution students_t; // Convenience typedef for double version. template inline const std::pair range(const students_t_distribution& /*dist*/) { // Range of permissible values for random variable x. - // No including infinity. + // NOT including infinity. using boost::math::tools::max_value; return std::pair(-max_value(), max_value()); } @@ -81,81 +95,89 @@ template inline RealType pdf(const students_t_distribution& dist, const RealType& x) { BOOST_FPU_EXCEPTION_GUARD - BOOST_MATH_STD_USING // for ADL of std functions + BOOST_MATH_STD_USING // for ADL of std functions. - RealType degrees_of_freedom = dist.degrees_of_freedom(); - // common handling Error check is for finite and > 0: - // Might conceivably permit df = +infinity too? RealType error_result; - if(false == detail::check_df( - "boost::math::pdf(const students_t_distribution<%1%>&, %1%)", degrees_of_freedom, &error_result, Policy())) - return error_result; if(false == detail::check_x( "boost::math::pdf(const students_t_distribution<%1%>&, %1%)", x, &error_result, Policy())) return error_result; + RealType df = dist.degrees_of_freedom(); + if(false == check_df( // Check that df > 0 or == +infinity. + "boost::math::pdf(const students_t_distribution<%1%>&, %1%)", df, &error_result, Policy())) + return error_result; RealType result; - + if (boost::math::isinf(x)) + { // +infinity. + normal_distribution n(0, 1); + RealType result = pdf(n, x); + return result; + } RealType limit = policies::get_epsilon(); // Use policies so that if policy requests lower precision, // then get the normal distribution approximation earlier. limit = static_cast(1) / limit; // 1/eps // for 64-bit double 1/eps = 4503599627370496 - if (degrees_of_freedom > limit) - { // Special case for really big degrees_of_freedom > 1 / eps (perhaps infinite?) + if (df > limit) + { // Special case for really big degrees_of_freedom > 1 / eps // - use normal distribution which is much faster and more accurate. normal_distribution n(0, 1); result = pdf(n, x); } else { // - RealType basem1 = x * x / degrees_of_freedom; + RealType basem1 = x * x / df; if(basem1 < 0.125) { - result = exp(-boost::math::log1p(basem1, Policy()) * (1+degrees_of_freedom) / 2); + result = exp(-boost::math::log1p(basem1, Policy()) * (1+df) / 2); } else { - result = pow(1 / (1 + basem1), (degrees_of_freedom + 1) / 2); + result = pow(1 / (1 + basem1), (df + 1) / 2); } - result /= sqrt(degrees_of_freedom) * boost::math::beta(degrees_of_freedom / 2, RealType(0.5f), Policy()); + result /= sqrt(df) * boost::math::beta(df / 2, RealType(0.5f), Policy()); } return result; } // pdf template -inline RealType cdf(const students_t_distribution& dist, const RealType& t) +inline RealType cdf(const students_t_distribution& dist, const RealType& x) { - RealType degrees_of_freedom = dist.degrees_of_freedom(); - // Error check: RealType error_result; - if(false == detail::check_df( - "boost::math::cdf(const students_t_distribution<%1%>&, %1%)", degrees_of_freedom, &error_result, Policy())) - return error_result; if(false == detail::check_x( - "boost::math::pdf(const students_t_distribution<%1%>&, %1%)", t, &error_result, Policy())) + "boost::math::pdf(const students_t_distribution<%1%>&, %1%)", x, &error_result, Policy())) + return error_result; + RealType df = dist.degrees_of_freedom(); + // Error check: + + if(false == check_df( // Check that df > 0 or == +infinity. + "boost::math::cdf(const students_t_distribution<%1%>&, %1%)", df, &error_result, Policy())) return error_result; - if (t == 0) - { - return 0.5; + if (x == 0) + { // Special case with exact result. + return static_cast(0.5); + } + if (boost::math::isinf(x)) + { // +infinity. + normal_distribution n(0, 1); + RealType result = cdf(n, x); + return result; } - RealType limit = policies::get_epsilon(); // Use policies so that if policy requests lower precision, // then get the normal distribution approximation earlier. limit = static_cast(1) / limit; // 1/eps // for 64-bit double 1/eps = 4503599627370496 - if (degrees_of_freedom > limit) + if (df > limit) { // Special case for really big degrees_of_freedom > 1 / eps (perhaps infinite?) // - use normal distribution which is much faster and more accurate. normal_distribution n(0, 1); - RealType result = cdf(n, t); + RealType result = cdf(n, x); return result; } else - { // normal case. - + { // normal df case. // // Calculate probability of Student's t using the incomplete beta function. // probability = ibeta(degrees_of_freedom / 2, 1/2, degrees_of_freedom / (degrees_of_freedom + t*t)) @@ -174,19 +196,19 @@ inline RealType cdf(const students_t_distribution& dist, const // // 1 - x = t^2 / (df + t^2) // - RealType t2 = t * t; + RealType x2 = x * x; RealType probability; - if(degrees_of_freedom > 2 * t2) + if(df > 2 * x2) { - RealType z = t2 / (degrees_of_freedom + t2); - probability = ibetac(static_cast(0.5), degrees_of_freedom / 2, z, Policy()) / 2; + RealType z = x2 / (df + x2); + probability = ibetac(static_cast(0.5), df / 2, z, Policy()) / 2; } else { - RealType z = degrees_of_freedom / (degrees_of_freedom + t2); - probability = ibeta(degrees_of_freedom / 2, static_cast(0.5), z, Policy()) / 2; + RealType z = df / (df + x2); + probability = ibeta(df / 2, static_cast(0.5), z, Policy()) / 2; } - return (t > 0 ? 1 - probability : probability); + return (x > 0 ? 1 - probability : probability); } } // cdf @@ -196,26 +218,23 @@ inline RealType quantile(const students_t_distribution& dist, BOOST_MATH_STD_USING // for ADL of std functions // // Obtain parameters: - // - RealType degrees_of_freedom = dist.degrees_of_freedom(); RealType probability = p; - // + // Check for domain errors: - // + RealType df = dist.degrees_of_freedom(); static const char* function = "boost::math::quantile(const students_t_distribution<%1%>&, %1%)"; RealType error_result; - if(false == (detail::check_df( - function, degrees_of_freedom, &error_result, Policy()) + if(false == (check_df( // Check that df > 0 or == +infinity. + function, df, &error_result, Policy()) && detail::check_probability(function, probability, &error_result, Policy()))) return error_result; - // Special cases, regardless of degrees_of_freedom. if (probability == 0) return -policies::raise_overflow_error(function, 0, Policy()); if (probability == 1) return policies::raise_overflow_error(function, 0, Policy()); if (probability == static_cast(0.5)) - return 0; + return 0; // // #if 0 // This next block is disabled in favour of a faster method than @@ -245,7 +264,7 @@ inline RealType quantile(const students_t_distribution& dist, // and a couple of epsilon at double precision and in the central // region where most use cases will occur... // - return boost::math::detail::fast_students_t_quantile(degrees_of_freedom, probability, Policy()); + return boost::math::detail::fast_students_t_quantile(df, probability, Policy()); } // quantile template @@ -276,7 +295,9 @@ struct sample_size_func RealType operator()(const RealType& df) { if(df <= tools::min_value()) + { // return 1; + } students_t_distribution t(df); RealType qa = quantile(complement(t, alpha)); RealType qb = quantile(complement(t, beta)); @@ -329,13 +350,15 @@ RealType students_t_distribution::find_degrees_of_freedom( template inline RealType mode(const students_t_distribution& /*dist*/) { - return 0; + // Assume no checks on degrees of freedom are useful (unlike mean). + return 0; // Always zero by definition. } template inline RealType median(const students_t_distribution& /*dist*/) { - return 0; + // Assume no checks on degrees of freedom are useful (unlike mean). + return 0; // Always zero by definition. } // See section 5.1 on moments at http://en.wikipedia.org/wiki/Student%27s_t-distribution @@ -344,37 +367,53 @@ template inline RealType mean(const students_t_distribution& dist) { // Revised for https://svn.boost.org/trac/boost/ticket/7177 RealType df = dist.degrees_of_freedom(); - if((!(boost::math::isfinite)(df)) || (df <= 1) )// Undefined for moment <= 1 - { + if(((boost::math::isnan)(df)) || (df <= 1) ) + { // mean is undefined for moment <= 1! policies::raise_domain_error( "boost::math::mean(students_t_distribution<%1%> const&, %1%)", "Mean is undefined for degrees of freedom < 1 but got %1%.", df, Policy()); return std::numeric_limits::quiet_NaN(); } return 0; -} +} // mean template inline RealType variance(const students_t_distribution& dist) { // http://en.wikipedia.org/wiki/Student%27s_t-distribution // Revised for https://svn.boost.org/trac/boost/ticket/7177 RealType df = dist.degrees_of_freedom(); - if (!(boost::math::isfinite)(df) || (df <= 2)) - { // Infinity or NaN. + if ((boost::math::isnan)(df) || (df <= 2)) + { // NaN or undefined for <= 2. policies::raise_domain_error( "boost::math::variance(students_t_distribution<%1%> const&, %1%)", "variance is undefined for degrees of freedom <= 2, but got %1%.", df, Policy()); return std::numeric_limits::quiet_NaN(); // Undefined. } - return df / (df - 2); + if (boost::math::isinf(df)) + { // +infinity. + return 1; + } + RealType limit = policies::get_epsilon(); + // Use policies so that if policy requests lower precision, + // then get the normal distribution approximation earlier. + limit = static_cast(1) / limit; // 1/eps + // for 64-bit double 1/eps = 4503599627370496 + if (df > limit) + { // Special case for really big degrees_of_freedom > 1 / eps. + return 1; + } + else + { + return df / (df - 2); + } } // variance template inline RealType skewness(const students_t_distribution& dist) { RealType df = dist.degrees_of_freedom(); - if( (!(boost::math::isfinite)(df)) || (dist.degrees_of_freedom() <= 3)) + if( ((boost::math::isnan)(df)) || (dist.degrees_of_freedom() <= 3)) { // Undefined for moment k = 3. policies::raise_domain_error( "boost::math::skewness(students_t_distribution<%1%> const&, %1%)", @@ -382,14 +421,14 @@ inline RealType skewness(const students_t_distribution& dist) dist.degrees_of_freedom(), Policy()); return std::numeric_limits::quiet_NaN(); } - return 0; -} + return 0; // For all valid df, including infinity. +} // skewness template inline RealType kurtosis(const students_t_distribution& dist) { RealType df = dist.degrees_of_freedom(); - if((!(boost::math::isfinite)(df)) || (df <= 4)) + if(((boost::math::isnan)(df)) || (df <= 4)) { // Undefined or infinity for moment k = 4. policies::raise_domain_error( "boost::math::kurtosis(students_t_distribution<%1%> const&, %1%)", @@ -397,9 +436,25 @@ inline RealType kurtosis(const students_t_distribution& dist) df, Policy()); return std::numeric_limits::quiet_NaN(); // Undefined. } - //return 3 * (df - 2) / (df - 4); - return 6 / (df - 4) + 3; -} + if (boost::math::isinf(df)) + { // +infinity. + return 3; + } + RealType limit = policies::get_epsilon(); + // Use policies so that if policy requests lower precision, + // then get the normal distribution approximation earlier. + limit = static_cast(1) / limit; // 1/eps + // for 64-bit double 1/eps = 4503599627370496 + if (df > limit) + { // Special case for really big degrees_of_freedom > 1 / eps. + return 3; + } + else + { + //return 3 * (df - 2) / (df - 4); re-arranged to + return 6 / (df - 4) + 3; + } +} // kurtosis template inline RealType kurtosis_excess(const students_t_distribution& dist) @@ -407,7 +462,7 @@ inline RealType kurtosis_excess(const students_t_distribution& // see http://mathworld.wolfram.com/Kurtosis.html RealType df = dist.degrees_of_freedom(); - if((!(boost::math::isfinite)(df)) || (df <= 4)) + if(((boost::math::isnan)(df)) || (df <= 4)) { // Undefined or infinity for moment k = 4. policies::raise_domain_error( "boost::math::kurtosis_excess(students_t_distribution<%1%> const&, %1%)", @@ -415,7 +470,23 @@ inline RealType kurtosis_excess(const students_t_distribution& df, Policy()); return std::numeric_limits::quiet_NaN(); // Undefined. } - return 6 / (df - 4); + if (boost::math::isinf(df)) + { // +infinity. + return 0; + } + RealType limit = policies::get_epsilon(); + // Use policies so that if policy requests lower precision, + // then get the normal distribution approximation earlier. + limit = static_cast(1) / limit; // 1/eps + // for 64-bit double 1/eps = 4503599627370496 + if (df > limit) + { // Special case for really big degrees_of_freedom > 1 / eps. + return 0; + } + else + { + return 6 / (df - 4); + } } } // namespace math From 7737ce6a06a5a316ea4715546b73c3938198ba85 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Tue, 7 Aug 2012 15:56:27 +0000 Subject: [PATCH 086/115] Tets for Major update to allow df == +infinity. [SVN r79912] --- test/test_constant_generate.cpp | 1 + 1 file changed, 1 insertion(+) diff --git a/test/test_constant_generate.cpp b/test/test_constant_generate.cpp index 58b37f6f4..1da7408cc 100644 --- a/test/test_constant_generate.cpp +++ b/test/test_constant_generate.cpp @@ -32,6 +32,7 @@ int main() BOOST_CONSTANTS_GENERATE(root_three); BOOST_CONSTANTS_GENERATE(half_root_two); BOOST_CONSTANTS_GENERATE(ln_two); + BOOST_CONSTANTS_GENERATE(ln_ten); BOOST_CONSTANTS_GENERATE(ln_ln_two); BOOST_CONSTANTS_GENERATE(root_ln_four); BOOST_CONSTANTS_GENERATE(one_div_root_two); From f2e2e0890856c6be846ae7dda66a83016f0eed3e Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Wed, 8 Aug 2012 09:26:47 +0000 Subject: [PATCH 087/115] Changed to use if (typeid(RealType) != typeid(boost::math::concepts::real_concept)) { // Ordinary floats only. to avoid failure of previous string name comparison by gcc and other platforms. [SVN r79921] --- test/test_students_t.cpp | 56 ++++++++++++++++++++++++++++++---------- 1 file changed, 42 insertions(+), 14 deletions(-) diff --git a/test/test_students_t.cpp b/test/test_students_t.cpp index 6b15cdcb1..150905d54 100644 --- a/test/test_students_t.cpp +++ b/test/test_students_t.cpp @@ -472,10 +472,13 @@ void test_spots(RealType) 9); // Test for large degrees of freedom when should be same as normal. + RealType inf = std::numeric_limits::infinity(); + RealType nan = std::numeric_limits::quiet_NaN(); std::string type = typeid(RealType).name(); - if (type != "class boost::math::concepts::real_concept") - { +// if (type != "class boost::math::concepts::real_concept") fails for gcc + if (typeid(RealType) != typeid(boost::math::concepts::real_concept)) + { // Ordinary floats only. RealType limit = 1/ boost::math::tools::epsilon(); // Default policy to get full accuracy. // std::cout << "Switch over to normal if df > " << limit << std::endl; @@ -492,12 +495,20 @@ void test_spots(RealType) // CDF BOOST_CHECK_EQUAL(cdf(st, 0), cdf(n, 0.)); // should be exactly equal. BOOST_CHECK_CLOSE_FRACTION(cdf(st2, 0), cdf(n, 0.), tolerance); // should be very close to normal. - } + // Tests for df = infinity. + students_t_distribution infdf(inf); + BOOST_CHECK_EQUAL(infdf.degrees_of_freedom(), inf); + BOOST_CHECK_EQUAL(mean(infdf), 0); // OK. + BOOST_CHECK_THROW(students_t_distribution minfdf(-inf), std::domain_error); + BOOST_CHECK_THROW(students_t_distribution minfdf(nan), std::domain_error); + BOOST_CHECK_THROW(students_t_distribution minfdf(-nan), std::domain_error); + + // BOOST_CHECK_CLOSE_FRACTION(pdf(infdf, 0), static_cast(0.3989422804014326779399460599343818684759L), tolerance); + BOOST_CHECK_CLOSE_FRACTION(pdf(infdf, 0),boost::math::constants::one_div_root_two_pi() , tolerance); + BOOST_CHECK_CLOSE_FRACTION(cdf(infdf, 0),boost::math::constants::half() , tolerance); // Checks added for Trac #7717 report by Thomas Mang. - RealType inf = std::numeric_limits::infinity(); - RealType nan = std::numeric_limits::quiet_NaN(); BOOST_CHECK_THROW(quantile(dist, -1), std::domain_error); BOOST_CHECK_THROW(quantile(dist, 2), std::domain_error); @@ -505,15 +516,18 @@ void test_spots(RealType) BOOST_CHECK_THROW(pdf(students_t_distribution(-1), 0), std::domain_error); // Check on df for mean (moment k = 1) + BOOST_CHECK_THROW(mean(students_t_distribution(nan)), std::domain_error); +// BOOST_CHECK_THROW(mean(students_t_distribution(inf)), std::domain_error); inf is now OK BOOST_CHECK_THROW(mean(students_t_distribution(-1)), std::domain_error); BOOST_CHECK_THROW(mean(students_t_distribution(0)), std::domain_error); BOOST_CHECK_THROW(mean(students_t_distribution(1)), std::domain_error); // df == k BOOST_CHECK_EQUAL(mean(students_t_distribution(2)), 0); // OK. + BOOST_CHECK_EQUAL(mean(students_t_distribution(inf)), 0); // OK. // Check on df for variance (moment 2) BOOST_CHECK_THROW(variance(students_t_distribution(nan)), std::domain_error); - BOOST_CHECK_THROW(variance(students_t_distribution(inf)), std::domain_error); +// BOOST_CHECK_THROW(variance(students_t_distribution(inf)), std::domain_error); // inf is now OK. BOOST_CHECK_THROW(variance(students_t_distribution(-1)), std::domain_error); BOOST_CHECK_THROW(variance(students_t_distribution(0)), std::domain_error); BOOST_CHECK_THROW(variance(students_t_distribution(1)), std::domain_error); @@ -522,8 +536,10 @@ void test_spots(RealType) BOOST_CHECK_THROW(variance(students_t_distribution(2)), std::domain_error); // df == BOOST_CHECK_EQUAL(variance(students_t_distribution(2.5)), 5); // OK. BOOST_CHECK_EQUAL(variance(students_t_distribution(3)), 3); // OK. + BOOST_CHECK_EQUAL(variance(students_t_distribution(inf)), 1); // OK. // Check on df for skewness (moment 3) + BOOST_CHECK_THROW(skewness(students_t_distribution(nan)), std::domain_error); BOOST_CHECK_THROW(skewness(students_t_distribution(-1)), std::domain_error); BOOST_CHECK_THROW(skewness(students_t_distribution(0)), std::domain_error); BOOST_CHECK_THROW(skewness(students_t_distribution(1)), std::domain_error); @@ -532,8 +548,10 @@ void test_spots(RealType) BOOST_CHECK_THROW(skewness(students_t_distribution(3)), std::domain_error); // df == k BOOST_CHECK_EQUAL(skewness(students_t_distribution(3.5)), 0); // OK. BOOST_CHECK_EQUAL(skewness(students_t_distribution(4)), 0); // OK. + BOOST_CHECK_EQUAL(skewness(students_t_distribution(inf)), 0); // OK. // Check on df for kurtosis_excess (moment 4) + BOOST_CHECK_THROW(kurtosis_excess(students_t_distribution(nan)), std::domain_error); BOOST_CHECK_THROW(kurtosis_excess(students_t_distribution(-1)), std::domain_error); BOOST_CHECK_THROW(kurtosis_excess(students_t_distribution(0)), std::domain_error); BOOST_CHECK_THROW(kurtosis_excess(students_t_distribution(1)), std::domain_error); @@ -543,8 +561,10 @@ void test_spots(RealType) BOOST_CHECK_THROW(kurtosis_excess(students_t_distribution(3)), std::domain_error); BOOST_CHECK_THROW(kurtosis_excess(students_t_distribution(4)), std::domain_error); // df == k BOOST_CHECK_EQUAL(kurtosis_excess(students_t_distribution(5)), 6); // OK. + BOOST_CHECK_EQUAL(kurtosis_excess(students_t_distribution(inf)), 0); // OK. // Check on df for kurtosis (moment 4) + BOOST_CHECK_THROW(kurtosis(students_t_distribution(nan)), std::domain_error); BOOST_CHECK_THROW(kurtosis(students_t_distribution(-1)), std::domain_error); BOOST_CHECK_THROW(kurtosis(students_t_distribution(0)), std::domain_error); BOOST_CHECK_THROW(kurtosis(students_t_distribution(1)), std::domain_error); @@ -553,23 +573,29 @@ void test_spots(RealType) BOOST_CHECK_THROW(kurtosis(students_t_distribution(3)), std::domain_error); BOOST_CHECK_THROW(kurtosis(students_t_distribution(4)), std::domain_error); // df == k BOOST_CHECK_EQUAL(kurtosis(students_t_distribution(5)), 9); // OK. + BOOST_CHECK_EQUAL(kurtosis(students_t_distribution(inf)), 3); // OK. + + } + // Use a new distribution ignore_error_students_t with a custom policy to ignore all errors, // and check returned values are as expected. - /* + /* Sandia-darwin-intel-12.0 - math - test_students_t / intel-darwin-12.0 - ../libs/math/test/test_students_t.cpp(544): error: "domain_error" has already been declared in the current scope using boost::math::policies::domain_error; - ^ ../libs/math/test/test_students_t.cpp(552): error: "pole_error" has already been declared in the current scope using boost::math::policies::pole_error; - Unclear where previous declaration is. Does seem to be in student_t.hpp or any included files??? + Unclear where previous declaration is. + Does not seem to be in student_t.hpp or any included files??? + So to avoid this perceived problem by this compiler, + the ignore policy below uses fully specified names. */ + using boost::math::policies::policy; // Types of error whose action can be altered by policies:. //using boost::math::policies::evaluation_error; @@ -618,7 +644,6 @@ void test_spots(RealType) BOOST_CHECK(boost::math::isnan(variance(ignore_error_students_t(2)))); // Skewness - BOOST_CHECK(boost::math::isnan(skewness(ignore_error_students_t(std::numeric_limits::quiet_NaN())))); BOOST_CHECK(boost::math::isnan(skewness(ignore_error_students_t(std::numeric_limits::quiet_NaN())))); BOOST_CHECK(boost::math::isnan(skewness(ignore_error_students_t(-1)))); BOOST_CHECK(boost::math::isnan(skewness(ignore_error_students_t(0)))); @@ -628,7 +653,6 @@ void test_spots(RealType) // Kurtosis BOOST_CHECK(boost::math::isnan(kurtosis(ignore_error_students_t(std::numeric_limits::quiet_NaN())))); - BOOST_CHECK(boost::math::isnan(kurtosis(ignore_error_students_t(std::numeric_limits::infinity())))); BOOST_CHECK(boost::math::isnan(kurtosis(ignore_error_students_t(-1)))); BOOST_CHECK(boost::math::isnan(kurtosis(ignore_error_students_t(0)))); BOOST_CHECK(boost::math::isnan(kurtosis(ignore_error_students_t(1)))); @@ -639,7 +663,6 @@ void test_spots(RealType) // Kurtosis excess BOOST_CHECK(boost::math::isnan(kurtosis_excess(ignore_error_students_t(std::numeric_limits::quiet_NaN())))); - BOOST_CHECK(boost::math::isnan(kurtosis_excess(ignore_error_students_t(std::numeric_limits::infinity())))); BOOST_CHECK(boost::math::isnan(kurtosis_excess(ignore_error_students_t(-1)))); BOOST_CHECK(boost::math::isnan(kurtosis_excess(ignore_error_students_t(0)))); BOOST_CHECK(boost::math::isnan(kurtosis_excess(ignore_error_students_t(1)))); @@ -657,7 +680,12 @@ void test_spots(RealType) BOOST_CHECK(boost::math::isfinite(kurtosis(ignore_error_students_t(4 + 4 * std::numeric_limits::epsilon())))); BOOST_CHECK(boost::math::isfinite(kurtosis(ignore_error_students_t(static_cast(4.0001L))))); - check_out_of_range >(1); + // check_out_of_range >(1); + // Cannot be used because fails "exception std::domain_error is expected" + // because df = +infinity is allowed. + + check_support >(students_t_distribution(1)); + } // template void test_spots(RealType) int test_main(int, char* []) From 29a0fa9d5892ce46b5e21900b429cc0ca0426dcd Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Thu, 9 Aug 2012 17:57:27 +0000 Subject: [PATCH 088/115] Changes to deal with broken links (and rebuilt so that Inspection tool can check too) [SVN r79948] --- doc/sf_and_dist/dist_tutorial.qbk | 1 + doc/sf_and_dist/distributions/binomial.qbk | 2 +- doc/sf_and_dist/html/index.html | 2 +- doc/sf_and_dist/html/index/s13.html | 4 ++-- doc/sf_and_dist/html/index/s14.html | 4 ++-- doc/sf_and_dist/html/index/s15.html | 4 ++-- doc/sf_and_dist/html/index/s16.html | 4 ++-- doc/sf_and_dist/html/index/s17.html | 4 ++-- .../math_toolkit/dist/dist_ref/dists/binomial_dist.html | 9 +++++---- .../html/math_toolkit/main_overview/conventions.html | 2 +- .../html/math_toolkit/main_overview/navigation.html | 2 +- 11 files changed, 20 insertions(+), 18 deletions(-) diff --git a/doc/sf_and_dist/dist_tutorial.qbk b/doc/sf_and_dist/dist_tutorial.qbk index 521eb0d50..361492717 100644 --- a/doc/sf_and_dist/dist_tutorial.qbk +++ b/doc/sf_and_dist/dist_tutorial.qbk @@ -1,4 +1,5 @@ [/ def names all end in distrib to avoid clashes with names of functions] + [def __binomial_distrib [link math_toolkit.dist.dist_ref.dists.binomial_dist Binomial Distribution]] [def __chi_squared_distrib [link math_toolkit.dist.dist_ref.dists.chi_squared_dist Chi Squared Distribution]] [def __normal_distrib [link math_toolkit.dist.dist_ref.dists.normal_dist Normal Distribution]] diff --git a/doc/sf_and_dist/distributions/binomial.qbk b/doc/sf_and_dist/distributions/binomial.qbk index bbe532836..9b31a3750 100644 --- a/doc/sf_and_dist/distributions/binomial.qbk +++ b/doc/sf_and_dist/distributions/binomial.qbk @@ -58,7 +58,7 @@ The class type `binomial_distribution` represents a it is used when there are exactly two mutually exclusive outcomes of a trial. These outcomes are labelled "success" and "failure". The -[@ binomial distribution] is used to obtain +__binomial_distrib is used to obtain the probability of observing k successes in N trials, with the probability of success on a single trial denoted by p. The binomial distribution assumes that p is fixed for all trials. diff --git a/doc/sf_and_dist/html/index.html b/doc/sf_and_dist/html/index.html index 93f657e4a..4e09592d7 100644 --- a/doc/sf_and_dist/html/index.html +++ b/doc/sf_and_dist/html/index.html @@ -579,7 +579,7 @@

    - +

    Last revised: August 02, 2012 at 14:37:58 GMT

    Last revised: August 09, 2012 at 17:01:44 GMT


    diff --git a/doc/sf_and_dist/html/index/s13.html b/doc/sf_and_dist/html/index/s13.html index e11b3ddc2..a80dabc70 100644 --- a/doc/sf_and_dist/html/index/s13.html +++ b/doc/sf_and_dist/html/index/s13.html @@ -22,9 +22,9 @@
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    diff --git a/doc/sf_and_dist/html/index/s16.html b/doc/sf_and_dist/html/index/s16.html index 06856a35b..352ae5031 100644 --- a/doc/sf_and_dist/html/index/s16.html +++ b/doc/sf_and_dist/html/index/s16.html @@ -22,9 +22,9 @@
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    diff --git a/doc/sf_and_dist/html/index/s17.html b/doc/sf_and_dist/html/index/s17.html index 4ff6d32c4..8b155eea0 100644 --- a/doc/sf_and_dist/html/index/s17.html +++ b/doc/sf_and_dist/html/index/s17.html @@ -21,9 +21,9 @@
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    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html index 95121b8fb..85d983501 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html @@ -88,10 +88,11 @@ represents a binomial distribution: it is used when there are exactly two mutually exclusive outcomes of a trial. These outcomes are labelled "success" - and "failure". The distribution - is used to obtain the probability of observing k successes in N trials, - with the probability of success on a single trial denoted by p. The binomial - distribution assumes that p is fixed for all trials. + and "failure". The Binomial + Distribution is used to obtain the probability of observing k + successes in N trials, with the probability of success on a single trial + denoted by p. The binomial distribution assumes that p is fixed for all + trials.

    diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html b/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html index c2edc3872..bb99eeb4e 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html @@ -27,7 +27,7 @@ Document Conventions

    - +

    This documentation aims to use of the following naming and formatting conventions. diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html index 1af20cbf7..4e84084c0 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html @@ -27,7 +27,7 @@ Navigation

    - +

    Boost.Math documentation is provided in both HTML and PDF formats. From e4cf24554b75747adaeb9788d498ed0ad78128c9 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Thu, 9 Aug 2012 17:58:46 +0000 Subject: [PATCH 089/115] Changes to deal with copyright and tabs from inspection report [SVN r79949] --- include/boost/math/distributions/skew_normal.hpp | 14 +++++++------- include/boost/math/special_functions/owens_t.hpp | 2 +- 2 files changed, 8 insertions(+), 8 deletions(-) diff --git a/include/boost/math/distributions/skew_normal.hpp b/include/boost/math/distributions/skew_normal.hpp index af89817f2..8ef9b5669 100644 --- a/include/boost/math/distributions/skew_normal.hpp +++ b/include/boost/math/distributions/skew_normal.hpp @@ -1,4 +1,4 @@ -// (C) Benjamin Sobotta 2012 +// Copyright Benjamin Sobotta 2012 // Use, modification and distribution are subject to the // Boost Software License, Version 1.0. (See accompanying file @@ -645,23 +645,23 @@ namespace boost{ namespace math{ if(false == detail::check_probability(function, p, &result, Policy())) return result; - // compute initial guess via Cornish-Fisher expansion + // Compute initial guess via Cornish-Fisher expansion. RealType x = -boost::math::erfc_inv(2 * p, Policy()) * constants::root_two(); - // avoid unnecessary computations if there is no skew + // Avoid unnecessary computations if there is no skew. if(shape != 0) { const RealType skew = skewness(dist); const RealType exk = kurtosis_excess(dist); x = x + (x*x-static_cast(1))*skew/static_cast(6) - + x*(x*x-static_cast(3))*exk/static_cast(24) - - x*(static_cast(2)*x*x-static_cast(5))*skew*skew/static_cast(36); + + x*(x*x-static_cast(3))*exk/static_cast(24) + - x*(static_cast(2)*x*x-static_cast(5))*skew*skew/static_cast(36); } // if(shape != 0) result = standard_deviation(dist)*x+mean(dist); - // handle special case of non-skew normal distribution + // handle special case of non-skew normal distribution. if(shape == 0) return result; @@ -681,7 +681,7 @@ namespace boost{ namespace math{ template inline RealType quantile(const complemented2_type, RealType>& c) - { + { const RealType scale = c.dist.scale(); const RealType location = c.dist.location(); const RealType shape = c.dist.shape(); diff --git a/include/boost/math/special_functions/owens_t.hpp b/include/boost/math/special_functions/owens_t.hpp index c632bd553..0765b2a49 100644 --- a/include/boost/math/special_functions/owens_t.hpp +++ b/include/boost/math/special_functions/owens_t.hpp @@ -1,4 +1,4 @@ -// (C) Benjamin Sobotta 2012 +// Copyright Benjamin Sobotta 2012 // Use, modification and distribution are subject to the // Boost Software License, Version 1.0. (See accompanying file From 889b73605179d29237b9e38d9b978a7b559abfa7 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Sat, 11 Aug 2012 08:58:51 +0000 Subject: [PATCH 090/115] Rebuilt html sf & dist html docs after minor edits. [SVN r79959] --- doc/sf_and_dist/html/index.html | 2 +- doc/sf_and_dist/html/index/s13.html | 4 ++-- doc/sf_and_dist/html/index/s14.html | 4 ++-- doc/sf_and_dist/html/index/s15.html | 4 ++-- doc/sf_and_dist/html/index/s16.html | 4 ++-- doc/sf_and_dist/html/index/s17.html | 4 ++-- .../html/math_toolkit/main_overview/conventions.html | 2 +- .../html/math_toolkit/main_overview/navigation.html | 2 +- 8 files changed, 13 insertions(+), 13 deletions(-) diff --git a/doc/sf_and_dist/html/index.html b/doc/sf_and_dist/html/index.html index 4e09592d7..d4d2f13da 100644 --- a/doc/sf_and_dist/html/index.html +++ b/doc/sf_and_dist/html/index.html @@ -579,7 +579,7 @@

    - +

    Last revised: August 09, 2012 at 17:01:44 GMT

    Last revised: August 11, 2012 at 08:36:53 GMT


    diff --git a/doc/sf_and_dist/html/index/s13.html b/doc/sf_and_dist/html/index/s13.html index a80dabc70..f101927c2 100644 --- a/doc/sf_and_dist/html/index/s13.html +++ b/doc/sf_and_dist/html/index/s13.html @@ -22,9 +22,9 @@
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    diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html b/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html index bb99eeb4e..7baeff9e2 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html @@ -27,7 +27,7 @@ Document Conventions

    - +

    This documentation aims to use of the following naming and formatting conventions. diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html index 4e84084c0..b911d5561 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html @@ -27,7 +27,7 @@ Navigation

    - +

    Boost.Math documentation is provided in both HTML and PDF formats. From 777defb1451f27fbb3f70d2fbdf8b02ae01091a8 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Sun, 12 Aug 2012 11:19:21 +0000 Subject: [PATCH 091/115] Added (correct) copyright and non-ASCII chars. [SVN r79975] --- example/error_handling_example.cpp | 3 +++ example/owens_t_example.cpp | 6 +++++- example/skew_normal_example.cpp | 4 ++-- 3 files changed, 10 insertions(+), 3 deletions(-) diff --git a/example/error_handling_example.cpp b/example/error_handling_example.cpp index 22c100c4a..4691e06da 100644 --- a/example/error_handling_example.cpp +++ b/example/error_handling_example.cpp @@ -51,6 +51,9 @@ is a certain sign that it will /not/ have the desired effect. We'll begin our sample program with the needed includes: */ + + #define BOOST_MATH_DOMAIN_ERROR_POLICY ignore_error + // Boost #include using boost::math::students_t; // Probability of students_t(df, t). diff --git a/example/owens_t_example.cpp b/example/owens_t_example.cpp index ecf630574..6c6d20417 100644 --- a/example/owens_t_example.cpp +++ b/example/owens_t_example.cpp @@ -1,9 +1,13 @@ -// (C) Benjamin Sobotta 2012 +// Copyright Benjamin Sobotta 2012 // Use, modification and distribution are subject to the // Boost Software License, Version 1.0. (See accompanying file // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) +#ifdef _MSC_VER +# pragma warning(disable : 4127) // conditional expression is constant. +#endif + #include #include diff --git a/example/skew_normal_example.cpp b/example/skew_normal_example.cpp index cdf20a4d2..5858aff35 100644 --- a/example/skew_normal_example.cpp +++ b/example/skew_normal_example.cpp @@ -1,4 +1,4 @@ -// (C) Benjamin Sobotta 2012 +// Copyright Benjamin Sobotta 2012 // Use, modification and distribution are subject to the // Boost Software License, Version 1.0. (See accompanying file @@ -69,7 +69,7 @@ int main() to install packages into? (y/n) y --- Please select a CRAN mirror for use in this session --- Loading Tcl/Tk interface ... done - also installing the dependency ‘mnormt’ + also installing the dependency mnormt trying URL 'http://mirrors.dotsrc.org/cran/src/contrib/mnormt_1.4-5.tar.gz' Content type 'application/x-gzip' length 34049 bytes (33 Kb) From 3a39099b41edcf9b89261d11c3d244749daf3526 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Sun, 12 Aug 2012 11:21:31 +0000 Subject: [PATCH 092/115] Added (correct) copyright and non-ASCII chars. [SVN r79976] --- test/test_out_of_range.hpp | 1 + 1 file changed, 1 insertion(+) diff --git a/test/test_out_of_range.hpp b/test/test_out_of_range.hpp index e4486552a..220684b3c 100644 --- a/test/test_out_of_range.hpp +++ b/test/test_out_of_range.hpp @@ -117,6 +117,7 @@ void check_out_of_range(typename Distro::value_type p1) if(std::numeric_limits::has_infinity) { BOOST_CHECK_THROW(pdf(Distro(std::numeric_limits::infinity()), range(d).first), std::domain_error); + // BOOST_CHECK_THROW(pdf(Distro(std::numeric_limits::infinity()), range(d).second), std::domain_error); } if(std::numeric_limits::has_quiet_NaN) { From cca8db714e6b67c9371cde7a4f6109921fdd5d89 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Sun, 12 Aug 2012 11:24:15 +0000 Subject: [PATCH 093/115] Added (correct) copyright and non-ASCII chars. [SVN r79977] --- test/test_owens_t.cpp | 284 +++--------------------------------------- 1 file changed, 17 insertions(+), 267 deletions(-) diff --git a/test/test_owens_t.cpp b/test/test_owens_t.cpp index e08981554..cdc45f4d4 100644 --- a/test/test_owens_t.cpp +++ b/test/test_owens_t.cpp @@ -1,7 +1,6 @@ -// test_owens_t.cpp - // Copyright Paul A. Bristow 2012. // Copyright Benjamin Sobotta 2012. +// Copyright John Maddock 2012. // Use, modification and distribution are subject to the // Boost Software License, Version 1.0. @@ -18,12 +17,10 @@ // not alter the result. The resultant values Tacc(h,a) say, were validated by evaluating (8) with // m = 48 (i.e. 96 point Gaussian quadrature). -#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error +// test_owens_t.cpp #ifdef _MSC_VER # pragma warning (disable : 4127) // conditional expression is constant -# pragma warning (disable : 4305) // 'initializing' : truncation from 'double' to 'const float' -// ?? TODO get rid of these warnings? #endif #include // for real_concept. @@ -31,41 +28,9 @@ using ::boost::math::concepts::real_concept; #include // for owens_t function. using boost::math::owens_t; -#include -#include -#include -#include - -#include "libs/math/test/handle_test_result.hpp" -#include "libs/math/test/table_type.hpp" -#include "libs/math/test/functor.hpp" - -// -// Defining TEST_CPP_DEC_FLOAT enables testing of multiprecision support. -// This requires the multiprecision library from sandbox/big_number. -// Note that these tests *do not pass*, but they do give an idea of the -// error rates that can be expected.... -// -#ifdef TEST_CPP_DEC_FLOAT -#include - -template -inline R convert_to(const char* s) -{ - try{ - return boost::lexical_cast(s); - } - catch(const boost::bad_lexical_cast&) - { - return 0; - } -} - -#define SC_(x) convert_to(BOOST_STRINGIZE(x)) -#endif - -#include "owens_t_T7.hpp" +#include // for test_main. +#include // for BOOST_CHECK_CLOSE and BOOST_CHECK_CLOSE_fraction. #include using std::cout; @@ -73,65 +38,13 @@ using std::endl; #include using std::numeric_limits; -void expected_results() -{ - // - // Define the max and mean errors expected for - // various compilers and platforms. - // - const char* largest_type; -#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS - if(boost::math::policies::digits >() == boost::math::policies::digits >()) - { - largest_type = "(long\\s+)?double|real_concept"; - } - else - { - largest_type = "long double|real_concept"; - } -#else - largest_type = "(long\\s+)?double"; -#endif - - // - // Catch all cases come last: - // - if(std::numeric_limits::digits > 60) - { - add_expected_result( - ".*", // compiler - ".*", // stdlib - ".*", // platform - largest_type, // test type(s) - ".*", // test data group - "boost::math::owens_t", 500, 100); // test function - } - else - { - add_expected_result( - ".*", // compiler - ".*", // stdlib - ".*", // platform - largest_type, // test type(s) - ".*", // test data group - "boost::math::owens_t", 60, 5); // test function - } - // - // Finish off by printing out the compiler/stdlib/platform names, - // we do this to make it easier to mark up expected error rates. - // - std::cout << "Tests run with " << BOOST_COMPILER << ", " - << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; -} - - template void test_spot( - RealType h, // - RealType a, // + RealType h, // + RealType a, // Chi Square statistic RealType tol) // Test tolerance { - BOOST_CHECK_CLOSE_FRACTION(owens_t(h, a), 3.89119302347013668966224771378e-2L, tol); + BOOST_CHECK_CLOSE_FRACTION(owens_t(h, a), 3.89119302347013668966224771378e-2, tol); } @@ -140,173 +53,33 @@ void test_spots(RealType) { // Basic sanity checks, test data is as accurate as long double, // so set tolerance to a few epsilon expressed as a fraction. - RealType tolerance = boost::math::tools::epsilon() * 30; // most OK with 3 eps tolerance. + RealType tolerance = boost::math::tools::epsilon() * 3; cout << "Tolerance = " << tolerance << "." << endl; using ::boost::math::owens_t; - using ::boost::math::normal_distribution; - BOOST_MATH_STD_USING // ADL of std names. - // Checks of six sub-methods T1 to T6. - BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(0.0625L), static_cast(0.25L)), static_cast(3.89119302347013668966224771378e-2L), tolerance); // T1 - BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(6.5L), static_cast(0.4375L)), static_cast(2.00057730485083154100907167685E-11L), tolerance); // T2 - BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(7L), static_cast( 0.96875L)), static_cast(6.39906271938986853083219914429E-13L), tolerance); // T3 - BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(4.78125L), static_cast(0.0625L)), static_cast(1.06329748046874638058307112826E-7L), tolerance); // T4 - BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(2.L), static_cast(0.5L)), static_cast(8.62507798552150713113488319155E-3L), tolerance); // T5 - BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(1.L), static_cast(0.9999975L)), static_cast(6.67418089782285927715589822405E-2L), tolerance); // T6 - //BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(L), static_cast(L)), static_cast(L), tolerance); + using namespace std; // ADL of std names. + + BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(0.0625L), static_cast(0.25L)), static_cast(3.89119302347013668966224771378e-2L), tolerance); -// BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(L), static_cast(L)), static_cast(L), tolerance); - // Spots values using Mathematica - BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(6.5L), static_cast(0.4375L)), static_cast(2.00057730485083154100907167684918851101649922551817956120806662022118024594547E-11L), tolerance); - BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(0.4375L), static_cast(6.5L)), static_cast(0.16540130125449396247498691826626273249659241838438244251206819782787761751256L), tolerance); - BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(7.L), static_cast(0.96875L)), static_cast(6.39906271938986853083219914428916013764797190941459233223182225724846022843930e-13L), tolerance); - BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(0.96875L), static_cast(7.L)), static_cast(0.08316748474602973770533230453272140919966614259525787470390475393923633179072L), tolerance); - BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(4.78125L), static_cast(0.0625L)), static_cast(1.06329748046874638058307112826015825291136503488102191050906959246644942646701e-7L), tolerance); - BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(0.0625L), static_cast(4.78125L)), static_cast(0.21571185819897989857261253680409017017649352928888660746045361855686569265171L), tolerance); - BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(2.L), static_cast(0.5L)), static_cast(0.00862507798552150713113488319154637187875641190390854291100809449487812876461L), tolerance); - BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(0.5L), static_cast(2L)), static_cast(0.14158060365397839346662819588111542648867283386549027383784843786494855594607L), tolerance); - - // check basic properties - BOOST_CHECK_EQUAL(owens_t(static_cast(0.5L), static_cast(2L)), owens_t(static_cast(-0.5L), static_cast(2L))); - BOOST_CHECK_EQUAL(owens_t(static_cast(0.5L), static_cast(2L)), -owens_t(static_cast(0.5L), static_cast(-2L))); - BOOST_CHECK_EQUAL(owens_t(static_cast(0.5L), static_cast(2L)), -owens_t(static_cast(-0.5L), static_cast(-2L))); - - // Special relations from Owen's original paper: - BOOST_CHECK_EQUAL(owens_t(static_cast(0.5), static_cast(0)), static_cast(0)); - BOOST_CHECK_EQUAL(owens_t(static_cast(10), static_cast(0)), static_cast(0)); - BOOST_CHECK_EQUAL(owens_t(static_cast(10000), static_cast(0)), static_cast(0)); - - BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(0), static_cast(2L)), atan(static_cast(2L)) / (boost::math::constants::pi() * 2), tolerance); - BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(0), static_cast(0.5L)), atan(static_cast(0.5L)) / (boost::math::constants::pi() * 2), tolerance); - BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(0), static_cast(2000L)), atan(static_cast(2000L)) / (boost::math::constants::pi() * 2), tolerance); - BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(5), static_cast(1)), cdf(normal_distribution(), 5) * cdf(complement(normal_distribution(), 5)) / 2, tolerance); - BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(0.125), static_cast(1)), cdf(normal_distribution(), 0.125) * cdf(complement(normal_distribution(), 0.125)) / 2, tolerance); - if(std::numeric_limits::has_infinity) - { - BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(0.125), std::numeric_limits::infinity()), cdf(complement(normal_distribution(), 0.125)) / 2, tolerance); - BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(5), std::numeric_limits::infinity()), cdf(complement(normal_distribution(), 5)) / 2, tolerance); - BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(-0.125), std::numeric_limits::infinity()), cdf(normal_distribution(), -0.125) / 2, tolerance); - BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(-5), std::numeric_limits::infinity()), cdf(normal_distribution(), -5) / 2, tolerance); - } } // template void test_spots(RealType) -template // Any floating-point type RealType. -void check_against_T7(RealType) -{ - // Basic sanity checks, test data is as accurate as long double, - // so set tolerance to a few epsilon expressed as a fraction. - RealType tolerance = boost::math::tools::epsilon() * 150; // most OK with 3 eps tolerance. - cout << "Tolerance = " << tolerance << "." << endl; - - using ::boost::math::owens_t; - using namespace std; // ADL of std names. - - // apply log scale because points near zero are more interesting - for(RealType a = static_cast(-10.0l); a < static_cast(3l); a+= static_cast(0.2l)) - for(RealType h = static_cast(-10.0l); h < static_cast(3.5l); h+= static_cast(0.2l)) - { - const RealType expa = exp(a); - const RealType exph = exp(h); - const RealType t = boost::math::owens_t(exph, expa); - RealType t7 = boost::math::owens_t_T7(exph,expa); - //if(!boost::math::isnormal(t) || !boost::math::isnormal(t7)) - // std::cout << "a = " << expa << " h = " << exph << " t = " << t << " t7 = " << t7 << std::endl; - BOOST_CHECK_CLOSE_FRACTION(t, t7, tolerance); - } - -} // template void test_spots(RealType) - -template -void do_test_owens_t(const T& data, const char* type_name, const char* test_name) -{ - typedef typename T::value_type row_type; - typedef Real value_type; - - typedef value_type (*pg)(value_type, value_type); -#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) - pg funcp = boost::math::owens_t; -#else - pg funcp = boost::math::owens_t; -#endif - - boost::math::tools::test_result result; - - std::cout << "Testing " << test_name << " with type " << type_name - << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n"; - - // - // test hermite against data: - // - result = boost::math::tools::test_hetero( - data, - bind_func(funcp, 0, 1), - extract_result(2)); - handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::owens_t", test_name); - - std::cout << std::endl; -} - -template -void test_owens_t(T, const char* name) -{ - // - // The actual test data is rather verbose, so it's in a separate file - // - // The contents are as follows, each row of data contains - // three items, input value a, input value b and erf(a, b): - // -# include "owens_t.ipp" - - do_test_owens_t(owens_t, name, "Owens T (medium small values)"); - -#include "owens_t_large_data.ipp" - - do_test_owens_t(owens_t_large_data, name, "Owens T (large and diverse values)"); -} - - int test_main(int, char* []) { BOOST_MATH_CONTROL_FP; - expected_results(); - // Basic sanity-check spot values. + // (Parameter value, arbitrarily zero, only communicates the floating point type). - test_spots(0.0F); // Test float. + test_spots(0.0F); // Test float. test_spots(0.0); // Test double. #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS test_spots(0.0L); // Test long double. #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582)) test_spots(boost::math::concepts::real_concept(0.)); // Test real concept. #endif -#endif - - check_against_T7(0.0F); // Test float. - check_against_T7(0.0); // Test double. -#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS - check_against_T7(0.0L); // Test long double. -#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582)) - check_against_T7(boost::math::concepts::real_concept(0.)); // Test real concept. -#endif -#endif - - test_owens_t(0.0F, "float"); // Test float. - test_owens_t(0.0, "double"); // Test double. -#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS - test_owens_t(0.0L, "long double"); // Test long double. -#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582)) - test_owens_t(boost::math::concepts::real_concept(0.), "real_concept"); // Test real concept. -#endif -#endif -#ifdef TEST_CPP_DEC_FLOAT - typedef boost::multiprecision::mp_number > cpp_dec_float_35; - test_owens_t(cpp_dec_float_35(0), "cpp_dec_float_35"); // Test real concept. - test_owens_t(boost::multiprecision::cpp_dec_float_50(0), "cpp_dec_float_50"); // Test real concept. - test_owens_t(boost::multiprecision::cpp_dec_float_100(0), "cpp_dec_float_100"); // Test real concept. #endif return 0; } // int test_main(int, char* []) @@ -314,40 +87,17 @@ int test_main(int, char* []) /* Output: ------- Rebuild All started: Project: test_owens_t_sandbox, Configuration: Release Win32 ------ - test_owens_t.cpp + +test_owens_t.cpp Generating code Finished generating code - test_owens_t_sandbox.vcxproj -> J:\Cpp\MathToolkit\test\Math_test\Release\test_owens_t_sandbox.exe + test_owens_t.vcxproj -> J:\Cpp\MathToolkit\test\Math_test\Release\test_owens_t.exe Running 1 test case... - Platform: Win32 - Compiler: Microsoft Visual C++ version 10.0 - STL : Dinkumware standard library version 520 - Boost : 1.49.0 - Tolerance = 3.57628e-007. Tolerance = 6.66134e-016. Tolerance = 6.66134e-016. Tolerance = 6.66134e-016. - + *** No errors detected -========== Rebuild All: 1 succeeded, 0 failed, 0 skipped ========== - - ------- Build started: Project: test_owens_t_sandbox, Configuration: Debug Win32 ------ - test_owens_t.cpp - test_owens_t_sandbox.vcxproj -> J:\Cpp\MathToolkit\test\Math_test\Debug\test_owens_t_sandbox.exe - Running 1 test case... - Platform: Win32 - Compiler: Microsoft Visual C++ version 10.0 - STL : Dinkumware standard library version 520 - Boost : 1.49.0 - Tolerance = 3.57628e-006. - Tolerance = 6.66134e-015. - Tolerance = 6.66134e-015. - Tolerance = 6.66134e-015. - - *** No errors detected -========== Build: 1 succeeded, 0 failed, 0 up-to-date, 0 skipped ========== */ From fc6532902a2187f77474d4e6108f8c9e18770c4f Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Sun, 12 Aug 2012 11:27:43 +0000 Subject: [PATCH 094/115] Items that missed the roadmap for 1.51 [SVN r79978] --- doc/sf_and_dist/roadmap.qbk | 3 --- 1 file changed, 3 deletions(-) diff --git a/doc/sf_and_dist/roadmap.qbk b/doc/sf_and_dist/roadmap.qbk index ff0c4176b..41fa6f842 100644 --- a/doc/sf_and_dist/roadmap.qbk +++ b/doc/sf_and_dist/roadmap.qbk @@ -8,9 +8,6 @@ All bug reports including closed ones can be viewed [h4 Boost-1.52] * Corrected moments for small degrees of freedom [@https://svn.boost.org/trac/boost/ticket/7177 #7177] (reported by Thomas Mang). - -[h4 Boost-1.51] - * Added [link math_toolkit.special.airy Airy functions] and [link math_toolkit.special.jacobi Jacobi Elliptic functions]. * Corrected failure to detect bad parameters in many distributions [@https://svn.boost.org/trac/boost/ticket/6934 #6934] (reported by Florian Schoppmann) From a4640b3cf48989dbaed59e2b5da7834e229fd262 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Sun, 12 Aug 2012 17:03:26 +0000 Subject: [PATCH 095/115] Fix typo in algorithm selection. [SVN r79982] --- include/boost/math/special_functions/hankel.hpp | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/include/boost/math/special_functions/hankel.hpp b/include/boost/math/special_functions/hankel.hpp index 9702fd5d9..76ceb65d0 100644 --- a/include/boost/math/special_functions/hankel.hpp +++ b/include/boost/math/special_functions/hankel.hpp @@ -83,7 +83,7 @@ template inline std::complex hankel_imp(int v, T x, const bessel_int_tag&, const Policy& pol, int sign) { BOOST_MATH_STD_USING - if((std::abs(v < 200)) && (x > 0)) + if((std::abs(v) < 200) && (x > 0)) return std::complex(bessel_jn(v, x, pol), sign * bessel_yn(v, x, pol)); return hankel_imp(static_cast(v), x, bessel_no_int_tag(), pol, sign); } From e650b22aca43a0356e0bdbaf7ebfa7d158374d40 Mon Sep 17 00:00:00 2001 From: "Paul A. Bristow" Date: Tue, 14 Aug 2012 07:56:17 +0000 Subject: [PATCH 096/115] Reverted to previous version to get back lost content. [SVN r80028] --- test/test_owens_t.cpp | 323 +++++++++++++++++++++++++++++++++++++++--- 1 file changed, 303 insertions(+), 20 deletions(-) diff --git a/test/test_owens_t.cpp b/test/test_owens_t.cpp index cdc45f4d4..074375c2c 100644 --- a/test/test_owens_t.cpp +++ b/test/test_owens_t.cpp @@ -1,6 +1,7 @@ +// test_owens_t.cpp + // Copyright Paul A. Bristow 2012. // Copyright Benjamin Sobotta 2012. -// Copyright John Maddock 2012. // Use, modification and distribution are subject to the // Boost Software License, Version 1.0. @@ -17,10 +18,12 @@ // not alter the result. The resultant values Tacc(h,a) say, were validated by evaluating (8) with // m = 48 (i.e. 96 point Gaussian quadrature). -// test_owens_t.cpp +#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error #ifdef _MSC_VER # pragma warning (disable : 4127) // conditional expression is constant +# pragma warning (disable : 4305) // 'initializing' : truncation from 'double' to 'const float' +// ?? TODO get rid of these warnings? #endif #include // for real_concept. @@ -28,9 +31,41 @@ using ::boost::math::concepts::real_concept; #include // for owens_t function. using boost::math::owens_t; +#include -#include // for test_main. -#include // for BOOST_CHECK_CLOSE and BOOST_CHECK_CLOSE_fraction. +#include +#include +#include + +#include "libs/math/test/handle_test_result.hpp" +#include "libs/math/test/table_type.hpp" +#include "libs/math/test/functor.hpp" + +// +// Defining TEST_CPP_DEC_FLOAT enables testing of multiprecision support. +// This requires the multiprecision library from sandbox/big_number. +// Note that these tests *do not pass*, but they do give an idea of the +// error rates that can be expected.... +// +#ifdef TEST_CPP_DEC_FLOAT +#include + +template +inline R convert_to(const char* s) +{ + try{ + return boost::lexical_cast(s); + } + catch(const boost::bad_lexical_cast&) + { + return 0; + } +} + +#define SC_(x) convert_to(BOOST_STRINGIZE(x)) +#endif + +#include "owens_t_T7.hpp" #include using std::cout; @@ -38,13 +73,65 @@ using std::endl; #include using std::numeric_limits; +void expected_results() +{ + // + // Define the max and mean errors expected for + // various compilers and platforms. + // + const char* largest_type; +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + if(boost::math::policies::digits >() == boost::math::policies::digits >()) + { + largest_type = "(long\\s+)?double|real_concept"; + } + else + { + largest_type = "long double|real_concept"; + } +#else + largest_type = "(long\\s+)?double"; +#endif + + // + // Catch all cases come last: + // + if(std::numeric_limits::digits > 60) + { + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + largest_type, // test type(s) + ".*", // test data group + "boost::math::owens_t", 500, 100); // test function + } + else + { + add_expected_result( + ".*", // compiler + ".*", // stdlib + ".*", // platform + largest_type, // test type(s) + ".*", // test data group + "boost::math::owens_t", 60, 5); // test function + } + // + // Finish off by printing out the compiler/stdlib/platform names, + // we do this to make it easier to mark up expected error rates. + // + std::cout << "Tests run with " << BOOST_COMPILER << ", " + << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; +} + + template void test_spot( - RealType h, // - RealType a, // Chi Square statistic + RealType h, // + RealType a, // RealType tol) // Test tolerance { - BOOST_CHECK_CLOSE_FRACTION(owens_t(h, a), 3.89119302347013668966224771378e-2, tol); + BOOST_CHECK_CLOSE_FRACTION(owens_t(h, a), 3.89119302347013668966224771378e-2L, tol); } @@ -53,33 +140,173 @@ void test_spots(RealType) { // Basic sanity checks, test data is as accurate as long double, // so set tolerance to a few epsilon expressed as a fraction. - RealType tolerance = boost::math::tools::epsilon() * 3; + RealType tolerance = boost::math::tools::epsilon() * 30; // most OK with 3 eps tolerance. cout << "Tolerance = " << tolerance << "." << endl; using ::boost::math::owens_t; + using ::boost::math::normal_distribution; + BOOST_MATH_STD_USING // ADL of std names. - using namespace std; // ADL of std names. - - BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(0.0625L), static_cast(0.25L)), static_cast(3.89119302347013668966224771378e-2L), tolerance); + // Checks of six sub-methods T1 to T6. + BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(0.0625L), static_cast(0.25L)), static_cast(3.89119302347013668966224771378e-2L), tolerance); // T1 + BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(6.5L), static_cast(0.4375L)), static_cast(2.00057730485083154100907167685E-11L), tolerance); // T2 + BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(7L), static_cast( 0.96875L)), static_cast(6.39906271938986853083219914429E-13L), tolerance); // T3 + BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(4.78125L), static_cast(0.0625L)), static_cast(1.06329748046874638058307112826E-7L), tolerance); // T4 + BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(2.L), static_cast(0.5L)), static_cast(8.62507798552150713113488319155E-3L), tolerance); // T5 + BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(1.L), static_cast(0.9999975L)), static_cast(6.67418089782285927715589822405E-2L), tolerance); // T6 + //BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(L), static_cast(L)), static_cast(L), tolerance); +// BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(L), static_cast(L)), static_cast(L), tolerance); + // Spots values using Mathematica + BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(6.5L), static_cast(0.4375L)), static_cast(2.00057730485083154100907167684918851101649922551817956120806662022118024594547E-11L), tolerance); + BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(0.4375L), static_cast(6.5L)), static_cast(0.16540130125449396247498691826626273249659241838438244251206819782787761751256L), tolerance); + BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(7.L), static_cast(0.96875L)), static_cast(6.39906271938986853083219914428916013764797190941459233223182225724846022843930e-13L), tolerance); + BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(0.96875L), static_cast(7.L)), static_cast(0.08316748474602973770533230453272140919966614259525787470390475393923633179072L), tolerance); + BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(4.78125L), static_cast(0.0625L)), static_cast(1.06329748046874638058307112826015825291136503488102191050906959246644942646701e-7L), tolerance); + BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(0.0625L), static_cast(4.78125L)), static_cast(0.21571185819897989857261253680409017017649352928888660746045361855686569265171L), tolerance); + BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(2.L), static_cast(0.5L)), static_cast(0.00862507798552150713113488319154637187875641190390854291100809449487812876461L), tolerance); + BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(0.5L), static_cast(2L)), static_cast(0.14158060365397839346662819588111542648867283386549027383784843786494855594607L), tolerance); + + // check basic properties + BOOST_CHECK_EQUAL(owens_t(static_cast(0.5L), static_cast(2L)), owens_t(static_cast(-0.5L), static_cast(2L))); + BOOST_CHECK_EQUAL(owens_t(static_cast(0.5L), static_cast(2L)), -owens_t(static_cast(0.5L), static_cast(-2L))); + BOOST_CHECK_EQUAL(owens_t(static_cast(0.5L), static_cast(2L)), -owens_t(static_cast(-0.5L), static_cast(-2L))); + + // Special relations from Owen's original paper: + BOOST_CHECK_EQUAL(owens_t(static_cast(0.5), static_cast(0)), static_cast(0)); + BOOST_CHECK_EQUAL(owens_t(static_cast(10), static_cast(0)), static_cast(0)); + BOOST_CHECK_EQUAL(owens_t(static_cast(10000), static_cast(0)), static_cast(0)); + + BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(0), static_cast(2L)), atan(static_cast(2L)) / (boost::math::constants::pi() * 2), tolerance); + BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(0), static_cast(0.5L)), atan(static_cast(0.5L)) / (boost::math::constants::pi() * 2), tolerance); + BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(0), static_cast(2000L)), atan(static_cast(2000L)) / (boost::math::constants::pi() * 2), tolerance); + BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(5), static_cast(1)), cdf(normal_distribution(), 5) * cdf(complement(normal_distribution(), 5)) / 2, tolerance); + BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(0.125), static_cast(1)), cdf(normal_distribution(), 0.125) * cdf(complement(normal_distribution(), 0.125)) / 2, tolerance); + if(std::numeric_limits::has_infinity) + { + BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(0.125), std::numeric_limits::infinity()), cdf(complement(normal_distribution(), 0.125)) / 2, tolerance); + BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(5), std::numeric_limits::infinity()), cdf(complement(normal_distribution(), 5)) / 2, tolerance); + BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(-0.125), std::numeric_limits::infinity()), cdf(normal_distribution(), -0.125) / 2, tolerance); + BOOST_CHECK_CLOSE_FRACTION(owens_t(static_cast(-5), std::numeric_limits::infinity()), cdf(normal_distribution(), -5) / 2, tolerance); + } } // template void test_spots(RealType) +template // Any floating-point type RealType. +void check_against_T7(RealType) +{ + // Basic sanity checks, test data is as accurate as long double, + // so set tolerance to a few epsilon expressed as a fraction. + RealType tolerance = boost::math::tools::epsilon() * 150; // most OK with 3 eps tolerance. + cout << "Tolerance = " << tolerance << "." << endl; + + using ::boost::math::owens_t; + using namespace std; // ADL of std names. + + // apply log scale because points near zero are more interesting + for(RealType a = static_cast(-10.0l); a < static_cast(3l); a+= static_cast(0.2l)) + for(RealType h = static_cast(-10.0l); h < static_cast(3.5l); h+= static_cast(0.2l)) + { + const RealType expa = exp(a); + const RealType exph = exp(h); + const RealType t = boost::math::owens_t(exph, expa); + RealType t7 = boost::math::owens_t_T7(exph,expa); + //if(!boost::math::isnormal(t) || !boost::math::isnormal(t7)) + // std::cout << "a = " << expa << " h = " << exph << " t = " << t << " t7 = " << t7 << std::endl; + BOOST_CHECK_CLOSE_FRACTION(t, t7, tolerance); + } + +} // template void test_spots(RealType) + +template +void do_test_owens_t(const T& data, const char* type_name, const char* test_name) +{ + typedef typename T::value_type row_type; + typedef Real value_type; + + typedef value_type (*pg)(value_type, value_type); +#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) + pg funcp = boost::math::owens_t; +#else + pg funcp = boost::math::owens_t; +#endif + + boost::math::tools::test_result result; + + std::cout << "Testing " << test_name << " with type " << type_name + << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n"; + + // + // test hermite against data: + // + result = boost::math::tools::test_hetero( + data, + bind_func(funcp, 0, 1), + extract_result(2)); + handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::owens_t", test_name); + + std::cout << std::endl; +} + +template +void test_owens_t(T, const char* name) +{ + // + // The actual test data is rather verbose, so it's in a separate file + // + // The contents are as follows, each row of data contains + // three items, input value a, input value b and erf(a, b): + // +# include "owens_t.ipp" + + do_test_owens_t(owens_t, name, "Owens T (medium small values)"); + +#include "owens_t_large_data.ipp" + + do_test_owens_t(owens_t_large_data, name, "Owens T (large and diverse values)"); +} + + int test_main(int, char* []) { BOOST_MATH_CONTROL_FP; + expected_results(); + // Basic sanity-check spot values. - // (Parameter value, arbitrarily zero, only communicates the floating point type). - test_spots(0.0F); // Test float. + test_spots(0.0F); // Test float. test_spots(0.0); // Test double. #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS test_spots(0.0L); // Test long double. #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582)) test_spots(boost::math::concepts::real_concept(0.)); // Test real concept. #endif +#endif + + check_against_T7(0.0F); // Test float. + check_against_T7(0.0); // Test double. +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + check_against_T7(0.0L); // Test long double. +#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582)) + check_against_T7(boost::math::concepts::real_concept(0.)); // Test real concept. +#endif +#endif + + test_owens_t(0.0F, "float"); // Test float. + test_owens_t(0.0, "double"); // Test double. +#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS + test_owens_t(0.0L, "long double"); // Test long double. +#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582)) + test_owens_t(boost::math::concepts::real_concept(0.), "real_concept"); // Test real concept. +#endif +#endif +#ifdef TEST_CPP_DEC_FLOAT + typedef boost::multiprecision::mp_number > cpp_dec_float_35; + test_owens_t(cpp_dec_float_35(0), "cpp_dec_float_35"); // Test real concept. + test_owens_t(boost::multiprecision::cpp_dec_float_50(0), "cpp_dec_float_50"); // Test real concept. + test_owens_t(boost::multiprecision::cpp_dec_float_100(0), "cpp_dec_float_100"); // Test real concept. #endif return 0; } // int test_main(int, char* []) @@ -88,17 +315,73 @@ int test_main(int, char* []) Output: -test_owens_t.cpp - Generating code - Finished generating code - test_owens_t.vcxproj -> J:\Cpp\MathToolkit\test\Math_test\Release\test_owens_t.exe + Description: Autorun "J:\Cpp\MathToolkit\test\Math_test\Debug\test_owens_t.exe" Running 1 test case... - Tolerance = 6.66134e-016. - Tolerance = 6.66134e-016. - Tolerance = 6.66134e-016. + Tests run with Microsoft Visual C++ version 10.0, Dinkumware standard library version 520, Win32 + Tolerance = 3.57628e-006. + Tolerance = 6.66134e-015. + Tolerance = 6.66134e-015. + Tolerance = 6.66134e-015. + Tolerance = 1.78814e-005. + Tolerance = 3.33067e-014. + Tolerance = 3.33067e-014. + Tolerance = 3.33067e-014. + Testing Owens T (medium small values) with type float + ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + boost::math::owens_t Max = 0 RMS Mean=0 + + + Testing Owens T (large and diverse values) with type float + ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + boost::math::owens_t Max = 0 RMS Mean=0 + + + Testing Owens T (medium small values) with type double + ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + boost::math::owens_t Max = 4.375 RMS Mean=0.9728 + worst case at row: 81 + { 4.4206809997558594, 0.1269868016242981, 1.0900281236140834e-006 } + + + Testing Owens T (large and diverse values) with type double + ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + boost::math::owens_t Max = 3.781 RMS Mean=0.6206 + worst case at row: 430 + { 3.4516773223876953, 0.0010718167759478092, 4.413983645332431e-007 } + + + Testing Owens T (medium small values) with type long double + ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + boost::math::owens_t Max = 4.375 RMS Mean=0.9728 + worst case at row: 81 + { 4.4206809997558594, 0.1269868016242981, 1.0900281236140834e-006 } + + + Testing Owens T (large and diverse values) with type long double + ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + boost::math::owens_t Max = 3.781 RMS Mean=0.6206 + worst case at row: 430 + { 3.4516773223876953, 0.0010718167759478092, 4.413983645332431e-007 } + + + Testing Owens T (medium small values) with type real_concept + ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + boost::math::owens_t Max = 4.375 RMS Mean=1.032 + worst case at row: 81 + { 4.4206809997558594, 0.1269868016242981, 1.0900281236140834e-006 } + + + Testing Owens T (large and diverse values) with type real_concept + ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + boost::math::owens_t Max = 21.04 RMS Mean=1.102 + worst case at row: 439 + { 3.4516773223876953, 0.98384737968444824, 0.00013923002576038691 } + + *** No errors detected + */ From bf39b3834ad73c639d17ecc6382910a3d2e4dae4 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Thu, 16 Aug 2012 15:27:40 +0000 Subject: [PATCH 097/115] Fix bug in incomplete beta which causes an exception to be thrown in itrunc when one argument is very large. Fix several similar issue in the non-central T which cause cancellation errors if we let the starting iteration be zero. Remove dead code that results from above changes. Minor fixes to table_type and test_next.cpp. [SVN r80061] --- .../math/distributions/non_central_beta.hpp | 11 +- .../math/distributions/non_central_t.hpp | 105 ++++++------------ include/boost/math/special_functions/beta.hpp | 2 +- test/nct_small_delta.ipp | 59 ++++++++++ test/table_type.hpp | 13 --- test/test_nc_t.cpp | 17 ++- test/test_next.cpp | 10 +- 7 files changed, 118 insertions(+), 99 deletions(-) create mode 100644 test/nct_small_delta.ipp diff --git a/include/boost/math/distributions/non_central_beta.hpp b/include/boost/math/distributions/non_central_beta.hpp index ebb6e91fa..6e699e509 100644 --- a/include/boost/math/distributions/non_central_beta.hpp +++ b/include/boost/math/distributions/non_central_beta.hpp @@ -51,17 +51,8 @@ namespace boost int k = itrunc(l2); if(k == 0) k = 1; - T pois; - if(k == 0) - { // Starting Poisson weight: - pois = exp(-l2); - } - else - { - // Starting Poisson weight: - pois = gamma_p_derivative(T(k+1), l2, pol); - } + T pois = gamma_p_derivative(T(k+1), l2, pol); if(pois == 0) return init_val; // recurance term: diff --git a/include/boost/math/distributions/non_central_t.hpp b/include/boost/math/distributions/non_central_t.hpp index e46980fc2..95cef8b6e 100644 --- a/include/boost/math/distributions/non_central_t.hpp +++ b/include/boost/math/distributions/non_central_t.hpp @@ -38,43 +38,26 @@ namespace boost T d2 = delta * delta / 2; // // k is the starting point for iteration, and is the - // maximum of the poisson weighting term: + // maximum of the poisson weighting term, we don't + // ever allow k == 0 as this can lead to catastrophic + // cancellation errors later (test case is v = 1621286869049072.3 + // delta = 0.16212868690490723, x = 0.86987415482475994). // int k = itrunc(d2); T pois; - if(k < 15) - { - // Since we'll likely need 30-40 terms anyway, start from zero - // since this simplifies the arithmetic, don't go too overboard though - // as this is the *unstable* direction: - k = 0; - // Starting Poisson weight: - pois = exp(-d2) * 2 / constants::root_pi(); - pois *= delta / constants::root_two(); - } - else - { - // Starting Poisson weight: - pois = gamma_p_derivative(T(k+1), d2, pol) - * tgamma_delta_ratio(T(k + 1), T(0.5f)) - * delta / constants::root_two(); - } + if(k == 0) k = 1; + // Starting Poisson weight: + pois = gamma_p_derivative(T(k+1), d2, pol) + * tgamma_delta_ratio(T(k + 1), T(0.5f)) + * delta / constants::root_two(); if(pois == 0) return init_val; T xterm, beta; // Recurrance & starting beta terms: - if(k == 0) - { - beta = -boost::math::powm1(y, n / 2, pol); - xterm = beta > 0.5f ? T(pow(y, n / 2)) : T(1 - beta); - } - else - { - beta = x < y - ? detail::ibeta_imp(T(k + 1), T(n / 2), x, pol, false, true, &xterm) - : detail::ibeta_imp(T(n / 2), T(k + 1), y, pol, true, true, &xterm); - xterm *= y / (n / 2 + k); - } + beta = x < y + ? detail::ibeta_imp(T(k + 1), T(n / 2), x, pol, false, true, &xterm) + : detail::ibeta_imp(T(n / 2), T(k + 1), y, pol, true, true, &xterm); + xterm *= y / (n / 2 + k); T poisf(pois), betaf(beta), xtermf(xterm); T sum = init_val; if((xterm == 0) && (beta == 0)) @@ -89,7 +72,8 @@ namespace boost { T term = beta * pois; sum += term; - if(fabs(term/sum) < errtol) + // Don't terminate on first term in case we "fixed" k above: + if((i != k) && fabs(term/sum) < errtol) break; pois *= (i + 0.5f) / d2; beta += xterm; @@ -128,23 +112,16 @@ namespace boost T d2 = delta * delta / 2; // // k is the starting point for iteration, and is the - // maximum of the poisson weighting term: + // maximum of the poisson weighting term, we don't allow + // k == 0 as this can cause catastrophic cancellation errors + // (test case is v = 561908036470413.25, delta = 0.056190803647041321, + // x = 1.6155232703966216): // int k = itrunc(d2); - if(k < 30) - { - // We typically need around 40 terms so may as well start at 0 - // and gain faster computation of starting conditions: - k = 0; - } + if(k == 0) k = 1; // Starting Poisson weight: T pois; - if(k == 0) - { - pois = exp(-d2) * 2 / constants::root_pi(); - pois *= delta / constants::root_two(); - } - else if((k < (int)(max_factorial::value)) && (d2 < tools::log_max_value()) && (log(d2) * k < tools::log_max_value())) + if((k < (int)(max_factorial::value)) && (d2 < tools::log_max_value()) && (log(d2) * k < tools::log_max_value())) { // // For small k we can optimise this calculation by using @@ -205,7 +182,8 @@ namespace boost } sum += term; - if(fabs(term/sum) < errtol) + // Don't terminate on first term in case we "fixed" the value of k above: + if((j != k) && fabs(term/sum) < errtol) break; if(count > max_iter) { @@ -370,31 +348,16 @@ namespace boost // int k = itrunc(d2); T pois, xterm; - if(k < 30) - { - // - // Since we'll need at least 30-40 terms anyway, start from 0 - // since this simplifies the starting arithmetic: - // - k = 0; - // Starting Poisson weight: - pois = exp(-d2) - * (2 / constants::root_pi()) - * delta / constants::root_two(); - // Starting beta term: - xterm = pow(y, n / 2 - 1) * n / 2; - } - else - { - // Starting Poisson weight: - pois = gamma_p_derivative(T(k+1), d2, pol) - * tgamma_delta_ratio(T(k + 1), T(0.5f)) - * delta / constants::root_two(); - // Starting beta term: - xterm = x < y - ? ibeta_derivative(T(k + 1), n / 2, x, pol) - : ibeta_derivative(n / 2, T(k + 1), y, pol); - } + if(k == 0) + k = 1; + // Starting Poisson weight: + pois = gamma_p_derivative(T(k+1), d2, pol) + * tgamma_delta_ratio(T(k + 1), T(0.5f)) + * delta / constants::root_two(); + // Starting beta term: + xterm = x < y + ? ibeta_derivative(T(k + 1), n / 2, x, pol) + : ibeta_derivative(n / 2, T(k + 1), y, pol); T poisf(pois), xtermf(xterm); T sum = init_val; if((pois == 0) || (xterm == 0)) @@ -409,7 +372,7 @@ namespace boost { T term = xterm * pois; sum += term; - if((fabs(term/sum) < errtol) || (term == 0)) + if(((fabs(term/sum) < errtol) && (i != k)) || (term == 0)) break; pois *= (i + 0.5f) / d2; xterm *= (i) / (x * (n / 2 + i)); diff --git a/include/boost/math/special_functions/beta.hpp b/include/boost/math/special_functions/beta.hpp index 1177f44d6..440e762b4 100644 --- a/include/boost/math/special_functions/beta.hpp +++ b/include/boost/math/special_functions/beta.hpp @@ -1115,7 +1115,7 @@ T ibeta_imp(T a, T b, T x, const Policy& pol, bool inv, bool normalised, T* p_de if(b < 40) { - if((floor(a) == a) && (floor(b) == b)) + if((floor(a) == a) && (floor(b) == b) && (a < (std::numeric_limits::max)() - 100)) { // relate to the binomial distribution and use a finite sum: T k = a - 1; diff --git a/test/nct_small_delta.ipp b/test/nct_small_delta.ipp new file mode 100644 index 000000000..c22e6d8d1 --- /dev/null +++ b/test/nct_small_delta.ipp @@ -0,0 +1,59 @@ +#ifndef SC_ +# define SC_(x) static_cast(BOOST_JOIN(x, L)) +#endif + static const boost::array, 52> nct_small_delta = {{ + { SC_(528154.0625), SC_(0.5281540482737767661092220805585384368896484375e-10), SC_(-0.0438658893108367919921875), SC_(0.48250566102131993419090032097993141749629366237354), SC_(0.51749433897868006580909967902006858250370633762646) }, + { SC_(528154.0625), SC_(0.5281540482737767661092220805585384368896484375e-10), SC_(0.944180071353912353515625), SC_(0.82746096542548677580028882735723708488758715357832), SC_(0.17253903457451322419971117264276291511241284642168) }, + { SC_(660934.625), SC_(0.6609346403507743161753751337528228759765625e-10), SC_(-1.09356248378753662109375), SC_(0.13707365461620354384117941652933126383612908392123), SC_(0.86292634538379645615882058347066873616387091607877) }, + { SC_(660934.625), SC_(0.6609346403507743161753751337528228759765625e-10), SC_(0.8943269252777099609375), SC_(0.81442633822735887388224244171117444649106453395369), SC_(0.18557366177264112611775755828882555350893546604631) }, + { SC_(2218633.5), SC_(0.221863361016261251279502175748348236083984375e-9), SC_(0.900856673717498779296875), SC_(0.81616768606164643627773468420573729773227964864232), SC_(0.18383231393835356372226531579426270226772035135768) }, + { SC_(2218633.5), SC_(0.221863361016261251279502175748348236083984375e-9), SC_(1.2173912525177001953125), SC_(0.88827224039054756935944165341219624193195834170515), SC_(0.11172775960945243064055834658780375806804165829485) }, + { SC_(4272462.5), SC_(0.427246238388079291325993835926055908203125e-9), SC_(-0.608891189098358154296875), SC_(0.27129829842994003638790396047987351547260466368909), SC_(0.72870170157005996361209603952012648452739533631091) }, + { SC_(4272462.5), SC_(0.427246238388079291325993835926055908203125e-9), SC_(1.00504648685455322265625), SC_(0.84256273846140526398141847027259437264491990536997), SC_(0.15743726153859473601858152972740562735508009463003) }, + { SC_(5247940), SC_(0.524793986045324345468543469905853271484375e-9), SC_(-1.11901676654815673828125), SC_(0.13156651861218774164823859585016794860626893918254), SC_(0.86843348138781225835176140414983205139373106081746) }, + { SC_(5247940), SC_(0.524793986045324345468543469905853271484375e-9), SC_(-1.0743181705474853515625), SC_(0.14134007648961033259203628094925336577210835950473), SC_(0.85865992351038966740796371905074663422789164049527) }, + { SC_(18336510), SC_(0.1833651008809056293102912604808807373046875e-8), SC_(-1.48560678958892822265625), SC_(0.068691587407182335464773960988799828434588100829723), SC_(0.93130841259281766453522603901120017156541189917028) }, + { SC_(18336510), SC_(0.1833651008809056293102912604808807373046875e-8), SC_(1.40664613246917724609375), SC_(0.92023381810537925932116820364336353453322062034513), SC_(0.079766181894620740678831796356636465466779379654875) }, + { SC_(35639400), SC_(0.3563940254025510512292385101318359375e-8), SC_(-0.2346564829349517822265625), SC_(0.40723768241459441841438282814230236027330099372549), SC_(0.59276231758540558158561717185769763972669900627451) }, + { SC_(35639400), SC_(0.3563940254025510512292385101318359375e-8), SC_(1.24018728733062744140625), SC_(0.89254693057186762829174224773340895165093032749745), SC_(0.10745306942813237170825775226659104834906967250255) }, + { SC_(45487064), SC_(0.4548706300511184963397681713104248046875e-8), SC_(-1.162539005279541015625), SC_(0.12250829730838957792258003981798522875055846989729), SC_(0.87749170269161042207741996018201477124944153010271) }, + { SC_(45487064), SC_(0.4548706300511184963397681713104248046875e-8), SC_(-0.8368303775787353515625), SC_(0.20134396068806204684905953847272082011338589718573), SC_(0.79865603931193795315094046152727917988661410281427) }, + { SC_(121620224), SC_(0.12162022500206148833967745304107666015625e-7), SC_(0.39718806743621826171875), SC_(0.6543856047457196617262494109772647455321658941725), SC_(0.3456143952542803382737505890227352544678341058275) }, + { SC_(121620224), SC_(0.12162022500206148833967745304107666015625e-7), SC_(1.24731695652008056640625), SC_(0.89385934536068351965787494087690986211211985166153), SC_(0.10614065463931648034212505912309013788788014833847) }, + { SC_(194932064), SC_(0.1949320704852652852423489093780517578125e-7), SC_(-0.575359284877777099609375), SC_(0.28252416082756836234341731346566281326700494104297), SC_(0.71747583917243163765658268653433718673299505895703) }, + { SC_(194932064), SC_(0.1949320704852652852423489093780517578125e-7), SC_(0.4194296896457672119140625), SC_(0.66254892777524155315670363767975247199405361778407), SC_(0.33745107222475844684329636232024752800594638221593) }, + { SC_(327092512), SC_(0.327092521956728887744247913360595703125e-7), SC_(-1.2071979045867919921875), SC_(0.11367796276232027931825008133662930047269775407393), SC_(0.88632203723767972068174991866337069952730224592607) }, + { SC_(327092512), SC_(0.327092521956728887744247913360595703125e-7), SC_(0.876802742481231689453125), SC_(0.80970309616765211535813735932417404262765601883988), SC_(0.19029690383234788464186264067582595737234398116012) }, + { SC_(922215104), SC_(0.922215122045599855482578277587890625e-7), SC_(0.141965448856353759765625), SC_(0.55644631504480191279462370740448518366492417190403), SC_(0.44355368495519808720537629259551481633507582809597) }, + { SC_(922215104), SC_(0.922215122045599855482578277587890625e-7), SC_(1.13559567928314208984375), SC_(0.87193707155023294863968629343839663906062875149397), SC_(0.12806292844976705136031370656160336093937124850603) }, + { SC_(1524088576), SC_(0.15240885886669275350868701934814453125e-6), SC_(-0.664114892482757568359375), SC_(0.25330834087624892647434930428222142994198568419577), SC_(0.74669165912375107352565069571777857005801431580423) }, + { SC_(1524088576), SC_(0.15240885886669275350868701934814453125e-6), SC_(1.37886774539947509765625), SC_(0.91603220911482167517950113163803628076090836350073), SC_(0.083967790885178324820498868361963719239091636499269) }, + { SC_(2833322752), SC_(0.2833322696460527367889881134033203125e-6), SC_(-0.934321820735931396484375), SC_(0.1750688828424918771805411797628815067286394341076), SC_(0.8249311171575081228194588202371184932713605658924) }, + { SC_(2833322752), SC_(0.2833322696460527367889881134033203125e-6), SC_(0.01152040623128414154052734375), SC_(0.50459576244612621592734255378527979154430257136497), SC_(0.49540423755387378407265744621472020845569742863503) }, + { SC_(7376104448), SC_(0.737610434953239746391773223876953125e-6), SC_(0.14150333404541015625), SC_(0.55626354548618560623653714942035371801766096231359), SC_(0.44373645451381439376346285057964628198233903768641) }, + { SC_(7376104448), SC_(0.737610434953239746391773223876953125e-6), SC_(0.46808087825775146484375), SC_(0.68013635973699279491605645205785045329423814366365), SC_(0.31986364026300720508394354794214954670576185633635) }, + { SC_(19005597696), SC_(0.190055970961111597716808319091796875e-5), SC_(0.89516448974609375), SC_(0.81464991000540683634213811269861642939018294670759), SC_(0.18535008999459316365786188730138357060981705329241) }, + { SC_(19005597696), SC_(0.190055970961111597716808319091796875e-5), SC_(1.48002254962921142578125), SC_(0.93056613193114394805618686943760965268036694876176), SC_(0.069433868068856051943813130562390347319633051238245) }, + { SC_(37336477696), SC_(0.37336476452765055000782012939453125e-5), SC_(-1.39093267917633056640625), SC_(0.08212235488316398659317034137786838544688552825868), SC_(0.91787764511683601340682965862213161455311447174132) }, + { SC_(37336477696), SC_(0.37336476452765055000782012939453125e-5), SC_(1.37445271015167236328125), SC_(0.91534882988245816934090108875322008488528628081311), SC_(0.084651170117541830659098911246779915114713719186888) }, + { SC_(76158959616), SC_(0.7615895810886286199092864990234375e-5), SC_(-0.4133583009243011474609375), SC_(0.33966927100300125337615080987310920514534610032036), SC_(0.66033072899699874662384919012689079485465389967964) }, + { SC_(76158959616), SC_(0.7615895810886286199092864990234375e-5), SC_(1.4921436309814453125), SC_(0.93216825396603974510969367870165246570825488483101), SC_(0.067831746033960254890306321298347534291745115168994) }, + { SC_(149909094400), SC_(0.149909101310186088085174560546875e-4), SC_(1.0512597560882568359375), SC_(0.85342690591562485295243723515889796180107709178638), SC_(0.14657309408437514704756276484110203819892290821362) }, + { SC_(149909094400), SC_(0.149909101310186088085174560546875e-4), SC_(1.39853727817535400390625), SC_(0.91902185764013358458014118954726949359893649842036), SC_(0.080978142359866415419858810452730506401063501579643) }, + { SC_(300246401024), SC_(0.300246392725966870784759521484375e-4), SC_(-0.858747541904449462890625), SC_(0.19523162330012228777050408978728209345121805498577), SC_(0.80476837669987771222949591021271790654878194501423) }, + { SC_(300246401024), SC_(0.300246392725966870784759521484375e-4), SC_(1.40856420993804931640625), SC_(0.92051352414116507572847602921599610498310359056324), SC_(0.079486475858834924271523970784003895016896409436761) }, + { SC_(353275379712), SC_(0.3532753908075392246246337890625e-4), SC_(-1.0212171077728271484375), SC_(0.15356742764115001237771940686359565408937029456416), SC_(0.84643257235884998762228059313640434591062970543584) }, + { SC_(353275379712), SC_(0.3532753908075392246246337890625e-4), SC_(1.30792331695556640625), SC_(0.90454434807153994552344182822189877220821074884107), SC_(0.09545565192846005447655817177810122779178925115893) }, + { SC_(0.105336832e13), SC_(0.0001053368323482573032379150390625), SC_(0.554341971874237060546875), SC_(0.71029154537084727662513596094978928595259300760913), SC_(0.28970845462915272337486403905021071404740699239087) }, + { SC_(0.105336832e13), SC_(0.0001053368323482573032379150390625), SC_(0.68778026103973388671875), SC_(0.75417124280258349801796658501621988164110540869668), SC_(0.24582875719741650198203341498378011835889459130332) }, + { SC_(2405508317184), SC_(0.0002405508421361446380615234375), SC_(0.5517151355743408203125), SC_(0.70934580778979545712784947970550407070754829519999), SC_(0.29065419221020454287215052029449592929245170480001) }, + { SC_(2405508317184), SC_(0.0002405508421361446380615234375), SC_(1.42728817462921142578125), SC_(0.92321691603357102065464321251307839682832539201822), SC_(0.076783083966428979345356787486921603171674607981778) }, + { SC_(4836693114880), SC_(0.000483669340610504150390625), SC_(-0.2817919254302978515625), SC_(0.38886609876734874792671065039736370377189209526496), SC_(0.61113390123265125207328934960263629622810790473504) }, + { SC_(4836693114880), SC_(0.000483669340610504150390625), SC_(1.46532154083251953125), SC_(0.92851742167955783637755823728448115497442142134004), SC_(0.071482578320442163622441762715518845025578578659958) }, + { SC_(9556477345792), SC_(0.000955647788941860198974609375), SC_(0.804133951663970947265625), SC_(0.78906415810449876562078794471829514693427758064696), SC_(0.21093584189550123437921205528170485306572241935304) }, + { SC_(9556477345792), SC_(0.000955647788941860198974609375), SC_(1.4024145603179931640625), SC_(0.91946155703754481352479238346787859905335082869119), SC_(0.080538442962455186475207616532121400946649171308807) }, + { SC_(10838489432064), SC_(0.00108384899795055389404296875), SC_(-1.13749277591705322265625), SC_(0.12743989126870304346542317478912987226157104995751), SC_(0.87256010873129695653457682521087012773842895004249) }, + { SC_(10838489432064), SC_(0.00108384899795055389404296875), SC_(0.75486361980438232421875), SC_(0.77450926357298223779984584559741400272890293481015), SC_(0.22549073642701776220015415440258599727109706518985) } + }}; +//#undef SC_ + diff --git a/test/table_type.hpp b/test/table_type.hpp index ed3fe0bfe..b8f16cfdf 100644 --- a/test/table_type.hpp +++ b/test/table_type.hpp @@ -26,17 +26,4 @@ struct table_type typedef long double type; }; -namespace boost{ namespace multiprecision{ - - template - class mp_number; - -}} - -template -struct table_type > -{ - typedef const char* type; -}; - #endif diff --git a/test/test_nc_t.cpp b/test/test_nc_t.cpp index 05639f3ff..6bb9907da 100644 --- a/test/test_nc_t.cpp +++ b/test/test_nc_t.cpp @@ -443,8 +443,9 @@ void quantile_sanity_check(T& data, const char* type_name, const char* test) try{ value_type m = mode(boost::math::non_central_t_distribution(data[i][0], data[i][1])); value_type p = pdf(boost::math::non_central_t_distribution(data[i][0], data[i][1]), m); - BOOST_CHECK_EX(pdf(boost::math::non_central_t_distribution(data[i][0], data[i][1]), m * (1 + sqrt(precision) * 100)) <= p, i); - BOOST_CHECK_EX(pdf(boost::math::non_central_t_distribution(data[i][0], data[i][1]), m * (1 - sqrt(precision)) * 100) <= p, i); + value_type delta = (std::max)(fabs(m * sqrt(precision) * 50), sqrt(precision) * 50); + BOOST_CHECK_EX(pdf(boost::math::non_central_t_distribution(data[i][0], data[i][1]), m + delta) <= p, i); + BOOST_CHECK_EX(pdf(boost::math::non_central_t_distribution(data[i][0], data[i][1]), m - delta) <= p, i); } catch(const boost::math::evaluation_error& ) {} #if 0 @@ -452,7 +453,7 @@ void quantile_sanity_check(T& data, const char* type_name, const char* test) // Sanity check degrees-of-freedom finder, don't bother at float // precision though as there's not enough data in the probability // values to get back to the correct degrees of freedom or - // non-cenrality parameter: + // non-centrality parameter: // try{ if((data[i][3] < 0.99) && (data[i][3] != 0)) @@ -489,6 +490,16 @@ void test_accuracy(T, const char* type_name) #include "nct.ipp" do_test_nc_t(nct, type_name, "Non Central T"); quantile_sanity_check(nct, type_name, "Non Central T"); + if(std::numeric_limits::is_specialized) + { + // + // Don't run these tests for real_concept: they take too long and don't converge + // without numeric_limits and lanczos support: + // +#include "nct_small_delta.ipp" + do_test_nc_t(nct_small_delta, type_name, "Non Central T (large parameters)"); + quantile_sanity_check(nct_small_delta, type_name, "Non Central T (large parameters)"); + } } int test_main(int, char* []) diff --git a/test/test_next.cpp b/test/test_next.cpp index a4dc84551..ea24d2d0b 100644 --- a/test/test_next.cpp +++ b/test/test_next.cpp @@ -15,7 +15,7 @@ #endif #if !defined(_CRAYC) && !defined(__CUDACC__) && (!defined(__GNUC__) || (__GNUC__ > 3) || ((__GNUC__ == 3) && (__GNUC_MINOR__ > 3))) -#if (defined(_M_IX86_FP) && (_M_IX86_FP >= 2)) || defined(__SSE2__) +#if (defined(_M_IX86_FP) && (_M_IX86_FP >= 2)) || defined(__SSE2__) || defined(TEST_SSE2) #include #include "xmmintrin.h" #define TEST_SSE2 @@ -157,6 +157,14 @@ int test_main(int, char* []) test_values(boost::math::concepts::real_concept(0), "real_concept"); #endif #if defined(TEST_SSE2) + +#ifdef _MSC_VER +# pragma message("Compiling SSE2 test code") +#endif +#ifdef __GNUC__ +# pragma message "Compiling SSE2 test code" +#endif + #ifdef _WIN32 // These tests fail pretty badly on Linux x64, especially with Intel-12.1 _MM_SET_FLUSH_ZERO_MODE(_MM_FLUSH_ZERO_ON); From 4be8acfe6884349f9f336e2c8c588bed4280908d Mon Sep 17 00:00:00 2001 From: John Maddock Date: Fri, 17 Aug 2012 11:18:18 +0000 Subject: [PATCH 098/115] Fix numerical stability problem in incomplete beta: ibeta_fraction2 sometimes has catastrophic cancellation errors when a and b are large and x is near 1. Change non central t series termination conditions to check for divergent series. Update tests with new larger test values. [SVN r80065] --- .../math/distributions/non_central_t.hpp | 12 +- include/boost/math/special_functions/beta.hpp | 10 +- test/nct_asym.ipp | 33 +++++ test/nct_small_delta.ipp | 133 +++++++++++------- test/test_nc_t.cpp | 14 +- 5 files changed, 140 insertions(+), 62 deletions(-) create mode 100644 test/nct_asym.ipp diff --git a/include/boost/math/distributions/non_central_t.hpp b/include/boost/math/distributions/non_central_t.hpp index 95cef8b6e..6e04261b4 100644 --- a/include/boost/math/distributions/non_central_t.hpp +++ b/include/boost/math/distributions/non_central_t.hpp @@ -68,18 +68,21 @@ namespace boost // direction for recursion: // boost::uintmax_t count = 0; + T last_term = 0; for(int i = k; i >= 0; --i) { T term = beta * pois; sum += term; // Don't terminate on first term in case we "fixed" k above: - if((i != k) && fabs(term/sum) < errtol) + if((fabs(last_term) > fabs(term)) && fabs(term/sum) < errtol) break; + last_term = term; pois *= (i + 0.5f) / d2; beta += xterm; xterm *= (i) / (x * (n / 2 + i - 1)); ++count; } + last_term = 0; for(int i = k + 1; ; ++i) { poisf *= d2 / (i + 0.5f); @@ -87,8 +90,9 @@ namespace boost betaf -= xtermf; T term = poisf * betaf; sum += term; - if(fabs(term/sum) < errtol) + if((fabs(last_term) > fabs(term)) && (fabs(term/sum) < errtol)) break; + last_term = term; ++count; if(count > max_iter) { @@ -166,6 +170,7 @@ namespace boost // Fused forward and backwards recursion: // boost::uintmax_t count = 0; + T last_term = 0; for(int i = k + 1, j = k; ; ++i, --j) { poisf *= d2 / (i + 0.5f); @@ -183,8 +188,9 @@ namespace boost sum += term; // Don't terminate on first term in case we "fixed" the value of k above: - if((j != k) && fabs(term/sum) < errtol) + if((fabs(last_term) > fabs(term)) && fabs(term/sum) < errtol) break; + last_term = term; if(count > max_iter) { return policies::raise_evaluation_error( diff --git a/include/boost/math/special_functions/beta.hpp b/include/boost/math/special_functions/beta.hpp index 440e762b4..40cc9efa4 100644 --- a/include/boost/math/special_functions/beta.hpp +++ b/include/boost/math/special_functions/beta.hpp @@ -597,7 +597,7 @@ struct ibeta_fraction2_t { typedef std::pair result_type; - ibeta_fraction2_t(T a_, T b_, T x_) : a(a_), b(b_), x(x_), m(0) {} + ibeta_fraction2_t(T a_, T b_, T x_, T y_) : a(a_), b(b_), x(x_), y(y_), m(0) {} result_type operator()() { @@ -607,7 +607,7 @@ struct ibeta_fraction2_t T bN = m; bN += (m * (b - m) * x) / (a + 2*m - 1); - bN += ((a + m) * (a - (a + b) * x + 1 + m *(2 - x))) / (a + 2*m + 1); + bN += ((a + m) * (a * y - b * x + 1 + m *(2 - x))) / (a + 2*m + 1); ++m; @@ -615,7 +615,7 @@ struct ibeta_fraction2_t } private: - T a, b, x; + T a, b, x, y; int m; }; // @@ -635,8 +635,10 @@ inline T ibeta_fraction2(T a, T b, T x, T y, const Policy& pol, bool normalised, if(result == 0) return result; - ibeta_fraction2_t f(a, b, x); + ibeta_fraction2_t f(a, b, x, y); T fract = boost::math::tools::continued_fraction_b(f, boost::math::policies::get_epsilon()); + BOOST_MATH_INSTRUMENT_VARIABLE(fract); + BOOST_MATH_INSTRUMENT_VARIABLE(result); return result / fract; } // diff --git a/test/nct_asym.ipp b/test/nct_asym.ipp new file mode 100644 index 000000000..bd5022b62 --- /dev/null +++ b/test/nct_asym.ipp @@ -0,0 +1,33 @@ +#ifndef SC_ +# define SC_(x) static_cast(BOOST_JOIN(x, L)) +#endif + static const boost::array, 26> nct_asym = {{ + { SC_(4536808851374080), SC_(0.45368087291717529296875), SC_(-0.481173217296600341796875), SC_(0.1749317497754352460810908541491372795891542325487), SC_(0.8250682502245647539189091458508627204108457674513) }, + { SC_(4536808851374080), SC_(0.45368087291717529296875), SC_(1.3978519439697265625), SC_(0.82745888213761221622777144575509830758765026825781), SC_(0.17254111786238778377222855424490169241234973174219) }, + { SC_(5677385198338048), SC_(0.56773853302001953125), SC_(-0.5258305072784423828125), SC_(0.13707201688604064907083148328658590547016675560101), SC_(0.86292798311395935092916851671341409452983324439899) }, + { SC_(5677385198338048), SC_(0.56773853302001953125), SC_(0.708383023738861083984375), SC_(0.55592460048261968604418681822217801676118984510485), SC_(0.44407539951738031395581318177782198323881015489515) }, + { SC_(19057916648620032), SC_(1.905791759490966796875), SC_(3.123167514801025390625), SC_(0.88826935840310006680843037482396692978657176631796), SC_(0.11173064159689993319156962517603307021342823368204) }, + { SC_(19057916648620032), SC_(1.905791759490966796875), SC_(3.3844356536865234375), SC_(0.93038224262142835995452986318222481740507172432515), SC_(0.069617757378571640045470136817775182594928275674854) }, + { SC_(36700173421772800), SC_(3.670017242431640625), SC_(4.6750431060791015625), SC_(0.84255780194329132905115240305424746317298104246855), SC_(0.15744219805670867094884759694575253682701895753145) }, + { SC_(36700173421772800), SC_(3.670017242431640625), SC_(5.042537689208984375), SC_(0.91504926091817108755289153804799207257503305462555), SC_(0.084950739081828912447108461952007927424966945374453) }, + { SC_(45079461342740480), SC_(4.507946014404296875), SC_(3.3889064788818359375), SC_(0.13156163646802619543156433884136170088487556815931), SC_(0.86843836353197380456843566115863829911512443184069) }, + { SC_(45079461342740480), SC_(4.507946014404296875), SC_(5.9973297119140625), SC_(0.93180682050435927369046460493686411555287073533266), SC_(0.068193179495640726309535395063135884447129264667335) }, + { SC_(157509421545553920), SC_(15.750942230224609375), SC_(17.14560699462890625), SC_(0.91844152246389020936377208106238904518645300898785), SC_(0.081558477536109790636227918937610954813546991012154) }, + { SC_(157509421545553920), SC_(15.750942230224609375), SC_(17.1575450897216796875), SC_(0.92022740765138483503818882082673489052943410104556), SC_(0.079772592348615164961811179173265109470565898954439) }, + { SC_(306140114898124800), SC_(30.614013671875), SC_(31.8541412353515625), SC_(0.89253589230213680868361632253582462638850083853234), SC_(0.10746410769786319131638367746417537361149916146766) }, + { SC_(306140114898124800), SC_(30.614013671875), SC_(32.01709747314453125), SC_(0.91970407450026572598532504589599032507374844769296), SC_(0.080295925499734274014674954104009674926251552307043) }, + { SC_(390730904542117888), SC_(39.073089599609375), SC_(38.045928955078125), SC_(0.15217241315852103004776349323469720103276253578469), SC_(0.84782758684147896995223650676530279896723746421531) }, + { SC_(390730904542117888), SC_(39.073089599609375), SC_(38.2361907958984375), SC_(0.20132472643110592660423913551748708698902279471476), SC_(0.79867527356889407339576086448251291301097720528524) }, + { SC_(1044709769224388608), SC_(104.470977783203125), SC_(104.8680572509765625), SC_(0.65434556985043816570960826185482905142969403857975), SC_(0.34565443014956183429039173814517094857030596142025) }, + { SC_(1044709769224388608), SC_(104.470977783203125), SC_(105.14849090576171875), SC_(0.75095977650749132960934905238656630719173158415557), SC_(0.24904022349250867039065094761343369280826841584443) }, + { SC_(1674453679643557888), SC_(167.44537353515625), SC_(166.869873046875), SC_(0.28247643026063070467278298745564297946418695359089), SC_(0.71752356973936929532721701254435702053581304640911) }, + { SC_(1674453679643557888), SC_(167.44537353515625), SC_(168.857147216796875), SC_(0.92099169494016061238522995952802645037178736022794), SC_(0.079008305059839387614770040471973549628212639772055) }, + { SC_(2809703283612975104), SC_(280.9703369140625), SC_(279.762969970703125), SC_(0.11364543011784098836896955307019184576823123795544), SC_(0.88635456988215901163103044692980815423176876204456) }, + { SC_(2809703283612975104), SC_(280.9703369140625), SC_(282.413665771484375), SC_(0.92553607281289461499104965729721028764390548597727), SC_(0.074463927187105385008950342702789712356094514022729) }, + { SC_(7921767423114477568), SC_(792.1767578125), SC_(792.31842041015625), SC_(0.5563267401667033086322021527186481547238720682263), SC_(0.4436732598332966913677978472813518452761279317737) }, + { SC_(7921767423114477568), SC_(792.1767578125), SC_(793.54827880859375), SC_(0.91489369852628004292795662749916567238372650186026), SC_(0.085106301473719957072043372500834327616273498139738) }, + { SC_(13091821180254420992), SC_(1309.18212890625), SC_(1308.01171875), SC_(0.12091797523015676375913420093212297337117969426545), SC_(0.87908202476984323624086579906787702662882030573455) }, + { SC_(13091821180254420992), SC_(1309.18212890625), SC_(1308.517578125), SC_(0.25316892936238242974380182772830364755920164172871), SC_(0.74683107063761757025619817227169635244079835827129) } + }}; +//#undef SC_ + diff --git a/test/nct_small_delta.ipp b/test/nct_small_delta.ipp index c22e6d8d1..f95518178 100644 --- a/test/nct_small_delta.ipp +++ b/test/nct_small_delta.ipp @@ -1,59 +1,86 @@ #ifndef SC_ # define SC_(x) static_cast(BOOST_JOIN(x, L)) #endif - static const boost::array, 52> nct_small_delta = {{ - { SC_(528154.0625), SC_(0.5281540482737767661092220805585384368896484375e-10), SC_(-0.0438658893108367919921875), SC_(0.48250566102131993419090032097993141749629366237354), SC_(0.51749433897868006580909967902006858250370633762646) }, - { SC_(528154.0625), SC_(0.5281540482737767661092220805585384368896484375e-10), SC_(0.944180071353912353515625), SC_(0.82746096542548677580028882735723708488758715357832), SC_(0.17253903457451322419971117264276291511241284642168) }, - { SC_(660934.625), SC_(0.6609346403507743161753751337528228759765625e-10), SC_(-1.09356248378753662109375), SC_(0.13707365461620354384117941652933126383612908392123), SC_(0.86292634538379645615882058347066873616387091607877) }, - { SC_(660934.625), SC_(0.6609346403507743161753751337528228759765625e-10), SC_(0.8943269252777099609375), SC_(0.81442633822735887388224244171117444649106453395369), SC_(0.18557366177264112611775755828882555350893546604631) }, - { SC_(2218633.5), SC_(0.221863361016261251279502175748348236083984375e-9), SC_(0.900856673717498779296875), SC_(0.81616768606164643627773468420573729773227964864232), SC_(0.18383231393835356372226531579426270226772035135768) }, - { SC_(2218633.5), SC_(0.221863361016261251279502175748348236083984375e-9), SC_(1.2173912525177001953125), SC_(0.88827224039054756935944165341219624193195834170515), SC_(0.11172775960945243064055834658780375806804165829485) }, - { SC_(4272462.5), SC_(0.427246238388079291325993835926055908203125e-9), SC_(-0.608891189098358154296875), SC_(0.27129829842994003638790396047987351547260466368909), SC_(0.72870170157005996361209603952012648452739533631091) }, - { SC_(4272462.5), SC_(0.427246238388079291325993835926055908203125e-9), SC_(1.00504648685455322265625), SC_(0.84256273846140526398141847027259437264491990536997), SC_(0.15743726153859473601858152972740562735508009463003) }, - { SC_(5247940), SC_(0.524793986045324345468543469905853271484375e-9), SC_(-1.11901676654815673828125), SC_(0.13156651861218774164823859585016794860626893918254), SC_(0.86843348138781225835176140414983205139373106081746) }, - { SC_(5247940), SC_(0.524793986045324345468543469905853271484375e-9), SC_(-1.0743181705474853515625), SC_(0.14134007648961033259203628094925336577210835950473), SC_(0.85865992351038966740796371905074663422789164049527) }, - { SC_(18336510), SC_(0.1833651008809056293102912604808807373046875e-8), SC_(-1.48560678958892822265625), SC_(0.068691587407182335464773960988799828434588100829723), SC_(0.93130841259281766453522603901120017156541189917028) }, - { SC_(18336510), SC_(0.1833651008809056293102912604808807373046875e-8), SC_(1.40664613246917724609375), SC_(0.92023381810537925932116820364336353453322062034513), SC_(0.079766181894620740678831796356636465466779379654875) }, - { SC_(35639400), SC_(0.3563940254025510512292385101318359375e-8), SC_(-0.2346564829349517822265625), SC_(0.40723768241459441841438282814230236027330099372549), SC_(0.59276231758540558158561717185769763972669900627451) }, - { SC_(35639400), SC_(0.3563940254025510512292385101318359375e-8), SC_(1.24018728733062744140625), SC_(0.89254693057186762829174224773340895165093032749745), SC_(0.10745306942813237170825775226659104834906967250255) }, - { SC_(45487064), SC_(0.4548706300511184963397681713104248046875e-8), SC_(-1.162539005279541015625), SC_(0.12250829730838957792258003981798522875055846989729), SC_(0.87749170269161042207741996018201477124944153010271) }, - { SC_(45487064), SC_(0.4548706300511184963397681713104248046875e-8), SC_(-0.8368303775787353515625), SC_(0.20134396068806204684905953847272082011338589718573), SC_(0.79865603931193795315094046152727917988661410281427) }, - { SC_(121620224), SC_(0.12162022500206148833967745304107666015625e-7), SC_(0.39718806743621826171875), SC_(0.6543856047457196617262494109772647455321658941725), SC_(0.3456143952542803382737505890227352544678341058275) }, - { SC_(121620224), SC_(0.12162022500206148833967745304107666015625e-7), SC_(1.24731695652008056640625), SC_(0.89385934536068351965787494087690986211211985166153), SC_(0.10614065463931648034212505912309013788788014833847) }, - { SC_(194932064), SC_(0.1949320704852652852423489093780517578125e-7), SC_(-0.575359284877777099609375), SC_(0.28252416082756836234341731346566281326700494104297), SC_(0.71747583917243163765658268653433718673299505895703) }, - { SC_(194932064), SC_(0.1949320704852652852423489093780517578125e-7), SC_(0.4194296896457672119140625), SC_(0.66254892777524155315670363767975247199405361778407), SC_(0.33745107222475844684329636232024752800594638221593) }, - { SC_(327092512), SC_(0.327092521956728887744247913360595703125e-7), SC_(-1.2071979045867919921875), SC_(0.11367796276232027931825008133662930047269775407393), SC_(0.88632203723767972068174991866337069952730224592607) }, - { SC_(327092512), SC_(0.327092521956728887744247913360595703125e-7), SC_(0.876802742481231689453125), SC_(0.80970309616765211535813735932417404262765601883988), SC_(0.19029690383234788464186264067582595737234398116012) }, - { SC_(922215104), SC_(0.922215122045599855482578277587890625e-7), SC_(0.141965448856353759765625), SC_(0.55644631504480191279462370740448518366492417190403), SC_(0.44355368495519808720537629259551481633507582809597) }, - { SC_(922215104), SC_(0.922215122045599855482578277587890625e-7), SC_(1.13559567928314208984375), SC_(0.87193707155023294863968629343839663906062875149397), SC_(0.12806292844976705136031370656160336093937124850603) }, - { SC_(1524088576), SC_(0.15240885886669275350868701934814453125e-6), SC_(-0.664114892482757568359375), SC_(0.25330834087624892647434930428222142994198568419577), SC_(0.74669165912375107352565069571777857005801431580423) }, - { SC_(1524088576), SC_(0.15240885886669275350868701934814453125e-6), SC_(1.37886774539947509765625), SC_(0.91603220911482167517950113163803628076090836350073), SC_(0.083967790885178324820498868361963719239091636499269) }, - { SC_(2833322752), SC_(0.2833322696460527367889881134033203125e-6), SC_(-0.934321820735931396484375), SC_(0.1750688828424918771805411797628815067286394341076), SC_(0.8249311171575081228194588202371184932713605658924) }, - { SC_(2833322752), SC_(0.2833322696460527367889881134033203125e-6), SC_(0.01152040623128414154052734375), SC_(0.50459576244612621592734255378527979154430257136497), SC_(0.49540423755387378407265744621472020845569742863503) }, - { SC_(7376104448), SC_(0.737610434953239746391773223876953125e-6), SC_(0.14150333404541015625), SC_(0.55626354548618560623653714942035371801766096231359), SC_(0.44373645451381439376346285057964628198233903768641) }, - { SC_(7376104448), SC_(0.737610434953239746391773223876953125e-6), SC_(0.46808087825775146484375), SC_(0.68013635973699279491605645205785045329423814366365), SC_(0.31986364026300720508394354794214954670576185633635) }, - { SC_(19005597696), SC_(0.190055970961111597716808319091796875e-5), SC_(0.89516448974609375), SC_(0.81464991000540683634213811269861642939018294670759), SC_(0.18535008999459316365786188730138357060981705329241) }, - { SC_(19005597696), SC_(0.190055970961111597716808319091796875e-5), SC_(1.48002254962921142578125), SC_(0.93056613193114394805618686943760965268036694876176), SC_(0.069433868068856051943813130562390347319633051238245) }, - { SC_(37336477696), SC_(0.37336476452765055000782012939453125e-5), SC_(-1.39093267917633056640625), SC_(0.08212235488316398659317034137786838544688552825868), SC_(0.91787764511683601340682965862213161455311447174132) }, - { SC_(37336477696), SC_(0.37336476452765055000782012939453125e-5), SC_(1.37445271015167236328125), SC_(0.91534882988245816934090108875322008488528628081311), SC_(0.084651170117541830659098911246779915114713719186888) }, - { SC_(76158959616), SC_(0.7615895810886286199092864990234375e-5), SC_(-0.4133583009243011474609375), SC_(0.33966927100300125337615080987310920514534610032036), SC_(0.66033072899699874662384919012689079485465389967964) }, - { SC_(76158959616), SC_(0.7615895810886286199092864990234375e-5), SC_(1.4921436309814453125), SC_(0.93216825396603974510969367870165246570825488483101), SC_(0.067831746033960254890306321298347534291745115168994) }, - { SC_(149909094400), SC_(0.149909101310186088085174560546875e-4), SC_(1.0512597560882568359375), SC_(0.85342690591562485295243723515889796180107709178638), SC_(0.14657309408437514704756276484110203819892290821362) }, - { SC_(149909094400), SC_(0.149909101310186088085174560546875e-4), SC_(1.39853727817535400390625), SC_(0.91902185764013358458014118954726949359893649842036), SC_(0.080978142359866415419858810452730506401063501579643) }, - { SC_(300246401024), SC_(0.300246392725966870784759521484375e-4), SC_(-0.858747541904449462890625), SC_(0.19523162330012228777050408978728209345121805498577), SC_(0.80476837669987771222949591021271790654878194501423) }, - { SC_(300246401024), SC_(0.300246392725966870784759521484375e-4), SC_(1.40856420993804931640625), SC_(0.92051352414116507572847602921599610498310359056324), SC_(0.079486475858834924271523970784003895016896409436761) }, - { SC_(353275379712), SC_(0.3532753908075392246246337890625e-4), SC_(-1.0212171077728271484375), SC_(0.15356742764115001237771940686359565408937029456416), SC_(0.84643257235884998762228059313640434591062970543584) }, - { SC_(353275379712), SC_(0.3532753908075392246246337890625e-4), SC_(1.30792331695556640625), SC_(0.90454434807153994552344182822189877220821074884107), SC_(0.09545565192846005447655817177810122779178925115893) }, - { SC_(0.105336832e13), SC_(0.0001053368323482573032379150390625), SC_(0.554341971874237060546875), SC_(0.71029154537084727662513596094978928595259300760913), SC_(0.28970845462915272337486403905021071404740699239087) }, - { SC_(0.105336832e13), SC_(0.0001053368323482573032379150390625), SC_(0.68778026103973388671875), SC_(0.75417124280258349801796658501621988164110540869668), SC_(0.24582875719741650198203341498378011835889459130332) }, - { SC_(2405508317184), SC_(0.0002405508421361446380615234375), SC_(0.5517151355743408203125), SC_(0.70934580778979545712784947970550407070754829519999), SC_(0.29065419221020454287215052029449592929245170480001) }, - { SC_(2405508317184), SC_(0.0002405508421361446380615234375), SC_(1.42728817462921142578125), SC_(0.92321691603357102065464321251307839682832539201822), SC_(0.076783083966428979345356787486921603171674607981778) }, - { SC_(4836693114880), SC_(0.000483669340610504150390625), SC_(-0.2817919254302978515625), SC_(0.38886609876734874792671065039736370377189209526496), SC_(0.61113390123265125207328934960263629622810790473504) }, - { SC_(4836693114880), SC_(0.000483669340610504150390625), SC_(1.46532154083251953125), SC_(0.92851742167955783637755823728448115497442142134004), SC_(0.071482578320442163622441762715518845025578578659958) }, - { SC_(9556477345792), SC_(0.000955647788941860198974609375), SC_(0.804133951663970947265625), SC_(0.78906415810449876562078794471829514693427758064696), SC_(0.21093584189550123437921205528170485306572241935304) }, - { SC_(9556477345792), SC_(0.000955647788941860198974609375), SC_(1.4024145603179931640625), SC_(0.91946155703754481352479238346787859905335082869119), SC_(0.080538442962455186475207616532121400946649171308807) }, - { SC_(10838489432064), SC_(0.00108384899795055389404296875), SC_(-1.13749277591705322265625), SC_(0.12743989126870304346542317478912987226157104995751), SC_(0.87256010873129695653457682521087012773842895004249) }, - { SC_(10838489432064), SC_(0.00108384899795055389404296875), SC_(0.75486361980438232421875), SC_(0.77450926357298223779984584559741400272890293481015), SC_(0.22549073642701776220015415440258599727109706518985) } + static const boost::array, 78> nct_small_delta = {{ + { SC_(528154.0625), SC_(0.5281540482737767661092220805585384368896484375e-10), SC_(-0.043873153626918792724609375), SC_(0.48250276576722336046483816401534117826515884583867), SC_(0.51749723423277663953516183598465882173484115416133) }, + { SC_(528154.0625), SC_(0.5281540482737767661092220805585384368896484375e-10), SC_(0.729398787021636962890625), SC_(0.76712095847007040756161950500140014007502095546645), SC_(0.23287904152992959243838049499859985992497904453355) }, + { SC_(528154.0625), SC_(0.5281540482737767661092220805585384368896484375e-10), SC_(0.944172799587249755859375), SC_(0.82745910775138122060234718854881274437593644597231), SC_(0.17254089224861877939765281145118725562406355402769) }, + { SC_(660934.625), SC_(0.6609346403507743161753751337528228759765625e-10), SC_(-1.09357059001922607421875), SC_(0.13707187615241828790447496643413251920933193961981), SC_(0.86292812384758171209552503356586748079066806038019) }, + { SC_(660934.625), SC_(0.6609346403507743161753751337528228759765625e-10), SC_(-0.075724057853221893310546875), SC_(0.46981932920499526656408951192932529155640100686028), SC_(0.53018067079500473343591048807067470844359899313972) }, + { SC_(660934.625), SC_(0.6609346403507743161753751337528228759765625e-10), SC_(0.894318759441375732421875), SC_(0.8144241543253204424707276799726958127232605442998), SC_(0.1855758456746795575292723200273041872767394557002) }, + { SC_(2218633.5), SC_(0.221863361016261251279502175748348236083984375e-9), SC_(-0.32331907749176025390625), SC_(0.37322681889304995092918136348422956501557638199648), SC_(0.62677318110695004907081863651577043498442361800352) }, + { SC_(2218633.5), SC_(0.221863361016261251279502175748348236083984375e-9), SC_(0.900841772556304931640625), SC_(0.81616372411403034488699018804029514822710817134975), SC_(0.18383627588596965511300981195970485177289182865025) }, + { SC_(2218633.5), SC_(0.221863361016261251279502175748348236083984375e-9), SC_(1.21737635135650634765625), SC_(0.88826940695840047354018486823128837280979546898275), SC_(0.11173059304159952645981513176871162719020453101725) }, + { SC_(4272462.5), SC_(0.427246238388079291325993835926055908203125e-9), SC_(-0.608911812305450439453125), SC_(0.27129146314707937854382467984874644387201484012076), SC_(0.72870853685292062145617532015125355612798515987924) }, + { SC_(4272462.5), SC_(0.427246238388079291325993835926055908203125e-9), SC_(-0.233737051486968994140625), SC_(0.40759456615456790965120565572754800087372105257581), SC_(0.59240543384543209034879434427245199912627894742419) }, + { SC_(4272462.5), SC_(0.427246238388079291325993835926055908203125e-9), SC_(1.0050258636474609375), SC_(0.84255777338099392090018173116713612691826495532429), SC_(0.15744222661900607909981826883286387308173504467571) }, + { SC_(5247940), SC_(0.524793986045324345468543469905853271484375e-9), SC_(-1.11903965473175048828125), SC_(0.13156163653841524718807085637540033587741857268684), SC_(0.86843836346158475281192914362459966412258142731316) }, + { SC_(5247940), SC_(0.524793986045324345468543469905853271484375e-9), SC_(-1.0743410587310791015625), SC_(0.14133494913380490957172969254766861098247075035799), SC_(0.85866505086619509042827030745233138901752924964201) }, + { SC_(5247940), SC_(0.524793986045324345468543469905853271484375e-9), SC_(0.466433703899383544921875), SC_(0.67954744448251303029682738870296370754546775710788), SC_(0.32045255551748696970317261129703629245453224289212) }, + { SC_(18336510), SC_(0.1833651008809056293102912604808807373046875e-8), SC_(-1.485649585723876953125), SC_(0.068685924351077450776106805057666756267354379116941), SC_(0.93131407564892254922389319494233324373264562088306) }, + { SC_(18336510), SC_(0.1833651008809056293102912604808807373046875e-8), SC_(-0.978404521942138671875), SC_(0.1639371522987393851111295873413950142583525211773), SC_(0.8360628477012606148888704126586049857416474788227) }, + { SC_(18336510), SC_(0.1833651008809056293102912604808807373046875e-8), SC_(1.406603336334228515625), SC_(0.92022746964275550779312032818254511021364287700111), SC_(0.079772530357244492206879671817454889786357122998891) }, + { SC_(35639400), SC_(0.3563940254025510512292385101318359375e-8), SC_(-0.9864399433135986328125), SC_(0.16195863866320448164806483040777245446296140149356), SC_(0.83804136133679551835193516959222754553703859850644) }, + { SC_(35639400), SC_(0.3563940254025510512292385101318359375e-8), SC_(-0.2347161769866943359375), SC_(0.40721451480880048322798573509892024502193304263547), SC_(0.59278548519119951677201426490107975497806695736453) }, + { SC_(35639400), SC_(0.3563940254025510512292385101318359375e-8), SC_(1.2401275634765625), SC_(0.89253588756079690951410755269677773042628883005293), SC_(0.10746411243920309048589244730322226957371116994707) }, + { SC_(45487064), SC_(0.4548706300511184963397681713104248046875e-8), SC_(-1.1626064777374267578125), SC_(0.12249460282273418971343108523190852402322477087166), SC_(0.87750539717726581028656891476809147597677522912834) }, + { SC_(45487064), SC_(0.4548706300511184963397681713104248046875e-8), SC_(-0.83689785003662109375), SC_(0.20132499540381076102236383246070664744644381565087), SC_(0.79867500459618923897763616753929335255355618434913) }, + { SC_(45487064), SC_(0.4548706300511184963397681713104248046875e-8), SC_(-0.594260692596435546875), SC_(0.27616888228432564767719590034089174423793663334908), SC_(0.72383111771567435232280409965910825576206336665092) }, + { SC_(121620224), SC_(0.12162022500206148833967745304107666015625e-7), SC_(0.3970777988433837890625), SC_(0.65434494968481063069505183722213499438179132868887), SC_(0.34565505031518936930494816277786500561820867131113) }, + { SC_(121620224), SC_(0.12162022500206148833967745304107666015625e-7), SC_(0.61813831329345703125), SC_(0.73175791107603006961198160308845586981919324758164), SC_(0.26824208892396993038801839691154413018080675241836) }, + { SC_(121620224), SC_(0.12162022500206148833967745304107666015625e-7), SC_(1.24720668792724609375), SC_(0.8938391359252750533876681559850381133400744586929), SC_(0.1061608640747249466123318440149618866599255413071) }, + { SC_(194932064), SC_(0.1949320704852652852423489093780517578125e-7), SC_(-0.575498878955841064453125), SC_(0.28247696804790908448299598525508816339233446215666), SC_(0.71752303195209091551700401474491183660766553784334) }, + { SC_(194932064), SC_(0.1949320704852652852423489093780517578125e-7), SC_(0.4192900955677032470703125), SC_(0.66249792556950493924206051736760665840039674490309), SC_(0.33750207443049506075793948263239334159960325509691) }, + { SC_(194932064), SC_(0.1949320704852652852423489093780517578125e-7), SC_(0.891839683055877685546875), SC_(0.81376056011022270595841292021652342060820308429614), SC_(0.18623943988977729404158707978347657939179691570386) }, + { SC_(327092512), SC_(0.327092521956728887744247913360595703125e-7), SC_(-1.404501438140869140625), SC_(0.080084787472122488844415495242012312453561424134301), SC_(0.9199152125278775111555845047579876875464385758657) }, + { SC_(327092512), SC_(0.327092521956728887744247913360595703125e-7), SC_(-1.20737874507904052734375), SC_(0.11364315277765295082194817827847616199631048415041), SC_(0.88635684722234704917805182172152383800368951584959) }, + { SC_(327092512), SC_(0.327092521956728887744247913360595703125e-7), SC_(0.8766219615936279296875), SC_(0.80965398752936883769527309841930163032620924932467), SC_(0.19034601247063116230472690158069836967379075067533) }, + { SC_(922215104), SC_(0.922215122045599855482578277587890625e-7), SC_(-0.550348579883575439453125), SC_(0.29104012336625227702044178467603355057145302194928), SC_(0.70895987663374772297955821532396644942854697805072) }, + { SC_(922215104), SC_(0.922215122045599855482578277587890625e-7), SC_(0.1416618525981903076171875), SC_(0.55632640945989957068387202865702682448619885466383), SC_(0.44367359054010042931612797134297317551380114533617) }, + { SC_(922215104), SC_(0.922215122045599855482578277587890625e-7), SC_(1.13529217243194580078125), SC_(0.87187352013277999854694556458228781398877720084173), SC_(0.12812647986722000145305443541771218601122279915827) }, + { SC_(1524088576), SC_(0.15240885886669275350868701934814453125e-6), SC_(-0.669230878353118896484375), SC_(0.25167405732584667576513293514194252242977450905894), SC_(0.74832594267415332423486706485805747757022549094106) }, + { SC_(1524088576), SC_(0.15240885886669275350868701934814453125e-6), SC_(-0.66450512409210205078125), SC_(0.25318348652085408643723791160561950141473919546181), SC_(0.74681651347914591356276208839438049858526080453819) }, + { SC_(1524088576), SC_(0.15240885886669275350868701934814453125e-6), SC_(1.37847745418548583984375), SC_(0.9159720143264452800722709073773563686088927059612), SC_(0.084027985673554719927729092622643631391107294038796) }, + { SC_(2833322752), SC_(0.2833322696460527367889881134033203125e-6), SC_(-0.9348537921905517578125), SC_(0.17493175360129918436210468793967574035560766123375), SC_(0.82506824639870081563789531206032425964439233876625) }, + { SC_(2833322752), SC_(0.2833322696460527367889881134033203125e-6), SC_(0.01098839938640594482421875), SC_(0.50438353586498884681723519205661827951453610911603), SC_(0.49561646413501115318276480794338172048546389088397) }, + { SC_(2833322752), SC_(0.2833322696460527367889881134033203125e-6), SC_(1.11728668212890625), SC_(0.86806405541813070462577859975991426774401640081913), SC_(0.13193594458186929537422140024008573225598359918087) }, + { SC_(7376104448), SC_(0.737610434953239746391773223876953125e-6), SC_(-1.36148512363433837890625), SC_(0.086680099352107115152692238918143641020516123095345), SC_(0.91331990064789288484730776108185635897948387690466) }, + { SC_(7376104448), SC_(0.737610434953239746391773223876953125e-6), SC_(0.1406452357769012451171875), SC_(0.55592460342263048867879490949555684169178196778873), SC_(0.44407539657736951132120509050444315830821803221127) }, + { SC_(7376104448), SC_(0.737610434953239746391773223876953125e-6), SC_(0.4672227799892425537109375), SC_(0.6798294875609898291245772837764000326600691290926), SC_(0.3201705124390101708754227162235999673399308709074) }, + { SC_(19005597696), SC_(0.190055970961111597716808319091796875e-5), SC_(-1.0526561737060546875), SC_(0.14624886521046919412989626895906939222407293206212), SC_(0.85375113478953080587010373104093060777592706793788) }, + { SC_(19005597696), SC_(0.190055970961111597716808319091796875e-5), SC_(0.893787801265716552734375), SC_(0.81428177283808104910080873651678647035668255855401), SC_(0.18571822716191895089919126348321352964331744144599) }, + { SC_(19005597696), SC_(0.190055970961111597716808319091796875e-5), SC_(1.478645801544189453125), SC_(0.9303822435208431945428692571159084817569960338472), SC_(0.069617756479156805457130742884091518243003966152798) }, + { SC_(37336477696), SC_(0.37336476452765055000782012939453125e-5), SC_(-1.39286124706268310546875), SC_(0.081830311952030386950958528699491776784138181119043), SC_(0.91816968804796961304904147130050822321586181888096) }, + { SC_(37336477696), SC_(0.37336476452765055000782012939453125e-5), SC_(-1.2086009979248046875), SC_(0.11340736887699187293262662688976277518450464408822), SC_(0.88659263112300812706737337311023722481549535591178) }, + { SC_(37336477696), SC_(0.37336476452765055000782012939453125e-5), SC_(1.37252414226531982421875), SC_(0.91504925497864847245117739324928896561477482544626), SC_(0.084950745021351527548822606750711034385225174553738) }, + { SC_(76158959616), SC_(0.7615895810886286199092864990234375e-5), SC_(-0.4161103665828704833984375), SC_(0.33866183595792209794153109645293698407273819046339), SC_(0.66133816404207790205846890354706301592726180953661) }, + { SC_(76158959616), SC_(0.7615895810886286199092864990234375e-5), SC_(1.48221313953399658203125), SC_(0.93085719135108164633155760685918105899871704889272), SC_(0.069142808648918353668442393140818941001282951107282) }, + { SC_(76158959616), SC_(0.7615895810886286199092864990234375e-5), SC_(1.4893915653228759765625), SC_(0.93180685365187513633521575127608504580804034566387), SC_(0.068193146348124863664784248723914954191959654336133) }, + { SC_(149909094400), SC_(0.149909101310186088085174560546875e-4), SC_(0.97038853168487548828125), SC_(0.83406983375988250630225384732975974640680046980811), SC_(0.16593016624011749369774615267024025359319953019189) }, + { SC_(149909094400), SC_(0.149909101310186088085174560546875e-4), SC_(1.04740297794342041015625), SC_(0.85253966501367083089932755397065936180784831841043), SC_(0.14746033498632916910067244602934063819215168158957) }, + { SC_(149909094400), SC_(0.149909101310186088085174560546875e-4), SC_(1.394680500030517578125), SC_(0.91844163480163429797669181827603427319262632792639), SC_(0.08155836519836570202330818172396572680737367207361) }, + { SC_(300246401024), SC_(0.300246392725966870784759521484375e-4), SC_(-0.864196956157684326171875), SC_(0.19373160667651853950263712162705732018958798823552), SC_(0.80626839332348146049736287837294267981041201176448) }, + { SC_(300246401024), SC_(0.300246392725966870784759521484375e-4), SC_(0.965739905834197998046875), SC_(0.83290531317191357846564987870102532533516215684712), SC_(0.16709468682808642153435012129897467466483784315288) }, + { SC_(300246401024), SC_(0.300246392725966870784759521484375e-4), SC_(1.403114795684814453125), SC_(0.91970421907553442085361472793817522857066471337247), SC_(0.080295780924465579146385272061824771429335286627532) }, + { SC_(353275379712), SC_(0.3532753908075392246246337890625e-4), SC_(-1.02712547779083251953125), SC_(0.15217237530683021166365655887378113611916101492035), SC_(0.84782762469316978833634344112621886388083898507965) }, + { SC_(353275379712), SC_(0.3532753908075392246246337890625e-4), SC_(0.584521234035491943359375), SC_(0.72055327773828199091011436164660463547526546920033), SC_(0.27944672226171800908988563835339536452473453079967) }, + { SC_(353275379712), SC_(0.3532753908075392246246337890625e-4), SC_(1.30201494693756103515625), SC_(0.90353832363228799912881142113287687617562615688939), SC_(0.096461676367712000871188578867123123824373843110611) }, + { SC_(0.105336832e13), SC_(0.0001053368323482573032379150390625), SC_(-1.12434637546539306640625), SC_(0.13041072232576106505759370992705369062839357686989), SC_(0.86958927767423893494240629007294630937160642313011) }, + { SC_(0.105336832e13), SC_(0.0001053368323482573032379150390625), SC_(0.544183909893035888671875), SC_(0.70680629772915567856214841102838580323130470572332), SC_(0.29319370227084432143785158897161419676869529427668) }, + { SC_(0.105336832e13), SC_(0.0001053368323482573032379150390625), SC_(0.67762219905853271484375), SC_(0.75096096245833210774398163041302339076159056835009), SC_(0.24903903754166789225601836958697660923840943164991) }, + { SC_(2405508317184), SC_(0.0002405508421361446380615234375), SC_(-0.54846096038818359375), SC_(0.29160515445821290109615211658532752777534929659883), SC_(0.70839484554178709890384788341467247222465070340117) }, + { SC_(2405508317184), SC_(0.0002405508421361446380615234375), SC_(0.53644597530364990234375), SC_(0.70409170751851223796496285006888224216192038796279), SC_(0.29590829248148776203503714993111775783807961203721) }, + { SC_(2405508317184), SC_(0.0002405508421361446380615234375), SC_(1.4120190143585205078125), SC_(0.92099239916220010887823964338845316029716642789693), SC_(0.079007600837799891121760356611546839702833572103074) }, + { SC_(4836693114880), SC_(0.000483669340610504150390625), SC_(-0.30330073833465576171875), SC_(0.38064607328786833329129434720920126565403722909458), SC_(0.61935392671213166670870565279079873434596277090542) }, + { SC_(4836693114880), SC_(0.000483669340610504150390625), SC_(0.79173374176025390625), SC_(0.78560096142991773065052672400091405076291446132892), SC_(0.21439903857008226934947327599908594923708553867108) }, + { SC_(4836693114880), SC_(0.000483669340610504150390625), SC_(1.44381272792816162109375), SC_(0.92553610113350895085593676928879838003706656547384), SC_(0.074463898866491049144063230711201619962933434526164) }, + { SC_(9556477345792), SC_(0.000955647788941860198974609375), SC_(0.774176061153411865234375), SC_(0.78030402643947053525294588392940945045026100828356), SC_(0.21969597356052946474705411607059054954973899171644) }, + { SC_(9556477345792), SC_(0.000955647788941860198974609375), SC_(1.35162198543548583984375), SC_(0.91159882995045713756961834701249644548104352714108), SC_(0.088401170049542862430381652987503554518956472858921) }, + { SC_(9556477345792), SC_(0.000955647788941860198974609375), SC_(1.37245666980743408203125), SC_(0.91489058742913963764590136168317114106740895702093), SC_(0.085109412570860362354098638316828858932591042979068) }, + { SC_(10838489432064), SC_(0.00108384899795055389404296875), SC_(-1.1693308353424072265625), SC_(0.12091706455667160284074085853324054976433257083915), SC_(0.87908293544332839715925914146675945023566742916085) }, + { SC_(10838489432064), SC_(0.00108384899795055389404296875), SC_(-0.02714899368584156036376953125), SC_(0.48873822149228296214357093419224183546582949284801), SC_(0.51126177850771703785642906580775816453417050715199) }, + { SC_(10838489432064), SC_(0.00108384899795055389404296875), SC_(0.723025619983673095703125), SC_(0.76483486081732755088858031522414884241973724382194), SC_(0.23516513918267244911141968477585115758026275617806) } }}; //#undef SC_ + diff --git a/test/test_nc_t.cpp b/test/test_nc_t.cpp index 6bb9907da..397d66cb0 100644 --- a/test/test_nc_t.cpp +++ b/test/test_nc_t.cpp @@ -94,6 +94,13 @@ void expected_results() "real_concept", // test type(s) "[^|]*", // test data group "[^|]*", 300000, 100000); // test function + add_expected_result( + "[^|]*", // compiler + "[^|]*", // stdlib + "[^|]*", // platform + largest_type, // test type(s) + "[^|]*large[^|]*", // test data group + "[^|]*", 1500, 300); // test function add_expected_result( "[^|]*", // compiler "[^|]*", // stdlib @@ -497,8 +504,11 @@ void test_accuracy(T, const char* type_name) // without numeric_limits and lanczos support: // #include "nct_small_delta.ipp" - do_test_nc_t(nct_small_delta, type_name, "Non Central T (large parameters)"); - quantile_sanity_check(nct_small_delta, type_name, "Non Central T (large parameters)"); + do_test_nc_t(nct_small_delta, type_name, "Non Central T (small non-centrality)"); + quantile_sanity_check(nct_small_delta, type_name, "Non Central T (small non-centrality)"); +#include "nct_asym.ipp" + do_test_nc_t(nct_asym, type_name, "Non Central T (large parameters)"); + quantile_sanity_check(nct_asym, type_name, "Non Central T (large parameters)"); } } From 29d598eb970c6c231f127fe359de7266ab0384a3 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Fri, 17 Aug 2012 12:21:57 +0000 Subject: [PATCH 099/115] Add student's t approximations for large v. [SVN r80066] --- .../math/distributions/non_central_t.hpp | 19 +++++++++++++++++++ 1 file changed, 19 insertions(+) diff --git a/include/boost/math/distributions/non_central_t.hpp b/include/boost/math/distributions/non_central_t.hpp index 6e04261b4..cef8606c9 100644 --- a/include/boost/math/distributions/non_central_t.hpp +++ b/include/boost/math/distributions/non_central_t.hpp @@ -214,6 +214,16 @@ namespace boost delta = -delta; invert = !invert; } + if(fabs(delta / (4 * n)) < policies::get_epsilon()) + { + // Approximate with a Student's T centred on delta, + // the crossover point is based on eq 2.6 from + // "A Comparison of Approximations To Persentiles of the + // Noncentral t-Distribution". H. Sahai and M. M. Ojeda, + // Revista Investigacion Operacional Vol 21, No 2, 2000. + T result = cdf(students_t_distribution(n), t - delta); + return invert ? 1 - result : result; + } // // x and y are the corresponding random // variables for the noncentral beta distribution, @@ -437,6 +447,15 @@ namespace boost * sqrt(n / constants::pi()) * exp(-delta * delta / 2) / 2; } + if(fabs(delta / (4 * n)) < policies::get_epsilon()) + { + // Approximate with a Student's T centred on delta, + // the crossover point is based on eq 2.6 from + // "A Comparison of Approximations To Persentiles of the + // Noncentral t-Distribution". H. Sahai and M. M. Ojeda, + // Revista Investigacion Operacional Vol 21, No 2, 2000. + return pdf(students_t_distribution(n), t - delta); + } // // x and y are the corresponding random // variables for the noncentral beta distribution, From 1f9cdaf16ff3357508945f87d1e903bb47f36ce7 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Fri, 17 Aug 2012 15:32:12 +0000 Subject: [PATCH 100/115] Add needed using declarations. [SVN r80068] --- include/boost/math/distributions/non_central_t.hpp | 1 + 1 file changed, 1 insertion(+) diff --git a/include/boost/math/distributions/non_central_t.hpp b/include/boost/math/distributions/non_central_t.hpp index cef8606c9..195a395fe 100644 --- a/include/boost/math/distributions/non_central_t.hpp +++ b/include/boost/math/distributions/non_central_t.hpp @@ -205,6 +205,7 @@ namespace boost template T non_central_t_cdf(T n, T delta, T t, bool invert, const Policy& pol) { + BOOST_MATH_STD_USING // // For t < 0 we have to use reflect: // From 9cef5e424d7bf41beb4c63058f7fb0a3b305137d Mon Sep 17 00:00:00 2001 From: John Maddock Date: Fri, 17 Aug 2012 16:04:15 +0000 Subject: [PATCH 101/115] Change variable names to match common usage. [SVN r80069] --- .../math/distributions/non_central_t.hpp | 42 +++++++++---------- 1 file changed, 21 insertions(+), 21 deletions(-) diff --git a/include/boost/math/distributions/non_central_t.hpp b/include/boost/math/distributions/non_central_t.hpp index 195a395fe..661bb6dc6 100644 --- a/include/boost/math/distributions/non_central_t.hpp +++ b/include/boost/math/distributions/non_central_t.hpp @@ -27,7 +27,7 @@ namespace boost namespace detail{ template - T non_central_t2_p(T n, T delta, T x, T y, const Policy& pol, T init_val) + T non_central_t2_p(T v, T delta, T x, T y, const Policy& pol, T init_val) { BOOST_MATH_STD_USING // @@ -55,9 +55,9 @@ namespace boost T xterm, beta; // Recurrance & starting beta terms: beta = x < y - ? detail::ibeta_imp(T(k + 1), T(n / 2), x, pol, false, true, &xterm) - : detail::ibeta_imp(T(n / 2), T(k + 1), y, pol, true, true, &xterm); - xterm *= y / (n / 2 + k); + ? detail::ibeta_imp(T(k + 1), T(v / 2), x, pol, false, true, &xterm) + : detail::ibeta_imp(T(v / 2), T(k + 1), y, pol, true, true, &xterm); + xterm *= y / (v / 2 + k); T poisf(pois), betaf(beta), xtermf(xterm); T sum = init_val; if((xterm == 0) && (beta == 0)) @@ -79,14 +79,14 @@ namespace boost last_term = term; pois *= (i + 0.5f) / d2; beta += xterm; - xterm *= (i) / (x * (n / 2 + i - 1)); + xterm *= (i) / (x * (v / 2 + i - 1)); ++count; } last_term = 0; for(int i = k + 1; ; ++i) { poisf *= d2 / (i + 0.5f); - xtermf *= (x * (n / 2 + i - 1)) / (i); + xtermf *= (x * (v / 2 + i - 1)) / (i); betaf -= xtermf; T term = poisf * betaf; sum += term; @@ -105,7 +105,7 @@ namespace boost } template - T non_central_t2_q(T n, T delta, T x, T y, const Policy& pol, T init_val) + T non_central_t2_q(T v, T delta, T x, T y, const Policy& pol, T init_val) { BOOST_MATH_STD_USING // @@ -151,14 +151,14 @@ namespace boost if(k != 0) { beta = x < y - ? detail::ibeta_imp(T(k + 1), T(n / 2), x, pol, true, true, &xterm) - : detail::ibeta_imp(T(n / 2), T(k + 1), y, pol, false, true, &xterm); + ? detail::ibeta_imp(T(k + 1), T(v / 2), x, pol, true, true, &xterm) + : detail::ibeta_imp(T(v / 2), T(k + 1), y, pol, false, true, &xterm); - xterm *= y / (n / 2 + k); + xterm *= y / (v / 2 + k); } else { - beta = pow(y, n / 2); + beta = pow(y, v / 2); xterm = beta; } T poisf(pois), betaf(beta), xtermf(xterm); @@ -174,7 +174,7 @@ namespace boost for(int i = k + 1, j = k; ; ++i, --j) { poisf *= d2 / (i + 0.5f); - xtermf *= (x * (n / 2 + i - 1)) / (i); + xtermf *= (x * (v / 2 + i - 1)) / (i); betaf += xtermf; T term = poisf * betaf; @@ -183,7 +183,7 @@ namespace boost term += beta * pois; pois *= (j + 0.5f) / d2; beta -= xterm; - xterm *= (j) / (x * (n / 2 + j - 1)); + xterm *= (j) / (x * (v / 2 + j - 1)); } sum += term; @@ -203,7 +203,7 @@ namespace boost } template - T non_central_t_cdf(T n, T delta, T t, bool invert, const Policy& pol) + T non_central_t_cdf(T v, T delta, T t, bool invert, const Policy& pol) { BOOST_MATH_STD_USING // @@ -215,14 +215,14 @@ namespace boost delta = -delta; invert = !invert; } - if(fabs(delta / (4 * n)) < policies::get_epsilon()) + if(fabs(delta / (4 * v)) < policies::get_epsilon()) { // Approximate with a Student's T centred on delta, // the crossover point is based on eq 2.6 from // "A Comparison of Approximations To Persentiles of the // Noncentral t-Distribution". H. Sahai and M. M. Ojeda, // Revista Investigacion Operacional Vol 21, No 2, 2000. - T result = cdf(students_t_distribution(n), t - delta); + T result = cdf(students_t_distribution(v), t - delta); return invert ? 1 - result : result; } // @@ -230,11 +230,11 @@ namespace boost // variables for the noncentral beta distribution, // with y = 1 - x: // - T x = t * t / (n + t * t); - T y = n / (n + t * t); + T x = t * t / (v + t * t); + T y = v / (v + t * t); T d2 = delta * delta; T a = 0.5f; - T b = n / 2; + T b = v / 2; T c = a + b + d2 / 2; // // Crossover point for calculating p or q is the same @@ -250,7 +250,7 @@ namespace boost if(x != 0) { result = non_central_beta_p(a, b, d2, x, y, pol); - result = non_central_t2_p(n, delta, x, y, pol, result); + result = non_central_t2_p(v, delta, x, y, pol, result); result /= 2; } else @@ -266,7 +266,7 @@ namespace boost if(x != 0) { result = non_central_beta_q(a, b, d2, x, y, pol); - result = non_central_t2_q(n, delta, x, y, pol, result); + result = non_central_t2_q(v, delta, x, y, pol, result); result /= 2; } else From 885e35a8fdd8f4017d679fad9942a6c033a7a346 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Fri, 17 Aug 2012 16:19:23 +0000 Subject: [PATCH 102/115] Update reference in comments. [SVN r80070] --- include/boost/math/distributions/non_central_t.hpp | 10 ++++++++++ 1 file changed, 10 insertions(+) diff --git a/include/boost/math/distributions/non_central_t.hpp b/include/boost/math/distributions/non_central_t.hpp index 661bb6dc6..d89944f05 100644 --- a/include/boost/math/distributions/non_central_t.hpp +++ b/include/boost/math/distributions/non_central_t.hpp @@ -222,6 +222,11 @@ namespace boost // "A Comparison of Approximations To Persentiles of the // Noncentral t-Distribution". H. Sahai and M. M. Ojeda, // Revista Investigacion Operacional Vol 21, No 2, 2000. + // Original sources referenced in the above are: + // "Some Approximations to the Persentage Points of the Noncentral + // t-Distribution". C. van Eeden. International Statistical Review, 29, 4-31. + // "Continuous Univariate Distributions". N.L. Johnson, S. Kotz and + // N. Balkrishnan. 1995. John Wiley and Sons New York. T result = cdf(students_t_distribution(v), t - delta); return invert ? 1 - result : result; } @@ -455,6 +460,11 @@ namespace boost // "A Comparison of Approximations To Persentiles of the // Noncentral t-Distribution". H. Sahai and M. M. Ojeda, // Revista Investigacion Operacional Vol 21, No 2, 2000. + // Original sources referenced in the above are: + // "Some Approximations to the Persentage Points of the Noncentral + // t-Distribution". C. van Eeden. International Statistical Review, 29, 4-31. + // "Continuous Univariate Distributions". N.L. Johnson, S. Kotz and + // N. Balkrishnan. 1995. John Wiley and Sons New York. return pdf(students_t_distribution(n), t - delta); } // From 15ac117d4ad75d3b764bd5357f27fb3fb9858a9e Mon Sep 17 00:00:00 2001 From: John Maddock Date: Fri, 17 Aug 2012 16:57:11 +0000 Subject: [PATCH 103/115] Update docs to reflect code changes. Regenerate. [SVN r80071] --- doc/sf_and_dist/distributions/nc_t.qbk | 13 + doc/sf_and_dist/html/index.html | 6 +- doc/sf_and_dist/html/index/s13.html | 2766 +++---- doc/sf_and_dist/html/index/s14.html | 176 +- doc/sf_and_dist/html/index/s15.html | 382 +- doc/sf_and_dist/html/index/s16.html | 284 +- doc/sf_and_dist/html/index/s17.html | 6494 ++++++++--------- .../html/math_toolkit/backgrounders.html | 4 +- .../backgrounders/implementation.html | 26 +- .../math_toolkit/backgrounders/lanczos.html | 20 +- .../html/math_toolkit/backgrounders/refs.html | 4 +- .../backgrounders/relative_error.html | 4 +- .../math_toolkit/backgrounders/remez.html | 30 +- .../html/math_toolkit/constants.html | 4 +- .../html/math_toolkit/constants/FAQ.html | 94 +- .../math_toolkit/constants/constants.html | 4 +- .../html/math_toolkit/constants/intro.html | 40 +- .../math_toolkit/constants/new_const.html | 5 +- .../html/math_toolkit/constants/tutorial.html | 4 +- .../constants/tutorial/non_templ.html | 4 +- .../constants/tutorial/templ.html | 4 +- .../constants/tutorial/user_def.html | 28 +- doc/sf_and_dist/html/math_toolkit/dist.html | 4 +- .../html/math_toolkit/dist/dist_ref.html | 4 +- .../dist/dist_ref/dist_algorithms.html | 4 +- .../math_toolkit/dist/dist_ref/dists.html | 4 +- .../dist/dist_ref/dists/bernoulli_dist.html | 10 +- .../dist/dist_ref/dists/beta_dist.html | 4 +- .../dist/dist_ref/dists/binomial_dist.html | 12 +- .../dist/dist_ref/dists/cauchy_dist.html | 12 +- .../dist/dist_ref/dists/chi_squared_dist.html | 12 +- .../dist/dist_ref/dists/exp_dist.html | 16 +- .../dist/dist_ref/dists/extreme_dist.html | 4 +- .../dist/dist_ref/dists/f_dist.html | 4 +- .../dist/dist_ref/dists/gamma_dist.html | 4 +- .../dist/dist_ref/dists/geometric_dist.html | 4 +- .../dist_ref/dists/hypergeometric_dist.html | 4 +- .../dists/inverse_chi_squared_dist.html | 22 +- .../dist_ref/dists/inverse_gamma_dist.html | 4 +- .../dist_ref/dists/inverse_gaussian_dist.html | 26 +- 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.../html/math_toolkit/using_udt/concepts.html | 12 +- .../math_toolkit/using_udt/dist_concept.html | 4 +- .../html/math_toolkit/using_udt/e_float.html | 4 +- .../html/math_toolkit/using_udt/use_mpfr.html | 4 +- .../html/math_toolkit/using_udt/use_ntl.html | 4 +- doc/sf_and_dist/html/math_toolkit/utils.html | 4 +- .../html/math_toolkit/utils/fp_facets.html | 4 +- .../utils/fp_facets/examples.html | 5 +- .../math_toolkit/utils/fp_facets/intro.html | 15 +- .../utils/fp_facets/portability.html | 4 +- .../utils/fp_facets/rationale.html | 10 +- .../utils/fp_facets/reference.html | 26 +- .../html/math_toolkit/utils/fpclass.html | 4 +- .../html/math_toolkit/utils/next_float.html | 4 +- .../utils/next_float/float_advance.html | 4 +- .../utils/next_float/float_distance.html | 12 +- .../utils/next_float/float_next.html | 4 +- .../utils/next_float/float_prior.html | 4 +- .../utils/next_float/nextafter.html | 4 +- .../html/math_toolkit/utils/rounding.html | 4 +- .../math_toolkit/utils/rounding/modf.html | 4 +- .../math_toolkit/utils/rounding/round.html | 4 +- .../math_toolkit/utils/rounding/trunc.html | 4 +- .../math_toolkit/utils/sign_functions.html | 50 +- 288 files changed, 6899 insertions(+), 6706 deletions(-) diff --git a/doc/sf_and_dist/distributions/nc_t.qbk b/doc/sf_and_dist/distributions/nc_t.qbk index bfee6490f..c0420682b 100644 --- a/doc/sf_and_dist/distributions/nc_t.qbk +++ b/doc/sf_and_dist/distributions/nc_t.qbk @@ -159,6 +159,19 @@ The PDF can be computed by a very similar method using: Where I[sub x][super '](a,b) is the derivative of the incomplete beta function. +For both the PDF and CDF we switch to approximating the distribution by a +Student's t distribution centred on [delta] when [nu] is very large. +The crossover location appears to be when [delta]/(4[nu]) < [epsilon], +this location was estimated by inspection of equation 2.6 in +"A Comparison of Approximations To Persentiles of the +Noncentral t-Distribution". H. Sahai and M. M. Ojeda, +Revista Investigacion Operacional Vol 21, No 2, 2000, and confirmed by +experimental testing. See also +"Some Approximations to the Persentage Points of the Noncentral +t-Distribution". C. van Eeden. International Statistical Review, 29, 4-31. +"Continuous Univariate Distributions". N.L. Johnson, S. Kotz and +N. Balkrishnan. 1995. John Wiley and Sons New York. + The quantile is calculated via the usual [link math_toolkit.toolkit.internals1.roots2 derivative-free root-finding techniques], diff --git a/doc/sf_and_dist/html/index.html b/doc/sf_and_dist/html/index.html index d4d2f13da..1d199e012 100644 --- a/doc/sf_and_dist/html/index.html +++ b/doc/sf_and_dist/html/index.html @@ -3,7 +3,7 @@ Math Toolkit - + @@ -18,7 +18,7 @@


    Next
    -
    +

    @@ -579,7 +579,7 @@

    - +

    Last revised: August 11, 2012 at 08:36:53 GMT

    Last revised: August 17, 2012 at 16:25:49 GMT


    diff --git a/doc/sf_and_dist/html/index/s13.html b/doc/sf_and_dist/html/index/s13.html index f101927c2..c6f1be6ed 100644 --- a/doc/sf_and_dist/html/index/s13.html +++ b/doc/sf_and_dist/html/index/s13.html @@ -3,7 +3,7 @@ Function Index - + @@ -22,2336 +22,2336 @@
    PrevUpHomeNext
    -
    +

    -Function Index

    +Function Index

    A B C D E F G H I J K L M N O P Q R S T U V W Z

    A
    -
    diff --git a/doc/sf_and_dist/html/index/s14.html b/doc/sf_and_dist/html/index/s14.html index dec99e6f3..f700616fe 100644 --- a/doc/sf_and_dist/html/index/s14.html +++ b/doc/sf_and_dist/html/index/s14.html @@ -3,7 +3,7 @@ Class Index - + @@ -22,210 +22,210 @@
    PrevUpHomeNext
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    +

    -Class Index

    +Class Index

    B C D E F G H I L M N P R S T U W

    B
    -
    diff --git a/doc/sf_and_dist/html/index/s15.html b/doc/sf_and_dist/html/index/s15.html index 301fbbd15..4338ab203 100644 --- a/doc/sf_and_dist/html/index/s15.html +++ b/doc/sf_and_dist/html/index/s15.html @@ -3,7 +3,7 @@ Typedef Index - + @@ -22,369 +22,369 @@
    PrevUpHomeNext
    -
    +

    -Typedef Index

    +Typedef Index

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    A
    -
    diff --git a/doc/sf_and_dist/html/index/s16.html b/doc/sf_and_dist/html/index/s16.html index b613d3dd5..af63c89a7 100644 --- a/doc/sf_and_dist/html/index/s16.html +++ b/doc/sf_and_dist/html/index/s16.html @@ -3,7 +3,7 @@ Macro Index - + @@ -22,266 +22,266 @@
    PrevUpHomeNext
    -
    +

    -Macro Index

    +Macro Index

    B F

    B
    -
    diff --git a/doc/sf_and_dist/html/index/s17.html b/doc/sf_and_dist/html/index/s17.html index e9b9baeb0..f856c372f 100644 --- a/doc/sf_and_dist/html/index/s17.html +++ b/doc/sf_and_dist/html/index/s17.html @@ -3,7 +3,7 @@ Index - + @@ -21,4912 +21,4912 @@
    PrevUpHome
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    -Index

    +Index

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    diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders.html b/doc/sf_and_dist/html/math_toolkit/backgrounders.html index 0e5065f9f..c90615900 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders.html @@ -3,7 +3,7 @@ Backgrounders - + @@ -22,7 +22,7 @@
    PrevUpHomeNext
    -
    +
    diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html b/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html index 189a1abad..4e664d29f 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html @@ -3,7 +3,7 @@ Additional Implementation Notes - + @@ -22,7 +22,7 @@
    PrevUpHomeNext
    -
    +

    Additional Implementation Notes @@ -137,11 +137,11 @@

    The tolerances need to be set to the maximum of:

    -
      -
    • +
        +
      • Some epsilon value.
      • -
      • +
      • The accuracy of the data (often only near 64-bit double).
      @@ -166,7 +166,7 @@ it is proposed that signalling a domain error is mandatory when the argument would give an mathematically undefined result.

      -

    -
    • +
      • Default parameters for the Triangular Distribution. We are uncertain about the best default parameters. Some sources suggest that the Standard Triangular Distribution has lower = 0, mode = half and upper = 1. However @@ -593,17 +593,17 @@

        Checks made are:

        -
          -
        • +
            +
          • Infinity or NaN (if available) passed in place of each of the valid params.
          • -
          • +
          • Infinity or NaN (if available) as a random variable.
          • -
          • +
          • Out-of-range random variable passed to pdf and cdf (ie outside of "range(DistributionType)").
          • -
          • +
          • Out-of-range probability passed to quantile function and complement.
          diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html b/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html index 022dd417d..f3ef1ee6f 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html @@ -3,7 +3,7 @@ The Lanczos Approximation - + @@ -22,7 +22,7 @@
          PrevUpHomeNext
          -
          +
          @@ -45,8 +45,8 @@ Lanczos approximation does have a couple of properties that make it worthy of further consideration:

          -
            -
          • +
              +
            • The approximation has an easy to compute truncation error that holds for all z > 0. In practice that means we can use the same approximation for all z > 0, and @@ -54,7 +54,7 @@ the truncation error will at worst be bounded by some finite value.
            • -
            • +
            • The approximation has a form that is particularly amenable to analytic manipulation, in particular ratios of gamma or gamma-like functions are particularly easy to compute without resorting to logarithms. @@ -537,21 +537,21 @@ References -
                -
              1. +
                  +
                1. Paul Godfrey, "A note on the computation of the convergent Lanczos complex Gamma approximation".
                2. -
                3. +
                4. Glendon Ralph Pugh, "An Analysis of the Lanczos Gamma Approximation", PhD Thesis November 2004.
                5. -
                6. +
                7. Viktor T. Toth, "Calculators and the Gamma Function".
                8. -
                9. +
                10. Mathworld, The Lanczos Approximation.
                11. diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html b/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html index 99b3eb9c0..236f5da6c 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html @@ -3,7 +3,7 @@ References - + @@ -22,7 +22,7 @@
                  PrevUpHomeNext
                  -
                  +
                  diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html b/doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html index 86a079e87..f3f749d05 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html @@ -3,7 +3,7 @@ Relative Error - + @@ -22,7 +22,7 @@
                  PrevUpHomeNext
                  -
                  +
                  diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html b/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html index ba8a6237a..370a8d95b 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html @@ -3,7 +3,7 @@ The Remez Method - + @@ -22,7 +22,7 @@
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                  @@ -65,15 +65,15 @@ yields the smallest maximal value of the error function. Chebyshev showed that there is a unique minimax solution for R(x) that has the following properties:

                  -
                    -
                  • +
                      +
                    • If R(x) is a polynomial of degree N, then there are N+2 unknowns: the N+1 coefficients of the polynomial, and maximal value of the error function.
                    • -
                    • +
                    • The error function has N+1 roots, and N+2 extrema (minima and maxima).
                    • -
                    • +
                    • The extrema alternate in sign, and all have the same magnitude.
                    @@ -416,18 +416,18 @@ wrong, it is by no means an exhaustive list, but is provided in the hopes that it will prove useful.

                    -
                      -
                    • +
                        +
                      • Is the function smooth enough? Can it be better separated into a rapidly changing part, and an asymptotic part?
                      • -
                      • +
                      • Does the function being approximated have any "blips" in it? Check for problems as the function changes computation method, or if a root, or an infinity has been divided out. The telltale sign is if there is a narrow region where the Remez method will not converge.
                      • -
                      • +
                      • Check you have enough accuracy in your calculations: remember that the Remez method works on the difference between the approximation and the function being approximated: so you must have more digits of precision @@ -435,27 +435,27 @@ So for example at double precision, you shouldn't expect to be able to get better than a float precision approximation.
                      • -
                      • +
                      • Try skewing the initial interpolated approximation to minimise the error before you begin the Remez steps.
                      • -
                      • +
                      • If the approximation won't converge or is ill-conditioned from one starting location, try starting from a different location.
                      • -
                      • +
                      • If a rational function won't converge, one can minimise a polynomial (which presents no problems), then rotate one term from the numerator to the denominator and minimise again. In theory one can continue moving terms one at a time from numerator to denominator, and then re-minimising, retaining the last set of control points at each stage.
                      • -
                      • +
                      • Try using a smaller interval. It may also be possible to optimise over one (small) interval, rescale the control points over a larger interval, and then re-minimise.
                      • -
                      • +
                      • Keep absissa values small: use a change of variable to keep the abscissa over, say [0, b], for some smallish value b.
                      • diff --git a/doc/sf_and_dist/html/math_toolkit/constants.html b/doc/sf_and_dist/html/math_toolkit/constants.html index 764de778d..ac07998d5 100644 --- a/doc/sf_and_dist/html/math_toolkit/constants.html +++ b/doc/sf_and_dist/html/math_toolkit/constants.html @@ -3,7 +3,7 @@ Mathematical Constants - + @@ -22,7 +22,7 @@
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                        diff --git a/doc/sf_and_dist/html/math_toolkit/constants/FAQ.html b/doc/sf_and_dist/html/math_toolkit/constants/FAQ.html index 22e3559b6..d2c275d49 100644 --- a/doc/sf_and_dist/html/math_toolkit/constants/FAQ.html +++ b/doc/sf_and_dist/html/math_toolkit/constants/FAQ.html @@ -3,7 +3,7 @@ FAQs - + @@ -22,7 +22,7 @@
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                        @@ -37,24 +37,24 @@

                        Some of the criteria we have used are:

                        -
                          -
                        • +
                            +
                          • Used in Boost.Math.
                          • -
                          • +
                          • Commonly used.
                          • -
                          • +
                          • Expensive to compute.
                          • -
                          • +
                          • Requested by users.
                          • -
                          • +
                          • Used in science and mathematics.
                          • -
                          • +
                          • No integer values (because so cheap to construct).
                            (You can easily define your own if found convenient, for example: FPT one =static_cast<FPT>(42);). @@ -65,57 +65,57 @@ How are constants named? -
                              -
                            • +
                                +
                              • Not macros, so no upper case.
                              • -
                              • +
                              • All lower case (following C++ standard names).
                              • -
                              • +
                              • No CamelCase.
                              • -
                              • +
                              • Underscore as _ delimiter between words.
                              • -
                              • +
                              • Numbers spelt as words rather than decimal digits (except following pow).
                              • -
                              • +
                              • Abbreviation conventions: -
                                  -
                                • +
                                    +
                                  • root for square root.
                                  • -
                                  • +
                                  • cbrt for cube root.
                                  • -
                                  • +
                                  • pow for pow function using decimal digits like pow23 for n2/3.
                                  • -
                                  • +
                                  • div for divided by or operator /.
                                  • -
                                  • +
                                  • minus for operator -, plus for operator +.
                                  • -
                                  • +
                                  • sqr for squared.
                                  • -
                                  • +
                                  • cubed for cubed n3.
                                  • -
                                  • +
                                  • words for greek, like π, ζ and Γ.
                                  • -
                                  • +
                                  • words like half, third, three_quarters, sixth for fractions. (Digit(s) can get muddled).
                                  • -
                                  • +
                                  • log10 for log10
                                  • -
                                  • +
                                  • ln for loge
                                  @@ -146,24 +146,24 @@ How are the constants tested? -
                                    -
                                  1. +
                                      +
                                    1. Comparison using Boost.Test BOOST_CHECK_CLOSE_FRACTION using long double literals, with at least 35 decimal digits, enough to be accurate for all long double implementations. The tolerance is usually twice long double epsilon.
                                    2. -
                                    3. +
                                    4. Comparison with calculation at long double precision. This often requires a slightly higher tolerance than two epsilon because of computational noise from round-off etc, especially when trig and other functions are called.
                                    5. -
                                    6. +
                                    7. Comparison with independent published values, for example, using The On-Line Encyclopedia of Integer Sequences (OEIS) again using at least 35 decimal digits strings.
                                    8. -
                                    9. +
                                    10. Comparison with independely calculated values using arbitrary precision tools like Mathematica, again using at least 35 decimal digits literal strings. @@ -397,40 +397,40 @@ Where can I find other high precision constants? -
                                        -
                                      1. +
                                          +
                                        1. Constants with very high precision and good accuracy (>40 decimal digits) from Simon Plouffe's web based collection http://pi.lacim.uqam.ca/eng/.
                                        2. -
                                        3. +
                                        4. The On-Line Encyclopedia of Integer Sequences (OEIS)
                                        5. -
                                        6. +
                                        7. Checks using printed text optically scanned values and converted from: D. E. Knuth, Art of Computer Programming, Appendix A, Table 1, Vol 1, ISBN 0 201 89683 4 (1997)
                                        8. -
                                        9. +
                                        10. M. Abrahamovitz & I. E. Stegun, National Bureau of Standards, Handbook of Mathematical Functions, a reference source for formulae now superceded by
                                        11. -
                                        12. +
                                        13. Frank W. Olver, Daniel W. Lozier, Ronald F. Boisvert, Charles W. Clark, NIST Handbook of Mathemetical Functions, Cambridge University Press, ISBN 978-0-521-14063-8, 2010.
                                        14. -
                                        15. +
                                        16. John F Hart, Computer Approximations, Kreiger (1978) ISBN 0 88275 642 7.
                                        17. -
                                        18. +
                                        19. Some values from Cephes Mathematical Library, Stephen L. Moshier and CALC100 100 decimal digit Complex Variable Calculator Program, a DOS utility.
                                        20. -
                                        21. +
                                        22. Xavier Gourdon, Pascal Sebah, 50 decimal digits constants at Number, constants and computation.
                                        23. @@ -443,18 +443,18 @@

                                          Not here in this Boost.Math collection, because physical constants:

                                          -
                                            -
                                          • +
                                              +
                                            • Are measurements.
                                            • -
                                            • +
                                            • Are not truly constant and keeping changing as mensuration technology improves.
                                            • -
                                            • +
                                            • Have a instrinsic uncertainty.
                                            • -
                                            • +
                                            • Mathematical constants are stored and represented at varying precision, but should never be inaccurate.
                                            • diff --git a/doc/sf_and_dist/html/math_toolkit/constants/constants.html b/doc/sf_and_dist/html/math_toolkit/constants/constants.html index e869ebe7b..9bb34f5bd 100644 --- a/doc/sf_and_dist/html/math_toolkit/constants/constants.html +++ b/doc/sf_and_dist/html/math_toolkit/constants/constants.html @@ -3,7 +3,7 @@ The Mathematical Constants - + @@ -22,7 +22,7 @@
                                              PrevUpHomeNext
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                                              +
                                              diff --git a/doc/sf_and_dist/html/math_toolkit/constants/intro.html b/doc/sf_and_dist/html/math_toolkit/constants/intro.html index 72d6a519a..e0cfc6586 100644 --- a/doc/sf_and_dist/html/math_toolkit/constants/intro.html +++ b/doc/sf_and_dist/html/math_toolkit/constants/intro.html @@ -3,7 +3,7 @@ Introduction - + @@ -22,7 +22,7 @@
                                              PrevUpHomeNext
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                                              +
                                              @@ -34,68 +34,68 @@ Why use Boost.Math mathematical constants? -
                                                -
                                              • +
                                                  +
                                                • Readable. For the very many jobs just using built-in like double, you can just write expressions like
                                                  double area = pi * r * r;
                                                  (If that's all you want, jump direct to use in non-template code!)
                                                • -
                                                • +
                                                • Effortless - avoiding a search of reference sources.
                                                • -
                                                • +
                                                • Usable with both builtin floating point types, and user-defined, possibly extended precision, types such as NTL, MPFR/GMP, mp_float: in the latter case the constants are computed to the necessary precision and then cached.
                                                • -
                                                • +
                                                • Accurate - ensuring that the values are as accurate as possible for the chosen floating-point type -
                                                    -
                                                  • +
                                                      +
                                                    • No loss of accuracy from repeated rounding of intermediate computations.
                                                    • -
                                                    • +
                                                    • Result is computed with higher precision and only rounded once.
                                                    • -
                                                    • +
                                                    • Less risk of inaccurate result from functions pow, trig and log at corner cases.
                                                    • -
                                                    • +
                                                    • Less risk of cancellation error.
                                                  • -
                                                  • +
                                                  • Faster - can avoid (re-)calculation at runtime. This can be significant if: -
                                                      -
                                                    • +
                                                        +
                                                      • Functions pow, trig or log are used.
                                                      • -
                                                      • +
                                                      • Inside an inner loop.
                                                      • -
                                                      • +
                                                      • Using a high-precision UDT.
                                                      • -
                                                      • +
                                                      • Compiler optimizations possible with built-in types, especially double, are not available.
                                                    • -
                                                    • +
                                                    • Portable - as possible between different systems using different floating-point precisions: see use in template code.
                                                    • -
                                                    • +
                                                    • Tested - by comparison with other published sources, or separately computed at long double precision.
                                                    • diff --git a/doc/sf_and_dist/html/math_toolkit/constants/new_const.html b/doc/sf_and_dist/html/math_toolkit/constants/new_const.html index 712c7c863..75e90fa9e 100644 --- a/doc/sf_and_dist/html/math_toolkit/constants/new_const.html +++ b/doc/sf_and_dist/html/math_toolkit/constants/new_const.html @@ -3,7 +3,7 @@ Defining New Constants - + @@ -22,7 +22,7 @@
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                                                      @@ -246,7 +246,6 @@ } // namespace constants } // namespace math } // namespace boost -

                                                      diff --git a/doc/sf_and_dist/html/math_toolkit/constants/tutorial.html b/doc/sf_and_dist/html/math_toolkit/constants/tutorial.html index 24c8d2ecb..cfecd8783 100644 --- a/doc/sf_and_dist/html/math_toolkit/constants/tutorial.html +++ b/doc/sf_and_dist/html/math_toolkit/constants/tutorial.html @@ -3,7 +3,7 @@ Tutorial - + @@ -22,7 +22,7 @@
                                                      PrevUpHomeNext
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                                                      diff --git a/doc/sf_and_dist/html/math_toolkit/constants/tutorial/non_templ.html b/doc/sf_and_dist/html/math_toolkit/constants/tutorial/non_templ.html index 64a88431b..34de38b24 100644 --- a/doc/sf_and_dist/html/math_toolkit/constants/tutorial/non_templ.html +++ b/doc/sf_and_dist/html/math_toolkit/constants/tutorial/non_templ.html @@ -3,7 +3,7 @@ Use in non-template code - + @@ -22,7 +22,7 @@
                                                      PrevUpHomeNext
                                                      -
                                                      +

                                                      Use in non-template code diff --git a/doc/sf_and_dist/html/math_toolkit/constants/tutorial/templ.html b/doc/sf_and_dist/html/math_toolkit/constants/tutorial/templ.html index 5656451d0..6ecb83209 100644 --- a/doc/sf_and_dist/html/math_toolkit/constants/tutorial/templ.html +++ b/doc/sf_and_dist/html/math_toolkit/constants/tutorial/templ.html @@ -3,7 +3,7 @@ Use in template code - + @@ -22,7 +22,7 @@
                                                      PrevUpHomeNext
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                                                      +

                                                      Use in template code diff --git a/doc/sf_and_dist/html/math_toolkit/constants/tutorial/user_def.html b/doc/sf_and_dist/html/math_toolkit/constants/tutorial/user_def.html index 57ed9902c..4f83f5d11 100644 --- a/doc/sf_and_dist/html/math_toolkit/constants/tutorial/user_def.html +++ b/doc/sf_and_dist/html/math_toolkit/constants/tutorial/user_def.html @@ -3,7 +3,7 @@ Use With User Defined Types - + @@ -22,7 +22,7 @@
                                                      PrevUpHomeNext
                                                      -
                                                      +

                                                      Use With User Defined Types @@ -40,25 +40,25 @@ than that of the built-in floating pointer types, how the value returned is created is as follows:

                                                      -
                                                        -
                                                      • +
                                                          +
                                                        • If the precision of the type is known at compile time: -
                                                            -
                                                          • +
                                                              +
                                                            • If the precision is less than or equal to that of a float and the type is constructable from a float then our code returns a float literal. If the user-defined type is a literal type then the function call that returns the constant will be a constexp.
                                                            • -
                                                            • +
                                                            • If the precision is less than or equal to that of a double and the type is constructable from a double then our code returns a double literal. If the user-defined type is a literal type then the function call that returns the constant will be a constexp.
                                                            • -
                                                            • +
                                                            • If the precision is less than or equal to that of a long double and the type is constructable from a long double then our code returns @@ -66,27 +66,27 @@ literal. If the user-defined type is a literal type then the function call that returns the constant will be a constexp.
                                                            • -
                                                            • +
                                                            • If the precision is less than 100 decimal digits, then the constant will be constructed (just the once, then cached in a thread-safe manner) from a string representation of the constant.
                                                            • -
                                                            • +
                                                            • Otherwise the value is computed (just once, then cached in a thread-safe manner).
                                                          • -
                                                          • +
                                                          • If the precision is unknown at compile time then: -
                                                              -
                                                            • +
                                                                +
                                                              • If the runtime precision (obtained from a call to boost::math::tools::digits<T>()) is less than 100 decimal digits, then the constant is constructed "on the fly" from the string representation of the constant.
                                                              • -
                                                              • +
                                                              • Otherwise the value is constructed "on the fly" by calculating then value of the constant using the current default precision of the type. Note that this can make use of the constants diff --git a/doc/sf_and_dist/html/math_toolkit/dist.html b/doc/sf_and_dist/html/math_toolkit/dist.html index 2a5cdeb07..b82807d67 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist.html @@ -3,7 +3,7 @@ Statistical Distributions and Functions - + @@ -22,7 +22,7 @@
                                                                PrevUpHomeNext
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                                                                +
                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref.html index 851ed3a04..f5894db88 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref.html @@ -3,7 +3,7 @@ Statistical Distributions Reference - + @@ -22,7 +22,7 @@
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                                                                +

                                                                Statistical Distributions Reference diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html index 95258344d..1eb55821a 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html @@ -3,7 +3,7 @@ Distribution Algorithms - + @@ -22,7 +22,7 @@
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                                                                Distribution Algorithms diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists.html index 37918a159..fdad85808 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists.html @@ -3,7 +3,7 @@ Distributions - + @@ -22,7 +22,7 @@
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                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html index 8dcda1d1e..55f0ede0f 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html @@ -3,7 +3,7 @@ Bernoulli Distribution - + @@ -22,7 +22,7 @@
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                                                                +
                                                                Bernoulli Distribution @@ -329,12 +329,12 @@ References
                                                                -
                                                                  -
                                                                • +
                                                                    +
                                                                  • Wikpedia Bernoulli distribution
                                                                  • -
                                                                  • +
                                                                  • Weisstein, Eric W. "Bernoulli Distribution." From MathWorld--A Wolfram Web Resource. diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html index b636547a1..bbc7f3cb5 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html @@ -3,7 +3,7 @@ Beta Distribution - + @@ -22,7 +22,7 @@
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                                                                    +
                                                                    Beta Distribution diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html index 85d983501..aea5344d5 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html @@ -3,7 +3,7 @@ Binomial Distribution - + @@ -22,7 +22,7 @@
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                                                                    +
                                                                    Binomial Distribution @@ -886,17 +886,17 @@ References
                                                                    -
                                                                      -
                                                                    • +
                                                                        +
                                                                      • Weisstein, Eric W. "Binomial Distribution." From MathWorld--A Wolfram Web Resource.
                                                                      • -
                                                                      • +
                                                                      • Wikipedia binomial distribution.
                                                                      • -
                                                                      • +
                                                                      • NIST Explorary Data Analysis.
                                                                      • diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html index 85844f1fc..8d19fa1b1 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html @@ -3,7 +3,7 @@ Cauchy-Lorentz Distribution - + @@ -22,7 +22,7 @@
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                                                                        Cauchy-Lorentz Distribution @@ -275,16 +275,16 @@ References
                                                                        -
                                                                          -
                                                                        • +
                                                                            +
                                                                          • Cauchy-Lorentz distribution
                                                                          • -
                                                                          • +
                                                                          • NIST Exploratory Data Analysis
                                                                          • -
                                                                          • +
                                                                          • Weisstein, Eric W. "Cauchy Distribution." From MathWorld--A Wolfram Web Resource. diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html index 3ce8af145..133854cc8 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html @@ -3,7 +3,7 @@ Chi Squared Distribution - + @@ -22,7 +22,7 @@
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                                                                            Chi Squared Distribution @@ -381,16 +381,16 @@ independent, normally distributed random References
                                                                            -
                                                                              -
                                                                            • +
                                                                                +
                                                                              • NIST Exploratory Data Analysis
                                                                              • -
                                                                              • +
                                                                              • Chi-square distribution
                                                                              • -
                                                                              • +
                                                                              • Weisstein, Eric W. "Chi-Squared Distribution." From MathWorld--A Wolfram Web Resource. diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html index dd005309f..5f1fc1083 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html @@ -3,7 +3,7 @@ Exponential Distribution - + @@ -22,7 +22,7 @@
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                                                                                Exponential Distribution @@ -285,21 +285,21 @@ references
                                                                                -
                                                                                  -
                                                                                • +
                                                                                    +
                                                                                  • Weisstein, Eric W. "Exponential Distribution." From MathWorld--A Wolfram Web Resource
                                                                                  • -
                                                                                  • +
                                                                                  • Wolfram Mathematica calculator
                                                                                  • -
                                                                                  • +
                                                                                  • NIST Exploratory Data Analysis
                                                                                  • -
                                                                                  • +
                                                                                  • Wikipedia Exponential distribution
                                                                                  • @@ -308,7 +308,7 @@ (See also the reference documentation for the related Extreme Distributions.)

                                                                                    -
                                                                                    • +
                                                                                      • Extreme Value Distributions, Theory and Applications Samuel Kotz & Saralees Nadarajah discuss the relationship of the types of extreme diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/extreme_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/extreme_dist.html index 7c26112b8..b4e1b90e8 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/extreme_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/extreme_dist.html @@ -3,7 +3,7 @@ Extreme Value Distribution - + @@ -22,7 +22,7 @@
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                                                                                        Extreme Value Distribution diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html index 236493a55..05a0f6a21 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html @@ -3,7 +3,7 @@ F Distribution - + @@ -22,7 +22,7 @@
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                                                                                        +
                                                                                        diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html index 25b80cce6..d4bfb8b27 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html @@ -3,7 +3,7 @@ Gamma (and Erlang) Distribution - + @@ -22,7 +22,7 @@
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                                                                                        -
                                                                                        +
                                                                                        Gamma (and Erlang) Distribution diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/geometric_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/geometric_dist.html index 61cf4b5b5..fe09827a1 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/geometric_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/geometric_dist.html @@ -3,7 +3,7 @@ Geometric Distribution - + @@ -22,7 +22,7 @@
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                                                                                        -
                                                                                        +
                                                                                        Geometric Distribution diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html index ddc58adca..5ab8ced41 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html @@ -3,7 +3,7 @@ Hypergeometric Distribution - + @@ -22,7 +22,7 @@
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                                                                                        -
                                                                                        +
                                                                                        Hypergeometric Distribution diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_chi_squared_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_chi_squared_dist.html index 46c8b11cc..2436766a3 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_chi_squared_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_chi_squared_dist.html @@ -3,7 +3,7 @@ Inverse Chi Squared Distribution - + @@ -22,7 +22,7 @@
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                                                                                        +
                                                                                        Inverse Chi Squared Distribution @@ -84,23 +84,23 @@

                                                                                        See

                                                                                        -
                                                                                        -
                                                                                          -
                                                                                        1. +
                                                                                            +
                                                                                          1. Bayesian Data Analysis, Andrew Gelman, John B. Carlin, Hal S. Stern, Donald B. Rubin, ISBN-13: 978-1584883883, Chapman & Hall; 2 edition (29 July 2003).
                                                                                          2. -
                                                                                          3. +
                                                                                          4. Bayesian Computation with R, Jim Albert, ISBN-13: 978-0387922973, Springer; 2nd ed. edition (10 Jun 2009)
                                                                                          5. diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gamma_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gamma_dist.html index 0a6be5f41..0a9f625a9 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gamma_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gamma_dist.html @@ -3,7 +3,7 @@ Inverse Gamma Distribution - + @@ -22,7 +22,7 @@
                                                                                            PrevUpHomeNext
                                                                                            -
                                                                                            +
                                                                                            Inverse Gamma Distribution diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gaussian_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gaussian_dist.html index 3b36b4aa1..16dc6afca 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gaussian_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/inverse_gaussian_dist.html @@ -3,7 +3,7 @@ Inverse Gaussian (or Inverse Normal) Distribution - + @@ -22,7 +22,7 @@
                                                                                            PrevUpHomeNext
                                                                                            -
                                                                                            +
                                                                                            Inverse Gaussian (or Inverse Normal) Distribution @@ -391,44 +391,44 @@ References
                                                                                            -
                                                                                              -
                                                                                            1. +
                                                                                                +
                                                                                              1. Wald, A. (1947). Sequential analysis. Wiley, NY.
                                                                                              2. -
                                                                                              3. +
                                                                                              4. The Inverse Gaussian distribution : theory, methodology, and applications, Raj S. Chhikara, J. Leroy Folks. ISBN 0824779975 (1989).
                                                                                              5. -
                                                                                              6. +
                                                                                              7. The Inverse Gaussian distribution : statistical theory and applications, Seshadri, V , ISBN - 0387986189 (pbk) (Dewey 519.2) (1998).
                                                                                              8. -
                                                                                              9. +
                                                                                              10. Numpy and Scipy Documentation.
                                                                                              11. -
                                                                                              12. +
                                                                                              13. R statmod invgauss functions.
                                                                                              14. -
                                                                                              15. +
                                                                                              16. R SuppDists invGauss functions. (Note that these R implementations names differ in case).
                                                                                              17. -
                                                                                              18. +
                                                                                              19. StatSci.org invgauss help.
                                                                                              20. -
                                                                                              21. +
                                                                                              22. invgauss R source.
                                                                                              23. -
                                                                                              24. +
                                                                                              25. pwald, qwald.
                                                                                              26. -
                                                                                              27. +
                                                                                              28. Brighton Webs wald.
                                                                                              29. diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/laplace_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/laplace_dist.html index d5450a464..66a30cf10 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/laplace_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/laplace_dist.html @@ -3,7 +3,7 @@ Laplace Distribution - + @@ -22,7 +22,7 @@
                                                                                                PrevUpHomeNext
                                                                                                -
                                                                                                +
                                                                                                Laplace Distribution @@ -331,17 +331,17 @@ References
                                                                                                -
                                                                                                  -
                                                                                                • +
                                                                                                    +
                                                                                                  • Weisstein, Eric W. "Laplace Distribution." From MathWorld--A Wolfram Web Resource.
                                                                                                  • -
                                                                                                  • +
                                                                                                  • Laplace Distribution
                                                                                                  • -
                                                                                                  • +
                                                                                                  • M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 1972, p. 930.
                                                                                                  • diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/logistic_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/logistic_dist.html index 0fc2c4523..e3c1e1c2e 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/logistic_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/logistic_dist.html @@ -3,7 +3,7 @@ Logistic Distribution - + @@ -22,7 +22,7 @@
                                                                                                    PrevUpHomeNext
                                                                                                    -
                                                                                                    +
                                                                                                    Logistic Distribution diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/lognormal_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/lognormal_dist.html index d8e588168..d1f470575 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/lognormal_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/lognormal_dist.html @@ -3,7 +3,7 @@ Log Normal Distribution - + @@ -22,7 +22,7 @@
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                                                                                                    +
                                                                                                    Log Normal Distribution diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_beta_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_beta_dist.html index 2eaac3b59..a04e51808 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_beta_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_beta_dist.html @@ -3,7 +3,7 @@ Noncentral Beta Distribution - + @@ -22,7 +22,7 @@
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                                                                                                    +
                                                                                                    Noncentral Beta Distribution diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html index 499e9e1da..2a8271538 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html @@ -3,7 +3,7 @@ Noncentral Chi-Squared Distribution - + @@ -22,7 +22,7 @@
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                                                                                                    +
                                                                                                    Noncentral Chi-Squared Distribution diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_f_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_f_dist.html index 20c11cfde..84603934b 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_f_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_f_dist.html @@ -3,7 +3,7 @@ Noncentral F Distribution - + @@ -22,7 +22,7 @@
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                                                                                                    +
                                                                                                    Noncentral F Distribution diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_t_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_t_dist.html index ea139038d..ab70fafc7 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_t_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_t_dist.html @@ -3,7 +3,7 @@ Noncentral T Distribution - + @@ -22,7 +22,7 @@
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                                                                                                    +
                                                                                                    Noncentral T Distribution @@ -323,6 +323,19 @@

                                                                                                    Where Ix'(a,b) is the derivative of the incomplete beta function.

                                                                                                    +

                                                                                                    + For both the PDF and CDF we switch to approximating the distribution + by a Student's t distribution centred on δ when ν is very large. The crossover + location appears to be when δ/(4ν) < ε, this location was estimated by + inspection of equation 2.6 in "A Comparison of Approximations To + Persentiles of the Noncentral t-Distribution". H. Sahai and M. M. + Ojeda, Revista Investigacion Operacional Vol 21, No 2, 2000, and confirmed + by experimental testing. See also "Some Approximations to the Persentage + Points of the Noncentral t-Distribution". C. van Eeden. International + Statistical Review, 29, 4-31. "Continuous Univariate Distributions". + N.L. Johnson, S. Kotz and N. Balkrishnan. 1995. John Wiley and Sons New + York. +

                                                                                                    The quantile is calculated via the usual derivative-free root-finding techniques, with the initial guess taken as the quantile diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html index 332c3dcce..66794effd 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html @@ -3,7 +3,7 @@ Negative Binomial Distribution - + @@ -22,7 +22,7 @@

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                                                                                                    +
                                                                                                    Negative Binomial Distribution @@ -878,13 +878,13 @@

                                                                                                    Implementation notes:

                                                                                                    -
                                                                                                      -
                                                                                                    • +
                                                                                                        +
                                                                                                      • The real concept type (that deliberately lacks the Lanczos approximation), was found to take several minutes to evaluate some extreme test values, so the test has been disabled for this type.
                                                                                                      • -
                                                                                                      • +
                                                                                                      • Much greater speed, and perhaps greater accuracy, might be achieved for extreme values by using a normal approximation. This is NOT been tested or implemented. diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html index 28c6ecf90..33143f135 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html @@ -3,7 +3,7 @@ Normal (Gaussian) Distribution - + @@ -22,7 +22,7 @@
                                                                                                        PrevUpHomeNext
                                                                                                        -
                                                                                                        +
                                                                                                        Normal (Gaussian) Distribution diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html index e0f9976f9..2a7331a6f 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html @@ -3,7 +3,7 @@ Pareto Distribution - + @@ -22,7 +22,7 @@
                                                                                                        PrevUpHomeNext
                                                                                                        -
                                                                                                        +
                                                                                                        @@ -320,17 +320,17 @@ References
                                                                                                        -
                                                                                                          -
                                                                                                        • +
                                                                                                            +
                                                                                                          • Pareto Distribution
                                                                                                          • -
                                                                                                          • +
                                                                                                          • Weisstein, Eric W. "Pareto Distribution." From MathWorld--A Wolfram Web Resource.
                                                                                                          • -
                                                                                                          • +
                                                                                                          • Handbook of Statistical Distributions with Applications, K Krishnamoorthy, ISBN 1-58488-635-8, Chapter 23, pp 257 - 267. (Note the meaning of a and b is reversed in Wolfram and Krishnamoorthy). diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/poisson_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/poisson_dist.html index 5ac44182a..5f7b4d590 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/poisson_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/poisson_dist.html @@ -3,7 +3,7 @@ Poisson Distribution - + @@ -22,7 +22,7 @@
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                                                                                                            +
                                                                                                            Poisson Distribution diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html index 7a7390307..0663b5d26 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html @@ -3,7 +3,7 @@ Rayleigh Distribution - + @@ -22,7 +22,7 @@
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                                                                                                            +
                                                                                                            Rayleigh Distribution @@ -322,11 +322,11 @@ References
                                                                                                            -
                                                                                                            -
                                                                                                              -
                                                                                                            • + diff --git a/doc/sf_and_dist/html/math_toolkit/dist/future.html b/doc/sf_and_dist/html/math_toolkit/dist/future.html index cc81b9be1..9d909633a 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/future.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/future.html @@ -3,7 +3,7 @@ Extras/Future Directions - + @@ -22,7 +22,7 @@
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                                                                                                              +
                                                                                                              diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut.html index 18cb69c3e..e9f0a041a 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut.html @@ -3,7 +3,7 @@ Statistical Distributions Tutorial - + @@ -22,7 +22,7 @@
                                                                                                              PrevUpHomeNext
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                                                                                                              +

                                                                                                              Statistical Distributions Tutorial diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/dist_params.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/dist_params.html index 044e097bf..5f747760c 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/dist_params.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/dist_params.html @@ -3,7 +3,7 @@ Discrete Probability Distributions - + @@ -22,7 +22,7 @@
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                                                                                                              +

                                                                                                              Discrete Probability Distributions diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview.html index c735e125c..ebe9959f2 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview.html @@ -3,7 +3,7 @@ Overview of Distributions - + @@ -22,7 +22,7 @@
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                                                                                                              +
                                                                                                              diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/complements.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/complements.html index 35379df86..e3f7a3bba 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/complements.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/complements.html @@ -3,7 +3,7 @@ Complements are supported too - and when to use them - + @@ -22,7 +22,7 @@
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                                                                                                              +
                                                                                                              Complements are supported too - and when to use them diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/generic.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/generic.html index 2b348fb26..9d20e9604 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/generic.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/generic.html @@ -3,7 +3,7 @@ Generic operations common to all distributions are non-member functions - + @@ -22,7 +22,7 @@
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                                                                                                              +
                                                                                                              Generic operations common to all distributions are non-member functions diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/headers.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/headers.html index d9b9fb8a1..e37ec40b5 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/headers.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/headers.html @@ -3,7 +3,7 @@ Headers and Namespaces - + @@ -22,7 +22,7 @@
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                                                                                                              +
                                                                                                              Headers and Namespaces diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/objects.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/objects.html index 8b85f9e1a..dc772c078 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/objects.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/objects.html @@ -3,7 +3,7 @@ Distributions are Objects - + @@ -22,7 +22,7 @@
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                                                                                                              -
                                                                                                              +
                                                                                                              Distributions are Objects @@ -50,13 +50,13 @@

                                                                                                              Making distributions class types does two things:

                                                                                                              -
                                                                                                                -
                                                                                                              • +
                                                                                                                  +
                                                                                                                • It encapsulates the kind of distribution in the C++ type system; so, for example, Students-t distributions are always a different C++ type from Chi-Squared distributions.
                                                                                                                • -
                                                                                                                • +
                                                                                                                • The distribution objects store any parameters associated with the distribution: for example, the Students-t distribution has a degrees of freedom parameter that controls the shape of the distribution. diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/parameters.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/parameters.html index e99532dd6..c56b7bcb0 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/parameters.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/parameters.html @@ -3,7 +3,7 @@ Parameters can be calculated - + @@ -22,7 +22,7 @@
                                                                                                                  PrevUpHomeNext
                                                                                                                  -
                                                                                                                  +
                                                                                                                  Parameters can be calculated diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/summary.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/summary.html index de7c68333..ee92a5a19 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/summary.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/summary.html @@ -3,7 +3,7 @@ Summary - + @@ -22,32 +22,32 @@
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                                                                                                                  +
                                                                                                                  -
                                                                                                                    -
                                                                                                                  • +
                                                                                                                      +
                                                                                                                    • Distributions are objects, which are constructed from whatever parameters the distribution may have.
                                                                                                                    • -
                                                                                                                    • +
                                                                                                                    • Member functions allow you to retrieve the parameters of a distribution.
                                                                                                                    • -
                                                                                                                    • +
                                                                                                                    • Generic non-member functions provide access to the properties that are common to all the distributions (PDF, CDF, quantile etc).
                                                                                                                    • -
                                                                                                                    • +
                                                                                                                    • Complements of probabilities are calculated by wrapping the function's arguments in a call to complement(...).
                                                                                                                    • -
                                                                                                                    • +
                                                                                                                    • Functions that accept a probability can accept a complement of the probability as well, by wrapping the function's arguments in a call to complement(...).
                                                                                                                    • -
                                                                                                                    • +
                                                                                                                    • Static member functions allow the parameters of a distribution to be found from other information.
                                                                                                                    • diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/variates.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/variates.html index 5a023500c..13bb6242d 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/variates.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/variates.html @@ -3,7 +3,7 @@ Random Variates and Distribution Parameters - + @@ -22,7 +22,7 @@
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                                                                                                                      +

                                                                                                                      Random Variates and Distribution Parameters diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg.html index 1ace5d9e3..1ff7ff852 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg.html @@ -3,7 +3,7 @@ Worked Examples - + @@ -22,7 +22,7 @@
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                                                                                                                      -
                                                                                                                      +
                                                                                                                      diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg.html index c8385a7c2..39cee9096 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg.html @@ -3,7 +3,7 @@ Binomial Distribution Examples - + @@ -22,7 +22,7 @@
                                                                                                                      PrevUpHomeNext
                                                                                                                      -
                                                                                                                      +
                                                                                                                      Binomial Distribution Examples diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html index 504bb9e3b..901a98ea4 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html @@ -3,7 +3,7 @@ Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution - + @@ -22,7 +22,7 @@
                                                                                                                      PrevUpHomeNext
                                                                                                                      -
                                                                                                                      +
                                                                                                                      Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution @@ -103,13 +103,13 @@ interval. Had we calculate two single-sided intervals each with a risk that the true value is outside the interval of α, then:

                                                                                                                      -
                                                                                                                      • +
                                                                                                                        • The risk that it is less than the lower bound is α.

                                                                                                                        and

                                                                                                                        -
                                                                                                                        • +
                                                                                                                          • The risk that it is greater than the upper bound is also α.

                                                                                                                          diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_size_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_size_eg.html index 89e280018..707e16e49 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_size_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_size_eg.html @@ -3,7 +3,7 @@ Estimating Sample Sizes for a Binomial Distribution. - + @@ -22,7 +22,7 @@

                                                                                                                          PrevUpHomeNext
                                                                                                                          -
                                                                                                                          +
                                                                                                                          Estimating Sample Sizes for a Binomial Distribution. diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html index 062c4e21b..546c83e69 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html @@ -3,7 +3,7 @@ Binomial Coin-Flipping Example - + @@ -22,7 +22,7 @@
                                                                                                                          PrevUpHomeNext
                                                                                                                          -
                                                                                                                          +
                                                                                                                          Binomial Coin-Flipping Example @@ -66,7 +66,8 @@ { cout << "Using Binomial distribution to predict how many heads and tails." << endl; try - { + { +

                                                                                                                          @@ -83,7 +84,8 @@ int flips = 10; binomial flip(flips, success_fraction); -cout.precision(4); +cout.precision(4); +

                                                                                                                          @@ -103,7 +105,8 @@ // if success_fraction is exactly one half, // for example, when flipping 'fair' coins. cout << "Skewness if success_fraction is " << flip.success_fraction() - << " is " << skewness(flip) << endl << endl; // Expect zero for a 'fair' coin. + << " is " << skewness(flip) << endl << endl; // Expect zero for a 'fair' coin. +

                                                                                                                          @@ -113,7 +116,8 @@

                                                                                                                          cout << "For " << flip.trials() << " coin flips: " << endl;
                                                                                                                           cout << "Probability of getting no heads is " << pdf(flip, 0) << endl;
                                                                                                                          -cout << "Probability of getting at least one head is " << 1. - pdf(flip, 0) << endl;
                                                                                                                          +cout << "Probability of getting at least one head is " << 1. - pdf(flip, 0) << endl; +

                                                                                                                          @@ -123,7 +127,8 @@

                                                                                                                          cout << "Probability of getting 0 or 1 heads is "
                                                                                                                          -  << pdf(flip, 0) + pdf(flip, 1) << endl; // sum of exactly == probabilities
                                                                                                                          + << pdf(flip, 0) + pdf(flip, 1) << endl; // sum of exactly == probabilities +

                                                                                                                          @@ -132,7 +137,8 @@

                                                                                                                          cout << "Probability of getting 0 or 1 (<= 1) heads is " << cdf(flip, 1) << endl;
                                                                                                                          -cout << "Probability of getting 9 or 10 heads is " << pdf(flip, 9) + pdf(flip, 10) << endl;
                                                                                                                          +cout << "Probability of getting 9 or 10 heads is " << pdf(flip, 9) + pdf(flip, 10) << endl; +

                                                                                                                          @@ -140,7 +146,8 @@

                                                                                                                          -
                                                                                                                          cout << "Probability of getting 9 or 10 heads is " << 1. - cdf(flip, 8) << endl;
                                                                                                                          +
                                                                                                                          cout << "Probability of getting 9 or 10 heads is " << 1. - cdf(flip, 8) << endl;
                                                                                                                          +

                                                                                                                          @@ -148,7 +155,8 @@

                                                                                                                          -
                                                                                                                          cout << "Probability of getting 9 or 10 heads is " << cdf(complement(flip, 8)) << endl;
                                                                                                                          +
                                                                                                                          cout << "Probability of getting 9 or 10 heads is " << cdf(complement(flip, 8)) << endl;
                                                                                                                          +

                                                                                                                          @@ -165,7 +173,8 @@

                                                                                                                          cout << "Probability of between 4 and 6 heads (4 or 5 or 6) is "
                                                                                                                             //  P(X == 4) + P(X == 5) + P(X == 6)
                                                                                                                          -  << pdf(flip, 4) + pdf(flip, 5) + pdf(flip, 6) << endl;
                                                                                                                          + << pdf(flip, 4) + pdf(flip, 5) + pdf(flip, 6) << endl; +

                                                                                                                          @@ -175,7 +184,8 @@

                                                                                                                          cout << "Probability of between 4 and 6 heads (4 or 5 or 6) is "
                                                                                                                             // P(X <= 6) - P(X <= 3) == P(X < 4)
                                                                                                                          -  << cdf(flip, 6) - cdf(flip, 3) << endl;
                                                                                                                          + << cdf(flip, 6) - cdf(flip, 3) << endl; +

                                                                                                                          @@ -186,7 +196,8 @@

                                                                                                                          cout << "Probability of between 3 and 7 heads (3, 4, 5, 6 or 7) is "
                                                                                                                             // P(X <= 7) - P(X <= 2) == P(X < 3)
                                                                                                                             << cdf(flip, 7) - cdf(flip, 2) << endl;
                                                                                                                          -cout << endl;
                                                                                                                          +cout << endl; +

                                                                                                                          @@ -215,7 +226,8 @@ cout << setw(2) << successes << " " << setw(10) << left << probability << " or 1 in " << 1. / probability << ", or " << probability * 100. << "%"<< endl; -} // for i +} // for i +

                                                                                                                          @@ -226,7 +238,8 @@

                                                                                                                          }
                                                                                                                           catch(const std::exception& e)
                                                                                                                           {
                                                                                                                          -  //
                                                                                                                          + // +

                                                                                                                          diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html index 9a5330d01..2259eba73 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html @@ -3,7 +3,7 @@ Binomial Quiz Example - + @@ -22,7 +22,7 @@

                                                                                                                          PrevUpHomeNext
                                                                                                                          -
                                                                                                                          +
                                                                                                                          Binomial Quiz Example @@ -55,8 +55,6 @@ using std::setw; using std::setprecision; #include <exception> using std::exception; - -

                                                                                                                          @@ -70,7 +68,8 @@
                                                                                                                          int questions = 16; // All the questions in the quiz.
                                                                                                                           int answers = 4; // Possible answers to each question.
                                                                                                                           double success_fraction = 1. / answers; // If a random guess, p = 1/4 = 0.25.
                                                                                                                          -binomial quiz(questions, success_fraction);
                                                                                                                          +binomial quiz(questions, success_fraction); +

                                                                                                                          @@ -81,7 +80,8 @@

                                                                                                                          cout << "In a quiz with " << quiz.trials()
                                                                                                                             << " questions and with a probability of guessing right of "
                                                                                                                             << quiz.success_fraction() * 100 << " %"
                                                                                                                          -  << " or 1 in " << static_cast<int>(1. / quiz.success_fraction()) << endl;
                                                                                                                          + << " or 1 in " << static_cast<int>(1. / quiz.success_fraction()) << endl; +

                                                                                                                          @@ -96,7 +96,8 @@ cout << "Probability of getting exactly " << pass_score << " answers right by chance is " << pdf(quiz, pass_score) << endl; cout << "Probability of getting all " << questions << " answers right by chance is " - << pdf(quiz, questions) << endl; + << pdf(quiz, questions) << endl; +

                                                                                                                          Probability of getting none right is 0.0100226
                                                                                                                          @@ -119,7 +120,8 @@ Probability of getting exactly all 16 answers right by chance is 2.32831e-010
                                                                                                                             double probability = pdf(quiz, successes);
                                                                                                                             cout << setw(2) << successes << "      " << probability << endl;
                                                                                                                           }
                                                                                                                          -cout << endl;
                                                                                                                          +cout << endl; +

                                                                                                                          Guessed Probability
                                                                                                                          @@ -146,7 +148,8 @@ Probability of getting exactly all 16 answers right by chance is 2.32831e-010
                                                                                                                                       

                                                                                                                          -
                                                                                                                          cout << "Probability of getting none or one right is " << pdf(quiz, 0) + pdf(quiz, 1) << endl;
                                                                                                                          +
                                                                                                                          cout << "Probability of getting none or one right is " << pdf(quiz, 0) + pdf(quiz, 1) << endl;
                                                                                                                          +

                                                                                                                          Probability of getting none or one right is 0.0634764
                                                                                                                          @@ -158,7 +161,8 @@ Probability of getting exactly all 16 answers right by chance is 2.32831e-010
                                                                                                                                       

                                                                                                                          -
                                                                                                                          cout << "Probability of getting none or one right is " << cdf(quiz, 1) << endl;
                                                                                                                          +
                                                                                                                          cout << "Probability of getting none or one right is " << cdf(quiz, 1) << endl;
                                                                                                                          +

                                                                                                                          Probability of getting none or one right is 0.0634764
                                                                                                                          @@ -169,7 +173,8 @@ Probability of getting exactly all 16 answers right by chance is 2.32831e-010
                                                                                                                                       

                                                                                                                          -
                                                                                                                          cout << "Probability of getting <= 10 right (to fail) is " << cdf(quiz, 10) << endl;
                                                                                                                          +
                                                                                                                          cout << "Probability of getting <= 10 right (to fail) is " << cdf(quiz, 10) << endl;
                                                                                                                          +

                                                                                                                          Probability of getting <= 10 right (to fail) is 0.999715
                                                                                                                          @@ -184,7 +189,8 @@ Probability of getting exactly all 16 answers right by chance is 2.32831e-010
                                                                                                                                       

                                                                                                                          -
                                                                                                                          cout << "Probability of getting > 10 right (to pass) is " << 1 - cdf(quiz, 10) << endl;
                                                                                                                          +
                                                                                                                          cout << "Probability of getting > 10 right (to pass) is " << 1 - cdf(quiz, 10) << endl;
                                                                                                                          +

                                                                                                                          Probability of getting > 10 right (to pass) is 0.000285239
                                                                                                                          @@ -195,7 +201,8 @@ Probability of getting exactly all 16 answers right by chance is 2.32831e-010
                                                                                                                                       

                                                                                                                          -
                                                                                                                          cout << "Probability of getting > 10 right (to pass) is " << cdf(complement(quiz, 10)) << endl;
                                                                                                                          +
                                                                                                                          cout << "Probability of getting > 10 right (to pass) is " << cdf(complement(quiz, 10)) << endl;
                                                                                                                          +

                                                                                                                          Probability of getting > 10 right (to pass) is 0.000285239
                                                                                                                          @@ -205,7 +212,8 @@ Probability of getting exactly all 16 answers right by chance is 2.32831e-010
                                                                                                                                       

                                                                                                                          -
                                                                                                                          BOOST_ASSERT((cdf(quiz, 10) + cdf(complement(quiz, 10))) == 1.);
                                                                                                                          +
                                                                                                                          BOOST_ASSERT((cdf(quiz, 10) + cdf(complement(quiz, 10))) == 1.);
                                                                                                                          +

                                                                                                                          @@ -216,7 +224,8 @@ Probability of getting exactly all 16 answers right by chance is 2.32831e-010

                                                                                                                          cout << "Probability of getting less than " << pass_score
                                                                                                                             << " (< " << pass_score << ") answers right by guessing is "
                                                                                                                          -  << cdf(quiz, pass_score -1) << endl;
                                                                                                                          + << cdf(quiz, pass_score -1) << endl; +

                                                                                                                          Probability of getting less than 11 (< 11) answers right by guessing is 0.999715
                                                                                                                          @@ -235,7 +244,8 @@ Probability of getting exactly all 16 answers right by chance is 2.32831e-010
                                                                                                                             << cdf(complement(quiz, pass_score-1))
                                                                                                                             << ", only 1 in " << 1/cdf(complement(quiz, pass_score-1)) << endl;
                                                                                                                           
                                                                                                                          -BOOST_ASSERT((cdf(quiz, pass_score -1) + cdf(complement(quiz, pass_score-1))) == 1);
                                                                                                                          +BOOST_ASSERT((cdf(quiz, pass_score -1) + cdf(complement(quiz, pass_score-1))) == 1); +

                                                                                                                          Probability of getting at least 11 (>= 11) answers right by guessing is 0.000285239, only 1 in 3505.83
                                                                                                                          @@ -251,7 +261,8 @@ Probability of getting exactly all 16 answers right by chance is 2.32831e-010
                                                                                                                             cout << setw(2) << score << "           " << setprecision(10)
                                                                                                                               << cdf(quiz, score) << endl;
                                                                                                                           }
                                                                                                                          -cout << endl;
                                                                                                                          +cout << endl; +

                                                                                                                          At most (<=)
                                                                                                                          @@ -281,7 +292,8 @@ Guessed OK   Probability
                                                                                                                           {
                                                                                                                             cout << setw(2) << score << "           "  << setprecision(10)
                                                                                                                               << cdf(complement(quiz, score)) << endl;
                                                                                                                          -}
                                                                                                                          +} +

                                                                                                                          At least (>)
                                                                                                                          @@ -324,7 +336,8 @@ Guessed OK   Probability
                                                                                                                           cout.precision(4);
                                                                                                                           cout << "Probability of getting between "
                                                                                                                             << low << " and " << high << " answers right by guessing is "
                                                                                                                          -  << sum  << endl; // 0.61323
                                                                                                                          + << sum << endl; // 0.61323 +

                                                                                                                          Probability of getting between 3 and 5 answers right by guessing is 0.6132
                                                                                                                          @@ -335,7 +348,8 @@ Guessed OK   Probability
                                                                                                                           

                                                                                                                          cout << "Probability of getting between " << low << " and " << high << " answers right by guessing is "
                                                                                                                          -  <<  cdf(quiz, high) - cdf(quiz, low - 1) << endl; // 0.61323
                                                                                                                          + << cdf(quiz, high) - cdf(quiz, low - 1) << endl; // 0.61323 +

                                                                                                                          Probability of getting between 3 and 5 answers right by guessing is 0.6132
                                                                                                                          @@ -353,7 +367,8 @@ Guessed OK   Probability
                                                                                                                             <<  cdf(quiz, high) - cdf(quiz, low - 1) << endl; // 1 <= x 8 P = 0.9825
                                                                                                                           low = 4; high = 4;
                                                                                                                           cout << "Probability of getting between " << low << " and " << high << " answers right by guessing is "
                                                                                                                          -  <<  cdf(quiz, high) - cdf(quiz, low - 1) << endl; // 4 <= x 4 P = 0.22520
                                                                                                                          + << cdf(quiz, high) - cdf(quiz, low - 1) << endl; // 4 <= x 4 P = 0.22520 +

                                                                                                                          Probability of getting between 1 and 6 answers right by guessing is 0.9104
                                                                                                                          @@ -377,7 +392,8 @@ Probability of getting between 4 and 4 answers right by guessing is 0.2252
                                                                                                                             <<  ceil(mean(quiz) - standard_deviation(quiz))  << " and "
                                                                                                                             << floor(mean(quiz) + standard_deviation(quiz)) << " correct." << endl;
                                                                                                                           cout << "Mode (the most frequent) is " << mode(quiz) << endl;
                                                                                                                          -cout << "Skewness is " << skewness(quiz) << endl;
                                                                                                                          +cout << "Skewness is " << skewness(quiz) << endl; +

                                                                                                                          By guessing, on average, one can expect to get 4 correct answers.
                                                                                                                          @@ -410,7 +426,8 @@ Skewness is 0.2887
                                                                                                                             << quantile(complement(quiz, 0.02)) << endl; //  2 to 98%
                                                                                                                           
                                                                                                                           cout << "If guessing then percentiles 1 to 99% will get " << quantile(quiz, 0.01)
                                                                                                                          -  << " to " << quantile(complement(quiz, 0.01)) << " right." << endl;
                                                                                                                          + << " to " << quantile(complement(quiz, 0.01)) << " right." << endl; +

                                                                                                                          @@ -457,7 +474,8 @@ Deciles 1 to 6 using boost::math::policies::discrete_quantile; using boost::math::policies::real; using boost::math::policies::integer_round_outwards; // Default. -typedef boost::math::policies::policy<discrete_quantile<real> > real_quantile_policy; +typedef boost::math::policies::policy<discrete_quantile<real> > real_quantile_policy; +

                                                                                                                          @@ -473,7 +491,8 @@ Deciles 1 to 6

                                                                                                                          using boost::math::binomial_distribution;
                                                                                                                          -typedef binomial_distribution<double, real_quantile_policy> real_quantile_binomial;
                                                                                                                          +typedef binomial_distribution<double, real_quantile_policy> real_quantile_binomial; +

                                                                                                                          @@ -481,7 +500,8 @@ Deciles 1 to 6

                                                                                                                          -
                                                                                                                          real_quantile_binomial quiz_real(questions, success_fraction);
                                                                                                                          +
                                                                                                                          real_quantile_binomial quiz_real(questions, success_fraction);
                                                                                                                          +

                                                                                                                          @@ -504,7 +524,8 @@ Deciles 1 to 6 << quantile(complement(quiz_real, 0.02)) << endl; // 2 to 98% 0.31311 7.7880 cout << "If guessing, then percentiles 1 to 99% will get " << quantile(quiz_real, 0.01) - << " to " << quantile(complement(quiz_real, 0.01)) << " right." << endl; + << " to " << quantile(complement(quiz_real, 0.01)) << " right." << endl; +

                                                                                                                          Real Quantiles
                                                                                                                          diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/c_sharp.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/c_sharp.html
                                                                                                                          index 626f75249..51d811b54 100644
                                                                                                                          --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/c_sharp.html
                                                                                                                          +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/c_sharp.html
                                                                                                                          @@ -3,7 +3,7 @@
                                                                                                                           
                                                                                                                           Using the Distributions from Within C#
                                                                                                                           
                                                                                                                          -
                                                                                                                          +
                                                                                                                           
                                                                                                                           
                                                                                                                           
                                                                                                                          @@ -22,7 +22,7 @@
                                                                                                                           
                                                                                                                          PrevUpHomeNext
                                                                                                                          -
                                                                                                                          +
                                                                                                                          Using the Distributions from Within C# diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg.html index 4f3af08fe..09256043b 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg.html @@ -3,7 +3,7 @@ Chi Squared Distribution Examples - + @@ -22,7 +22,7 @@
                                                                                                                          PrevUpHomeNext
                                                                                                                          -
                                                                                                                          +
                                                                                                                          Chi Squared Distribution Examples diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html index 27131bbcf..6be1a9d28 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html @@ -3,7 +3,7 @@ Confidence Intervals on the Standard Deviation - + @@ -22,7 +22,7 @@
                                                                                                                          PrevUpHomeNext
                                                                                                                          -
                                                                                                                          +
                                                                                                                          Confidence Intervals on the Standard Deviation diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html index 72b9579ee..bb2197d59 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html @@ -3,7 +3,7 @@ Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation - + @@ -22,7 +22,7 @@
                                                                                                                          PrevUpHomeNext
                                                                                                                          -
                                                                                                                          +
                                                                                                                          Estimating the Required Sample Sizes for a Chi-Square Test for the Standard Deviation diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_test.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_test.html index 01aac83fa..4e154e43d 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_test.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_test.html @@ -3,7 +3,7 @@ Chi-Square Test for the Standard Deviation - + @@ -22,7 +22,7 @@
                                                                                                                          PrevUpHomeNext
                                                                                                                          -
                                                                                                                          +
                                                                                                                          Chi-Square Test for the Standard Deviation diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/dist_construct_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/dist_construct_eg.html index 4c772ca7d..a92b6cdf6 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/dist_construct_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/dist_construct_eg.html @@ -3,7 +3,7 @@ Distribution Construction Example - + @@ -22,7 +22,7 @@
                                                                                                                          PrevUpHomeNext
                                                                                                                          -
                                                                                                                          +
                                                                                                                          Distribution Construction Example @@ -52,7 +52,8 @@ #include <boost/math/distributions/binomial.hpp> // for binomial_distribution. #include <boost/math/distributions/beta.hpp> // for beta_distribution. #include <boost/math/distributions/gamma.hpp> // for gamma_distribution. -#include <boost/math/distributions/normal.hpp> // for normal_distribution.
                                                                                                                          +#include <boost/math/distributions/normal.hpp> // for normal_distribution. +

                                                                                                                          @@ -64,7 +65,8 @@

                                                                                                                          -
                                                                                                                          boost::math::negative_binomial_distribution<double> mydist0(8., 0.25);
                                                                                                                          +
                                                                                                                          boost::math::negative_binomial_distribution<double> mydist0(8., 0.25);
                                                                                                                          +

                                                                                                                          @@ -72,7 +74,8 @@

                                                                                                                          -
                                                                                                                          using namespace boost::math;
                                                                                                                          +
                                                                                                                          using namespace boost::math;
                                                                                                                          +

                                                                                                                          @@ -81,7 +84,8 @@

                                                                                                                          -
                                                                                                                          using boost::math::negative_binomial_distribution;
                                                                                                                          +
                                                                                                                          using boost::math::negative_binomial_distribution;
                                                                                                                          +

                                                                                                                          @@ -94,7 +98,8 @@

                                                                                                                          -
                                                                                                                          negative_binomial_distribution<> mydist9(8., 0.25); // Uses default RealType = double.
                                                                                                                          +
                                                                                                                          negative_binomial_distribution<> mydist9(8., 0.25); // Uses default RealType = double.
                                                                                                                          +

                                                                                                                          @@ -120,7 +125,8 @@

                                                                                                                          -
                                                                                                                          using boost::math::negative_binomial;
                                                                                                                          +
                                                                                                                          using boost::math::negative_binomial;
                                                                                                                          +

                                                                                                                          @@ -128,7 +134,8 @@

                                                                                                                          -
                                                                                                                          negative_binomial mydist(8., 0.25);
                                                                                                                          +
                                                                                                                          negative_binomial mydist(8., 0.25);
                                                                                                                          +

                                                                                                                          @@ -136,7 +143,8 @@

                                                                                                                          -
                                                                                                                          negative_binomial mydist10(5., 0.4); // Both arguments double.
                                                                                                                          +
                                                                                                                          negative_binomial mydist10(5., 0.4); // Both arguments double.
                                                                                                                          +

                                                                                                                          @@ -144,7 +152,8 @@

                                                                                                                          -
                                                                                                                          negative_binomial mydist11(5, 0.4); // Using provided typedef double, int and double arguments.
                                                                                                                          +
                                                                                                                          negative_binomial mydist11(5, 0.4); // Using provided typedef double, int and double arguments.
                                                                                                                          +

                                                                                                                          @@ -153,7 +162,8 @@

                                                                                                                          negative_binomial mydist12(5., 0.4F); // Double and float arguments.
                                                                                                                          -negative_binomial mydist13(5, 1); // Both arguments integer.
                                                                                                                          +negative_binomial mydist13(5, 1); // Both arguments integer. +

                                                                                                                          @@ -162,7 +172,8 @@

                                                                                                                          binomial mybinomial(1, 0.5); // is more concise than
                                                                                                                          -binomial_distribution<> mybinomd1(1, 0.5);
                                                                                                                          +binomial_distribution<> mybinomd1(1, 0.5); +

                                                                                                                          @@ -187,7 +198,8 @@ error C3861: 'mybetad0': identifier not found

                                                                                                                          using boost::math::beta_distribution;
                                                                                                                          -beta_distribution<> mybetad1(1, 0.5);
                                                                                                                          +beta_distribution<> mybetad1(1, 0.5); +

                                                                                                                          @@ -195,7 +207,8 @@ error C3861: 'mybetad0': identifier not found

                                                                                                                          -
                                                                                                                          gamma_distribution<> mygammad1(1, 0.5);
                                                                                                                          +
                                                                                                                          gamma_distribution<> mygammad1(1, 0.5);
                                                                                                                          +

                                                                                                                          @@ -222,7 +235,8 @@ error C3861: 'mybetad0': identifier not found negative_binomial_distribution<double> mydist6(8., 0.25); // Explicit long double precision: -negative_binomial_distribution<long double> mydist7(8., 0.25); +negative_binomial_distribution<long double> mydist7(8., 0.25); +

                                                                                                                          @@ -265,7 +279,8 @@ error C3861: 'mybetad0': identifier not found normal norm3(2, 3); // Mean = 2, std deviation = 3. return 0; -} // int main() +} // int main() +

                                                                                                                          diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/error_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/error_eg.html index 7dc6113f0..0f7f1a779 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/error_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/error_eg.html @@ -3,7 +3,7 @@ Error Handling Example - + @@ -22,7 +22,7 @@

                                                                                                                          PrevUpHomeNext
                                                                                                                          -
                                                                                                                          +
                                                                                                                          Error Handling Example @@ -95,7 +95,8 @@ using std::exception; #include <cstddef> - // using ::errno + // using ::errno +

                                                                                                                          @@ -137,7 +138,8 @@ "\n""Message from thrown exception was:\n " << e.what() << std::endl; } return 0; -} // int main() +} // int main() +

                                                                                                                          diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/f_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/f_eg.html index 04410b317..263781cd0 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/f_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/f_eg.html @@ -3,7 +3,7 @@ F Distribution Examples - + @@ -22,7 +22,7 @@

                                                                                                                          PrevUpHomeNext
                                                                                                                          -
                                                                                                                          +
                                                                                                                          F Distribution Examples diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg.html index a321584eb..43b01c9d6 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg.html @@ -3,7 +3,7 @@ Find Location and Scale Examples - + @@ -22,7 +22,7 @@
                                                                                                                          PrevUpHomeNext
                                                                                                                          -
                                                                                                                          +
                                                                                                                          Find Location and Scale Examples diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html index 2881c4bcf..c24476f50 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html @@ -3,7 +3,7 @@ Find Location (Mean) Example - + @@ -22,7 +22,7 @@
                                                                                                                          PrevUpHomeNext
                                                                                                                          -
                                                                                                                          +
                                                                                                                          Find Location (Mean) Example @@ -50,7 +50,6 @@ using std::setw; using std::setprecision; #include <limits> using std::numeric_limits; -

                                                                                                                          @@ -62,7 +61,8 @@

                                                                                                                          normal N01;  // Default 'standard' normal distribution with zero mean and 
                                                                                                                          -double sd = 1.; // normal default standard deviation is 1.
                                                                                                                          +double sd = 1.; // normal default standard deviation is 1. +

                                                                                                                          @@ -82,7 +82,8 @@ cout << "Normal distribution with mean = " << N01.location() << ", standard deviation " << N01.scale() << ", has " << "fraction > " << z - << ", p = " << cdf(complement(N01, z)) << endl; // Note: uses complement. + << ", p = " << cdf(complement(N01, z)) << endl; // Note: uses complement. +

                                                                                                                          Normal distribution with mean = 0, standard deviation 1, has fraction <= -2, p = 0.0227501
                                                                                                                          @@ -94,7 +95,8 @@ Normal distribution with mean = 0, standard deviation 1, has fraction > -2, p
                                                                                                                           

                                                                                                                          double l = find_location<normal>(z, p, sd);
                                                                                                                          -cout << "offset location (mean) = " << l << endl;
                                                                                                                          +cout << "offset location (mean) = " << l << endl; +

                                                                                                                          @@ -112,7 +114,8 @@ Normal distribution with mean = 0, standard deviation 1, has fraction > -2, p

                                                                                                                          -
                                                                                                                          normal np001pc(l, sd); // Same standard_deviation (scale) but with mean (location) shifted.
                                                                                                                          +
                                                                                                                          normal np001pc(l, sd); // Same standard_deviation (scale) but with mean (location) shifted.
                                                                                                                          +

                                                                                                                          @@ -125,7 +128,8 @@ Normal distribution with mean = 0, standard deviation 1, has fraction > -2, p << ", p = " << cdf(np001pc, z) << endl; cout << "Normal distribution with mean = " << l << " has " << "fraction > " << z - << ", p = " << cdf(complement(np001pc, z)) << endl; + << ", p = " << cdf(complement(np001pc, z)) << endl; +

                                                                                                                          Normal distribution with mean = 1.09023 has fraction <= -2, p = 0.001
                                                                                                                          @@ -148,7 +152,8 @@ Normal distribution with mean = 1.09023 has fraction > -2, p = 0.999
                                                                                                                           

                                                                                                                          using boost::math::policies::policy;
                                                                                                                           using boost::math::policies::domain_error;
                                                                                                                          -using boost::math::policies::ignore_error;
                                                                                                                          +using boost::math::policies::ignore_error; +

                                                                                                                          @@ -165,7 +170,8 @@ Normal distribution with mean = 1.09023 has fraction > -2, p = 0.999 // Default policy, fully specified. l = find_location<normal>(z, p, sd, boost::math::policies::policy<>()); // A new policy, ignoring domain errors, without using a typedef. -l = find_location<normal>(z, p, sd, policy<domain_error<ignore_error> >()); +l = find_location<normal>(z, p, sd, policy<domain_error<ignore_error> >()); +

                                                                                                                          diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html index b0cb0289f..39dec71bf 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html @@ -3,7 +3,7 @@ Find mean and standard deviation example - + @@ -22,7 +22,7 @@

                                                                                                                          PrevUpHomeNext
                                                                                                                          -
                                                                                                                          +
                                                                                                                          Find mean and standard deviation example @@ -77,7 +77,8 @@

                                                                                                                          double mean = 3.; // kg
                                                                                                                           double standard_deviation = 0.1; // kg
                                                                                                                          -normal packs(mean, standard_deviation);
                                                                                                                          +normal packs(mean, standard_deviation); +

                                                                                                                          @@ -88,7 +89,8 @@

                                                                                                                          double max_weight = 3.1; // kg
                                                                                                                           cout << "Percentage of packs > " << max_weight << " is "
                                                                                                                          -<< cdf(complement(packs, max_weight)) * 100. << endl; // P(X > 3.1)
                                                                                                                          +<< cdf(complement(packs, max_weight)) * 100. << endl; // P(X > 3.1) +

                                                                                                                          @@ -105,7 +107,8 @@

                                                                                                                          double minimum_weight = 2.9;
                                                                                                                           cout <<"Fraction of packs <= " << minimum_weight << " with a mean of " << mean
                                                                                                                             << " is " << cdf(complement(packs, minimum_weight)) << endl;
                                                                                                                          -// fraction of packs <= 2.9 with a mean of 3 is 0.841345
                                                                                                                          +// fraction of packs <= 2.9 with a mean of 3 is 0.841345 +

                                                                                                                          @@ -128,7 +131,8 @@ cout << "Fraction of packs >= " << minimum_weight << " with a mean of " << xpacks.mean() << " is " << cdf(complement(xpacks, minimum_weight)) << endl; -// fraction of packs >= 2.9 with a mean of 3.06449 is 0.950005 +// fraction of packs >= 2.9 with a mean of 3.06449 is 0.950005 +

                                                                                                                          @@ -147,7 +151,8 @@ cout << "Setting the packer to " << nominal_mean << " will mean that " << "fraction of packs >= " << minimum_weight << " is " << cdf(complement(nominal_packs, minimum_weight)) << endl; -// Setting the packer to 3.06449 will mean that fraction of packs >= 2.9 is 0.95 +// Setting the packer to 3.06449 will mean that fraction of packs >= 2.9 is 0.95 +

                                                                                                                          @@ -159,7 +164,8 @@

                                                                                                                          #include <boost/math/distributions/find_location.hpp>
                                                                                                                          -  using boost::math::find_location;
                                                                                                                          + using boost::math::find_location; +

                                                                                                                          @@ -169,7 +175,8 @@

                                                                                                                          double safe_mean = find_location<normal>(minimum_weight, under_fraction, standard_deviation);
                                                                                                                          -normal good_packs(safe_mean, standard_deviation);
                                                                                                                          +normal good_packs(safe_mean, standard_deviation); +

                                                                                                                          @@ -180,7 +187,8 @@

                                                                                                                          cout << "Setting the packer to " << nominal_mean << " will mean that "
                                                                                                                             << "fraction of packs >= " << minimum_weight
                                                                                                                             << " is " << cdf(complement(good_packs, minimum_weight)) << endl;
                                                                                                                          -// Setting the packer to 3.06449 will mean that fraction of packs >= 2.9 is 0.95
                                                                                                                          +// Setting the packer to 3.06449 will mean that fraction of packs >= 2.9 is 0.95 +

                                                                                                                          @@ -213,7 +221,8 @@ cout << "Cauchy Setting the packer to " << mean << " will mean that " << "fraction of packs >= " << minimum_weight << " is " << cdf(complement(cpacks, minimum_weight)) << endl; -// Cauchy Setting the packer to 3 will mean that fraction of packs >= 2.9 is 0.75 +// Cauchy Setting the packer to 3 will mean that fraction of packs >= 2.9 is 0.75 +

                                                                                                                          @@ -225,7 +234,8 @@

                                                                                                                          double lc = find_location<cauchy>(minimum_weight, under_fraction, standard_deviation);
                                                                                                                           cout << "find_location<cauchy>(minimum_weight, over fraction, standard_deviation); " << lc << endl;
                                                                                                                          -// find_location<cauchy>(minimum_weight, over fraction, packs.standard_deviation()); 3.53138
                                                                                                                          +// find_location<cauchy>(minimum_weight, over fraction, packs.standard_deviation()); 3.53138 +

                                                                                                                          @@ -241,7 +251,8 @@ cout << "Cauchy Setting the packer to " << lc << " will mean that " << "fraction of packs >= " << minimum_weight << " is " << cdf(complement(goodcpacks, minimum_weight)) << endl; -// Cauchy Setting the packer to 3.53138 will mean that fraction of packs >= 2.9 is 0.95 +// Cauchy Setting the packer to 3.53138 will mean that fraction of packs >= 2.9 is 0.95 +

                                                                                                                          @@ -254,7 +265,8 @@ << find_location<cauchy>(minimum_weight, 0.99, standard_deviation) << " will mean that " << "fraction of packs >= " << minimum_weight - << " is " << cdf(complement(goodcpacks, minimum_weight)) << endl; + << " is " << cdf(complement(goodcpacks, minimum_weight)) << endl; +

                                                                                                                          @@ -313,7 +325,8 @@

                                                                                                                          double p = 0.05; // wanted p th quantile.
                                                                                                                           cout << "Quantile of " << p << " = " << quantile(packs, p)
                                                                                                                          -  << ", mean = " << packs.mean() << ", sd = " << packs.standard_deviation() << endl;
                                                                                                                          + << ", mean = " << packs.mean() << ", sd = " << packs.standard_deviation() << endl; +

                                                                                                                          @@ -338,7 +351,8 @@ cout <<"Fraction of packs >= " << minimum_weight << " with a mean of " << mean << " and standard deviation of " << pack05.standard_deviation() << " is " << cdf(complement(pack05, minimum_weight)) << endl; -// Fraction of packs >= 2.9 with a mean of 3 and standard deviation of 0.05 is 0.97725 +// Fraction of packs >= 2.9 with a mean of 3 and standard deviation of 0.05 is 0.97725 +

                                                                                                                          @@ -357,7 +371,8 @@ cout <<"Fraction of packs >= " << minimum_weight << " with a mean of " << mean << " and standard deviation of " << pack06.standard_deviation() << " is " << cdf(complement(pack06, minimum_weight)) << endl; -// Fraction of packs >= 2.9 with a mean of 3 and standard deviation of 0.06 is 0.95221 +// Fraction of packs >= 2.9 with a mean of 3 and standard deviation of 0.06 is 0.95221 +

                                                                                                                          @@ -394,7 +409,8 @@ cout << "For the "<< p << "th quantile to be located at " << minimum_weight << ", would need a standard deviation of " << sd95 << endl; -// For the 0.05th quantile to be located at 2.9, would need a standard deviation of 0.0607957 +// For the 0.05th quantile to be located at 2.9, would need a standard deviation of 0.0607957 +

                                                                                                                          @@ -407,7 +423,8 @@ cout <<"Fraction of packs >= " << minimum_weight << " with a mean of " << mean << " and standard deviation of " << pack95.standard_deviation() << " is " << cdf(complement(pack95, minimum_weight)) << endl; -// Fraction of packs >= 2.9 with a mean of 3 and standard deviation of 0.0607957 is 0.95 +// Fraction of packs >= 2.9 with a mean of 3 and standard deviation of 0.0607957 is 0.95 +

                                                                                                                          @@ -418,7 +435,8 @@

                                                                                                                          double ss = find_scale<normal>(minimum_weight, under_fraction, packs.mean());
                                                                                                                           cout << "find_scale<normal>(minimum_weight, under_fraction, packs.mean()); " << ss << endl;
                                                                                                                          -// find_scale<normal>(minimum_weight, under_fraction, packs.mean()); 0.0607957
                                                                                                                          +// find_scale<normal>(minimum_weight, under_fraction, packs.mean()); 0.0607957 +

                                                                                                                          @@ -426,7 +444,8 @@

                                                                                                                          -
                                                                                                                          double over_fraction = 0.95;
                                                                                                                          +
                                                                                                                          double over_fraction = 0.95;
                                                                                                                          +

                                                                                                                          @@ -450,7 +469,8 @@

                                                                                                                          double ss1o = find_scale<normal>(minimum_weight, 1 - over_fraction, packs.mean());
                                                                                                                           cout << "find_scale<normal>(minimum_weight, under_fraction, packs.mean()); " << ss1o << endl;
                                                                                                                          -// find_scale<normal>(minimum_weight, under_fraction, packs.mean()); 0.0607957
                                                                                                                          +// find_scale<normal>(minimum_weight, under_fraction, packs.mean()); 0.0607957 +

                                                                                                                          @@ -463,7 +483,8 @@

                                                                                                                          double ssc = find_scale<normal>(complement(minimum_weight, over_fraction, packs.mean()));
                                                                                                                           cout << "find_scale<normal>(complement(minimum_weight, over_fraction, packs.mean())); " << ssc << endl;
                                                                                                                          -// find_scale<normal>(complement(minimum_weight, over_fraction, packs.mean())); 0.0607957
                                                                                                                          +// find_scale<normal>(complement(minimum_weight, over_fraction, packs.mean())); 0.0607957 +

                                                                                                                          @@ -478,20 +499,21 @@ cout <<"Fraction of packs >= " << minimum_weight << " with a mean of " << mean << " and standard deviation of " << pack95c.standard_deviation() << " is " << cdf(complement(pack95c, minimum_weight)) << endl; -// Fraction of packs >= 2.9 with a mean of 3 and standard deviation of 0.0607957 is 0.95 +// Fraction of packs >= 2.9 with a mean of 3 and standard deviation of 0.0607957 is 0.95 +

                                                                                                                          Notice that these two deceptively simple questions:

                                                                                                                          -
                                                                                                                          • +
                                                                                                                            • Do we over-fill to make sure we meet a minimum specification (or under-fill to avoid an overdose)?

                                                                                                                            and/or

                                                                                                                            -
                                                                                                                            • +
                                                                                                                              • Do we measure better?

                                                                                                                              diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html index a49aa351d..1ac81d7d4 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html @@ -3,7 +3,7 @@ Find Scale (Standard Deviation) Example - + @@ -22,7 +22,7 @@

                                                                                                                              PrevUpHomeNext
                                                                                                                              -
                                                                                                                              +
                                                                                                                              Find Scale (Standard Deviation) Example @@ -59,7 +59,8 @@

                                                                                                                              normal N01;  // Default 'standard' normal distribution with zero mean
                                                                                                                              -double sd = 1.; // and standard deviation is 1.
                                                                                                                              +double sd = 1.; // and standard deviation is 1. +

                                                                                                                              @@ -79,7 +80,8 @@ cout << "Normal distribution with mean = " << N01.location() << ", standard deviation " << N01.scale() << ", has " << "fraction > " << z - << ", p = " << cdf(complement(N01, z)) << endl; // Note: uses complement. + << ", p = " << cdf(complement(N01, z)) << endl; // Note: uses complement. +

                                                                                                                              Normal distribution with mean = 0 has fraction <= -2, p = 0.0227501
                                                                                                                              @@ -94,7 +96,8 @@ Normal distribution with mean = 0 has fraction > -2, p = 0.97725
                                                                                                                               

                                                                                                                              double l = N01.location();
                                                                                                                               double s = find_scale<normal>(z, p, l);
                                                                                                                              -cout << "scale (standard deviation) = " << s << endl;
                                                                                                                              +cout << "scale (standard deviation) = " << s << endl; +

                                                                                                                              @@ -111,7 +114,8 @@ Normal distribution with mean = 0 has fraction > -2, p = 0.97725

                                                                                                                              -
                                                                                                                              normal np001pc(N01.location(), s);
                                                                                                                              +
                                                                                                                              normal np001pc(N01.location(), s);
                                                                                                                              +

                                                                                                                              @@ -124,7 +128,8 @@ Normal distribution with mean = 0 has fraction > -2, p = 0.97725 << ", p = " << cdf(np001pc, z) << endl; cout << "Normal distribution with mean = " << l << " has " << "fraction > " << z - << ", p = " << cdf(complement(np001pc, z)) << endl; + << ", p = " << cdf(complement(np001pc, z)) << endl; +

                                                                                                                              Normal distribution with mean = 0 has fraction <= -2, p = 0.001
                                                                                                                              @@ -147,7 +152,8 @@ Normal distribution with mean = 0 has fraction > -2, p = 0.999
                                                                                                                               

                                                                                                                              using boost::math::policies::policy;
                                                                                                                               using boost::math::policies::domain_error;
                                                                                                                              -using boost::math::policies::ignore_error;
                                                                                                                              +using boost::math::policies::ignore_error; +

                                                                                                                              @@ -165,7 +171,8 @@ Normal distribution with mean = 0 has fraction > -2, p = 0.999 // Default policy, fully specified. l = find_scale<normal>(z, p, l, boost::math::policies::policy<>()); // New policy, without typedef. -l = find_scale<normal>(z, p, l, policy<domain_error<ignore_error> >()); +l = find_scale<normal>(z, p, l, policy<domain_error<ignore_error> >()); +

                                                                                                                              @@ -185,7 +192,8 @@ Normal distribution with mean = 0 has fraction > -2, p = 0.999 cout << "Normal distribution with mean = " << l << " has " << "fraction <= " << z << " = " << cdf(np95pc, z) << endl; cout << "Normal distribution with mean = " << l << " has " - << "fraction > " << z << " = " << cdf(complement(np95pc, z)) << endl; + << "fraction > " << z << " = " << cdf(complement(np95pc, z)) << endl; +

                                                                                                                              diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/geometric_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/geometric_eg.html index d231a1014..6a56334ae 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/geometric_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/geometric_eg.html @@ -3,7 +3,7 @@ Geometric Distribution Examples - + @@ -22,7 +22,7 @@

                                                                                                                              PrevUpHomeNext
                                                                                                                              -
                                                                                                                              +
                                                                                                                              Geometric Distribution Examples @@ -37,7 +37,8 @@

                                                                                                                              #define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
                                                                                                                              -#define BOOST_MATH_DISCRETE_QUANTILE_POLICY real
                                                                                                                              +#define BOOST_MATH_DISCRETE_QUANTILE_POLICY real +

    @@ -109,7 +110,8 @@

    double success_fraction = 1./6; // success_fraction (p) = 0.1666
    -// (so failure_fraction is 1 - success_fraction = 5./6 = 1- 0.1666 = 0.8333)
    +// (so failure_fraction is 1 - success_fraction = 5./6 = 1- 0.1666 = 0.8333) +

    @@ -126,7 +128,8 @@

    -
    geometric g6(success_fraction); // type double by default.
    +
    geometric g6(success_fraction); // type double by default.
    +

    @@ -134,7 +137,8 @@

    -
    cout << "success fraction of a six-sided dice is " << g6.success_fraction() << endl;
    +
    cout << "success fraction of a six-sided dice is " << g6.success_fraction() << endl;
    +

    @@ -144,7 +148,8 @@

    cout << pdf(g6, 0) << endl; // 0.1667
    -cout << cdf(g6, 0) << endl; // 0.1667
    +cout<<cdf(g6,0)<<endl;// 0.1667 +

    @@ -154,7 +159,8 @@

    -
    cout << pdf(g6, 1) << endl; // 0.1389
    +
    cout << pdf(g6, 1) << endl; // 0.1389
    +

    @@ -163,7 +169,8 @@

    -
    cout << "pdf(g6, 0) + pdf(g6, 1) = " << pdf(g6, 0) + pdf(g6, 1) << endl;
    +
    cout << "pdf(g6, 0) + pdf(g6, 1) = " << pdf(g6, 0) + pdf(g6, 1) << endl;
    +

    @@ -172,7 +179,8 @@

    -
    cout << "cdf(g6, 1) = " << cdf(g6, 1) << endl; // 0.3056
    +
    cout << "cdf(g6, 1) = " << cdf(g6, 1) << endl; // 0.3056
    +

    @@ -181,7 +189,8 @@

    -
    cout << "cdf(g6, 12) = " << cdf(g6, 12) << endl; // 0.9065 or 90% probability.
    +
    cout << "cdf(g6, 12) = " << cdf(g6, 12) << endl; // 0.9065 or 90% probability.
    +

    @@ -190,7 +199,8 @@

    -
    cout << "quantile(g6, 0.99) = " << quantile(g6, 0.99) << endl; // 24.26
    +
    cout << "quantile(g6, 0.99) = " << quantile(g6, 0.99) << endl; // 24.26
    +

    @@ -210,7 +220,8 @@

    negative_binomial nb(1, success_fraction);
     cout << pdf(nb, 1) << endl; // 0.1389
    -cout << cdf(nb, 1) << endl; // 0.3056
    +cout<<cdf(nb,1)<<endl;// 0.3056 +

    @@ -219,7 +230,8 @@

    -
    cout << "quantile(complement(g6, 1 - p))  " << quantile(complement(g6, 0.01)) << endl; // 24.26
    +
    cout << "quantile(complement(g6, 1 - p))  " << quantile(complement(g6, 0.01)) << endl; // 24.26
    +

    @@ -251,7 +263,8 @@ << max_digits10 << endl; cout.precision(max_digits10); // - cout << cdf(g05, 0.0001) << endl; // returns 0.5000346561579232, not exact 0.5. + cout << cdf(g05, 0.0001) << endl; // returns 0.5000346561579232, not exact 0.5. +

    @@ -260,7 +273,8 @@

    -
    cout << cdf(g05, floor(0.0001)) << endl; // returns exactly 0.5
    +
    cout << cdf(g05, floor(0.0001)) << endl; // returns exactly 0.5
    +

    > formatC(pgeom(0.9999999,0.5, FALSE), digits=17) [1] "              0.25"
    @@ -313,7 +327,8 @@
     c = 0.80; // Only reasonably confident.
     cout << "To be " << c * 100
       << "% confident of finding we customer with a fault, need to survey "
    -  <<  ceil(quantile(g, c)) << " customers." << endl; // 79
    + <<ceil(quantile(g,c))<<" customers."<<endl;// 79 +

    @@ -332,7 +347,8 @@

    cout.precision(2);
    -geometric gav(0.75); // Shooter averages 7.5 out of 10 in the basket.
    +geometric gav(0.75); // Shooter averages 7.5 out of 10 in the basket. +

    @@ -341,7 +357,8 @@

    -
    cout << "Probability of score on 1st try = " << pdf(gav, 0) << endl; // 0.75
    +
    cout << "Probability of score on 1st try = " << pdf(gav, 0) << endl; // 0.75
    +

    @@ -351,7 +368,8 @@

    -
    cout << "Probability of score on 5th try = " << pdf(gav, 4) << endl; // 0.0029
    +
    cout << "Probability of score on 5th try = " << pdf(gav, 4) << endl; // 0.0029
    +

    @@ -365,7 +383,8 @@

    geometric gbest(0.95);
     cout << "Probability of score on 5th try = " << pdf(gbest, 4) << endl; // 5.9e-6
     geometric gmediocre(0.50);
    -cout << "Probability of score on 5th try = " << pdf(gmediocre, 4) << endl; // 0.031
    +cout << "Probability of score on 5th try = " << pdf(gmediocre, 4) << endl; // 0.031 +

    @@ -408,7 +427,8 @@ << t << endl; // 0.00025 t = geometric::find_upper_bound_on_p(k, alpha/2); cout << "geometric::find_upper_bound_on_p(" << int(k) << ", " << alpha/2 << ") = " - << t << endl; // 0.037 + << t << endl; // 0.037 +

    @@ -433,7 +453,8 @@ << t << endl; // 5e-005 t = geometric::find_upper_bound_on_p(k, alpha/2); cout << "geometric::find_upper_bound_on_p(" << int(k) << ", " << alpha/2 << ") = " - << t << endl; // 0.052 + << t << endl; // 0.052 +

    @@ -451,7 +472,8 @@ catch(const std::exception& e) { // Since we have set an overflow policy of ignore_error, // an overflow exception should never be thrown. - std::cout << "\nMessage from thrown exception was:\n " << e.what() << std::endl; + std::cout << "\nMessage from thrown exception was:\n " << e.what() << std::endl; +

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/inverse_chi_squared_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/inverse_chi_squared_eg.html index 79dd07586..96fccf19c 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/inverse_chi_squared_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/inverse_chi_squared_eg.html @@ -3,7 +3,7 @@ Inverse Chi-Squared Distribution Bayes Example - + @@ -22,7 +22,7 @@

    PrevUpHomeNext
    -
    +
    Inverse Chi-Squared Distribution Bayes Example @@ -46,12 +46,12 @@

    For more general information on Bayesian type of analyses, see:

    -
      -
    • +
        +
      • Andrew Gelman, John B. Carlin, Hal E. Stern, Donald B. Rubin, Bayesian Data Analysis, 2003, ISBN 978-1439840955.
      • -
      • +
      • Jim Albert, Bayesian Compution with R, Springer, 2009, ISBN 978-0387922973.
      @@ -130,7 +130,6 @@ cout << " 2.5% quantile: " << quantile(prior, 0.025) << endl; cout << " 50% quantile: " << quantile(prior, 0.5) << endl; cout << " 97.5% quantile: " << quantile(prior, 0.975) << endl << endl; -

      @@ -244,7 +243,8 @@ double posteriorScale = (priorDF * priorScale + (ballsSampleVariance * (ballsSampleSize - 1))) / posteriorDF; cout << "prior scale: " << priorScale << endl; -cout << "posterior scale: " << posteriorScale << endl; +cout << "posterior scale: " << posteriorScale << endl; +

      @@ -262,6 +262,7 @@ posterior degrees-of-freedom: 120 prior scale: 25 posterior scale: 49.5 +

      To compare the generic machinery performance with our suspect machine, @@ -284,7 +285,6 @@ cout << " probability variance <= 25: " << boost::math::cdf(posterior, 25.0) << endl; cout << " probability variance > 50: " << boost::math::cdf(boost::math::complement(posterior, 50.0)) << endl; -

      diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nag_library.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nag_library.html index 32215d1f6..07f39002b 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nag_library.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nag_library.html @@ -3,7 +3,7 @@ Comparison with C, R, FORTRAN-style Free Functions - + @@ -22,7 +22,7 @@
      PrevUpHomeNext
      -
      +
      Comparison with C, R, FORTRAN-style Free Functions diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg.html index f0aaa6bf0..080f80ce2 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg.html @@ -3,7 +3,7 @@ Non Central Chi Squared Example - + @@ -22,7 +22,7 @@
      PrevUpHomeNext
      -
      +
      Non Central Chi Squared Example diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg/nccs_power_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg/nccs_power_eg.html index f0e3a9ba3..841e8e6ff 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg/nccs_power_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nccs_eg/nccs_power_eg.html @@ -3,7 +3,7 @@ Tables of the power function of the chi2 test. - + @@ -22,7 +22,7 @@
      PrevUpHomeNext
      -
      +
      Tables of the power function of the chi2 test. @@ -50,7 +50,8 @@ test at the 5% significance using std::setprecision; int main() -{ +{ +

      @@ -64,7 +65,8 @@ test at the 5% significance { cout << "[[lambda]=" << lam << "]"; } -cout << "]\n"; +cout << "]\n"; +

      @@ -80,7 +82,8 @@ test at the 5% significance { cout << "[[" << n << "]"; for(int lam = 2; lam <= 20; lam += 2) - { + { +

      @@ -88,7 +91,8 @@ test at the 5% significance

      -
      double cs = quantile(complement(chi_squared(n), 0.05));
      +
      double cs = quantile(complement(chi_squared(n), 0.05));
      +

      @@ -97,7 +101,8 @@ test at the 5% significance

      -
      double beta = cdf(complement(non_central_chi_squared(n, lam), cs));
      +
      double beta = cdf(complement(non_central_chi_squared(n, lam), cs));
      +

      @@ -110,7 +115,8 @@ test at the 5% significance cout << "]" << endl; } cout << "]" << endl; -} +} +

      diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg.html index 5ad0dd62e..0ddf31ea5 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg.html @@ -3,7 +3,7 @@ Negative Binomial Distribution Examples - + @@ -22,7 +22,7 @@

      PrevUpHomeNext
      -
      +
      Negative Binomial Distribution Examples diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html index 2762a0ae3..523eb5e66 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html @@ -3,7 +3,7 @@ Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial Distribution - + @@ -22,7 +22,7 @@
      PrevUpHomeNext
      -
      +
      Calculating Confidence Limits on the Frequency of Occurrence for the Negative Binomial @@ -67,7 +67,8 @@ using std::cout; using std::endl; #include <iomanip> using std::setprecision; -using std::setw; using std::left; using std::fixed; using std::right; +using std::setw; using std::left; using std::fixed; using std::right; +

      @@ -76,7 +77,8 @@

      -
      double alpha[] = { 0.5, 0.25, 0.1, 0.05, 0.01, 0.001, 0.0001, 0.00001 };
      +
      double alpha[] = { 0.5, 0.25, 0.1, 0.05, 0.01, 0.001, 0.0001, 0.00001 };
      +

      @@ -112,7 +114,8 @@ "___________________________________________\n" "Confidence Lower Upper\n" " Value (%) Limit Limit\n" - "___________________________________________\n"; + "___________________________________________\n"; +

      @@ -142,7 +145,8 @@ cout << fixed << setprecision(5) << setw(15) << right << upper << endl; } cout << endl; -} // void confidence_limits_on_frequency(unsigned trials, unsigned successes) +} // void confidence_limits_on_frequency(unsigned trials, unsigned successes) +

      @@ -159,7 +163,6 @@ return 0; } // int main() -

      diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html index 93674e17d..2171cbfca 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html @@ -3,7 +3,7 @@ Estimating Sample Sizes for the Negative Binomial. - + @@ -22,7 +22,7 @@
      -
      +
      Estimating Sample Sizes for the Negative Binomial. @@ -48,7 +48,8 @@

      -
      void find_number_of_trials(double failures, double p);
      +
      void find_number_of_trials(double failures, double p);
      +

      @@ -58,7 +59,8 @@

      -
      double alpha[] = { 0.5, 0.25, 0.1, 0.05, 0.01, 0.001, 0.0001, 0.00001 };
      +
      double alpha[] = { 0.5, 0.25, 0.1, 0.05, 0.01, 0.001, 0.0001, 0.00001 };
      +

      @@ -80,8 +82,7 @@

      -
      -void find_number_of_trials(double failures, double p)
      +
      void find_number_of_trials(double failures, double p)
       {
          // trials = number of trials
          // failures = number of failures before achieving required success(es).
      @@ -107,7 +108,8 @@
             << endl;
          }
          cout << endl;
      -} // void find_number_of_trials(double failures, double p)
      +} // void find_number_of_trials(double failures, double p) +

      @@ -127,7 +129,6 @@ return 0; } // int main() -

      diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html index f30f63f88..3380bd50d 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html @@ -3,7 +3,7 @@ Negative Binomial Sales Quota Example. - + @@ -22,7 +22,7 @@
      PrevUpHomeNext
      -
      +
      Negative Binomial Sales Quota Example. @@ -73,7 +73,8 @@

      #define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
      -#define BOOST_MATH_DISCRETE_QUANTILE_POLICY real
      +#define BOOST_MATH_DISCRETE_QUANTILE_POLICY real +

      @@ -124,7 +125,8 @@

      try
      -{
      +{ +

      @@ -134,7 +136,8 @@

      -
      double sales_quota = 5; // Pat's sales quota - successes (r).
      +
      double sales_quota = 5; // Pat's sales quota - successes (r).
      +

      @@ -143,7 +146,8 @@

      -
      double success_fraction = 0.4; // success_fraction (p) - so failure_fraction is 0.6.
      +
      double success_fraction = 0.4; // success_fraction (p) - so failure_fraction is 0.6.
      +

      @@ -160,7 +164,8 @@

      -
      negative_binomial nb(sales_quota, success_fraction); // type double by default.
      +
      negative_binomial nb(sales_quota, success_fraction); // type double by default.
      +

      @@ -178,7 +183,8 @@ cout << "With a success rate of " << nb.success_fraction() << ", he might expect, on average,\n" "to need to visit about " << success_fraction * all_houses - << " houses in order to sell all " << nb.successes() << " bars. " << endl; + << " houses in order to sell all " << nb.successes() << " bars. " << endl; +

      Pat has a sales per house success rate of 0.4.
      @@ -200,7 +206,8 @@ to need to visit about 12 houses in order to sell all 5 bars.
       

      cout << "Probability that Pat finishes on the " << sales_quota << "th house is "
      -  << pdf(nb, 5 - sales_quota) << endl; // == pdf(nb, 0)
      + << pdf(nb, 5 - sales_quota) << endl; // == pdf(nb, 0) +

      @@ -220,7 +227,8 @@ to need to visit about 12 houses in order to sell all 5 bars. cout << "Probability that Pat finishes on the 7th house is " << pdf(nb, 7 - sales_quota) << endl; cout << "Probability that Pat finishes on the 8th house is " - << pdf(nb, 8 - sales_quota) << endl; + << pdf(nb, 8 - sales_quota) << endl; +

      Probability that Pat finishes on the 6th house is 0.03072
      @@ -240,7 +248,8 @@ Probability that Pat finishes on the 8th house is 0.077414
           + pdf(nb, 6 - sales_quota) // 1 failure.
           + pdf(nb, 7 - sales_quota) // 2 failures.
           + pdf(nb, 8 - sales_quota) // 3 failures.
      -  << endl;
      + << endl; +

      pdf(sales_quota) + pdf(6) + pdf(7) + pdf(8) = 0.17367
      @@ -253,7 +262,8 @@ Probability that Pat finishes on the 8th house is 0.077414
       

      cout << "\nProbability of selling his quota of " << sales_quota
         << " bars\non or before the " << 8 << "th house is "
      -  << cdf(nb, 8 - sales_quota) << endl;
      + << cdf(nb, 8 - sales_quota) << endl; +

      Probability of selling his quota of 5 bars on or before the 8th house is 0.17367
      @@ -264,7 +274,8 @@ Probability that Pat finishes on the 8th house is 0.077414
         << pdf(nb, 10 - sales_quota) << endl;
       cout << "\nProbability of selling his quota of " << sales_quota
         << " bars\non or before the " << 10 << "th house is "
      -  << cdf(nb, 10 - sales_quota) << endl;
      + << cdf(nb, 10 - sales_quota) << endl; +

      Probability that Pat finishes exactly on the 10th house is 0.10033
      @@ -276,7 +287,8 @@ Probability of selling his quota of 5 bars on or before the 10th house is 0.3669
         << pdf(nb, 11 - sales_quota) << endl;
       cout << "\nProbability of selling his quota of " << sales_quota
         << " bars\non or before the " << 11 << "th house is "
      -  << cdf(nb, 11 - sales_quota) << endl;
      + << cdf(nb, 11 - sales_quota) << endl; +

      Probability that Pat finishes on the 11th house is 0.10033
      @@ -290,7 +302,8 @@ on or before the 11th house is 0.46723
       
       cout << "\nProbability of selling his quota of " << sales_quota
         << " bars\non or before the " << 12 << "th house is "
      -  << cdf(nb, 12 - sales_quota) << endl;
      + << cdf(nb, 12 - sales_quota) << endl; +

      Probability that Pat finishes on the 12th house is 0.094596
      @@ -306,7 +319,8 @@ on or before the 12th house is 0.56182
       

      cout << "Probability that Pat finishes on the " << all_houses
      -  << " house is " << pdf(nb, all_houses - sales_quota) << endl;
      + << " house is " << pdf(nb, all_houses - sales_quota) << endl; +

      @@ -326,7 +340,8 @@ on or before the 12th house is 0.56182

      cout << "\nProbability of selling his quota of " << sales_quota
         << " bars\non or before the " << all_houses << "th house is "
      -  << cdf(nb, all_houses - sales_quota) << endl;
      + << cdf(nb, all_houses - sales_quota) << endl; +

      Probability of selling his quota of 5 bars
      @@ -367,7 +382,8 @@ on or before the 30th house is 0.99849
       

      cout << "\nProbability of failing to sell his quota of " << sales_quota
         << " bars\neven after visiting all " << all_houses << " houses is "
      -  << cdf(complement(nb, all_houses - sales_quota)) << endl;
      + << cdf(complement(nb, all_houses - sales_quota)) << endl; +

      Probability of failing to sell his quota of 5 bars
      @@ -380,7 +396,8 @@ even after visiting all 30 houses is 0.0015101
       

      double p = cdf(nb, (8 - sales_quota));
      -cout << "Probability of meeting sales quota on or before 8th house is "<< p << endl;
      +cout << "Probability of meeting sales quota on or before 8th house is "<< p << endl; +

      Probability of meeting sales quota on or before 8th house is 0.174
      @@ -390,7 +407,8 @@ even after visiting all 30 houses is 0.0015101
       
      cout << "If the confidence of meeting sales quota is " << p
           << ", then the finishing house is " << quantile(nb, p) + sales_quota << endl;
       
      -cout<< " quantile(nb, p) = " << quantile(nb, p) << endl;
      +cout<< " quantile(nb, p) = " << quantile(nb, p) << endl; +

      If the confidence of meeting sales quota is 0.17367, then the finishing house is 8
      @@ -405,7 +423,8 @@ even after visiting all 30 houses is 0.0015101
       

      cout << "If the confidence of meeting sales quota is " << 1.
           << ", then the finishing house is " << quantile(nb, 1) + sales_quota << endl;
      -//  1.#INF == infinity.
      +// 1.#INF == infinity. +

      If the confidence of meeting sales quota is 1, then the finishing house is 1.#INF
      @@ -422,7 +441,8 @@ even after visiting all 30 houses is 0.0015101
           << ", then the finishing house is " << quantile(nb, 0.5) + sales_quota << endl;
       
       cout << "If the confidence of meeting sales quota is " << 1 - 0.00151 // 30 th
      -    << ", then the finishing house is " << quantile(nb, 1 - 0.00151) + sales_quota << endl;
      + << ", then the finishing house is " << quantile(nb, 1 - 0.00151) + sales_quota << endl; +

      If the confidence of meeting sales quota is 0, then the finishing house is 5
      @@ -441,7 +461,8 @@ If the confidence of meeting sales quota is 0.99849, then the finishing house is
       

      cout << "If confidence of meeting quota is zero\n(we assume all houses are successful sales)"
      -  ", then finishing house is " << sales_quota << endl;
      + ", then finishing house is " << sales_quota << endl; +

      If confidence of meeting quota is zero (we assume all houses are successful sales), then finishing house is 5
      @@ -460,7 +481,8 @@ If confidence of meeting quota is 0, then finishing house is 5
          cout << "If confidence of meeting quota is " << ps[i]
            << ", then finishing house is " << quantile(nb, ps[i]) + sales_quota
            << endl;
      -}
      +} +

      If confidence of meeting quota is 0, then finishing house is 5
      @@ -514,7 +536,8 @@ If confidence of meeting quota is 0.95, then finishing house is 21
       {
         cout << left << setw(3) << i << "                             " << setw(8) << cdf(nb, i - sales_quota)  << endl;
       }
      -cout << endl;
      +cout << endl; +

      House for 5 th (last) sale.  Probability (%)
      @@ -555,7 +578,8 @@ If confidence of meeting quota is 0.95, then finishing house is 21
       catch(const std::exception& e)
       { // Since we have set an overflow policy of ignore_error,
         // an overflow exception should never be thrown.
      -   std::cout << "\nMessage from thrown exception was:\n " << e.what() << std::endl;
      + std::cout << "\nMessage from thrown exception was:\n " << e.what() << std::endl; +

      diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html index af3dfa805..a0d451a75 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html @@ -3,7 +3,7 @@ Negative Binomial Table Printing Example. - + @@ -22,7 +22,7 @@

      PrevUpHomeNext
      -
      +
      Negative Binomial Table Printing Example. diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example.html index 845fbc943..447cc2737 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example.html @@ -3,7 +3,7 @@ Normal Distribution Examples - + @@ -22,7 +22,7 @@
      PrevUpHomeNext
      -
      +
      Normal Distribution Examples diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html index 07541a86e..6ac4cc272 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html @@ -3,7 +3,7 @@ Some Miscellaneous Examples of the Normal (Gaussian) Distribution - + @@ -22,7 +22,7 @@
      PrevUpHomeNext
      -
      +
      Some Miscellaneous Examples of the Normal (Gaussian) Distribution @@ -58,7 +58,8 @@ try { - { // Traditional tables and values. + { // Traditional tables and values. +

      @@ -77,7 +78,8 @@ // Construct a standard normal distribution s normal s; // (default mean = zero, and standard deviation = unity) cout << "Standard normal distribution, mean = "<< s.mean() - << ", standard deviation = " << s.standard_deviation() << endl; + << ", standard deviation = " << s.standard_deviation() << endl; +

      @@ -93,7 +95,8 @@ cout << left << setprecision(3) << setw(6) << z << " " << setprecision(precision) << setw(12) << pdf(s, z) << endl; } -cout.precision(6); // default +cout.precision(6); // default +

      @@ -112,7 +115,8 @@ cout << left << setprecision(3) << setw(6) << z << " " << setprecision(precision) << setw(12) << cdf(s, z) << endl; } -cout.precision(6); // default +cout.precision(6); // default +

      @@ -134,7 +138,8 @@

      double z = 2.;
      -cout << "Area for z = " << z << " is " << cdf(s, z) << endl; // to get the area for z.
      +cout << "Area for z = " << z << " is " << cdf(s, z) << endl; // to get the area for z. +

      @@ -146,7 +151,8 @@

        cout << "95% of area has a z below " << quantile(s, 0.95) << endl;
      -// 95% of area has a z below 1.64485
      +// 95% of area has a z below 1.64485 +

      @@ -157,7 +163,8 @@

        cout << "95% of area has a z between " << quantile(s, 0.975)
           << " and " << -quantile(s, 0.975) << endl;
      -// 95% of area has a z between 1.95996 and -1.95996
      +// 95% of area has a z between 1.95996 and -1.95996 +

      @@ -172,7 +179,8 @@

      double alpha1 = cdf(s, -1) * 2; // 0.3173105078629142
      -cout << setprecision(17) << "Significance level for z == 1 is " << alpha1 << endl;
      +cout << setprecision(17) << "Significance level for z == 1 is " << alpha1 << endl; +

      @@ -181,7 +189,8 @@

      double alpha[] = {0.3173105078629142, // z for 1 standard deviation.
      -  0.20, 0.1, 0.05, 0.01, 0.001, 0.0001, 0.00001 };
      + 0.20, 0.1, 0.05, 0.01, 0.001, 0.0001, 0.00001 }; +

      @@ -198,7 +207,8 @@ cout << setw(15) << alpha[i] << setw(15) << alpha[i] /2 << setw(10) << quantile(complement(s, alpha[i]/2)) << endl; // Use quantile(complement(s, alpha[i]/2)) to avoid potential loss of accuracy from quantile(s, 1 - alpha[i]/2) } -cout << endl; +cout << endl; +

      @@ -241,7 +251,8 @@ cout << "Fraction 2 standard deviations within either side of mean is " << 1 - cdf(complement(s, 2 * s.standard_deviation())) * 2 << endl; cout << "Fraction 3 standard deviations within either side of mean is " - << 1 - cdf(complement(s, 3 * s.standard_deviation())) * 2 << endl; + << 1 - cdf(complement(s, 3 * s.standard_deviation())) * 2 << endl; +

      @@ -289,7 +300,8 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740

      // K. Krishnamoorthy, Handbook of Statistical Distributions with Applications,
      - // ISBN 1 58488 635 8, page 125, example 10.3.5
      + // ISBN 1 58488 635 8, page 125, example 10.3.5 +

      @@ -303,7 +315,8 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740

      double mean_life = 1100.;
       double life_standard_deviation = 100.;
       normal bulbs(mean_life, life_standard_deviation);
      -double expected_life = 1000.;
      +double expected_life = 1000.; +

      @@ -321,7 +334,8 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740 cout << "Fraction of bulbs that will last between " << min_life << " and " << max_life << " is " << cdf(bulbs, max_life) // P(X <= 1200) - - cdf(bulbs, min_life) << endl; // P(X <= 900) + - cdf(bulbs, min_life) << endl; // P(X <= 900) +

    @@ -354,7 +368,8 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740 doublestock=160.;// per week.cout<<"Percentage of weeks overstocked "<<cdf(sacks,stock)*100.<<endl;// P(X <=160) -// Percentage of weeks overstocked 97.7 +// Percentage of weeks overstocked 97.7 +

    @@ -364,7 +379,8 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740

    double stock_95 = quantile(sacks, 0.95);
    -cout << "Store should stock " << int(stock_95) << " sacks to meet 95% of demands." << endl;
    +cout<<"Store should stock "<<int(stock_95)<<" sacks to meet 95% of demands."<<endl; +

    @@ -421,7 +437,8 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740 normal nominal_packs(nominal_mean, standard_deviation); cout << "Setting the packer to " << nominal_mean << " will mean that " << "fraction of packs >= " << under_weight - << " is " << cdf(complement(nominal_packs, under_weight)) << endl; + << " is " << cdf(complement(nominal_packs, under_weight)) << endl; +

    @@ -446,7 +463,8 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740

    double p = 0.05; // wanted p th quantile.
     cout << "Quantile of " << p << " = " << quantile(packs, p)
    -  << ", mean = " << packs.mean() << ", sd = " << packs.standard_deviation() << endl; //
    + <<", mean = "<<packs.mean()<<", sd = "<<packs.standard_deviation()<<endl;// +

    @@ -470,7 +488,8 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740 cout <<"Fraction of packs >= " << under_weight << " with a mean of " << mean << " and standard deviation of " << pack05.standard_deviation() << " is " << cdf(complement(pack05, under_weight)) << endl; -// +// +

    @@ -490,7 +509,8 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740 cout <<"Fraction of packs >= " << under_weight << " with a mean of " << mean << " and standard deviation of " << pack06.standard_deviation() - << " is " << cdf(complement(pack06, under_weight)) << endl; + << " is " << cdf(complement(pack06, under_weight)) << endl; +

    @@ -531,7 +551,8 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740 << " and standard deviation of " << pack95.standard_deviation() << " is " << cdf(complement(pack95, under_weight)) << endl; -// Fraction of packs >= 2.9 with a mean of 3 and standard deviation of 0.0608 is 0.95 +// Fraction of packs >= 2.9 with a mean of 3 and standard deviation of 0.0608 is 0.95 +

    @@ -570,7 +591,6 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740 << cdf(complement(bolts, top)) << endl; cout << "95% of bolts are shorter than " << quantile(bolts, 0.95) << endl; -

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg.html index 3619b9509..c888c5f48 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg.html @@ -3,7 +3,7 @@ Student's t Distribution Examples - + @@ -22,7 +22,7 @@
    PrevUpHomeNext
    -
    +
    Student's t Distribution Examples diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/paired_st.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/paired_st.html index 14b0fb82e..9e0bf08fa 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/paired_st.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/paired_st.html @@ -3,7 +3,7 @@ Comparing two paired samples with the Student's t distribution - + @@ -22,7 +22,7 @@
    PrevUpHomeNext
    -
    +
    Comparing two paired samples with the Student's t distribution @@ -42,20 +42,20 @@

    That means we can:

    -
      -
    • +
        +
      • Calculate confidence intervals of the mean. If the endpoints of the interval differ in sign then we are unable to reject the null-hypothesis that there is no change.
      • -
      • +
      • Test whether the true mean is zero. If the result is consistent with a true mean of zero, then we are unable to reject the null-hypothesis that there is no change.
      • -
      • +
      • Calculate how many pairs of readings we would need in order to obtain a significant result. diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_intervals.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_intervals.html index 391b5e54e..30c04a1ba 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_intervals.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_intervals.html @@ -3,7 +3,7 @@ Calculating confidence intervals on the mean with the Students-t distribution - + @@ -22,7 +22,7 @@
        PrevUpHomeNext
        -
        +
        Calculating confidence intervals on the mean with the Students-t distribution @@ -84,19 +84,19 @@

        From the formula, it should be clear that:

        -
          -
        • +
            +
          • The width of the confidence interval decreases as the sample size increases.
          • -
          • +
          • The width increases as the standard deviation increases.
          • -
          • +
          • The width increases as the confidence level increases (0.5 towards 0.99999 - stronger).
          • -
          • +
          • The width increases as the significance level decreases (0.5 towards 0.00000...01 - stronger).
          • diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_size.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_size.html index c05d0cd17..a05fa0da1 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_size.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_size.html @@ -3,7 +3,7 @@ Estimating how large a sample size would have to become in order to give a significant Students-t test result with a single sample test - + @@ -22,7 +22,7 @@
            PrevUpHomeNext
            -
            +
            Estimating how large a sample size would have to become in order to give a significant diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_test.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_test.html index c417f5660..51bad107c 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_test.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_test.html @@ -3,7 +3,7 @@ Testing a sample mean for difference from a "true" mean - + @@ -22,7 +22,7 @@ -
            +
            Testing a sample mean for difference from a "true" mean diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/two_sample_students_t.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/two_sample_students_t.html index 660fbb04e..2789de4bb 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/two_sample_students_t.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/two_sample_students_t.html @@ -3,7 +3,7 @@ Comparing the means of two samples with the Students-t test - + @@ -22,7 +22,7 @@
            PrevUpHomeNext
            -
            +
            Comparing the means of two samples with the Students-t test diff --git a/doc/sf_and_dist/html/math_toolkit/extern_c.html b/doc/sf_and_dist/html/math_toolkit/extern_c.html index f84c960d9..a530bb2e9 100644 --- a/doc/sf_and_dist/html/math_toolkit/extern_c.html +++ b/doc/sf_and_dist/html/math_toolkit/extern_c.html @@ -3,7 +3,7 @@ TR1 and C99 external "C" Functions - + @@ -22,7 +22,7 @@
            PrevUpHomeNext
            -
            +

            TR1 and C99 external "C" Functions diff --git a/doc/sf_and_dist/html/math_toolkit/extern_c/c99.html b/doc/sf_and_dist/html/math_toolkit/extern_c/c99.html index aeed4f50d..77cd4d152 100644 --- a/doc/sf_and_dist/html/math_toolkit/extern_c/c99.html +++ b/doc/sf_and_dist/html/math_toolkit/extern_c/c99.html @@ -3,7 +3,7 @@ C99 C Functions - + @@ -22,7 +22,7 @@
            PrevUpHomeNext
            -
            +
            diff --git a/doc/sf_and_dist/html/math_toolkit/extern_c/tr1.html b/doc/sf_and_dist/html/math_toolkit/extern_c/tr1.html index e381cc3b9..a503b2915 100644 --- a/doc/sf_and_dist/html/math_toolkit/extern_c/tr1.html +++ b/doc/sf_and_dist/html/math_toolkit/extern_c/tr1.html @@ -3,7 +3,7 @@ C99 and TR1 C Functions Overview - + @@ -22,7 +22,7 @@
            PrevUpHomeNext
            -
            +
            @@ -40,30 +40,30 @@

            Pros:

            -
              -
            • +
                +
              • The header to include is lightweight (i.e. fast to compile).
              • -
              • +
              • The functions have extern "C" linkage, and so are usable from other languages (not just C and C++).
              • -
              • +
              • C99 and C++ TR1 Standard compatibility.

              Cons:

              -
                -
              • +
                  +
                • You will need to compile and link to the external Boost.Math libraries.
                • -
                • +
                • Limited to support for the types, float, double and long double.
                • -
                • +
                • Error handling is handled via setting ::errno and returning NaN's and infinities: this may be less flexible than an C++ exception based approach.
                • @@ -265,12 +265,12 @@

                  This library now presents the user with a choice:

                  -
                    -
                  • +
                      +
                    • To include the header only versions of the functions and have an easier time linking, but a longer compile time.
                    • -
                    • +
                    • To include the TR1 headers and link against an external library.
                    diff --git a/doc/sf_and_dist/html/math_toolkit/extern_c/tr1_ref.html b/doc/sf_and_dist/html/math_toolkit/extern_c/tr1_ref.html index 35cf64682..322e382bb 100644 --- a/doc/sf_and_dist/html/math_toolkit/extern_c/tr1_ref.html +++ b/doc/sf_and_dist/html/math_toolkit/extern_c/tr1_ref.html @@ -3,7 +3,7 @@ TR1 C Functions Quick Reference - + @@ -22,7 +22,7 @@
                    PrevUpHomeNext
                    -
                    +

                    TR1 C Functions Quick Reference diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview.html b/doc/sf_and_dist/html/math_toolkit/main_overview.html index 5098226b9..fb3a92ee7 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview.html @@ -3,7 +3,7 @@ Overview - + @@ -22,7 +22,7 @@
                    PrevUpHomeNext
                    -
                    +
                    diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/building.html b/doc/sf_and_dist/html/math_toolkit/main_overview/building.html index 1f1a8af5b..e9aa84d6e 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/building.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/building.html @@ -3,7 +3,7 @@ If and How to Build a Boost.Math Library, and its Examples and Tests - + @@ -22,7 +22,7 @@
                    PrevUpHomeNext
                    -
                    +

                    If and How to Build a Boost.Math Library, and its Examples and Tests diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/compilers_overview.html b/doc/sf_and_dist/html/math_toolkit/main_overview/compilers_overview.html index 13070b190..bdb6ab8b6 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/compilers_overview.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/compilers_overview.html @@ -3,7 +3,7 @@ Compilers - + @@ -22,7 +22,7 @@
                    PrevUpHomeNext
                    -
                    +
                    diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/config_macros.html b/doc/sf_and_dist/html/math_toolkit/main_overview/config_macros.html index f5755bb94..cefc0a7f8 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/config_macros.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/config_macros.html @@ -3,7 +3,7 @@ Configuration Macros - + @@ -22,7 +22,7 @@
                    PrevUpHomeNext
                    -
                    +

                    Configuration Macros diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/contact.html b/doc/sf_and_dist/html/math_toolkit/main_overview/contact.html index 484a2e037..8b1526759 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/contact.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/contact.html @@ -3,7 +3,7 @@ Contact Info and Support - + @@ -22,7 +22,7 @@
                    PrevUpHomeNext
                    -
                    +

                    Contact Info and Support @@ -30,12 +30,12 @@

                    The main support for this library is via the Boost mailing lists:

                    -
                      -
                    • +
                        +
                      • Use the boost-user list for general support questions.
                      • -
                      • +
                      • Use the boost-developer list for discussion about implementation and or submission of extensions. diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html b/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html index 7baeff9e2..5730ce6e6 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/conventions.html @@ -3,7 +3,7 @@ Document Conventions - + @@ -22,46 +22,46 @@
                        PrevUpHomeNext
                        -
                        +

                        - +

                        This documentation aims to use of the following naming and formatting conventions.

                        -
                          -
                        • +
                            +
                          • C++ Code is in fixed width font and is syntax-highlighted in color, for example double.
                          • -
                          • +
                          • Other code is in block teletype fixed-width font.
                          • -
                          • +
                          • Replaceable text that you will need to supply is in italics.
                          • -
                          • +
                          • If a name refers to a free function, it is specified like this: free_function(); that is, it is in code font and its name is followed by () to indicate that it is a free function.
                          • -
                          • +
                          • If a name refers to a class template, it is specified like this: class_template<>; that is, it is in code font and its name is followed by <> to indicate that it is a class template.
                          • -
                          • +
                          • If a name refers to a function-like macro, it is specified like this: MACRO(); that is, it is uppercase in code font and its name is followed by () to indicate that it is a function-like macro. Object-like macros appear without the trailing ().
                          • -
                          • +
                          • Names that refer to concepts in the generic programming sense (like template parameter names) are specified in CamelCase.
                          • diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/directories.html b/doc/sf_and_dist/html/math_toolkit/main_overview/directories.html index 2ec7edcf9..f11c459cb 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/directories.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/directories.html @@ -3,7 +3,7 @@ Directory and File Structure - + @@ -22,7 +22,7 @@
                            PrevUpHomeNext
                            -
                            +

                            Directory and File Structure diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/error_handling.html b/doc/sf_and_dist/html/math_toolkit/main_overview/error_handling.html index 16dd51c81..745d53842 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/error_handling.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/error_handling.html @@ -3,7 +3,7 @@ Error Handling - + @@ -22,7 +22,7 @@
                            PrevUpHomeNext
                            -
                            +
                            @@ -34,11 +34,11 @@

                            Handling of errors by this library is split into two orthogonal parts:

                            -
                              -
                            • +
                                +
                              • What kind of error has been raised?
                              • -
                              • +
                              • What should be done when the error is raised?
                              @@ -766,16 +766,16 @@ the default behaviours were chosen based on feedback during the formal review of this library. It was felt that:

                              -
                                -
                              • +
                                  +
                                • Genuine errors should be flagged with exceptions rather than following C-compatible behaviour and setting ::errno.
                                • -
                                • +
                                • Numeric underflow and denormalised results were not considered to be fatal errors in most cases, so it was felt that these should be ignored.
                                • -
                                • +
                                • If there is more than one error, only the first detected will be reported in the throw message.
                                • diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/faq.html b/doc/sf_and_dist/html/math_toolkit/main_overview/faq.html index 697e39a76..aee1d0c02 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/faq.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/faq.html @@ -3,7 +3,7 @@ Frequently Asked Questions FAQ - + @@ -22,13 +22,13 @@
                                  PrevUpHomeNext
                                  -
                                  +
                                  -
                                    -
                                  1. +
                                      +
                                    1. I'm a FORTRAN/NAG/SPSS/SAS/Cephes/MathCad/R user and I don't see where the functions like dnorm(mean, sd) are in Boost.Math?
                                      Nearly all are provided, and many more like mean, skewness, quantiles, @@ -42,7 +42,7 @@ my_norm(0, 1); pdf(my_norm, 2.0);
                                    2. -
                                    3. +
                                    4. I'm a user of New SAS Functions for Computing Probabilities.
                                      You will find the interface more familar, but to be able to select a distribution (perhaps @@ -51,7 +51,7 @@ find useful): see Statistical Distribution Explorer
                                      .
                                    5. -
                                    6. +
                                    7. I'm allegic to reading manuals and prefer to learn from examples.
                                      Fear not - you are not alone! Many examples are available for functions and distributions. Some are referenced directly from the text. Others @@ -60,7 +60,7 @@ these, making sure that the Boost library is in the include directories list.
                                    8. -
                                    9. +
                                    10. How do I make sure that the Boost library is in the Visual Studio include directories list?
                                      You can add an include path, for example, your Boost place /boost-latest_release, for example @@ -72,7 +72,7 @@ sheets to assist. You may find it convenient to create a new one adding \boost-latest_release; to the existing include items in $(IncludePath).
                                    11. -
                                    12. +
                                    13. I'm a FORTRAN/NAG/SPSS/SAS/Cephes/MathCad/R user and I don't see where the properties like mean, median, mode, variance, skewness of distributions are in Boost.Math?
                                      They are all available @@ -86,13 +86,13 @@ kurtosis, kurtosis_excess, range and support.
                                    14. -
                                    15. +
                                    16. I am a C programmer. Can I user Boost.Math with C?
                                      Yes you can, including all the special functions, and TR1 functions like isnan. They appear as C functions, by being declared as "extern C".
                                    17. -
                                    18. +
                                    19. I am a C# (Basic? F# FORTRAN? Other CLI?) programmer. Can I use Boost.Math with C#?
                                      Yes you can, including all the special functions, and TR1 functions like isnan. But you must build the Boost.Math as a dynamic library (.dll) and @@ -101,7 +101,7 @@ app with a GUI. See Statistical Distribution Explorer
                                    20. -
                                    21. +
                                    22. What these "policies" things for?
                                      Policies are a powerful (if necessarily complex) fine-grain mechanism that allow you to customise the behaviour of the Boost.Math library according @@ -109,21 +109,21 @@ But if, very probably, the default behaviour suits you, you don't need to know more.
                                    23. -
                                    24. +
                                    25. I am a C user and expect to see global C-style::errno set for overflow/errors etc?
                                      You can achieve what you want - see error handling policies and user error handling and many examples.
                                    26. -
                                    27. +
                                    28. I am a C user and expect to silently return a max value for overflow?
                                      You (and C++ users too) can return whatever you want on overflow - see overflow_error and error handling policies and several examples.
                                    29. -
                                    30. +
                                    31. I don't want any error message for overflow etc?
                                      You can control exactly what happens for all the abnormal conditions, including the values returned. See domain_error, @@ -131,14 +131,14 @@ handling policies user error handling etc and examples.
                                    32. -
                                    33. +
                                    34. My environment doesn't allow and/or I don't want exceptions. Can I still user Boost.Math?
                                      Yes but you must customise the error handling: see user error handling and changing policies defaults .
                                    35. -
                                    36. +
                                    37. The docs are several hundreds of pages long! Can I read the docs off-line or on paper?
                                      Yes - you can download the Boost current release of most documentation as a zip of pdfs (including @@ -149,7 +149,7 @@ Reader, Edit, Find ... This can often find what you seek, a partial substitute for a full index.
                                    38. -
                                    39. +
                                    40. I want a compact version for an embedded application. Can I use float precision?
                                      Yes - by selecting RealType template parameter as float: for example normal_distribution<float> your_normal(mean, @@ -157,7 +157,7 @@ less that you hope for). You can also change the promotion policy, but accuracy might be much reduced.
                                    41. -
                                    42. +
                                    43. I seem to get somewhat different results compared to other programs. Why? We hope Boost.Math to be more accurate: our priority is accuracy (over speed). See the section on accuracy. But for @@ -165,7 +165,7 @@ the required accuracy. You might be able to squeeze a little more accuracy at the cost of runtime.
                                    44. -
                                    45. +
                                    46. Will my program run more slowly compared to other math functions and statistical libraries? Probably, thought not always, and not by too much: our priority is accuracy. For most functions, making @@ -174,18 +174,18 @@ be able to gain a little more speed at the expense of accuracy. See detailed suggestions and results on performance.
                                    47. -
                                    48. +
                                    49. How do I handle infinity and NaNs portably?
                                      See nonfinite fp_facets for Facets for Floating-Point Infinities and NaNs.
                                    50. -
                                    51. +
                                    52. Where are the pre-built libraries?
                                      Good news - you probably don't need any! - just #include <boost/math/distribution_you_want>. But in the unlikely event that you do, see building libraries.
                                    53. -
                                    54. +
                                    55. I don't see the function or distribution that I want.
                                      You could try an email to ask the authors - but no promises!
                                    56. diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/hints.html b/doc/sf_and_dist/html/math_toolkit/main_overview/hints.html index 0ccb9275c..53a2dae49 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/hints.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/hints.html @@ -3,7 +3,7 @@ Other Hints and tips - + @@ -22,28 +22,28 @@
                                      PrevUpHomeNext
                                      -
                                      +
                                      -
                                        -
                                      • +
                                          +
                                        • If you have a feature request, or if it appears that the implementation is in error, please search first in the Boost Trac.
                                        • -
                                        • +
                                        • Trac entries may indicate that updates or corrections that solve your problem are in Boost-trunk where changes are being assembled and tested ready for the next release. You may, at your own risk, download new versions from there.
                                        • -
                                        • +
                                        • If you do not understand why things work the way they do, see the rationale section.
                                        • -
                                        • +
                                        • If you do not find your idea/feature/complaint, please reach the author preferably through the Boost development list, or email the author(s) direct. diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html b/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html index 7c2f86b2b..37577bd5c 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html @@ -3,7 +3,7 @@ History and What's New - + @@ -22,7 +22,7 @@
                                          PrevUpHomeNext
                                          -
                                          +

                                          History and What's New @@ -37,31 +37,27 @@ Boost-1.52

                                          -
                                          • +
                                              +
                                            • Corrected moments for small degrees of freedom #7177 (reported by Thomas Mang). -
                                            -
                                            - - Boost-1.51 -
                                            -
                                              -
                                            • +
                                            • +
                                            • Added Airy functions and Jacobi Elliptic functions.
                                            • -
                                            • +
                                            • Corrected failure to detect bad parameters in many distributions #6934 (reported by Florian Schoppmann) by adding a function check_out_of_range to test many possible bad parameters. This test revealed several distributions where the checks for bad parameters were ineffective, and these have been rectified.
                                            • -
                                            • +
                                            • Fixed issue in Hankel functions that causes incorrect values to be returned for x < 0 and ν odd, see #7135.
                                            • -
                                            • +
                                            • Fixed issues #6517, #6362, #7053, @@ -71,32 +67,32 @@
                                            - + Boost-1.50
                                            -
                                              -
                                            • +
                                                +
                                              • Promoted math constants to be 1st class citizens, including convenient access to the most widely used built-in float, double, long double via three namespaces.
                                              • -
                                              • +
                                              • Added the Owen's T function and Skew Normal distribution written by Benjamin Sobotta: see Owens T and skew_normal_distrib.
                                              • -
                                              • +
                                              • Added Hankel functions cyl_hankel_1, cyl_hankel_2, sph_hankel_1 and sph_hankel_2.
                                              • -
                                              • +
                                              • Corrected issue #6627 nonfinite_num_put formatting of 0.0 is incorrect based on a patch submitted by K R Walker.
                                              • -
                                              • +
                                              • Changed constant initialization mechanism so that it is thread safe even for user-defined types, also so that user defined types get the full precision of the constant, even when long @@ -104,46 +100,46 @@ 128-bit rational approximations will work with UDT's and do the right thing, even though long double may be only 64 or 80 bits.
                                              • -
                                              • +
                                              • Fixed issue in bessel_jy which causes Y8.5(4π) to yield a NaN.
                                              - + Boost-1.49
                                              -
                                                -
                                              • +
                                                  +
                                                • Deprecated wrongly named twothirds math constant in favour of two_thirds (with underscore separator). (issue #6199).
                                                • -
                                                • +
                                                • Refactored test data and some special function code to improve support for arbitary precision and/or expression-template-enabled types.
                                                • -
                                                • +
                                                • Added new faster zeta function evaluation method.

                                                Fixed issues:

                                                -
                                                  -
                                                • +
                                                    +
                                                  • Corrected CDF complement for Laplace distribution (issue #6151).
                                                  • -
                                                  • +
                                                  • Corrected branch cuts on the complex inverse trig functions, to handle signed zeros (issue #6171).
                                                  • -
                                                  • +
                                                  • Fixed bug in bessel_yn which caused incorrect overflow errors to be raised for negative n (issue #6367).
                                                  • -
                                                  • +
                                                  • Also fixed minor/cosmetic/configuration issues #6120, #6191, #5982, @@ -154,356 +150,356 @@
                                                  - + Boost-1.48
                                                  -
                                                    -
                                                  • +
                                                      +
                                                    • Added new series evaluation methods to the cyclic Bessel I, J, K and Y functions. Also taken great care to avoid spurious over and underflow of these functions. Fixes issue #5560
                                                    • -
                                                    • +
                                                    • Added an example of using Inverse Chi-Squared distribution for Bayesian statistics, provided by Thomas Mang.
                                                    • -
                                                    • +
                                                    • Added tests to use improved version of lexical_cast which handles C99 nonfinites without using globale facets.
                                                    • -
                                                    • +
                                                    • Corrected wrong out-of-bound uniform distribution CDF complement values #5733.
                                                    • -
                                                    • +
                                                    • Enabled long double support on OpenBSD (issue #6014).
                                                    • -
                                                    • +
                                                    • Changed nextafter and related functions to behave in the same way as other implementations - so that nextafter(+INF, 0) is a finite value (issue #5832).
                                                    • -
                                                    • +
                                                    • Changed tuple include configuration to fix issue when using in conjunction with Boost.Tr1 (issue #5934).
                                                    • -
                                                    • +
                                                    • Changed class eps_tolerance to behave correctly when both ends of the range are zero (issue #6001).
                                                    • -
                                                    • +
                                                    • Fixed missing include guards on prime.hpp (issue #5927).
                                                    • -
                                                    • +
                                                    • Removed unused/undocumented constants from constants.hpp (issue #5982).
                                                    • -
                                                    • +
                                                    • Fixed missing std:: prefix in nonfinite_num_facets.hpp (issue #5914).
                                                    • -
                                                    • +
                                                    • Minor patches for Cray compiler compatibility.
                                                    - + Boost-1.47
                                                    -
                                                      -
                                                    • +
                                                        +
                                                      • Added changesign function to sign.hpp to facilitate addition of nonfinite facets.
                                                      • -
                                                      • +
                                                      • Addition of nonfinite facets from Johan Rade, with tests, examples of use for C99 format infinity and NaN, and documentation.
                                                      • -
                                                      • +
                                                      • Added tests and documentation of changesign from Johan Rade.
                                                      - + Boost-1.46.1
                                                      -
                                                      • +
                                                        - + Boost-1.46.0
                                                        -
                                                          -
                                                        • +
                                                            +
                                                          • Added Wald, Inverse Gaussian and geometric distributions.
                                                          • -
                                                          • +
                                                          • Added information about configuration macros.
                                                          • -
                                                          • +
                                                          • Added support for mpreal as a real-numbered type.
                                                          - + Boost-1.45.0
                                                          -
                                                            -
                                                          • +
                                                              +
                                                            • Added warnings about potential ambiguity with std random library in distribution and function names.
                                                            • -
                                                            • +
                                                            • Added inverse gamma distribution and inverse chi_square and scaled inverse chi_square.
                                                            • -
                                                            • +
                                                            • Editorial revision of documentation, and added FAQ.
                                                            - + Boost-1.44.0
                                                            -
                                                              -
                                                            • +
                                                                +
                                                              • Fixed incorrect range and support for Rayleigh distribution.
                                                              • -
                                                              • +
                                                              • Fixed numerical error in the quantile of the Student's T distribution: the function was returning garbage values for non-integer degrees of freedom between 2 and 3.
                                                              - + Boost-1.41.0
                                                              -
                                                              • +
                                                                • Significantly improved performance for the incomplete gamma function and its inverse.
                                                                - + Boost-1.40.0
                                                                -
                                                                  -
                                                                • +
                                                                    +
                                                                  • Added support for MPFR as a bignum type.
                                                                  • -
                                                                  • +
                                                                  • Added some full specializations of the policy classes to reduce compile times.
                                                                  • -
                                                                  • +
                                                                  • Added logistic and hypergeometric distributions, from Gautam Sewani's Google Summer of Code project.
                                                                  • -
                                                                  • +
                                                                  • Added Laplace distribution submitted by Thijs van den Berg.
                                                                  • -
                                                                  • +
                                                                  • Updated performance test code to include new distributions, and improved the performance of the non-central distributions.
                                                                  • -
                                                                  • +
                                                                  • Added SSE2 optimised Lanczos approximation code, from Gautam Sewani's Google Summer of Code project.
                                                                  • -
                                                                  • +
                                                                  • Fixed bug in cyl_bessel_i that used an incorrect approximation for ν = 0.5, also effects the non-central Chi Square Distribution when ν = 3, see bug report #2877.
                                                                  • -
                                                                  • +
                                                                  • Fixed minor bugs #2873.
                                                                  - + Boost-1.38.0
                                                                  -
                                                                    -
                                                                  • +
                                                                      +
                                                                    • Added Johan Råde's optimised floating point classification routines.
                                                                    • -
                                                                    • +
                                                                    • Fixed code so that it compiles in GCC's -pedantic mode (bug report #1451).
                                                                    - + Boost-1.37.0
                                                                    -
                                                                    • +
                                                                      • Improved accuracy and testing of the inverse hypergeometric functions.
                                                                      - + Boost-1.36.0
                                                                      -
                                                                        -
                                                                      • +
                                                                          +
                                                                        • Added Noncentral Chi Squared Distribution.
                                                                        • -
                                                                        • +
                                                                        • Added Noncentral Beta Distribution.
                                                                        • -
                                                                        • +
                                                                        • Added Noncentral F Distribution.
                                                                        • -
                                                                        • +
                                                                        • Added Noncentral T Distribution.
                                                                        • -
                                                                        • +
                                                                        • Added Exponential Integral Functions.
                                                                        • -
                                                                        • +
                                                                        • Added Zeta Function.
                                                                        • -
                                                                        • +
                                                                        • Added Rounding and Truncation functions.
                                                                        • -
                                                                        • +
                                                                        • Added Compile time powers of runtime bases.
                                                                        • -
                                                                        • +
                                                                        • Added SSE2 optimizations for Lanczos evaluation.
                                                                        - + Boost-1.35.0: Post Review First Official Release
                                                                        -
                                                                          -
                                                                        • +
                                                                            +
                                                                          • Added Policy based framework that allows fine grained control over function behaviour.
                                                                          • -
                                                                          • +
                                                                          • Breaking change: Changed default behaviour for domain, pole and overflow errors to throw an exception (based on review feedback), this behaviour can be customised using Policy's.
                                                                          • -
                                                                          • +
                                                                          • Breaking change: Changed exception thrown when an internal evaluation error occurs to boost::math::evaluation_error.
                                                                          • -
                                                                          • +
                                                                          • Breaking change: Changed discrete quantiles to return an integer result: this is anything up to 20 times faster than finding the true root, this behaviour can be customised using Policy's.
                                                                          • -
                                                                          • +
                                                                          • Polynomial/rational function evaluation is now customisable and hopefully faster than before.
                                                                          • -
                                                                          • +
                                                                          • Added performance test program.
                                                                          - + Milestone 4: Second Review Candidate (1st March 2007)
                                                                          -
                                                                            -
                                                                          • +
                                                                              +
                                                                            • Moved Xiaogang Zhang's Bessel Functions code into the library, and brought them into line with the rest of the code.
                                                                            • -
                                                                            • +
                                                                            • Added C# "Distribution Explorer" demo application.
                                                                            - + Milestone 3: First Review Candidate (31st Dec 2006)
                                                                            -
                                                                              -
                                                                            • +
                                                                                +
                                                                              • Implemented the main probability distribution and density functions.
                                                                              • -
                                                                              • +
                                                                              • Implemented digamma.
                                                                              • -
                                                                              • +
                                                                              • Added more factorial functions.
                                                                              • -
                                                                              • +
                                                                              • Implemented the Hermite, Legendre and Laguerre polynomials plus the spherical harmonic functions from TR1.
                                                                              • -
                                                                              • +
                                                                              • Moved Xiaogang Zhang's elliptic integral code into the library, and brought them into line with the rest of the code.
                                                                              • -
                                                                              • +
                                                                              • Moved Hubert Holin's existing Boost.Math special functions into this library and brought them into line with the rest of the code.
                                                                              - + Milestone 2: Released September 10th 2006
                                                                              -
                                                                                -
                                                                              • +
                                                                                  +
                                                                                • Implement preview release of the statistical distributions.
                                                                                • -
                                                                                • +
                                                                                • Added statistical distributions tutorial.
                                                                                • -
                                                                                • +
                                                                                • Implemented root finding algorithms.
                                                                                • -
                                                                                • +
                                                                                • Implemented the inverses of the incomplete gamma and beta functions.
                                                                                • -
                                                                                • +
                                                                                • Rewrite erf/erfc as rational approximations (valid to 128-bit precision).
                                                                                • -
                                                                                • +
                                                                                • Integrated the statistical results generated from the test data with Boost.Test: uses a database of expected results, indexed by test, floating point type, platform, and compiler.
                                                                                • -
                                                                                • +
                                                                                • Improved lgamma near 1 and 2 (rational approximations).
                                                                                • -
                                                                                • +
                                                                                • Improved erf/erfc inverses (rational approximations).
                                                                                • -
                                                                                • +
                                                                                • Implemented Rational function generation (the Remez method).
                                                                                - + Milestone 1: Released March 31st 2006
                                                                                -
                                                                                  -
                                                                                • +
                                                                                    +
                                                                                  • Implement gamma/beta/erf functions along with their incomplete counterparts.
                                                                                  • -
                                                                                  • +
                                                                                  • Generate high quality test data, against which future improvements can be judged.
                                                                                  • -
                                                                                  • +
                                                                                  • Provide tools for the evaluation of infinite series, continued fractions, and rational functions.
                                                                                  • -
                                                                                  • +
                                                                                  • Provide tools for testing against tabulated test data, and collecting statistics on error rates.
                                                                                  • -
                                                                                  • +
                                                                                  • Provide sufficient docs for people to be able to find their way around the library.
                                                                                  • diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/intro.html b/doc/sf_and_dist/html/math_toolkit/main_overview/intro.html index b6e272042..25b5f635f 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/intro.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/intro.html @@ -3,7 +3,7 @@ About the Math Toolkit - + @@ -22,7 +22,7 @@
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                                                                                    diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/namespaces.html b/doc/sf_and_dist/html/math_toolkit/main_overview/namespaces.html index 9d687619c..c1e51f122 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/namespaces.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/namespaces.html @@ -3,7 +3,7 @@ Namespaces - + @@ -22,7 +22,7 @@
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                                                                                    diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html index b911d5561..fcf929ceb 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html @@ -3,7 +3,7 @@ Navigation - + @@ -22,30 +22,30 @@
                                                                                    PrevUpHomeNext
                                                                                    -
                                                                                    +

                                                                                    - +

                                                                                    Boost.Math documentation is provided in both HTML and PDF formats.

                                                                                    -
                                                                                      -
                                                                                    • +
                                                                                        +
                                                                                      • Tutorials are listed in the Table of Contents and include many examples that should help you get started quickly.
                                                                                      • -
                                                                                      • +
                                                                                      • Source code of the many Examples will often be your quickest starting point.
                                                                                      • -
                                                                                      • +
                                                                                      • Index (general) includes all entries.
                                                                                      • -
                                                                                      • +
                                                                                      • Specific Indexes list only functions, class signatures, macros and typedefs.
                                                                                      • diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/perf_over.html b/doc/sf_and_dist/html/math_toolkit/main_overview/perf_over.html index 746f8f66b..a30695657 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/perf_over.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/perf_over.html @@ -3,7 +3,7 @@ Performance - + @@ -22,7 +22,7 @@
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                                                                                        @@ -46,13 +46,13 @@ The two most important things you can do to ensure the best performance from this library are:

                                                                                        -
                                                                                          -
                                                                                        1. +
                                                                                            +
                                                                                          1. Turn on your compilers optimisations: the difference between "release" and "debug" builds can easily be a factor of 20.
                                                                                          2. -
                                                                                          3. +
                                                                                          4. Pick your compiler carefully: performance differences of up to 8 fold have been found between some Windows compilers for example. diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/pol_overview.html b/doc/sf_and_dist/html/math_toolkit/main_overview/pol_overview.html index 48537d4ef..c52c2c652 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/pol_overview.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/pol_overview.html @@ -3,7 +3,7 @@ Policies - + @@ -22,7 +22,7 @@
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                                                                                            @@ -49,31 +49,31 @@

                                                                                            Using policies you can control:

                                                                                            -
                                                                                              -
                                                                                            • +
                                                                                                +
                                                                                              • How results from 'bad' arguments are handled, including those that cannot be fully evaluated.
                                                                                              • -
                                                                                              • +
                                                                                              • How accuracy is controlled by internal promotion to use more precise types.
                                                                                              • -
                                                                                              • +
                                                                                              • What working precision should be used to calculate results.
                                                                                              • -
                                                                                              • +
                                                                                              • What to do when a mathematically undefined function is used: Should this raise a run-time or compile-time error?
                                                                                              • -
                                                                                              • +
                                                                                              • Whether discrete functions, like the binomial, should return real or only integral values, and how they are rounded.
                                                                                              • -
                                                                                              • +
                                                                                              • How many iterations a special function is permitted to perform in a series evaluation or root finding algorithm before it gives up and raises an evaluation_error. @@ -82,18 +82,18 @@

                                                                                                You can control policies:

                                                                                                -
                                                                                                  -
                                                                                                • +
                                                                                                    +
                                                                                                  • Using macros to change any default policy: the is the prefered method for installation wide policies.
                                                                                                  • -
                                                                                                  • +
                                                                                                  • At your chosen namespace scope for distributions and/or functions: this is the prefered method for project, namespace, or translation unit scope policies.
                                                                                                  • -
                                                                                                  • +
                                                                                                  • In an ad-hoc manner by passing a specific policy to a special function, or to a statistical distribution. diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/result_type.html b/doc/sf_and_dist/html/math_toolkit/main_overview/result_type.html index 5055de925..8490bf68f 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/result_type.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/result_type.html @@ -3,7 +3,7 @@ Calculation of the Type of the Result - + @@ -22,7 +22,7 @@
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                                                                                                    Calculation of the Type of the Result @@ -40,7 +40,7 @@ two floating-point arguments. But that leaves the question:

    -

    [1] +

    [1] Cephes gets stuck in an infinite loop while trying to execute our test cases.

    -

    [2] +

    [2] The performance here is dominated by a few cases where the parameters grow very large: faster asymptotic expansions are available, but are of limited (or even frankly terrible) precision. The @@ -1811,28 +1811,28 @@

    -

    [1] +

    [1] There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result.

    -

    [2] +

    [2] This result is somewhat misleading: for small values of the parameters there is virtually no difference between the two libraries, but for large values the Boost implementation is much slower, albeit with much improved precision.

    -

    [3] +

    [3] The R library appears to use a linear-search strategy, that can perform very badly in a small number of pathological cases, but may or may not be more efficient in "typical" cases

    -

    [4] +

    [4] There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result.

    -

    [5] +

    [5] There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result. @@ -3088,28 +3088,28 @@

    -

    [1] +

    [1] There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result.

    -

    [2] +

    [2] This result is somewhat misleading: for small values of the parameters there is virtually no difference between the two libraries, but for large values the Boost implementation is much slower, albeit with much improved precision.

    -

    [3] +

    [3] The R library appears to use a linear-search strategy, that can perform very badly in a small number of pathological cases, but may or may not be more efficient in "typical" cases

    -

    [4] +

    [4] There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result.

    -

    [5] +

    [5] There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result. diff --git a/doc/sf_and_dist/html/math_toolkit/perf/getting_best.html b/doc/sf_and_dist/html/math_toolkit/perf/getting_best.html index e5324c20e..00838c3b5 100644 --- a/doc/sf_and_dist/html/math_toolkit/perf/getting_best.html +++ b/doc/sf_and_dist/html/math_toolkit/perf/getting_best.html @@ -3,7 +3,7 @@ Getting the Best Performance from this Library - + @@ -22,7 +22,7 @@

    PrevUpHomeNext
    -
    +

    Getting the Best Performance from this Library diff --git a/doc/sf_and_dist/html/math_toolkit/perf/interp.html b/doc/sf_and_dist/html/math_toolkit/perf/interp.html index 2d7c61fa9..9f2f2174c 100644 --- a/doc/sf_and_dist/html/math_toolkit/perf/interp.html +++ b/doc/sf_and_dist/html/math_toolkit/perf/interp.html @@ -3,7 +3,7 @@ Interpreting these Results - + @@ -22,7 +22,7 @@
    PrevUpHomeNext
    -
    +
    diff --git a/doc/sf_and_dist/html/math_toolkit/perf/perf_over.html b/doc/sf_and_dist/html/math_toolkit/perf/perf_over.html index d72678c3b..6da85de64 100644 --- a/doc/sf_and_dist/html/math_toolkit/perf/perf_over.html +++ b/doc/sf_and_dist/html/math_toolkit/perf/perf_over.html @@ -3,7 +3,7 @@ Performance Overview - + @@ -22,7 +22,7 @@
    PrevUpHomeNext
    -
    +
    @@ -46,13 +46,13 @@ The two most important things you can do to ensure the best performance from this library are:

    -
      -
    1. +
        +
      1. Turn on your compilers optimisations: the difference between "release" and "debug" builds can easily be a factor of 20.
      2. -
      3. +
      4. Pick your compiler carefully: performance differences of up to 8 fold have been found between some Windows compilers for example. diff --git a/doc/sf_and_dist/html/math_toolkit/perf/perf_test_app.html b/doc/sf_and_dist/html/math_toolkit/perf/perf_test_app.html index 69ea11452..68cbbd24c 100644 --- a/doc/sf_and_dist/html/math_toolkit/perf/perf_test_app.html +++ b/doc/sf_and_dist/html/math_toolkit/perf/perf_test_app.html @@ -3,7 +3,7 @@ The Performance Test Application - + @@ -22,7 +22,7 @@
        PrevUpHomeNext
        -
        +

        The Performance Test Application diff --git a/doc/sf_and_dist/html/math_toolkit/perf/tuning.html b/doc/sf_and_dist/html/math_toolkit/perf/tuning.html index 3213c2bda..e82a9a20d 100644 --- a/doc/sf_and_dist/html/math_toolkit/perf/tuning.html +++ b/doc/sf_and_dist/html/math_toolkit/perf/tuning.html @@ -3,7 +3,7 @@ Performance Tuning Macros - + @@ -22,7 +22,7 @@
        PrevUpHomeNext
        -
        +
        diff --git a/doc/sf_and_dist/html/math_toolkit/policy.html b/doc/sf_and_dist/html/math_toolkit/policy.html index 6cb913905..04f720d5a 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy.html +++ b/doc/sf_and_dist/html/math_toolkit/policy.html @@ -3,7 +3,7 @@ Policies - + @@ -22,7 +22,7 @@
        PrevUpHomeNext
        -
        +
        diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_overview.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_overview.html index da0f123d4..839e71e63 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_overview.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_overview.html @@ -3,7 +3,7 @@ Policy Overview - + @@ -22,7 +22,7 @@
        PrevUpHomeNext
        -
        +
        @@ -49,31 +49,31 @@

        Using policies you can control:

        -
          -
        • +
            +
          • How results from 'bad' arguments are handled, including those that cannot be fully evaluated.
          • -
          • +
          • How accuracy is controlled by internal promotion to use more precise types.
          • -
          • +
          • What working precision should be used to calculate results.
          • -
          • +
          • What to do when a mathematically undefined function is used: Should this raise a run-time or compile-time error?
          • -
          • +
          • Whether discrete functions, like the binomial, should return real or only integral values, and how they are rounded.
          • -
          • +
          • How many iterations a special function is permitted to perform in a series evaluation or root finding algorithm before it gives up and raises an evaluation_error. @@ -82,18 +82,18 @@

            You can control policies:

            -
              -
            • +
                +
              • Using macros to change any default policy: the is the prefered method for installation wide policies.
              • -
              • +
              • At your chosen namespace scope for distributions and/or functions: this is the prefered method for project, namespace, or translation unit scope policies.
              • -
              • +
              • In an ad-hoc manner by passing a specific policy to a special function, or to a statistical distribution. diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref.html index 1c02b07be..f204c9165 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref.html @@ -3,7 +3,7 @@ Policy Reference - + @@ -22,7 +22,7 @@
                PrevUpHomeNext
                -
                +
                diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/assert_undefined.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/assert_undefined.html index 61255c378..fdc82f522 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/assert_undefined.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/assert_undefined.html @@ -3,7 +3,7 @@ Mathematically Undefined Function Policies - + @@ -22,7 +22,7 @@
                PrevUpHomeNext
                -
                +

                Mathematically Undefined Function Policies diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/discrete_quant_ref.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/discrete_quant_ref.html index 0c4565c18..95cb6d4bb 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/discrete_quant_ref.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/discrete_quant_ref.html @@ -3,7 +3,7 @@ Discrete Quantile Policies - + @@ -22,7 +22,7 @@
                PrevUpHomeNext
                -
                +

                Discrete Quantile Policies @@ -78,7 +78,6 @@ double x = quantile(dist_type(20, 0.3), 0.05); // Upper 95% quantile: double y = quantile(complement(dist_type(20, 0.3), 0.05)); -

                @@ -94,12 +93,12 @@

                This is the default policy: an integer value is returned so that:

                -
                  -
                • +
                    +
                  • Lower quantiles (where the probability is less than 0.5) are rounded down.
                  • -
                  • +
                  • Upper quantiles (where the probability is greater than 0.5) are rounded up.
                  • @@ -119,7 +118,6 @@ double x = quantile(negative_binomial(20, 0.3), 0.05); // rounded up 27 from 27.3898 // Upper quantile rounded up: double y = quantile(complement(negative_binomial(20, 0.3), 0.05)); // rounded down to 69 from 68.1584 -

                    @@ -148,12 +146,12 @@ This is the opposite of integer_round_outwards: an integer value is returned so that:

                    -
                      -
                    • +
                        +
                      • Lower quantiles (where the probability is less than 0.5) are rounded up.
                      • -
                      • +
                      • Upper quantiles (where the probability is greater than 0.5) are rounded down.
                      • @@ -177,7 +175,6 @@ double x = quantile(dist_type(20, 0.3), 0.05); // 28 rounded up from 27.3898 // Upper quantile rounded down: double y = quantile(complement(dist_type(20, 0.3), 0.05)); // 68 rounded down from 68.1584 -

                        @@ -244,7 +241,6 @@ double x = quantile(dist_type(20, 0.3), 0.05); // 27 // Upper quantile rounded (down) to nearest: double y = quantile(complement(dist_type(20, 0.3), 0.05)); // 68 -

                        diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/error_handling_policies.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/error_handling_policies.html index 06749dbc1..7bf1bb9b1 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/error_handling_policies.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/error_handling_policies.html @@ -3,7 +3,7 @@ Error Handling Policies - + @@ -22,7 +22,7 @@
                        PrevUpHomeNext
                        -
                        +

                        Error Handling Policies @@ -30,11 +30,11 @@

                        There are two orthogonal aspects to error handling:

                        -
                          -
                        • +
                            +
                          • What to do (if anything) with the error.
                          • -
                          • +
                          • What kind of error is being raised.
                          @@ -760,7 +760,6 @@ // Construct a my_norm distribution, using default mean and standard deviation, // and get a 0.05 or 5% quantile: double q = quantile(my_norm(), 0.05); // = -1.64485 -

                          diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/internal_promotion.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/internal_promotion.html index 3965fa54a..e8aee2905 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/internal_promotion.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/internal_promotion.html @@ -3,7 +3,7 @@ Internal Floating-point Promotion Policies - + @@ -22,7 +22,7 @@
                          PrevUpHomeNext
                          -
                          +

                          Internal Floating-point Promotion Policies @@ -111,7 +111,6 @@ // Alternatively we could use helper function make_policy, // and concisely define everything at the call site: double t2 = tgamma(some_value, make_policy(promote_double<false>())); -

                          @@ -136,7 +135,6 @@ // Get a quantile: float q = quantile(my_norm(), 0.05f); -

                          diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/iteration_pol.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/iteration_pol.html index 740cecc43..8219eb7d2 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/iteration_pol.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/iteration_pol.html @@ -3,7 +3,7 @@ Iteration Limits Policies - + @@ -22,7 +22,7 @@
                          PrevUpHomeNext
                          -
                          +

                          Iteration Limits Policies diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/namespace_pol.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/namespace_pol.html index 09e511026..c66cc6e63 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/namespace_pol.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/namespace_pol.html @@ -3,7 +3,7 @@ Setting Polices at Namespace Scope - + @@ -22,7 +22,7 @@
                          PrevUpHomeNext
                          -
                          +

                          Setting Polices at Namespace Scope @@ -68,7 +68,6 @@ double t = myspace::tgamma(30.0); // Will *not* throw on overflow, // despite the large value of factorial 30 = 265252859812191058636308480000000 // unlike default policy boost::math::tgamma; -

                          @@ -133,7 +132,6 @@ cout << e.what() << endl; } } -

                          diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/pol_ref_ref.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/pol_ref_ref.html index 1c795737c..5735006e4 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/pol_ref_ref.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/pol_ref_ref.html @@ -3,7 +3,7 @@ Policy Class Reference - + @@ -22,7 +22,7 @@
                          PrevUpHomeNext
                          -
                          +

                          Policy Class Reference diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/policy_defaults.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/policy_defaults.html index 901387d61..7c0c1dd16 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/policy_defaults.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/policy_defaults.html @@ -3,7 +3,7 @@ Using Macros to Change the Policy Defaults - + @@ -22,7 +22,7 @@
                          PrevUpHomeNext
                          -
                          +

                          Using Macros to Change the Policy Defaults diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/precision_pol.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/precision_pol.html index 18e2fe4d5..d893131e7 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/precision_pol.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/precision_pol.html @@ -3,7 +3,7 @@ Precision Policies - + @@ -22,7 +22,7 @@
                          PrevUpHomeNext
                          -
                          +

                          Precision Policies @@ -82,7 +82,6 @@ using namespace boost::math::policies; double t = tgamma(12, policy<digits10<5> >()); // Concise make_policy. -

                          @@ -101,7 +100,6 @@ double q = quantile( normal_distribution<double, policy<digits2<bits> > >(), 0.05); // 5% quantile. -

                          diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial.html index 84c2943be..b098878e7 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial.html @@ -3,7 +3,7 @@ Policy Tutorial - + @@ -22,7 +22,7 @@
                          PrevUpHomeNext
                          -
                          +
                          diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html index 965afc00f..0ed804df9 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html @@ -3,7 +3,7 @@ Setting Policies for Distributions on an Ad Hoc Basis - + @@ -22,7 +22,7 @@
                          PrevUpHomeNext
                          -
                          +

                          Setting Policies for Distributions on an Ad Hoc Basis @@ -83,7 +83,6 @@ cout << "quantile(mybinom(200, 0.25), 0.05) is: " << quantile(mybinom(200, 0.25), 0.05) << endl; } -

                          diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html index fa210421b..142629ce8 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html @@ -3,7 +3,7 @@ Changing the Policy on an Ad Hoc Basis for the Special Functions - + @@ -22,7 +22,7 @@
                          PrevUpHomeNext
                          -
                          +

                          Changing the Policy on an Ad Hoc Basis for the Special Functions @@ -101,7 +101,6 @@ << boost::math::tgamma(-10, c_policy()) << endl; // Negative parameter. cout << "errno = " << errno << endl; // error 33 Numerical argument out of domain. } // int main() -

                          @@ -160,7 +159,6 @@ errno = 33 // Check errno was set: std::cout << "errno = " << errno << std::endl; } -

                          diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/changing_policy_defaults.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/changing_policy_defaults.html index 808ccb493..6982a086c 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/changing_policy_defaults.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/changing_policy_defaults.html @@ -3,7 +3,7 @@ Changing the Policy Defaults - + @@ -22,7 +22,7 @@
                          PrevUpHomeNext
                          -
                          +

                          Changing the Policy Defaults @@ -99,14 +99,14 @@

                          That means there are only two safe ways to use these macros:

                          -
                            -
                          • +
                              +
                            • Edit them in boost/math/tools/user.hpp, so that the defaults are set on an installation-wide basis. Unfortunately this may not be convenient if you are using a pre-installed Boost distribution (on Linux for example).
                            • -
                            • +
                            • Set the defines in your project's Makefile or build environment, so that they are set uniformly across all translation units.
                            • @@ -114,7 +114,7 @@

                              What you should not do is:

                              -
                              • +
                                • Set the defines in the source file using #define as doing so almost certainly will break your program, unless you're absolutely certain that the program is restricted to a single translation @@ -177,7 +177,8 @@ using std::exception; #include <cstddef> - // using ::errno + // using ::errno +

                                  @@ -219,7 +220,8 @@ "\n""Message from thrown exception was:\n " << e.what() << std::endl; } return 0; -} // int main() +} // int main() +

                                  diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/namespace_policies.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/namespace_policies.html index a58fe562d..b75c334c5 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/namespace_policies.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/namespace_policies.html @@ -3,7 +3,7 @@ Setting Policies at Namespace or Translation Unit Scope - + @@ -22,7 +22,7 @@

                                  PrevUpHomeNext
                                  -
                                  +

                                  Setting Policies at Namespace or Translation Unit Scope @@ -53,7 +53,8 @@

                                  #include <boost/math/special_functions.hpp>
                                  -//using boost::math::tgamma; // Not needed because using C::tgamma.
                                  +//using boost::math::tgamma; // Not needed because using C::tgamma. +

                                  @@ -82,7 +83,8 @@ pole_error<errno_on_error>, overflow_error<errno_on_error>, evaluation_error<errno_on_error> - > c_policy; + > c_policy; +

                                  @@ -93,7 +95,8 @@

                                  BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS(c_policy)
                                   
                                  -} // close namespace C
                                  +} // close namespace C +

                                  @@ -127,7 +130,8 @@ cout << "Result of tgamma(-10) is: " << C::tgamma(-10) << endl; cout << "errno = " << errno << endl; // errno = 33, overwriting previous value of 34. -} +} +

                                  @@ -167,7 +171,8 @@ errno = 33 evaluation_error<errno_on_error> > c_policy; -BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS(c_policy) +BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS(c_policy) +

                                  @@ -191,7 +196,6 @@ errno = 33 cout << "errno = " << errno << endl; // Default tgamma policy would throw an exception, and abort. } -

                                  @@ -214,14 +218,14 @@ errno = 33

                                  Suppose we want a set of distributions to behave as follows:

                                  -
                                    -
                                  • +
                                      +
                                    • Return infinity on overflow, rather than throwing an exception.
                                    • -
                                    • +
                                    • Don't perform any promotion from double to long double internally.
                                    • -
                                    • +
                                    • Return the closest integer result from the quantiles of discrete distributions.
                                    @@ -230,7 +234,8 @@ errno = 33

                                    -
                                    #include <boost/math/distributions.hpp>
                                    +
                                    #include <boost/math/distributions.hpp>
                                    +

                                    @@ -252,7 +257,8 @@ errno = 33 promote_double<false>, // Return the closest integer result for discrete quantiles: discrete_quantile<integer_round_nearest> - > my_policy; + > my_policy; +

                                    @@ -265,7 +271,8 @@ errno = 33

                                    BOOST_MATH_DECLARE_DISTRIBUTIONS(double, my_policy)
                                     
                                    -} // close namespace my_namespace
                                    +} // close namespace my_namespace +

                                    @@ -307,7 +314,8 @@ errno = 33 << quantile(binom, 0.05) << endl; // To check we get integer results. cout << "Result of quantile(complement(binom, 0.05)) is: " << quantile(complement(binom, 0.05)) << endl; -} +} +

                                    @@ -387,7 +395,6 @@ Result of quantile(complement(binom, 0.05)) is: 8 cout << "Result of quantile(complement(binom, 0.05)) is: " << quantile(complement(binom, 0.05)) << endl; } -

                                    diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_tut_defaults.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_tut_defaults.html index 836d7ac91..ff8c95913 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_tut_defaults.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_tut_defaults.html @@ -3,7 +3,7 @@ Policies Have Sensible Defaults - + @@ -22,7 +22,7 @@
                                    PrevUpHomeNext
                                    -
                                    +

                                    Policies Have Sensible Defaults diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_usage.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_usage.html index 3441e843d..bb66b9990 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_usage.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_usage.html @@ -3,7 +3,7 @@ So How are Policies Used Anyway? - + @@ -22,7 +22,7 @@
                                    PrevUpHomeNext
                                    -
                                    +

                                    So How are Policies Used Anyway? @@ -30,20 +30,20 @@

                                    The details follow later, but basically policies can be set by either:

                                    -
                                      -
                                    • +
                                        +
                                      • Defining some macros that change the default behaviour: this is the recommended method for setting installation-wide policies.
                                      • -
                                      • +
                                      • By instantiating a distribution object with an explicit policy: this is mainly reserved for ad hoc policy changes.
                                      • -
                                      • +
                                      • By passing a policy to a special function as an optional final argument: this is mainly reserved for ad hoc policy changes.
                                      • -
                                      • +
                                      • By using some helper macros to define a set of functions or distributions in the current namespace that use a specific policy: this is the recommended method for setting policies on a project- or translation-unit-wide diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/understand_dis_quant.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/understand_dis_quant.html index 109619d03..b251aae7b 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/understand_dis_quant.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/understand_dis_quant.html @@ -3,7 +3,7 @@ Understanding Quantiles of Discrete Distributions - + @@ -22,7 +22,7 @@
                                        PrevUpHomeNext
                                        -
                                        +

                                        Understanding Quantiles of Discrete Distributions @@ -53,11 +53,11 @@ As can be seen there is no random variable that corresponds to a probability of exactly 0.05, so we're left with two choices as shown in the figure:

                                        -
                                          -
                                        • +
                                            +
                                          • We could round the result down to 18.
                                          • -
                                          • +
                                          • We could round the result up to 19.
                                          @@ -77,12 +77,12 @@

                                          In coming to an answer we should realise that:

                                          -
                                            -
                                          • +
                                              +
                                            • Calculating an integer result is often much faster than calculating a real-valued result: in fact in our tests it was up to 20 times faster.
                                            • -
                                            • +
                                            • Normally people calculate quantiles so that they can perform a test of some kind: "If the random variable is less than N then we can reject our null-hypothesis with 90% confidence." @@ -256,7 +256,8 @@ using std::setw; using std::setprecision; -#include <boost/math/distributions/binomial.hpp> +#include <boost/math/distributions/binomial.hpp> +

                                              @@ -313,7 +314,8 @@ typedef binomial_distribution< double, policy<discrete_quantile<real> > > - binom_real_quantile; + binom_real_quantile; +

                                              @@ -387,7 +389,8 @@ << setw(18) << right << quantile(binom_real_quantile(50, 0.5), 0.95) << endl; -} // int main() +} // int main() +

                                              diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/user_def_err_pol.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/user_def_err_pol.html index 23ba349e6..b1cac051c 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/user_def_err_pol.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/user_def_err_pol.html @@ -3,7 +3,7 @@ Calling User Defined Error Handlers - + @@ -22,7 +22,7 @@

                                              PrevUpHomeNext
                                              -
                                              +

                                              Calling User Defined Error Handlers @@ -84,7 +84,8 @@ return std::numeric_limits<T>::quiet_NaN(); } } // namespace policies -}} // namespace boost{ namespace math +}} // namespace boost{ namespace math +

                                              @@ -104,7 +105,8 @@ BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS(user_error_policy) -} // close unnamed namespace +} // close unnamed namespace +

                                              @@ -136,7 +138,8 @@ << erf_inv(-10) << endl; cout << "Result of tgamma(-10) is: " << tgamma(-10) << endl; -} +} +

                                              @@ -196,7 +199,8 @@

                                              -
                                              #include <boost/math/special_functions.hpp>
                                              +
                                              #include <boost/math/special_functions.hpp>
                                              +

                                              @@ -211,7 +215,8 @@ template <class T> T user_domain_error(const char* function, const char* message, const T& val) -{ +{ +

                                              @@ -223,7 +228,8 @@

                                              if(function == 0)
                                                   function = "Unknown function with arguments of type %1%";
                                               if(message == 0)
                                              -    message = "Cause unknown with bad argument %1%";
                                              + message = "Cause unknown with bad argument %1%"; +

                                              @@ -233,7 +239,8 @@

                                              std::string msg("Error in function ");
                                              -msg += (boost::format(function) % typeid(T).name()).str();
                                              +msg += (boost::format(function) % typeid(T).name()).str(); +

                                              @@ -245,7 +252,8 @@

                                              msg += ": \n";
                                               int prec = 2 + (std::numeric_limits<T>::digits * 30103UL) / 100000UL;
                                               // int prec = std::numeric_limits<T>::max_digits10; //  For C++0X Standard Library
                                              -msg += (boost::format(message) % boost::io::group(std::setprecision(prec), val)).str();
                                              +msg += (boost::format(message) % boost::io::group(std::setprecision(prec), val)).str(); +

                                              @@ -254,7 +262,8 @@

                                              -
                                              std::cerr << msg << std::endl;
                                              +
                                              std::cerr << msg << std::endl;
                                              +

                                              @@ -264,7 +273,8 @@

                                                 return std::numeric_limits<T>::quiet_NaN();
                                              -}
                                              +} +

                                              @@ -277,7 +287,8 @@ T user_pole_error(const char* function, const char* message, const T& val) { return user_domain_error(function, message, val); -} +} +

                                              @@ -304,7 +315,8 @@ // Value passed to the function is an infinity, just return it: return val; -} +} +

                                              @@ -330,7 +342,8 @@ // Value passed to the function is zero, just return it: return val; -} +} +

                                              @@ -356,7 +369,8 @@ // Value passed to the function is denormalised, just return it: return val; -} +} +

                                              @@ -392,7 +406,8 @@ } } // policies -}} // boost::math +}} // boost::math +

                                              @@ -417,7 +432,8 @@ BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS(user_error_policy) -} // unnamed namespace +} // unnamed namespace +

                                              @@ -460,7 +476,8 @@ // Unfortunately we can't predicably raise a denormalised // result, nor can we raise an evaluation error in this example // since these should never really occur! -} // int main() +} // int main() +

                                              diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/what_is_a_policy.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/what_is_a_policy.html index 00c2d4dee..b211664e1 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/what_is_a_policy.html +++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/what_is_a_policy.html @@ -3,7 +3,7 @@ So Just What is a Policy Anyway? - + @@ -22,7 +22,7 @@

                                              PrevUpHomeNext
                                              -
                                              +

                                              So Just What is a Policy Anyway? @@ -32,23 +32,23 @@ special function, or a statistical distribution. With Policies you can control:

                                              -
                                                -
                                              • +
                                                  +
                                                • What action to take when an error occurs.
                                                • -
                                                • +
                                                • What happens when you call a function that is mathematically undefined (for example, if you ask for the mean of a Cauchy distribution).
                                                • -
                                                • +
                                                • What happens when you ask for a quantile of a discrete distribution.
                                                • -
                                                • +
                                                • Whether the library is allowed to internally promote float to double and double to long double in order to improve precision.
                                                • -
                                                • +
                                                • What precision to use when calculating the result.
                                                diff --git a/doc/sf_and_dist/html/math_toolkit/special.html b/doc/sf_and_dist/html/math_toolkit/special.html index 1ea84a1ff..370b4ce1b 100644 --- a/doc/sf_and_dist/html/math_toolkit/special.html +++ b/doc/sf_and_dist/html/math_toolkit/special.html @@ -3,7 +3,7 @@ Special Functions - + @@ -22,7 +22,7 @@
                                                PrevUpHomeNext
                                                -
                                                +
                                                diff --git a/doc/sf_and_dist/html/math_toolkit/special/airy.html b/doc/sf_and_dist/html/math_toolkit/special/airy.html index 62b7fb203..9b8a2cb4b 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/airy.html +++ b/doc/sf_and_dist/html/math_toolkit/special/airy.html @@ -3,7 +3,7 @@ Airy Functions - + @@ -22,7 +22,7 @@
                                                PrevUpHomeNext
                                                -
                                                +
                                                diff --git a/doc/sf_and_dist/html/math_toolkit/special/airy/ai.html b/doc/sf_and_dist/html/math_toolkit/special/airy/ai.html index 35c3a6eb7..56e702378 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/airy/ai.html +++ b/doc/sf_and_dist/html/math_toolkit/special/airy/ai.html @@ -3,7 +3,7 @@ Airy Ai Function - + @@ -22,7 +22,7 @@
                                                PrevUpHomeNext
                                                -
                                                +
                                                diff --git a/doc/sf_and_dist/html/math_toolkit/special/airy/aip.html b/doc/sf_and_dist/html/math_toolkit/special/airy/aip.html index 92c2b288e..3d57eebfd 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/airy/aip.html +++ b/doc/sf_and_dist/html/math_toolkit/special/airy/aip.html @@ -3,7 +3,7 @@ Airy Ai' Function - + @@ -22,7 +22,7 @@
                                                PrevUpHomeNext
                                                -
                                                +
                                                diff --git a/doc/sf_and_dist/html/math_toolkit/special/airy/bi.html b/doc/sf_and_dist/html/math_toolkit/special/airy/bi.html index a1ea19c47..9d4c1a38e 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/airy/bi.html +++ b/doc/sf_and_dist/html/math_toolkit/special/airy/bi.html @@ -3,7 +3,7 @@ Airy Bi Function - + @@ -22,7 +22,7 @@
                                                PrevUpHomeNext
                                                -
                                                +
                                                diff --git a/doc/sf_and_dist/html/math_toolkit/special/airy/bip.html b/doc/sf_and_dist/html/math_toolkit/special/airy/bip.html index e5b7e8ea8..76c62a2e3 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/airy/bip.html +++ b/doc/sf_and_dist/html/math_toolkit/special/airy/bip.html @@ -3,7 +3,7 @@ Airy Bi' Function - + @@ -22,7 +22,7 @@
                                                PrevUpHomeNext
                                                -
                                                +
                                                diff --git a/doc/sf_and_dist/html/math_toolkit/special/bessel.html b/doc/sf_and_dist/html/math_toolkit/special/bessel.html index 62e1a20e8..1e92928ad 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/bessel.html +++ b/doc/sf_and_dist/html/math_toolkit/special/bessel.html @@ -3,7 +3,7 @@ Bessel Functions - + @@ -22,7 +22,7 @@
                                                PrevUpHomeNext
                                                -
                                                +
                                                diff --git a/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel.html b/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel.html index 3f11f4018..fc23e89f1 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel.html +++ b/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel.html @@ -3,7 +3,7 @@ Bessel Functions of the First and Second Kinds - + @@ -22,7 +22,7 @@
                                                PrevUpHomeNext
                                                -
                                                +

                                                Bessel Functions of the First and Second Kinds diff --git a/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel_over.html b/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel_over.html index d074a0ecb..5ead6c678 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel_over.html +++ b/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel_over.html @@ -3,7 +3,7 @@ Bessel Function Overview - + @@ -22,7 +22,7 @@
                                                PrevUpHomeNext
                                                -
                                                +

                                                Bessel Function Overview diff --git a/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html b/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html index 64fb69d03..5d6adc8a1 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html +++ b/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html @@ -3,7 +3,7 @@ Modified Bessel Functions of the First and Second Kinds - + @@ -22,7 +22,7 @@
                                                PrevUpHomeNext
                                                -
                                                +

                                                Modified Bessel Functions of the First and Second Kinds @@ -339,13 +339,13 @@ The 0 and 1 cases use minimax rational approximations on finite and infinite intervals. The coefficients are from:

                                                -
                                                  -
                                                • +
                                                    +
                                                  • J.M. Blair and C.A. Edwards, Stable rational minimax approximations to the modified Bessel functions I_0(x) and I_1(x), Atomic Energy of Canada Limited Report 4928, Chalk River, 1974.
                                                  • -
                                                  • +
                                                  • S. Moshier, Methods and Programs for Mathematical Functions, Ellis Horwood Ltd, Chichester, 1989.
                                                  • diff --git a/doc/sf_and_dist/html/math_toolkit/special/bessel/sph_bessel.html b/doc/sf_and_dist/html/math_toolkit/special/bessel/sph_bessel.html index 3340fcb45..8bd007acc 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/bessel/sph_bessel.html +++ b/doc/sf_and_dist/html/math_toolkit/special/bessel/sph_bessel.html @@ -3,7 +3,7 @@ Spherical Bessel Functions of the First and Second Kinds - + @@ -22,7 +22,7 @@
                                                    PrevUpHomeNext
                                                    -
                                                    +

                                                    Spherical Bessel Functions of the First and Second Kinds diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint.html b/doc/sf_and_dist/html/math_toolkit/special/ellint.html index 35cd1efca..f27885254 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/ellint.html +++ b/doc/sf_and_dist/html/math_toolkit/special/ellint.html @@ -3,7 +3,7 @@ Elliptic Integrals - + @@ -22,7 +22,7 @@
                                                    PrevUpHomeNext
                                                    -
                                                    +
                                                    diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_1.html b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_1.html index 92dac8e30..c096ca02e 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_1.html +++ b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_1.html @@ -3,7 +3,7 @@ Elliptic Integrals of the First Kind - Legendre Form - + @@ -22,7 +22,7 @@
                                                    PrevUpHomeNext
                                                    -
                                                    +

                                                    Elliptic Integrals of the First Kind - Legendre Form diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_2.html b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_2.html index 78e46a1e6..e124a8fc5 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_2.html +++ b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_2.html @@ -3,7 +3,7 @@ Elliptic Integrals of the Second Kind - Legendre Form - + @@ -22,7 +22,7 @@
                                                    PrevUpHomeNext
                                                    -
                                                    +

                                                    Elliptic Integrals of the Second Kind - Legendre Form diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html index c9c2d5acc..34c7a0039 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html +++ b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html @@ -3,7 +3,7 @@ Elliptic Integrals of the Third Kind - Legendre Form - + @@ -22,7 +22,7 @@
                                                    PrevUpHomeNext
                                                    -
                                                    +

                                                    Elliptic Integrals of the Third Kind - Legendre Form @@ -297,7 +297,7 @@



                                                    -

                                                    [1] +

                                                    [1] I haven't been able to find a literature reference for this relation, but it appears to be the convention used by Mathematica. Intuitively the first 2 * m * Π(n, k) terms cancel out as the diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_carlson.html b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_carlson.html index c6533e398..dbc8d5ad3 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_carlson.html +++ b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_carlson.html @@ -3,7 +3,7 @@ Elliptic Integrals - Carlson Form - + @@ -22,7 +22,7 @@

                                                    PrevUpHomeNext
                                                    -
                                                    +

                                                    Elliptic Integrals - Carlson Form diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_intro.html b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_intro.html index 1b836c2ae..b65ccd86a 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_intro.html +++ b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_intro.html @@ -3,7 +3,7 @@ Elliptic Integral Overview - + @@ -22,7 +22,7 @@
                                                    PrevUpHomeNext
                                                    -
                                                    +

                                                    Elliptic Integral Overview @@ -300,65 +300,65 @@

                                                    However the main references are:

                                                    -
                                                      -
                                                    1. +
                                                        +
                                                      1. M. Abramowitz and I. A. Stegun (Eds.) (1964) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards Applied Mathematics Series, U.S. Government Printing Office, Washington, D.C.
                                                      2. -
                                                      3. +
                                                      4. B.C. Carlson, Computing elliptic integrals by duplication, Numerische Mathematik, vol 33, 1 (1979).
                                                      5. -
                                                      6. +
                                                      7. B.C. Carlson, Elliptic Integrals of the First Kind, SIAM Journal on Mathematical Analysis, vol 8, 231 (1977).
                                                      8. -
                                                      9. +
                                                      10. B.C. Carlson, Short Proofs of Three Theorems on Elliptic Integrals, SIAM Journal on Mathematical Analysis, vol 9, 524 (1978).
                                                      11. -
                                                      12. +
                                                      13. B.C. Carlson and E.M. Notis, ALGORITHM 577: Algorithms for Incomplete Elliptic Integrals, ACM Transactions on Mathematmal Software, vol 7, 398 (1981).
                                                      14. -
                                                      15. +
                                                      16. B. C. Carlson, On computing elliptic integrals and functions. J. Math. and Phys., 44 (1965), pp. 36-51.
                                                      17. -
                                                      18. +
                                                      19. B. C. Carlson, A table of elliptic integrals of the second kind. Math. Comp., 49 (1987), pp. 595-606. (Supplement, ibid., pp. S13-S17.)
                                                      20. -
                                                      21. +
                                                      22. B. C. Carlson, A table of elliptic integrals of the third kind. Math. Comp., 51 (1988), pp. 267-280. (Supplement, ibid., pp. S1-S5.)
                                                      23. -
                                                      24. +
                                                      25. B. C. Carlson, A table of elliptic integrals: cubic cases. Math. Comp., 53 (1989), pp. 327-333.
                                                      26. -
                                                      27. +
                                                      28. B. C. Carlson, A table of elliptic integrals: one quadratic factor. Math. Comp., 56 (1991), pp. 267-280.
                                                      29. -
                                                      30. +
                                                      31. B. C. Carlson, A table of elliptic integrals: two quadratic factors. Math. Comp., 59 (1992), pp. 165-180.
                                                      32. -
                                                      33. +
                                                      34. B. C. Carlson, Numerical computation of real or complex elliptic integrals. Numerical Algorithms, Volume 10, Number 1 / March, 1995, p13-26.
                                                      35. -
                                                      36. +
                                                      37. B. C. Carlson and John L. Gustafson, Asymptotic Approximations for Symmetric Elliptic Integrals, SIAM Journal on Mathematical Analysis, Volume 25, Issue 2 (March 1994), @@ -369,21 +369,21 @@ The following references, while not directly relevent to our implementation, may also be of interest:

                                                        -
                                                          -
                                                        1. +
                                                            +
                                                          1. R. Burlisch, Numerical Compuation of Elliptic Integrals and Elliptic Functions. Numerical Mathematik 7, 78-90.
                                                          2. -
                                                          3. +
                                                          4. R. Burlisch, An extension of the Bartky Transformation to Incomplete Elliptic Integrals of the Third Kind. Numerical Mathematik 13, 266-284.
                                                          5. -
                                                          6. +
                                                          7. R. Burlisch, Numerical Compuation of Elliptic Integrals and Elliptic Functions. III. Numerical Mathematik 13, 305-315.
                                                          8. -
                                                          9. +
                                                          10. T. Fukushima and H. Ishizaki, Numerical Computation of Incomplete Elliptic Integrals of a General Form. Celestial Mechanics and Dynamical Astronomy, Volume 59, Number 3 / diff --git a/doc/sf_and_dist/html/math_toolkit/special/expint.html b/doc/sf_and_dist/html/math_toolkit/special/expint.html index 9430aaf9e..7297239be 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/expint.html +++ b/doc/sf_and_dist/html/math_toolkit/special/expint.html @@ -3,7 +3,7 @@ Exponential Integrals - + @@ -22,7 +22,7 @@
                                                            PrevUpHomeNext
                                                            -
                                                            +
                                                            diff --git a/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html b/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html index 57014962c..6ae3a731f 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html +++ b/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html @@ -3,7 +3,7 @@ Exponential Integral Ei - + @@ -22,7 +22,7 @@
                                                            PrevUpHomeNext
                                                            -
                                                            +

                                                            Exponential Integral Ei @@ -276,7 +276,7 @@



                                                            -

                                                            [5] +

                                                            [5] W. J. Cody and H. C. Thacher, Jr., Rational Chebyshev approximations for the exponential integral E1(x), Math. Comp. 22 (1968), 641-649, and W. J. Cody and H. C. Thacher, Jr., Chebyshev approximations for the exponential diff --git a/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html b/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html index 860fe2198..69a8e91c1 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html +++ b/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html @@ -3,7 +3,7 @@ Exponential Integral En - + @@ -22,7 +22,7 @@

                                                            PrevUpHomeNext
                                                            -
                                                            +

                                                            Exponential Integral En diff --git a/doc/sf_and_dist/html/math_toolkit/special/factorials.html b/doc/sf_and_dist/html/math_toolkit/special/factorials.html index afbfe939c..976b1c5b0 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/factorials.html +++ b/doc/sf_and_dist/html/math_toolkit/special/factorials.html @@ -3,7 +3,7 @@ Factorials and Binomial Coefficients - + @@ -22,7 +22,7 @@
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                                                            -
                                                            +

                                                            Factorials and Binomial Coefficients diff --git a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_binomial.html b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_binomial.html index ab2e86828..c525b11db 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_binomial.html +++ b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_binomial.html @@ -3,7 +3,7 @@ Binomial Coefficients - + @@ -22,7 +22,7 @@
                                                            PrevUpHomeNext
                                                            -
                                                            +

                                                            Binomial Coefficients diff --git a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_double_factorial.html b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_double_factorial.html index 4bca14404..779003b06 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_double_factorial.html +++ b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_double_factorial.html @@ -3,7 +3,7 @@ Double Factorial - + @@ -22,7 +22,7 @@
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                                                            -
                                                            +

                                                            Double Factorial diff --git a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_factorial.html b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_factorial.html index 6423810a7..d4731e140 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_factorial.html +++ b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_factorial.html @@ -3,7 +3,7 @@ Factorial - + @@ -22,7 +22,7 @@
                                                            PrevUpHomeNext
                                                            -
                                                            +
                                                            diff --git a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_falling_factorial.html b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_falling_factorial.html index ea18b8163..3dcb4d48a 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_falling_factorial.html +++ b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_falling_factorial.html @@ -3,7 +3,7 @@ Falling Factorial - + @@ -22,7 +22,7 @@
                                                            PrevUpHomeNext
                                                            -
                                                            +

                                                            Falling Factorial diff --git a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_rising_factorial.html b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_rising_factorial.html index e0eac8547..809abcd4d 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_rising_factorial.html +++ b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_rising_factorial.html @@ -3,7 +3,7 @@ Rising Factorial - + @@ -22,7 +22,7 @@
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                                                            -
                                                            +

                                                            Rising Factorial diff --git a/doc/sf_and_dist/html/math_toolkit/special/hankel.html b/doc/sf_and_dist/html/math_toolkit/special/hankel.html index d58d2ef64..c37dc139a 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/hankel.html +++ b/doc/sf_and_dist/html/math_toolkit/special/hankel.html @@ -3,7 +3,7 @@ Hankel Functions - + @@ -22,7 +22,7 @@
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                                                            -
                                                            +
                                                            diff --git a/doc/sf_and_dist/html/math_toolkit/special/hankel/cyl_hankel.html b/doc/sf_and_dist/html/math_toolkit/special/hankel/cyl_hankel.html index af879f979..b4e890ea8 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/hankel/cyl_hankel.html +++ b/doc/sf_and_dist/html/math_toolkit/special/hankel/cyl_hankel.html @@ -3,7 +3,7 @@ Cyclic Hankel Functions - + @@ -22,7 +22,7 @@
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                                                            -
                                                            +

                                                            Cyclic Hankel Functions diff --git a/doc/sf_and_dist/html/math_toolkit/special/hankel/sph_hankel.html b/doc/sf_and_dist/html/math_toolkit/special/hankel/sph_hankel.html index 4a7397aa0..7c0d69afa 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/hankel/sph_hankel.html +++ b/doc/sf_and_dist/html/math_toolkit/special/hankel/sph_hankel.html @@ -3,7 +3,7 @@ Spherical Hankel Functions - + @@ -22,7 +22,7 @@
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                                                            Spherical Hankel Functions diff --git a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper.html b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper.html index e221ad879..af3e29f01 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper.html +++ b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper.html @@ -3,7 +3,7 @@ Inverse Hyperbolic Functions - + @@ -22,7 +22,7 @@
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                                                            diff --git a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/acosh.html b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/acosh.html index 0d3e0ef0e..2140a9e04 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/acosh.html +++ b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/acosh.html @@ -3,7 +3,7 @@ acosh - + @@ -22,7 +22,7 @@
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                                                            diff --git a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/asinh.html b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/asinh.html index cba70a3d3..a1d386ffc 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/asinh.html +++ b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/asinh.html @@ -3,7 +3,7 @@ asinh - + @@ -22,7 +22,7 @@
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                                                            diff --git a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/atanh.html b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/atanh.html index 7825f4585..6df001bed 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/atanh.html +++ b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/atanh.html @@ -3,7 +3,7 @@ atanh - + @@ -22,7 +22,7 @@
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                                                            diff --git a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/inv_hyper_over.html b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/inv_hyper_over.html index 58876d95f..d6579df64 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/inv_hyper_over.html +++ b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/inv_hyper_over.html @@ -3,7 +3,7 @@ Inverse Hyperbolic Functions Overview - + @@ -22,7 +22,7 @@
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                                                            Inverse Hyperbolic Functions Overview diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi.html index d59b20c8f..3f7129dd1 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi.html @@ -3,7 +3,7 @@ Jacobi Elliptic Functions - + @@ -22,7 +22,7 @@
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                                                            diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jac_over.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jac_over.html index 3ccc76b4d..c89461767 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jac_over.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jac_over.html @@ -3,7 +3,7 @@ Overvew of the Jacobi Elliptic Functions - + @@ -22,7 +22,7 @@
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                                                            Overvew of the Jacobi Elliptic Functions @@ -40,15 +40,15 @@

                                                            Like all elliptic functions these can be parameterised in a number of ways:

                                                            -
                                                              -
                                                            • +
                                                                +
                                                              • In terms of a parameter m.
                                                              • -
                                                              • +
                                                              • In terms of the elliptic modulus k where m = k2.
                                                              • -
                                                              • +
                                                              • In terms of the modular angle α, where m = sin2α.
                                                              @@ -94,16 +94,16 @@



                                                              -

                                                              [2] +

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                                                              [3] +

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                                                              [4] +

                                                              diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cd.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cd.html index 57226b5d1..a8ff7ac01 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cd.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cd.html @@ -3,7 +3,7 @@ Jacobi Elliptic Function cd - + @@ -22,7 +22,7 @@
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                                                              Jacobi Elliptic Function cd diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cn.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cn.html index 34dfe4d3e..d2ead927a 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cn.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cn.html @@ -3,7 +3,7 @@ Jacobi Elliptic Function cn - + @@ -22,7 +22,7 @@
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                                                              Jacobi Elliptic Function cn diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cs.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cs.html index 13efdf21c..890854164 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cs.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_cs.html @@ -3,7 +3,7 @@ Jacobi Elliptic Function cs - + @@ -22,7 +22,7 @@
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                                                              Jacobi Elliptic Function cs diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_dc.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_dc.html index d480f38e0..ba4d98855 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_dc.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_dc.html @@ -3,7 +3,7 @@ Jacobi Elliptic Function dc - + @@ -22,7 +22,7 @@
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                                                              Jacobi Elliptic Function dc diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_dn.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_dn.html index e31f43c6b..0afcd41c3 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_dn.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_dn.html @@ -3,7 +3,7 @@ Jacobi Elliptic Function dn - + @@ -22,7 +22,7 @@
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                                                              Jacobi Elliptic Function dn diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_ds.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_ds.html index bee68eecc..81fa28194 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_ds.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_ds.html @@ -3,7 +3,7 @@ Jacobi Elliptic Function ds - + @@ -22,7 +22,7 @@
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                                                              Jacobi Elliptic Function ds diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_elliptic.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_elliptic.html index ad43f6938..fdf945765 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_elliptic.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_elliptic.html @@ -3,7 +3,7 @@ Jacobi Elliptic SN, CN and DN - + @@ -22,7 +22,7 @@
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                                                              Jacobi Elliptic SN, CN and DN diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_nc.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_nc.html index 9ac08efea..4d0137f48 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_nc.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_nc.html @@ -3,7 +3,7 @@ Jacobi Elliptic Function nc - + @@ -22,7 +22,7 @@
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                                                              Jacobi Elliptic Function nc diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_nd.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_nd.html index 9c2dfea8a..c094ae4e1 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_nd.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_nd.html @@ -3,7 +3,7 @@ Jacobi Elliptic Function nd - + @@ -22,7 +22,7 @@
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                                                              Jacobi Elliptic Function nd diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_ns.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_ns.html index 0a9e5ccfd..4ff7a5024 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_ns.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_ns.html @@ -3,7 +3,7 @@ Jacobi Elliptic Function ns - + @@ -22,7 +22,7 @@
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                                                              Jacobi Elliptic Function ns diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sc.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sc.html index 3f54eca54..2c4a68220 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sc.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sc.html @@ -3,7 +3,7 @@ Jacobi Elliptic Function sc - + @@ -22,7 +22,7 @@
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                                                              Jacobi Elliptic Function sc diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sd.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sd.html index 0a849d476..54233b2cc 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sd.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sd.html @@ -3,7 +3,7 @@ Jacobi Elliptic Function sd - + @@ -22,7 +22,7 @@
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                                                              Jacobi Elliptic Function sd diff --git a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sn.html b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sn.html index 59fc551e1..9ed44383d 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sn.html +++ b/doc/sf_and_dist/html/math_toolkit/special/jacobi/jacobi_sn.html @@ -3,7 +3,7 @@ Jacobi Elliptic Function sn - + @@ -22,7 +22,7 @@
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                                                              Jacobi Elliptic Function sn diff --git a/doc/sf_and_dist/html/math_toolkit/special/owens_t.html b/doc/sf_and_dist/html/math_toolkit/special/owens_t.html index 7feb0183b..a80c5feba 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/owens_t.html +++ b/doc/sf_and_dist/html/math_toolkit/special/owens_t.html @@ -3,7 +3,7 @@ Owen's T function - + @@ -22,7 +22,7 @@
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                                                              @@ -131,15 +131,15 @@ Test data was generated by Patefield and Tandy algorithms T1 and T4, and also the suggested reference routine T7.

                                                              -
                                                                -
                                                              • +
                                                                  +
                                                                • T1 was rejected if the result was too small compared to atan(a) (ie cancellation),
                                                                • -
                                                                • +
                                                                • T4 was rejected if there was no convergence,
                                                                • -
                                                                • +
                                                                • Both were rejected if they didn't agree.
                                                                @@ -181,8 +181,8 @@ The Patefield-Tandy algorithm is accurate to approximately 20 decimal places, so for types with greater precision we use:

                                                                -
                                                                  -
                                                                • +
                                                                    +
                                                                  • A modified version of T1 which folds the calculation of atan(h) into the T1 series (to avoid subtracting two values similar in magnitude), and then accelerates the resulting alternating series using method 1 @@ -191,15 +191,15 @@ but doesn't always converge, or may become too divergent in the first few terms to sum accurately. This is used for ah < 1.
                                                                  • -
                                                                  • +
                                                                  • A modified version of T2 which is accelerated in the same manner as T1. This is used for h > 1.
                                                                  • -
                                                                  • +
                                                                  • A version of T4 only when both T1 and T2 have failed to produce an accurate answer.
                                                                  • -
                                                                  • +
                                                                  • Fallback to the Patefiled Tandy algorithm when all the above methods fail: this happens not at all for our test data at 100 decimal digits precision. However, there is a difficult area when a diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers.html b/doc/sf_and_dist/html/math_toolkit/special/powers.html index d8846168e..19307c012 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/powers.html +++ b/doc/sf_and_dist/html/math_toolkit/special/powers.html @@ -3,7 +3,7 @@ Logs, Powers, Roots and Exponentials - + @@ -22,7 +22,7 @@
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                                                                    Logs, Powers, Roots and Exponentials diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/cbrt.html b/doc/sf_and_dist/html/math_toolkit/special/powers/cbrt.html index ec7e83fb0..15be4ffa1 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/powers/cbrt.html +++ b/doc/sf_and_dist/html/math_toolkit/special/powers/cbrt.html @@ -3,7 +3,7 @@ cbrt - + @@ -22,7 +22,7 @@
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                                                                    diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/ct_pow.html b/doc/sf_and_dist/html/math_toolkit/special/powers/ct_pow.html index d0ba301ee..af3573014 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/powers/ct_pow.html +++ b/doc/sf_and_dist/html/math_toolkit/special/powers/ct_pow.html @@ -3,7 +3,7 @@ Compile Time Power of a Runtime Base - + @@ -22,7 +22,7 @@
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                                                                    Compile Time Power of a Runtime Base @@ -99,16 +99,16 @@ The return type of these functions is computed using the result type calculation rules. For example:

                                                                    -
                                                                      -
                                                                    • +
                                                                        +
                                                                      • If T is a float, the return type is a float.
                                                                      • -
                                                                      • +
                                                                      • If T is a long double, the return type is a long double.
                                                                      • -
                                                                      • +
                                                                      • Otherwise, the return type is a double.
                                                                      @@ -129,12 +129,12 @@

                                                                      Two cases of errors can occur when using pow:

                                                                      -
                                                                        -
                                                                      • +
                                                                          +
                                                                        • In case of null base and negative exponent, an overflow_error occurs since this operation is a division by 0 (it equals to 1/0).
                                                                        • -
                                                                        • +
                                                                        • In case of null base and null exponent, an indeterminate_result_error occurs since the result of this operation is indeterminate. Those errors follow the general @@ -147,18 +147,18 @@ exception. As shown in the link given above, other error handling policies can be used:

                                                                          -
                                                                            -
                                                                          • +
                                                                              +
                                                                            • errno_on_error: Sets ::errno to ERANGE and returns std::numeric_limits<T>::infinity().
                                                                            • -
                                                                            • +
                                                                            • ignore_error: Returns std::numeric_limits<T>::infinity().
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                                                                            • +
                                                                            • user_error: Returns the result of boost::math::policies::user_overflow_error: this function must be defined by the user. @@ -169,18 +169,18 @@ which for this function returns 1 since it's the most commonly chosen result for a power of 0. Here again, other error handling policies can be used:

                                                                              -
                                                                                -
                                                                              • +
                                                                                  +
                                                                                • throw_on_error: Throws std::domain_error
                                                                                • -
                                                                                • +
                                                                                • errno_on_error: Sets ::errno to EDOM and returns 1.
                                                                                • -
                                                                                • +
                                                                                • user_error: Returns the result of boost::math::policies::user_indeterminate_result_error: this function must be defined by the user. diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/expm1.html b/doc/sf_and_dist/html/math_toolkit/special/powers/expm1.html index bf40bd584..414973e33 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/powers/expm1.html +++ b/doc/sf_and_dist/html/math_toolkit/special/powers/expm1.html @@ -3,7 +3,7 @@ expm1 - + @@ -22,7 +22,7 @@ -
                                                                                  +
                                                                                  diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/hypot.html b/doc/sf_and_dist/html/math_toolkit/special/powers/hypot.html index b68021b90..56a162888 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/powers/hypot.html +++ b/doc/sf_and_dist/html/math_toolkit/special/powers/hypot.html @@ -3,7 +3,7 @@ hypot - + @@ -22,7 +22,7 @@
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                                                                                  diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/log1p.html b/doc/sf_and_dist/html/math_toolkit/special/powers/log1p.html index 42ef6f4b8..3ed0735f8 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/powers/log1p.html +++ b/doc/sf_and_dist/html/math_toolkit/special/powers/log1p.html @@ -3,7 +3,7 @@ log1p - + @@ -22,7 +22,7 @@
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                                                                                  diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/powm1.html b/doc/sf_and_dist/html/math_toolkit/special/powers/powm1.html index 7db13eb64..04cb2a344 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/powers/powm1.html +++ b/doc/sf_and_dist/html/math_toolkit/special/powers/powm1.html @@ -3,7 +3,7 @@ powm1 - + @@ -22,7 +22,7 @@
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                                                                                  diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/sqrt1pm1.html b/doc/sf_and_dist/html/math_toolkit/special/powers/sqrt1pm1.html index a29ebc16e..bd73cda14 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/powers/sqrt1pm1.html +++ b/doc/sf_and_dist/html/math_toolkit/special/powers/sqrt1pm1.html @@ -3,7 +3,7 @@ sqrt1pm1 - + @@ -22,7 +22,7 @@
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                                                                                  diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_beta.html b/doc/sf_and_dist/html/math_toolkit/special/sf_beta.html index bdcc39c44..d97dbc9ca 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_beta.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_beta.html @@ -3,7 +3,7 @@ Beta Functions - + @@ -22,7 +22,7 @@
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                                                                                  diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_derivative.html b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_derivative.html index fd509f234..4afd714dc 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_derivative.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_derivative.html @@ -3,7 +3,7 @@ Derivative of the Incomplete Beta Function - + @@ -22,7 +22,7 @@
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                                                                                  Derivative of the Incomplete Beta Function diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_function.html b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_function.html index 07e9d8de5..2e6166c58 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_function.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_function.html @@ -3,7 +3,7 @@ Beta - + @@ -22,7 +22,7 @@
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                                                                                  diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_function.html b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_function.html index f0efafef7..d96fb135a 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_function.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_function.html @@ -3,7 +3,7 @@ Incomplete Beta Functions - + @@ -22,7 +22,7 @@
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                                                                                  Incomplete Beta Functions diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_inv_function.html b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_inv_function.html index 99772503c..a0d993c6e 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_inv_function.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_inv_function.html @@ -3,7 +3,7 @@ The Incomplete Beta Function Inverses - + @@ -22,7 +22,7 @@
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                                                                                  The Incomplete Beta Function Inverses @@ -305,8 +305,8 @@

                                                                                  There are two sets of tests:

                                                                                  -
                                                                                    -
                                                                                  • +
                                                                                      +
                                                                                    • Basic sanity checks attempt to "round-trip" from a, b and x to p or q and back again. These tests have quite generous @@ -317,7 +317,7 @@ enough "information content" in the input to the inverse function to get back where you started.
                                                                                    • -
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                                                                                    • Accuracy checks using high precision test values. These measure the accuracy of the result, given exact input values.
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                                                                                      diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_inv.html b/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_inv.html index 51855afb9..43f849fa3 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_inv.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_inv.html @@ -3,7 +3,7 @@ Error Function Inverses - + @@ -22,7 +22,7 @@
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                                                                                      There are two sets of tests:

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                                                                                        • Basic sanity checks attempt to "round-trip" from x to p and back again. These tests have quite generous tolerances: in general both the error functions and their inverses @@ -124,7 +124,7 @@ enough "information content" in the input to the inverse function to get back where you started.
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                                                                                        • Accuracy checks using high-precision test values. These measure the accuracy of the result, given exact input values.
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                                                                                          Derivative of the Incomplete Gamma Function diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_ratios.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_ratios.html index 4f9bc5445..04181110e 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_ratios.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_ratios.html @@ -3,7 +3,7 @@ Ratios of Gamma Functions - + @@ -22,7 +22,7 @@
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                                                                                          Ratios of Gamma Functions diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html index 7f5b6de56..a7f1dbce7 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html @@ -3,7 +3,7 @@ Incomplete Gamma Functions - + @@ -22,7 +22,7 @@
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                                                                                          Incomplete Gamma Functions @@ -1010,21 +1010,21 @@ References

                                                                                          -
                                                                                            -
                                                                                          • +
                                                                                              +
                                                                                            • N. M. Temme, A Set of Algorithms for the Incomplete Gamma Functions, Probability in the Engineering and Informational Sciences, 8, 1994.
                                                                                            • -
                                                                                            • +
                                                                                            • N. M. Temme, The Asymptotic Expansion of the Incomplete Gamma Functions, Siam J. Math Anal. Vol 10 No 4, July 1979, p757.
                                                                                            • -
                                                                                            • +
                                                                                            • A. R. Didonato and A. H. Morris, Computation of the Incomplete Gamma Function Ratios and their Inverse. ACM TOMS, Vol 12, No 4, Dec 1986, p377.
                                                                                            • -
                                                                                            • +
                                                                                            • W. Gautschi, The Incomplete Gamma Functions Since Tricomi, In Tricomi's Ideas and Contemporary Applied Mathematics, Atti dei Convegni Lincei, n. 147, Accademia Nazionale dei Lincei, Roma, 1998, pp. 203--237. diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma_inv.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma_inv.html index 0bb16cfd5..d72923af9 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma_inv.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma_inv.html @@ -3,7 +3,7 @@ Incomplete Gamma Function Inverses - + @@ -22,7 +22,7 @@
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                                                                                              Incomplete Gamma Function Inverses @@ -187,8 +187,8 @@

                                                                                              There are two sets of tests:

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                                                                                              • +
                                                                                                  +
                                                                                                • Basic sanity checks attempt to "round-trip" from a and x to p or q and back again. These tests have quite generous tolerances: in general @@ -199,7 +199,7 @@ content" in the input to the inverse function to get back where you started.
                                                                                                • -
                                                                                                • +
                                                                                                • Accuracy checks using high precision test values. These measure the accuracy of the result, given exact input values.
                                                                                                • diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/lgamma.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/lgamma.html index ca010d54b..5786ff3e8 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/lgamma.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/lgamma.html @@ -3,7 +3,7 @@ Log Gamma - + @@ -22,7 +22,7 @@
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                                                                                                  diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_poly.html b/doc/sf_and_dist/html/math_toolkit/special/sf_poly.html index c00562719..7be55ec5c 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_poly.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_poly.html @@ -3,7 +3,7 @@ Polynomials - + @@ -22,7 +22,7 @@
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                                                                                                  diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/laguerre.html b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/laguerre.html index 8a03a812e..290de0bc9 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/laguerre.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/laguerre.html @@ -3,7 +3,7 @@ Laguerre (and Associated) Polynomials - + @@ -22,7 +22,7 @@
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                                                                                                  Laguerre (and Associated) Polynomials diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/legendre.html b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/legendre.html index 03dbd1685..fc14a2831 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/legendre.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/legendre.html @@ -3,7 +3,7 @@ Legendre (and Associated) Polynomials - + @@ -22,7 +22,7 @@
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                                                                                                  Legendre (and Associated) Polynomials diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/sph_harm.html b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/sph_harm.html index d4b546cdb..0d2432d31 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/sph_harm.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/sph_harm.html @@ -3,7 +3,7 @@ Spherical Harmonics - + @@ -22,7 +22,7 @@
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                                                                                                  diff --git a/doc/sf_and_dist/html/math_toolkit/special/sinc.html b/doc/sf_and_dist/html/math_toolkit/special/sinc.html index e25f029e0..5b4a51d63 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sinc.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sinc.html @@ -3,7 +3,7 @@ Sinus Cardinal and Hyperbolic Sinus Cardinal Functions - + @@ -22,7 +22,7 @@
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                                                                                                  Sinus Cardinal and Hyperbolic Sinus Cardinal Functions diff --git a/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_overview.html b/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_overview.html index 4fcf71107..02932e9a6 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_overview.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_overview.html @@ -3,7 +3,7 @@ Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview - + @@ -22,7 +22,7 @@
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                                                                                                  Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview diff --git a/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_pi.html b/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_pi.html index 41f4533f4..5985d4f96 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_pi.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_pi.html @@ -3,7 +3,7 @@ sinc_pi - + @@ -22,7 +22,7 @@
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                                                                                                  diff --git a/doc/sf_and_dist/html/math_toolkit/special/zetas.html b/doc/sf_and_dist/html/math_toolkit/special/zetas.html index 27e872e53..b50621460 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/zetas.html +++ b/doc/sf_and_dist/html/math_toolkit/special/zetas.html @@ -3,7 +3,7 @@ Zeta Functions - + @@ -22,7 +22,7 @@
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                                                                                                  diff --git a/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html b/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html index 60facf14f..572d5742b 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html +++ b/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html @@ -3,7 +3,7 @@ Riemann Zeta Function - + @@ -22,7 +22,7 @@
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                                                                                                  diff --git a/doc/sf_and_dist/html/math_toolkit/status.html b/doc/sf_and_dist/html/math_toolkit/status.html index b495e4b7f..9bb9ff048 100644 --- a/doc/sf_and_dist/html/math_toolkit/status.html +++ b/doc/sf_and_dist/html/math_toolkit/status.html @@ -3,7 +3,7 @@ Library Status - + @@ -22,7 +22,7 @@
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                                                                                                  diff --git a/doc/sf_and_dist/html/math_toolkit/status/credits.html b/doc/sf_and_dist/html/math_toolkit/status/credits.html index 3501fde05..04dd3d92b 100644 --- a/doc/sf_and_dist/html/math_toolkit/status/credits.html +++ b/doc/sf_and_dist/html/math_toolkit/status/credits.html @@ -3,7 +3,7 @@ Credits and Acknowledgements - + @@ -22,7 +22,7 @@
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                                                                                                  diff --git a/doc/sf_and_dist/html/math_toolkit/status/history1.html b/doc/sf_and_dist/html/math_toolkit/status/history1.html index 0882530c4..bfe9794d8 100644 --- a/doc/sf_and_dist/html/math_toolkit/status/history1.html +++ b/doc/sf_and_dist/html/math_toolkit/status/history1.html @@ -3,7 +3,7 @@ History and What's New - + @@ -22,7 +22,7 @@
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                                                                                                  @@ -36,31 +36,27 @@ Boost-1.52

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                                                                                                    • Corrected moments for small degrees of freedom #7177 (reported by Thomas Mang). -
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                                                                                                    • Corrected failure to detect bad parameters in many distributions #6934 (reported by Florian Schoppmann) by adding a function check_out_of_range to test many possible bad parameters. This test revealed several distributions where the checks for bad parameters were ineffective, and these have been rectified.
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                                                                                                    • Fixed issue in Hankel functions that causes incorrect values to be returned for x < 0 and ν odd, see #7135.
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                                                                                                    • Fixed issues #6517, #6362, #7053, @@ -70,32 +66,32 @@
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                                                                                                      • Promoted math constants to be 1st class citizens, including convenient access to the most widely used built-in float, double, long double via three namespaces.
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                                                                                                      • Added the Owen's T function and Skew Normal distribution written by Benjamin Sobotta: see Owens T and skew_normal_distrib.
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                                                                                                      • Added Hankel functions cyl_hankel_1, cyl_hankel_2, sph_hankel_1 and sph_hankel_2.
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                                                                                                      • Corrected issue #6627 nonfinite_num_put formatting of 0.0 is incorrect based on a patch submitted by K R Walker.
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                                                                                                      • Changed constant initialization mechanism so that it is thread safe even for user-defined types, also so that user defined types get the full precision of the constant, even when long @@ -103,46 +99,46 @@ 128-bit rational approximations will work with UDT's and do the right thing, even though long double may be only 64 or 80 bits.
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                                                                                                      • Fixed issue in bessel_jy which causes Y8.5(4π) to yield a NaN.
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                                                                                                        • Deprecated wrongly named twothirds math constant in favour of two_thirds (with underscore separator). (issue #6199).
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                                                                                                        • Refactored test data and some special function code to improve support for arbitary precision and/or expression-template-enabled types.
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                                                                                                        • Added new faster zeta function evaluation method.

                                                                                                        Fixed issues:

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                                                                                                          • Corrected CDF complement for Laplace distribution (issue #6151).
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                                                                                                          • Corrected branch cuts on the complex inverse trig functions, to handle signed zeros (issue #6171).
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                                                                                                          • Fixed bug in bessel_yn which caused incorrect overflow errors to be raised for negative n (issue #6367).
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                                                                                                          • Also fixed minor/cosmetic/configuration issues #6120, #6191, #5982, @@ -153,356 +149,356 @@
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                                                                                                            • Added new series evaluation methods to the cyclic Bessel I, J, K and Y functions. Also taken great care to avoid spurious over and underflow of these functions. Fixes issue #5560
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                                                                                                            • Added an example of using Inverse Chi-Squared distribution for Bayesian statistics, provided by Thomas Mang.
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                                                                                                            • Corrected wrong out-of-bound uniform distribution CDF complement values #5733.
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                                                                                                                      • Fixed incorrect range and support for Rayleigh distribution.
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                                                                                                                      • Fixed numerical error in the quantile of the Student's T distribution: the function was returning garbage values for non-integer degrees of freedom between 2 and 3.
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                                                                                                                        • Significantly improved performance for the incomplete gamma function and its inverse.
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                                                                                                                          • -
                                                                                                                          • +
                                                                                                                          • Fixed bug in cyl_bessel_i that used an incorrect approximation for ν = 0.5, also effects the non-central Chi Square Distribution when ν = 3, see bug report #2877.
                                                                                                                          • -
                                                                                                                          • +
                                                                                                                          • Fixed minor bugs #2873.
                                                                                                                          - + Boost-1.38.0
                                                                                                                          -
                                                                                                                            -
                                                                                                                          • +
                                                                                                                              +
                                                                                                                            • Added Johan Råde's optimised floating point classification routines.
                                                                                                                            • -
                                                                                                                            • +
                                                                                                                            • Fixed code so that it compiles in GCC's -pedantic mode (bug report #1451).
                                                                                                                            - + Boost-1.37.0
                                                                                                                            -
                                                                                                                            • +
                                                                                                                              • Improved accuracy and testing of the inverse hypergeometric functions.
                                                                                                                              - + Boost-1.36.0
                                                                                                                              -
                                                                                                                                -
                                                                                                                              • +
                                                                                                                                  +
                                                                                                                                • Added Noncentral Chi Squared Distribution.
                                                                                                                                • -
                                                                                                                                • +
                                                                                                                                • Added Noncentral Beta Distribution.
                                                                                                                                • -
                                                                                                                                • +
                                                                                                                                • Added Noncentral F Distribution.
                                                                                                                                • -
                                                                                                                                • +
                                                                                                                                • Added Noncentral T Distribution.
                                                                                                                                • -
                                                                                                                                • +
                                                                                                                                • Added Exponential Integral Functions.
                                                                                                                                • -
                                                                                                                                • +
                                                                                                                                • Added Zeta Function.
                                                                                                                                • -
                                                                                                                                • +
                                                                                                                                • Added Rounding and Truncation functions.
                                                                                                                                • -
                                                                                                                                • +
                                                                                                                                • Added Compile time powers of runtime bases.
                                                                                                                                • -
                                                                                                                                • +
                                                                                                                                • Added SSE2 optimizations for Lanczos evaluation.
                                                                                                                                - + Boost-1.35.0: Post Review First Official Release
                                                                                                                                -
                                                                                                                                  -
                                                                                                                                • +
                                                                                                                                    +
                                                                                                                                  • Added Policy based framework that allows fine grained control over function behaviour.
                                                                                                                                  • -
                                                                                                                                  • +
                                                                                                                                  • Breaking change: Changed default behaviour for domain, pole and overflow errors to throw an exception (based on review feedback), this behaviour can be customised using Policy's.
                                                                                                                                  • -
                                                                                                                                  • +
                                                                                                                                  • Breaking change: Changed exception thrown when an internal evaluation error occurs to boost::math::evaluation_error.
                                                                                                                                  • -
                                                                                                                                  • +
                                                                                                                                  • Breaking change: Changed discrete quantiles to return an integer result: this is anything up to 20 times faster than finding the true root, this behaviour can be customised using Policy's.
                                                                                                                                  • -
                                                                                                                                  • +
                                                                                                                                  • Polynomial/rational function evaluation is now customisable and hopefully faster than before.
                                                                                                                                  • -
                                                                                                                                  • +
                                                                                                                                  • Added performance test program.
                                                                                                                                  - + Milestone 4: Second Review Candidate (1st March 2007)
                                                                                                                                  -
                                                                                                                                    -
                                                                                                                                  • +
                                                                                                                                      +
                                                                                                                                    • Moved Xiaogang Zhang's Bessel Functions code into the library, and brought them into line with the rest of the code.
                                                                                                                                    • -
                                                                                                                                    • +
                                                                                                                                    • Added C# "Distribution Explorer" demo application.
                                                                                                                                    - + Milestone 3: First Review Candidate (31st Dec 2006)
                                                                                                                                    -
                                                                                                                                      -
                                                                                                                                    • +
                                                                                                                                        +
                                                                                                                                      • Implemented the main probability distribution and density functions.
                                                                                                                                      • -
                                                                                                                                      • +
                                                                                                                                      • Implemented digamma.
                                                                                                                                      • -
                                                                                                                                      • +
                                                                                                                                      • Added more factorial functions.
                                                                                                                                      • -
                                                                                                                                      • +
                                                                                                                                      • Implemented the Hermite, Legendre and Laguerre polynomials plus the spherical harmonic functions from TR1.
                                                                                                                                      • -
                                                                                                                                      • +
                                                                                                                                      • Moved Xiaogang Zhang's elliptic integral code into the library, and brought them into line with the rest of the code.
                                                                                                                                      • -
                                                                                                                                      • +
                                                                                                                                      • Moved Hubert Holin's existing Boost.Math special functions into this library and brought them into line with the rest of the code.
                                                                                                                                      - + Milestone 2: Released September 10th 2006
                                                                                                                                      -
                                                                                                                                        -
                                                                                                                                      • +
                                                                                                                                          +
                                                                                                                                        • Implement preview release of the statistical distributions.
                                                                                                                                        • -
                                                                                                                                        • +
                                                                                                                                        • Added statistical distributions tutorial.
                                                                                                                                        • -
                                                                                                                                        • +
                                                                                                                                        • Implemented root finding algorithms.
                                                                                                                                        • -
                                                                                                                                        • +
                                                                                                                                        • Implemented the inverses of the incomplete gamma and beta functions.
                                                                                                                                        • -
                                                                                                                                        • +
                                                                                                                                        • Rewrite erf/erfc as rational approximations (valid to 128-bit precision).
                                                                                                                                        • -
                                                                                                                                        • +
                                                                                                                                        • Integrated the statistical results generated from the test data with Boost.Test: uses a database of expected results, indexed by test, floating point type, platform, and compiler.
                                                                                                                                        • -
                                                                                                                                        • +
                                                                                                                                        • Improved lgamma near 1 and 2 (rational approximations).
                                                                                                                                        • -
                                                                                                                                        • +
                                                                                                                                        • Improved erf/erfc inverses (rational approximations).
                                                                                                                                        • -
                                                                                                                                        • +
                                                                                                                                        • Implemented Rational function generation (the Remez method).
                                                                                                                                        - + Milestone 1: Released March 31st 2006
                                                                                                                                        -
                                                                                                                                          -
                                                                                                                                        • +
                                                                                                                                            +
                                                                                                                                          • Implement gamma/beta/erf functions along with their incomplete counterparts.
                                                                                                                                          • -
                                                                                                                                          • +
                                                                                                                                          • Generate high quality test data, against which future improvements can be judged.
                                                                                                                                          • -
                                                                                                                                          • +
                                                                                                                                          • Provide tools for the evaluation of infinite series, continued fractions, and rational functions.
                                                                                                                                          • -
                                                                                                                                          • +
                                                                                                                                          • Provide tools for testing against tabulated test data, and collecting statistics on error rates.
                                                                                                                                          • -
                                                                                                                                          • +
                                                                                                                                          • Provide sufficient docs for people to be able to find their way around the library.
                                                                                                                                          • diff --git a/doc/sf_and_dist/html/math_toolkit/status/issues.html b/doc/sf_and_dist/html/math_toolkit/status/issues.html index 8db1f4aa5..89453779a 100644 --- a/doc/sf_and_dist/html/math_toolkit/status/issues.html +++ b/doc/sf_and_dist/html/math_toolkit/status/issues.html @@ -3,7 +3,7 @@ Known Issues, and TODO List - + @@ -22,7 +22,7 @@
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                                                                                                  -

                                                                                                  -
                                                                                                  • +
                                                                                                    • Investigate Didonato and Morris' asymptotic expansion for large a and b (medium priority).
                                                                                                    @@ -61,7 +61,7 @@ Inverse Gamma

                                                                                                  -
                                                                                                  • +
                                                                                                    • Investigate whether we can skip iteration altogether if the first approximation is good enough (Medium Priority).
                                                                                                    @@ -69,7 +69,7 @@ Polynomials

                                                                                              -
                                                                                              • +
                                                                                                • The Legendre and Laguerre Polynomials have surprisingly different error rates on different platforms, considering they are evaluated with only basic arithmetic operations. Maybe this is telling us something, or maybe @@ -80,8 +80,8 @@ Elliptic Integrals

                                                                                          -
                                                                                            -
                                                                                          • +
                                                                                              +
                                                                                            • Carlson's algorithms are essentially unchanged from Xiaogang Zhang's Google Summer of Code student project, and are based on Carlson's original papers. However, Carlson has revised his algorithms since then (refer @@ -89,7 +89,7 @@ performance and accuracy, we may be able to take advantage of these improvements too (Low Priority).
                                                                                            • -
                                                                                            • +
                                                                                            • Carlson's algorithms (mainly RJ) are somewhat prone to internal overflow/underflow when the arguments are very large or small. The homogeneity relations:

                                                                                              RF(ka, @@ -100,27 +100,27 @@ be used to sidestep trouble here: provided the problem domains can be accurately identified. (Medium Priority).

                                                                                            • -
                                                                                            • +
                                                                                            • Carlson's RC can be reduced to elementary funtions (asin and log), would it be more efficient evaluated this way, rather than by Carlson's algorithms? (Low Priority).
                                                                                            • -
                                                                                            • +
                                                                                            • Should we add an implementation of Carlson's RG? It's not required for the Legendre form integrals, but some people may find it useful (Low Priority).
                                                                                            • -
                                                                                            • +
                                                                                            • There are a several other integrals: D(φ, k), Z(β, k), Λ0(β, k) and Bulirsch's el functions that could be implemented using Carlson's integrals (Low Priority).
                                                                                            • -
                                                                                            • +
                                                                                            • The integrals K(k) and E(k) could be implemented using rational approximations (both for efficiency and accuracy), assuming we can find them. (Medium Priority).
                                                                                            • -
                                                                                            • +
                                                                                            • There is a sub-domain of ellint_3 that is unimplemented (see the docs for details), currently it's not clear how to solve this issue, or if it's ever likely to be an real problem @@ -158,7 +158,7 @@ Statistical distributions

                                                                                          -
                                                                                          • +
                                                                                            • Student's t Perhaps switch to normal distribution as a better approximation for very large degrees of freedom?
                                                                                            @@ -1211,16 +1211,16 @@

                                                                                            Also asked for more than once:

                                                                                            -
                                                                                              -
                                                                                            • +
                                                                                                +
                                                                                              • Add support for interpolated distributions, possibly combine with numeric integration and differentiation.
                                                                                              • -
                                                                                              • +
                                                                                              • Add support for bivariate and multivariate distributions: most especially the normal.
                                                                                              • -
                                                                                              • +
                                                                                              • Add support for the log of the cdf and pdf: this is mainly a performance optimisation since we can avoid some special function calls for some distributions by returning the log of the result. diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit.html b/doc/sf_and_dist/html/math_toolkit/toolkit.html index 1c4e25aad..96082d2bd 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit.html @@ -3,7 +3,7 @@ Tools and Internal Details - + @@ -22,7 +22,7 @@
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                                                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1.html index fd6e571c9..60873ae56 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1.html @@ -3,7 +3,7 @@ Utilities & Tools - + @@ -22,7 +22,7 @@
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                                                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/cf.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/cf.html index a279c0e20..0168e4770 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/cf.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/cf.html @@ -3,7 +3,7 @@ Continued Fraction Evaluation - + @@ -22,7 +22,7 @@
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                                                                                                Continued Fraction Evaluation diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/minima.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/minima.html index 34dda3ffe..befe42724 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/minima.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/minima.html @@ -3,7 +3,7 @@ Locating Function Minima: Brent's algorithm - + @@ -22,7 +22,7 @@
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                                                                                                Locating Function Minima: Brent's algorithm diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/rational.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/rational.html index 972f42f95..c2d8ad689 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/rational.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/rational.html @@ -3,7 +3,7 @@ Polynomial and Rational Function Evaluation - + @@ -22,7 +22,7 @@
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                                                                                                Polynomial and Rational Function Evaluation diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots.html index a184684a3..e0293aac3 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots.html @@ -3,7 +3,7 @@ Root Finding With Derivatives: Newton-Raphson, Halley & Schroeder - + @@ -22,7 +22,7 @@
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                                                                                                +

                                                                                                Root Finding With Derivatives: Newton-Raphson, Halley & Schroeder @@ -67,12 +67,12 @@

                                                                                                These functions all perform iterative root finding using derivatives:

                                                                                                -
                                                                                                  -
                                                                                                • +
                                                                                                    +
                                                                                                  • newton_raphson_iterateperforms second order Newton-Raphson iteration,
                                                                                                  • -
                                                                                                  • +
                                                                                                  • halley_iterate andschroeder_iterate perform third order Halley and Schroeder iteration. @@ -130,48 +130,48 @@

                                                                                                    When using these functions you should note that:

                                                                                                    -
                                                                                                      -
                                                                                                    • +
                                                                                                        +
                                                                                                      • Default max_iter = (std::numeric_limits<boost::uintmax_t>::max)() is effectively 'iterate for ever'!.
                                                                                                      • -
                                                                                                      • +
                                                                                                      • They may be very sensitive to the initial guess, typically they converge very rapidly if the initial guess has two or three decimal digits correct. However convergence can be no better than bisection, or in some rare cases, even worse than bisection if the initial guess is a long way from the correct value and the derivatives are close to zero.
                                                                                                      • -
                                                                                                      • +
                                                                                                      • These functions include special cases to handle zero first (and second where appropriate) derivatives, and fall back to bisection in this case. However, it is helpful if functor F is defined to return an arbitrarily small value of the correct sign rather than zero.
                                                                                                      • -
                                                                                                      • +
                                                                                                      • If the derivative at the current best guess for the result is infinite (or very close to being infinite) then these functions may terminate prematurely. A large first derivative leads to a very small next step, triggering the termination condition. Derivative based iteration may not be appropriate in such cases.
                                                                                                      • -
                                                                                                      • +
                                                                                                      • If the function is 'Really Well Behaved' (monotonic and has only one root) the bracket bounds min and max may as well be set to the widest limits like zero and numeric_limits<T>::max().
                                                                                                      • -
                                                                                                      • +
                                                                                                      • But if the function more complex and may have more than one root or a pole, the choice of bounds is protection against jumping out to seek the 'wrong' root.
                                                                                                      • -
                                                                                                      • +
                                                                                                      • These functions fall back to bisection if the next computed step would take the next value out of bounds. The bounds are updated after each step to ensure this leads to convergence. However, a good initial guess backed up by asymptotically-tight bounds will improve performance no end - rather than relying on bisection.
                                                                                                      • -
                                                                                                      • +
                                                                                                      • The value of digits is crucial to good performance of these functions, if it is set too high then at best you will get one extra (unnecessary) iteration, and at worst the last few steps @@ -186,17 +186,17 @@ final iteration just takes the next value into the zone where f(x) becomes inaccurate.
                                                                                                      • -
                                                                                                      • +
                                                                                                      • To get the binary digits of accuracy, use policies::get_max_root_iterations<Policy>()).
                                                                                                      • -
                                                                                                      • +
                                                                                                      • If you need some diagnostic output to see what is going on, you can #define BOOST_MATH_INSTRUMENT before the #include <boost/math/tools/roots.hpp>, and also ensure that display of all the possibly significant digits with cout.precision(std::numeric_limits<double>::max_digits10): but be warned, this may produce copious output!
                                                                                                      • -
                                                                                                      • +
                                                                                                      • Finally: you may well be able to do better than these functions by hand-coding the heuristics used so that they are tailored to a specific function. You may also be able to compute the ratio of derivatives diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots2.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots2.html index 879879c5f..cfb6db2e0 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots2.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots2.html @@ -3,7 +3,7 @@ Root Finding Without Derivatives: Bisection, Bracket and TOMS748 - + @@ -22,7 +22,7 @@
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                                                                                                        Root Finding Without Derivatives: Bisection, Bracket and TOMS748 diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/series_evaluation.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/series_evaluation.html index 2c460c339..d0e25f72d 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/series_evaluation.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/series_evaluation.html @@ -3,7 +3,7 @@ Series Evaluation - + @@ -22,7 +22,7 @@
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                                                                                                        Series Evaluation @@ -99,14 +99,14 @@ value of the sum to which the terms of the series should be added. This is useful in two situations:

                                                                                                        -
                                                                                                          -
                                                                                                        • +
                                                                                                            +
                                                                                                          • Where the first value of the series has a different formula to successive terms. In this case the first value in the series can be passed as the last argument and the logic of the function object can then be simplified to return subsequent terms.
                                                                                                          • -
                                                                                                          • +
                                                                                                          • Where the series is being added (or subtracted) from some other value: termination of the series will likely occur much more rapidly if that other value is passed as the last argument. For example, there are diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/tuples.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/tuples.html index 6abafa641..5e6a6f348 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/tuples.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/tuples.html @@ -3,7 +3,7 @@ Tuples - + @@ -22,7 +22,7 @@
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                                                                                                            @@ -50,17 +50,17 @@

                                                                                                            These types and functions are aliases for:

                                                                                                            -
                                                                                                              -
                                                                                                            • +
                                                                                                                +
                                                                                                              • std::tuple etc when available, otherwise:
                                                                                                              • -
                                                                                                              • +
                                                                                                              • std::tr1::tuple etc when available, otherwise:
                                                                                                              • -
                                                                                                              • +
                                                                                                              • boost::fusion::tuple etc if the compiler supports it, otherwise:
                                                                                                              • -
                                                                                                              • +
                                                                                                              • boost::tuple.
                                                                                                              diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2.html index 5631caf84..8e9cf4cf7 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2.html @@ -3,7 +3,7 @@ Testing and Development - + @@ -22,7 +22,7 @@
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                                                                                                              diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/error_test.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/error_test.html index 12ed5329f..b611e43cd 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/error_test.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/error_test.html @@ -3,7 +3,7 @@ Relative Error and Testing - + @@ -22,7 +22,7 @@
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                                                                                                              Relative Error and Testing @@ -60,11 +60,11 @@

                                                                                                              In addition the value returned is zero if:

                                                                                                              -
                                                                                                                -
                                                                                                              • +
                                                                                                                  +
                                                                                                                • Both a and v are infinite.
                                                                                                                • -
                                                                                                                • +
                                                                                                                • Both a and v are denormalised numbers or zero.
                                                                                                                • diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html index 6f3af82aa..f718e22a9 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html @@ -3,7 +3,7 @@ Minimax Approximations and the Remez Algorithm - + @@ -22,7 +22,7 @@
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                                                                                                                  Minimax Approximations and the Remez Algorithm diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/polynomials.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/polynomials.html index 9e8c4af1e..8f78f3de8 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/polynomials.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/polynomials.html @@ -3,7 +3,7 @@ Polynomials - + @@ -22,7 +22,7 @@
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                                                                                                                  diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/test_data.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/test_data.html index c386da4c8..a74246b25 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/test_data.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/test_data.html @@ -3,7 +3,7 @@ Graphing, Profiling, and Generating Test Data for Special Functions - + @@ -22,7 +22,7 @@
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                                                                                                                  Graphing, Profiling, and Generating Test Data for Special Functions @@ -32,16 +32,16 @@ associated helper functions are designed so that in just a few lines of code you should be able to:

                                                                                                                  -
                                                                                                                    -
                                                                                                                  • +
                                                                                                                      +
                                                                                                                    • Profile a continued fraction, or infinite series for convergence and accuracy.
                                                                                                                    • -
                                                                                                                    • +
                                                                                                                    • Generate csv data from a special function that can be imported into your favorite graphing program (or spreadsheet) for further analysis.
                                                                                                                    • -
                                                                                                                    • +
                                                                                                                    • Generate high precision test data.
                                                                                                                    @@ -156,22 +156,22 @@

                                                                                                                    The functionality of test_data is split into the following parts:

                                                                                                                    -
                                                                                                                      -
                                                                                                                    • +
                                                                                                                        +
                                                                                                                      • A functor that implements the function for which data is being generated: this is the bit you have to write.
                                                                                                                      • -
                                                                                                                      • +
                                                                                                                      • One of more parameters that are to be passed to the functor, these are described in fairly abstract terms: give me N points distributed like this etc.
                                                                                                                      • -
                                                                                                                      • +
                                                                                                                      • The class test_data, that takes the functor and descriptions of the parameters and computes how ever many output points have been requested, these are stored in a sorted container.
                                                                                                                      • -
                                                                                                                      • +
                                                                                                                      • Routines to iterate over the test_data container and output the data in either csv format, or as C++ source code (as a table using Boost.Array).
                                                                                                                      • @@ -354,14 +354,14 @@

                                                                                                                        The first #define serves two purposes:

                                                                                                                        -
                                                                                                                          -
                                                                                                                        • +
                                                                                                                            +
                                                                                                                          • It reduces the file sizes considerably: all those static_cast's add up to a lot of bytes otherwise (they are needed to suppress compiler warnings when T is narrower than a long double).
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                                                                                                                          • It provides a useful customisation point: for example if we were testing a user-defined type that has more precision than a long double we could change it to: diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals_overview.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals_overview.html index a6902f02b..6c3055ed0 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals_overview.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals_overview.html @@ -3,7 +3,7 @@ Overview - + @@ -22,7 +22,7 @@
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                                                                                                                            diff --git a/doc/sf_and_dist/html/math_toolkit/using_udt.html b/doc/sf_and_dist/html/math_toolkit/using_udt.html index b88cd1eb9..8d0659f94 100644 --- a/doc/sf_and_dist/html/math_toolkit/using_udt.html +++ b/doc/sf_and_dist/html/math_toolkit/using_udt.html @@ -3,7 +3,7 @@ Use with User-Defined Floating-Point Types - + @@ -22,7 +22,7 @@
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                                                                                                                            Use with User-Defined Floating-Point Types diff --git a/doc/sf_and_dist/html/math_toolkit/using_udt/archetypes.html b/doc/sf_and_dist/html/math_toolkit/using_udt/archetypes.html index 177f6c448..c0daf12e0 100644 --- a/doc/sf_and_dist/html/math_toolkit/using_udt/archetypes.html +++ b/doc/sf_and_dist/html/math_toolkit/using_udt/archetypes.html @@ -3,7 +3,7 @@ Conceptual Archetypes for Reals and Distributions - + @@ -22,7 +22,7 @@
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                                                                                                                            Conceptual Archetypes for Reals and Distributions @@ -30,11 +30,11 @@

                                                                                                                            There are a few concept archetypes available:

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                                                                                                                              • Real concept for floating-point types.
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                                                                                                                              • distribution Concept for statistical distributions.
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                                                                                                                              Conceptual Requirements for Real Number Types @@ -977,21 +977,21 @@

                                                                                                                              Note that:

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                                                                                                                                1. The functions log_max_value and log_min_value can be synthesised from the others, and so no explicit specialisation is required.
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                                                                                                                                4. The function epsilon can be synthesised from the others, so no explicit specialisation is required provided the precision of RealType does not vary at runtime (see the header boost/math/bindings/rr.hpp for an example where the precision does vary at runtime).
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                                                                                                                                7. The functions digits, max_value and min_value, all get synthesised automatically from std::numeric_limits. However, if numeric_limits is not specialised for diff --git a/doc/sf_and_dist/html/math_toolkit/using_udt/dist_concept.html b/doc/sf_and_dist/html/math_toolkit/using_udt/dist_concept.html index 7c3c4e5f1..f06d86e76 100644 --- a/doc/sf_and_dist/html/math_toolkit/using_udt/dist_concept.html +++ b/doc/sf_and_dist/html/math_toolkit/using_udt/dist_concept.html @@ -3,7 +3,7 @@ Conceptual Requirements for Distribution Types - + @@ -22,7 +22,7 @@
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                                                                                                                                  Conceptual Requirements for Distribution Types diff --git a/doc/sf_and_dist/html/math_toolkit/using_udt/e_float.html b/doc/sf_and_dist/html/math_toolkit/using_udt/e_float.html index 907d017ae..dbef5e7be 100644 --- a/doc/sf_and_dist/html/math_toolkit/using_udt/e_float.html +++ b/doc/sf_and_dist/html/math_toolkit/using_udt/e_float.html @@ -3,7 +3,7 @@ e_float Support - + @@ -22,7 +22,7 @@
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                                                                                                                                  diff --git a/doc/sf_and_dist/html/math_toolkit/using_udt/use_mpfr.html b/doc/sf_and_dist/html/math_toolkit/using_udt/use_mpfr.html index 1e6c37b7a..89927f5a8 100644 --- a/doc/sf_and_dist/html/math_toolkit/using_udt/use_mpfr.html +++ b/doc/sf_and_dist/html/math_toolkit/using_udt/use_mpfr.html @@ -3,7 +3,7 @@ Using With MPFR / GMP - a High-Precision Floating-Point Library - + @@ -22,7 +22,7 @@
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                                                                                                                                  Using With MPFR / GMP - a High-Precision Floating-Point Library diff --git a/doc/sf_and_dist/html/math_toolkit/using_udt/use_ntl.html b/doc/sf_and_dist/html/math_toolkit/using_udt/use_ntl.html index a681ef2ca..0aa490474 100644 --- a/doc/sf_and_dist/html/math_toolkit/using_udt/use_ntl.html +++ b/doc/sf_and_dist/html/math_toolkit/using_udt/use_ntl.html @@ -3,7 +3,7 @@ Using With NTL - a High-Precision Floating-Point Library - + @@ -22,7 +22,7 @@
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                                                                                                                                  Using With NTL - a High-Precision Floating-Point Library diff --git a/doc/sf_and_dist/html/math_toolkit/utils.html b/doc/sf_and_dist/html/math_toolkit/utils.html index 4611ee2fc..286a21a80 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils.html +++ b/doc/sf_and_dist/html/math_toolkit/utils.html @@ -3,7 +3,7 @@ Floating Point Utilities - + @@ -22,7 +22,7 @@
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                                                                                                                                  diff --git a/doc/sf_and_dist/html/math_toolkit/utils/fp_facets.html b/doc/sf_and_dist/html/math_toolkit/utils/fp_facets.html index 345bf8dc3..57eb7aa7b 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/fp_facets.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/fp_facets.html @@ -3,7 +3,7 @@ Facets for Floating-Point Infinities and NaNs - + @@ -22,7 +22,7 @@
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                                                                                                                                  Facets for Floating-Point Infinities and NaNs diff --git a/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/examples.html b/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/examples.html index 3dc34039a..5f80192ea 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/examples.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/examples.html @@ -3,7 +3,7 @@ Examples - + @@ -22,7 +22,7 @@
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                                                                                                                                  @@ -57,7 +57,6 @@ // with the new locale containing the nonfinite_numput facet. // So the cout output will be "1.#INF on MS platforms // and may be "inf" or other string representation on other platforms. -

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                                                                                                                                    • A NaN ordinal sequence is a left-parenthesis character '(', followed by a digit sequence representing an integer n, where 1 <= n <= INT_MAX-1, followed by a right-parenthesis character ')'.
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                                                                                                                                    • The integer value, n, is determined by the fraction bits of the NaN argument value as follows:
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                                                                                                                                    • For a signalling NaN value, NaN fraction bits are reversed (left to right) to produce bits (right to left) of an even integer value, 2*n. Then formatted output functions produce a (signalling) NaN ordinal sequence corresponding to the integer value n.
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                                                                                                                                    • For a quiet NaN value, NaN fraction bits are reversed (left to right) to produce bits (right to left) of an odd integer value, 2*n-1. Then formatted output functions produce a (quiet) NaN ordinal sequence corresponding diff --git a/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/portability.html b/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/portability.html index dc1df4357..76c457042 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/portability.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/portability.html @@ -3,7 +3,7 @@ Portability - + @@ -22,7 +22,7 @@
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                                                                                                                                      diff --git a/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/rationale.html b/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/rationale.html index a9df3e892..ac9360cf9 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/rationale.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/rationale.html @@ -3,7 +3,7 @@ Design Rationale - + @@ -22,12 +22,12 @@
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                                                                                                                                        • The flags are implemented as a const data member of the facet. Facets are reference counted, and locales can share facets. Therefore changing the flags of a facet would have effects that are hard to predict. An @@ -38,7 +38,7 @@ file would have to be added to the library. It was judged be more desirable to have a headers only library, than to have mutable flags and manipulators.
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                                                                                                                                        • The facet nonfinite_num_put throws an exception when the trap_infinity or trap_nan flag is diff --git a/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/reference.html b/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/reference.html index b2866fb00..aae5801ac 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/reference.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/fp_facets/reference.html @@ -3,7 +3,7 @@ Reference - + @@ -22,7 +22,7 @@
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