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Merge changes from sandbox to documentation.

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Puts all Math docs in one big whole with separate chapters for each part.

[SVN r84294]
This commit is contained in:
John Maddock
2013-05-16 09:04:28 +00:00
parent 411ffe225e 510e145450
commit e7384331ae
1977 changed files with 82835 additions and 84969 deletions
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64
doc/Jamfile.v2
View File

@@ -4,6 +4,11 @@
# file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
using quickbook ;
using auto-index ;
import modules ;
path-constant images_location : html ;
path-constant here : . ;
xml math : math.qbk ;
boostbook standalone
@@ -12,6 +17,7 @@ boostbook standalone
:
# Path for links to Boost:
<xsl:param>boost.root=../../../..
<xsl:param>html.stylesheet=boostbook.css
# Some general style settings:
<xsl:param>table.footnote.number.format=1
@@ -21,12 +27,64 @@ boostbook standalone
# Use graphics not text for navigation:
<xsl:param>navig.graphics=1
# How far down we chunk nested sections, basically all of them:
<xsl:param>chunk.section.depth=1
<xsl:param>chunk.section.depth=10
# Don't put the first section on the same page as the TOC:
<xsl:param>chunk.first.sections=0
<xsl:param>chunk.first.sections=1
# How far down sections get TOC's
<xsl:param>toc.section.depth=1
<xsl:param>toc.section.depth=10
# Max depth in each TOC:
<xsl:param>toc.max.depth=4
# How far down we go with TOC's
<xsl:param>generate.section.toc.level=10
# Index on type:
<xsl:param>index.on.type=1
<xsl:param>boost.noexpand.chapter.toc=1
#<xsl:param>root.filename="sf_dist_and_tools"
#<xsl:param>graphicsize.extension=1
#<xsl:param>use.extensions=1
# PDF Options:
# TOC Generation: this is needed for FOP-0.9 and later:
<xsl:param>fop1.extensions=0
<format>pdf:<xsl:param>xep.extensions=1
# TOC generation: this is needed for FOP 0.2, but must not be set to zero for FOP-0.9!
<format>pdf:<xsl:param>fop.extensions=0
<format>pdf:<xsl:param>fop1.extensions=0
# No indent on body text:
<format>pdf:<xsl:param>body.start.indent=0pt
# Margin size:
<format>pdf:<xsl:param>page.margin.inner=0.5in
# Margin size:
<format>pdf:<xsl:param>page.margin.outer=0.5in
# Paper type = A4
<format>pdf:<xsl:param>paper.type=A4
# Yes, we want graphics for admonishments:
<xsl:param>admon.graphics=1
# Set this one for PDF generation *only*:
# default pnd graphics are awful in PDF form,
# better use SVG's instead:
<format>pdf:<xsl:param>admon.graphics.extension=".svg"
<format>pdf:<xsl:param>use.role.for.mediaobject=1
<format>pdf:<xsl:param>preferred.mediaobject.role=print
<format>pdf:<xsl:param>img.src.path=$(images_location)/
<format>pdf:<xsl:param>draft.mode="no"
<format>pdf:<xsl:param>boost.url.prefix=http://www.boost.org/doc/libs/release/libs/math/doc/html
<auto-index>on <format>pdf:<auto-index-internal>off
<format>html:<auto-index-internal>on
<auto-index-script>$(here)/index.idx
<auto-index-prefix>$(here)/../../..
#<auto-index-verbose>on
<quickbook-define>enable_index
<format>pdf:<xsl:param>index.on.type=1
;
install pdfinstall : standalone/<format>pdf : <location>. <install-type>PDF <name>math.pdf ;
explicit pdfinstall ;

2
doc/sf_and_dist/error.qbk → doc/background/error.qbk
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@@ -41,7 +41,7 @@ In other words: two implementations of the same function, whose
maximum relative errors differ by a factor of 2, can actually be accurate
to the same number of binary digits. You have been warned!
[#zero_error][h4 The Impossibility of Zero Error]
[h4:zero_error The Impossibility of Zero Error]
For many of the functions in this library, it is assumed that the error is
"effectively zero" if the computation can be done with a number of guard

20
doc/sf_and_dist/implementation.qbk → doc/background/implementation.qbk
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@@ -1,4 +1,4 @@
[section:implementation Additional Implementation Notes]
[section:sf_implementation Additional Implementation Notes]
The majority of the implementation notes are included with the documentation
of each function or distribution. The notes here are of a more general nature,
@@ -125,16 +125,16 @@ This implementation is believed to follow these proposals and to assist compatib
['ISO/IEC 9899:1999 Programming languages - C]
and with the
[@http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1836.pdf Draft Technical Report on C++ Library Extensions, 2005-06-24, section 5.2.1, paragraph 5].
[link math_toolkit.main_overview.error_handling See also domain_error].
[link math_toolkit.error_handling See also domain_error].
See __policy_ref for details of the error handling policies that should allow
a user to comply with any of these recommendations, as well as other behaviour.
See [link math_toolkit.main_overview.error_handling error handling]
See [link math_toolkit.error_handling error handling]
for a detailed explanation of the mechanism, and
[link math_toolkit.dist.stat_tut.weg.error_eg error_handling example]
[link math_toolkit.stat_tut.weg.error_eg error_handling example]
and
[@../../../example/error_handling_example.cpp error_handling_example.cpp]
[@../../example/error_handling_example.cpp error_handling_example.cpp]
[caution If you enable throw but do NOT have try & catch block,
then the program will terminate with an uncaught exception and probably abort.
@@ -146,7 +146,7 @@ However, for simplicity, this is not done for most examples.]
Functions that are not mathematically defined,
like the Cauchy mean, fail to compile by default.
A [link math_toolkit.policy.pol_ref.assert_undefined policy]
A [link math_toolkit.pol_ref.assert_undefined policy]
allows control of this.
If the policy is to permit undefined functions, then calling them
@@ -267,7 +267,7 @@ the most common usage, lower = -1, mode = 0 and upper = 1 would be more suitable
Some of the special functions in this library are implemented via
rational approximations. These are either taken from the literature,
or devised by John Maddock using
[link math_toolkit.toolkit.internals2.minimax our Remez code].
[link math_toolkit.internals2.minimax our Remez code].
Rational rather than Polynomial approximations are used to ensure
accuracy: polynomial approximations are often wonderful up to
@@ -541,8 +541,8 @@ If you fail to do this you will get XEP warnings in the log file like
[pre \[warning\]could not find any font family matching "Times New Roman"; replaced by Helvetica]
(html is the default so it is generated at math_toolkit\libs\math\doc\sf_and_dist\html\index.html
using command line >bjam -a > math_docs.log).
(html is the default so it is generated at libs\math\doc\html\index.html
using command line >bjam -a > math_toolkit.docs.log).
<!-- Sample configuration for Windows TrueType fonts. -->
is provided in the xep.xml downloaded, but the Windows TrueType fonts are commented out.
@@ -638,7 +638,7 @@ project of Jacob Voytko (whose work so far,
considerably enhanced and now reasonably mature and usable, by Paul A. Bristow,
is at .\boost-sandbox\SOC\2007\visualization).
[endsect] [/section:implementation Implementation Notes]
[endsect] [/section:sf_implementation Implementation Notes]
[/
Copyright 2006, 2007, 2010 John Maddock and Paul A. Bristow.

4
doc/sf_and_dist/lanczos.qbk → doc/background/lanczos.qbk
View File

@@ -50,8 +50,8 @@ notoriously hard problem, but even so, analytic combinations of Lanczos
approximations can make the difference between obtaining a valid result, or
simply garbage. Refer to the implementation notes for the __beta function for
an example of this method in practice. The incomplete
[link math_toolkit.special.sf_gamma.igamma gamma_p gamma] and
[link math_toolkit.special.sf_beta.ibeta_function beta] functions
[link math_toolkit.sf_gamma.igamma gamma_p gamma] and
[link math_toolkit.sf_beta.ibeta_function beta] functions
use similar analytic combinations of power terms, to combine gamma and beta
functions divided by large powers into single (simpler) expressions.

2
doc/sf_and_dist/references.qbk → doc/background/references.qbk
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@@ -103,7 +103,7 @@ discusses using Boost.Math in finance.
Robert Demming & Daniel J. Duffy, Introduction to the C++ Boost Libraries - Volume I - Foundations
and Volume II ISBN 978-94-91028-01-4, Advanced Libraries and Applications, ISBN 978-94-91028-02-1
(to be published in 2011).
discusses application of Boost.Math, especially in finance.]
discusses application of Boost.Math, especially in finance.
[endsect] [/section:references References]
[/

0
doc/sf_and_dist/remez.qbk → doc/background/remez.qbk
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18
doc/common_factor.html
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@@ -1,18 +0,0 @@
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
<head>
<meta http-equiv="refresh" content="0; URL=gcd/html/index.html">
</head>
<body>
Automatic redirection failed, please go to
<a href="gcd/html/index.html">gcd/html/index.html</a>
<P>Copyright&nbsp;Daryle Walker 2006</P>
<P>Distributed under the Boost Software License, Version 1.0. (See accompanying file <A href="../../../LICENSE_1_0.txt">
LICENSE_1_0.txt</A> or copy at <A href="http://www.boost.org/LICENSE_1_0.txt">www.boost.org/LICENSE_1_0.txt</A>).</P>
</body>
</html>

77
doc/complex/Jamfile.v2
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@@ -1,77 +0,0 @@
# Copyright John Maddock 2005. 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)
using quickbook ;
path-constant images_location : html ;
xml complex-tr1 : complex-tr1.qbk ;
boostbook standalone
:
complex-tr1
:
# Path for links to Boost:
<xsl:param>boost.root=../../../../..
# Some general style settings:
<xsl:param>table.footnote.number.format=1
<xsl:param>footnote.number.format=1
# HTML options first:
# Use graphics not text for navigation:
<xsl:param>navig.graphics=1
# How far down we chunk nested sections, basically all of them:
<xsl:param>chunk.section.depth=10
# Don't put the first section on the same page as the TOC:
<xsl:param>chunk.first.sections=1
# How far down sections get TOC's
<xsl:param>toc.section.depth=10
# Max depth in each TOC:
<xsl:param>toc.max.depth=4
# How far down we go with TOC's
<xsl:param>generate.section.toc.level=10
#<xsl:param>root.filename="sf_dist_and_tools"
# PDF Options:
# TOC Generation: this is needed for FOP-0.9 and later:
# <xsl:param>fop1.extensions=1
<format>pdf:<xsl:param>xep.extensions=1
# TOC generation: this is needed for FOP 0.2, but must not be set to zero for FOP-0.9!
<format>pdf:<xsl:param>fop.extensions=0
<format>pdf:<xsl:param>fop1.extensions=0
# No indent on body text:
<format>pdf:<xsl:param>body.start.indent=0pt
# Margin size:
<format>pdf:<xsl:param>page.margin.inner=0.5in
# Margin size:
<format>pdf:<xsl:param>page.margin.outer=0.5in
# Paper type = A4
<format>pdf:<xsl:param>paper.type=A4
# Yes, we want graphics for admonishments:
<xsl:param>admon.graphics=1
# Set this one for PDF generation *only*:
# default pnd graphics are awful in PDF form,
# better use SVG's instead:
<format>pdf:<xsl:param>admon.graphics.extension=".svg"
<format>pdf:<xsl:param>use.role.for.mediaobject=1
<format>pdf:<xsl:param>preferred.mediaobject.role=print
<format>pdf:<xsl:param>img.src.path=$(images_location)/
<format>pdf:<xsl:param>draft.mode="no"
;

43
doc/complex/complex-tr1.qbk
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@@ -1,36 +1,16 @@
[article Complex Number TR1 Algorithms
[quickbook 1.4]
[copyright 2005 John Maddock]
[purpose Complex number arithmetic]
[license
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 http://www.boost.org/LICENSE_1_0.txt])
]
[authors [Maddock, John]]
[category math]
[last-revision $Date: 2006-12-29 11:08:32 +0000 (Fri, 29 Dec 2006) $]
]
[def __effects [*Effects: ]]
[def __formula [*Formula: ]]
[def __exm1 '''<code>e<superscript>x</superscript> - 1</code>''']
[def __ex '''<code>e<superscript>x</superscript></code>''']
[def __te '''2&#x03B5;''']
[template tr1[] [@http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1836.pdf Technical Report on C++ Library Extensions]]
This manual is also available in
[@http://sourceforge.net/projects/boost/files/boost-docs/
printer friendly PDF format].
[section:inverse_complex Complex Number Inverse Trigonometric Functions]
[mathpart inverse_complex..Complex Number Functions]
The following complex number algorithms are the inverses of trigonometric functions currently
present in the C++ standard. Equivalents to these functions are part of the C99 standard, and
are part of the [tr1].
[section:implementation Implementation and Accuracy]
[section:complex_implementation Implementation and Accuracy]
Although there are deceptively simple formulae available for all of these functions, a naive
implementation that used these formulae would fail catastrophically for some input
@@ -41,11 +21,12 @@ Vol. 23, No. 3, September 1997. This means that the functions are well defined
complex number range, and produce accurate values even at the extremes of that range, where as a naive
formula would cause overflow or underflow to occur during the calculation, even though the result is
actually a representable value. The maximum theoretical relative error for all of these functions
is less than 9.5E for every machine-representable point in the complex plane. Please refer to
is less than 9.5[epsilon] for every machine-representable point in the complex plane. Please refer to
comments in the header files themselves and to the above mentioned paper for more information
on the implementation methodology.
[endsect]
[section:asin asin]
[h4 Header:]
@@ -59,7 +40,7 @@ on the implementation methodology.
__effects returns the inverse sine of the complex number z.
__formula [$../../images/asin.png]
__formula [$../images/asin.png]
[endsect]
@@ -76,7 +57,7 @@ __formula [$../../images/asin.png]
__effects returns the inverse cosine of the complex number z.
__formula [$../../images/acos.png]
__formula [$../images/acos.png]
[endsect]
@@ -93,7 +74,7 @@ __formula [$../../images/acos.png]
__effects returns the inverse tangent of the complex number z.
__formula [$../../images/atan.png]
__formula [$../images/atan.png]
[endsect]
@@ -110,7 +91,7 @@ __formula [$../../images/atan.png]
__effects returns the inverse hyperbolic sine of the complex number z.
__formula [$../../images/asinh.png]
__formula [$../images/asinh.png]
[endsect]
@@ -127,7 +108,7 @@ __formula [$../../images/asinh.png]
__effects returns the inverse hyperbolic cosine of the complex number z.
__formula [$../../images/acosh.png]
__formula [$../images/acosh.png]
[endsect]
@@ -144,11 +125,11 @@ __formula [$../../images/acosh.png]
__effects returns the inverse hyperbolic tangent of the complex number z.
__formula [$../../images/atanh.png]
__formula [$../images/atanh.png]
[endsect]
[section History]
[section:complex_history History]
* 2005/12/17: Added support for platforms with no meaningful numeric_limits<>::infinity().
* 2005/12/01: Initial version, added as part of the TR1 library.
@@ -156,7 +137,7 @@ __formula [$../../images/atanh.png]
[endsect]
[endsect]
[endmathpart]

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doc/complex/html/complex_number_tr1_algorithms/inverse_complex.html
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@@ -1,61 +0,0 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Complex Number Inverse Trigonometric Functions</title>
<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../index.html" title="Complex Number TR1 Algorithms">
<link rel="up" href="../index.html" title="Complex Number TR1 Algorithms">
<link rel="prev" href="../index.html" title="Complex Number TR1 Algorithms">
<link rel="next" href="inverse_complex/implementation.html" title="Implementation and Accuracy">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
<td align="center"><a href="../../../../../../index.html">Home</a></td>
<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td>
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
<td align="center"><a href="../../../../../../more/index.htm">More</a></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="../index.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="inverse_complex/implementation.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="complex_number_tr1_algorithms.inverse_complex"></a><a class="link" href="inverse_complex.html" title="Complex Number Inverse Trigonometric Functions">Complex
Number Inverse Trigonometric Functions</a>
</h2></div></div></div>
<div class="toc"><dl>
<dt><span class="section"><a href="inverse_complex/implementation.html">Implementation
and Accuracy</a></span></dt>
<dt><span class="section"><a href="inverse_complex/asin.html">asin</a></span></dt>
<dt><span class="section"><a href="inverse_complex/acos.html">acos</a></span></dt>
<dt><span class="section"><a href="inverse_complex/atan.html">atan</a></span></dt>
<dt><span class="section"><a href="inverse_complex/asinh.html">asinh</a></span></dt>
<dt><span class="section"><a href="inverse_complex/acosh.html">acosh</a></span></dt>
<dt><span class="section"><a href="inverse_complex/atanh.html">atanh</a></span></dt>
<dt><span class="section"><a href="inverse_complex/history.html">History</a></span></dt>
</dl></div>
<p>
The following complex number algorithms are the inverses of trigonometric functions
currently present in the C++ standard. Equivalents to these functions are part
of the C99 standard, and are part of the <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1836.pdf" target="_top">Technical
Report on C++ Library Extensions</a>.
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2005 John Maddock<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>
</div></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="../index.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="inverse_complex/implementation.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

63
doc/complex/html/complex_number_tr1_algorithms/inverse_complex/acos.html
View File

@@ -1,63 +0,0 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>acos</title>
<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="home" href="../../index.html" title="Complex Number TR1 Algorithms">
<link rel="up" href="../inverse_complex.html" title="Complex Number Inverse Trigonometric Functions">
<link rel="prev" href="asin.html" title="asin">
<link rel="next" href="atan.html" title="atan">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td>
<td align="center"><a href="../../../../../../../index.html">Home</a></td>
<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td>
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
<td align="center"><a href="../../../../../../../more/index.htm">More</a></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="asin.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../inverse_complex.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="atan.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h3 class="title">
<a name="complex_number_tr1_algorithms.inverse_complex.acos"></a><a class="link" href="acos.html" title="acos">acos</a>
</h3></div></div></div>
<a name="complex_number_tr1_algorithms.inverse_complex.acos.header_"></a><h5>
<a name="id996888"></a>
<a class="link" href="acos.html#complex_number_tr1_algorithms.inverse_complex.acos.header_">Header:</a>
</h5>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">complex</span><span class="special">/</span><span class="identifier">acos</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
</pre>
<a name="complex_number_tr1_algorithms.inverse_complex.acos.synopsis_"></a><h5>
<a name="id996955"></a>
<a class="link" href="acos.html#complex_number_tr1_algorithms.inverse_complex.acos.synopsis_">Synopsis:</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">acos</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">z</span><span class="special">);</span>
</pre>
<p>
<span class="bold"><strong>Effects: </strong></span> returns the inverse cosine of
the complex number z.
</p>
<p>
<span class="bold"><strong>Formula: </strong></span> <span class="inlinemediaobject"><img src="../../../../images/acos.png" alt="acos"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2005 John Maddock<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>
</div></td>
</tr></table>
<hr>
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<a name="complex_number_tr1_algorithms.inverse_complex.acosh"></a><a class="link" href="acosh.html" title="acosh">acosh</a>
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<a name="complex_number_tr1_algorithms.inverse_complex.acosh.header_"></a><h5>
<a name="id997539"></a>
<a class="link" href="acosh.html#complex_number_tr1_algorithms.inverse_complex.acosh.header_">Header:</a>
</h5>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">complex</span><span class="special">/</span><span class="identifier">acosh</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
</pre>
<a name="complex_number_tr1_algorithms.inverse_complex.acosh.synopsis_"></a><h5>
<a name="id997606"></a>
<a class="link" href="acosh.html#complex_number_tr1_algorithms.inverse_complex.acosh.synopsis_">Synopsis:</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">acosh</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">z</span><span class="special">);</span>
</pre>
<p>
<span class="bold"><strong>Effects: </strong></span> returns the inverse hyperbolic
cosine of the complex number z.
</p>
<p>
<span class="bold"><strong>Formula: </strong></span> <span class="inlinemediaobject"><img src="../../../../images/acosh.png" alt="acosh"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2005 John Maddock<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>
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<a name="complex_number_tr1_algorithms.inverse_complex.asin"></a><a class="link" href="asin.html" title="asin">asin</a>
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<a name="complex_number_tr1_algorithms.inverse_complex.asin.header_"></a><h5>
<a name="id996670"></a>
<a class="link" href="asin.html#complex_number_tr1_algorithms.inverse_complex.asin.header_">Header:</a>
</h5>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">complex</span><span class="special">/</span><span class="identifier">asin</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
</pre>
<a name="complex_number_tr1_algorithms.inverse_complex.asin.synopsis_"></a><h5>
<a name="id996738"></a>
<a class="link" href="asin.html#complex_number_tr1_algorithms.inverse_complex.asin.synopsis_">Synopsis:</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">asin</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">z</span><span class="special">);</span>
</pre>
<p>
<span class="bold"><strong>Effects: </strong></span> returns the inverse sine of the
complex number z.
</p>
<p>
<span class="bold"><strong>Formula: </strong></span> <span class="inlinemediaobject"><img src="../../../../images/asin.png" alt="asin"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2005 John Maddock<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>
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63
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<div class="titlepage"><div><div><h3 class="title">
<a name="complex_number_tr1_algorithms.inverse_complex.asinh"></a><a class="link" href="asinh.html" title="asinh">asinh</a>
</h3></div></div></div>
<a name="complex_number_tr1_algorithms.inverse_complex.asinh.header_"></a><h5>
<a name="id997322"></a>
<a class="link" href="asinh.html#complex_number_tr1_algorithms.inverse_complex.asinh.header_">Header:</a>
</h5>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">complex</span><span class="special">/</span><span class="identifier">asinh</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
</pre>
<a name="complex_number_tr1_algorithms.inverse_complex.asinh.synopsis_"></a><h5>
<a name="id997389"></a>
<a class="link" href="asinh.html#complex_number_tr1_algorithms.inverse_complex.asinh.synopsis_">Synopsis:</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">asinh</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">z</span><span class="special">);</span>
</pre>
<p>
<span class="bold"><strong>Effects: </strong></span> returns the inverse hyperbolic
sine of the complex number z.
</p>
<p>
<span class="bold"><strong>Formula: </strong></span> <span class="inlinemediaobject"><img src="../../../../images/asinh.png" alt="asinh"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2005 John Maddock<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>
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63
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<div class="titlepage"><div><div><h3 class="title">
<a name="complex_number_tr1_algorithms.inverse_complex.atan"></a><a class="link" href="atan.html" title="atan">atan</a>
</h3></div></div></div>
<a name="complex_number_tr1_algorithms.inverse_complex.atan.header_"></a><h5>
<a name="id997105"></a>
<a class="link" href="atan.html#complex_number_tr1_algorithms.inverse_complex.atan.header_">Header:</a>
</h5>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">complex</span><span class="special">/</span><span class="identifier">atan</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
</pre>
<a name="complex_number_tr1_algorithms.inverse_complex.atan.synopsis_"></a><h5>
<a name="id997172"></a>
<a class="link" href="atan.html#complex_number_tr1_algorithms.inverse_complex.atan.synopsis_">Synopsis:</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">atan</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">z</span><span class="special">);</span>
</pre>
<p>
<span class="bold"><strong>Effects: </strong></span> returns the inverse tangent of
the complex number z.
</p>
<p>
<span class="bold"><strong>Formula: </strong></span> <span class="inlinemediaobject"><img src="../../../../images/atan.png" alt="atan"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2005 John Maddock<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>
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63
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<div class="section" lang="en">
<div class="titlepage"><div><div><h3 class="title">
<a name="complex_number_tr1_algorithms.inverse_complex.atanh"></a><a class="link" href="atanh.html" title="atanh">atanh</a>
</h3></div></div></div>
<a name="complex_number_tr1_algorithms.inverse_complex.atanh.header_"></a><h5>
<a name="id997756"></a>
<a class="link" href="atanh.html#complex_number_tr1_algorithms.inverse_complex.atanh.header_">Header:</a>
</h5>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">complex</span><span class="special">/</span><span class="identifier">atanh</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
</pre>
<a name="complex_number_tr1_algorithms.inverse_complex.atanh.synopsis_"></a><h5>
<a name="id997824"></a>
<a class="link" href="atanh.html#complex_number_tr1_algorithms.inverse_complex.atanh.synopsis_">Synopsis:</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">atanh</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">z</span><span class="special">);</span>
</pre>
<p>
<span class="bold"><strong>Effects: </strong></span> returns the inverse hyperbolic
tangent of the complex number z.
</p>
<p>
<span class="bold"><strong>Formula: </strong></span> <span class="inlinemediaobject"><img src="../../../../images/atanh.png" alt="atanh"></span>
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
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2005/12/17: Added support for platforms with no meaningful numeric_limits&lt;&gt;::infinity().
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2005/12/01: Initial version, added as part of the TR1 library.
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<p>
Although there are deceptively simple formulae available for all of these
functions, a naive implementation that used these formulae would fail catastrophically
for some input values. The Boost versions of these functions have been implemented
using the methodology described in "Implementing the Complex Arcsine
and Arccosine Functions Using Exception Handling" by T. E. Hull Thomas
F. Fairgrieve and Ping Tak Peter Tang, ACM Transactions on Mathematical Software,
Vol. 23, No. 3, September 1997. This means that the functions are well defined
over the entire complex number range, and produce accurate values even at
the extremes of that range, where as a naive formula would cause overflow
or underflow to occur during the calculation, even though the result is actually
a representable value. The maximum theoretical relative error for all of
these functions is less than 9.5E for every machine-representable point in
the complex plane. Please refer to comments in the header files themselves
and to the above mentioned paper for more information on the implementation
methodology.
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<a name="complex_number_tr1_algorithms"></a>Complex Number TR1 Algorithms</h2></div>
<div><div class="authorgroup"><div class="author"><h3 class="author">
<span class="firstname">John</span> <span class="surname">Maddock</span>
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<div><p class="copyright">Copyright &#169; 2005 John Maddock</p></div>
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<a name="id996589"></a><p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
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<dl>
<dt><span class="section"><a href="complex_number_tr1_algorithms/inverse_complex.html">Complex
Number Inverse Trigonometric Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="complex_number_tr1_algorithms/inverse_complex/implementation.html">Implementation
and Accuracy</a></span></dt>
<dt><span class="section"><a href="complex_number_tr1_algorithms/inverse_complex/asin.html">asin</a></span></dt>
<dt><span class="section"><a href="complex_number_tr1_algorithms/inverse_complex/acos.html">acos</a></span></dt>
<dt><span class="section"><a href="complex_number_tr1_algorithms/inverse_complex/atan.html">atan</a></span></dt>
<dt><span class="section"><a href="complex_number_tr1_algorithms/inverse_complex/asinh.html">asinh</a></span></dt>
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<dt><span class="section"><a href="complex_number_tr1_algorithms/inverse_complex/atanh.html">atanh</a></span></dt>
<dt><span class="section"><a href="complex_number_tr1_algorithms/inverse_complex/history.html">History</a></span></dt>
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This manual is also available in <a href="http://sourceforge.net/projects/boost/files/boost-docs/" target="_top">printer
friendly PDF format</a>.
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56
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View File

@@ -134,8 +134,8 @@ Ultimately these facilities should be provided by GCC and libstdc++.
The special functions and tools in this library can be used with
[@http://www.mpfr.org MPFR] (an arbitrary precision number type based on the __GMP),
either via the bindings in [@../../../../../boost/math/bindings/mpfr.hpp boost/math/bindings/mpfr.hpp],
or via [@../../../../../boost/math/bindings/mpfr.hpp boost/math/bindings/mpreal.hpp].
either via the bindings in [@../../../../boost/math/bindings/mpfr.hpp boost/math/bindings/mpfr.hpp],
or via [@../../../../boost/math/bindings/mpfr.hpp boost/math/bindings/mpreal.hpp].
[*New projects are recommended to use __multiprecision with GMP/MPFR backend instead.]
@@ -147,8 +147,8 @@ or [@http://www.holoborodko.com/pavel/mpfr/ mpfr-C++ (mpreal)].
Unfortunately neither `mpfr_class` nor `mpreal` quite satisfy our conceptual requirements,
so there is a very thin set of additional interfaces and some helper traits defined in
[@../../../../../boost/math/bindings/mpfr.hpp boost/math/bindings/mpfr.hpp] and
[@../../../../../boost/math/bindings/mpreal.hpp boost/math/bindings/mpreal.hpp]
[@../../../../boost/math/bindings/mpfr.hpp boost/math/bindings/mpfr.hpp] and
[@../../../../boost/math/bindings/mpreal.hpp boost/math/bindings/mpreal.hpp]
that you should use in place of including 'gmpfrxx.h' or 'mpreal.h' directly.
The classes `mpfr_class` or `mpreal` are
then usable unchanged once this header is included, so for example `mpfr_class`'s
@@ -186,8 +186,8 @@ up to approximately 3e-113. This therefore sets the upper limit for accuracy
to the majority of functions defined this library when used with either `mpfr_class` or `mpreal`.
There is a concept checking test program for mpfr support
[@../../../../../libs/math/test/mpfr_concept_check.cpp here] and
[@../../../../../libs/math/test/mpreal_concept_check.cpp here].
[@../../../../libs/math/test/mpfr_concept_check.cpp here] and
[@../../../../libs/math/test/mpreal_concept_check.cpp here].
[endsect] [/section:use_mpfr Using With MPFR / GMP - a High-Precision Floating-Point Library]
@@ -204,7 +204,7 @@ this type is a thin wrapper class around ::e_float which provides the necessary
syntactic sugar to make everything "just work".
There is also a concept checking test program for e_float support
[@../../../../../libs/math/test/e_float_concept_check.cpp here].
[@../../../../libs/math/test/e_float_concept_check.cpp here].
[*New projects are recommended to use __multiprecision with `cpp_float` backend instead.]
@@ -215,7 +215,7 @@ There is also a concept checking test program for e_float support
[@http://shoup.net/ntl/doc/RR.txt NTL::RR]
(an arbitrarily-fixed precision floating-point number type),
can be used via the bindings in
[@../../../../../boost/math/bindings/rr.hpp boost/math/bindings/rr.hpp].
[@../../../../boost/math/bindings/rr.hpp boost/math/bindings/rr.hpp].
For details, see [@http://shoup.net/ntl/ NTL: A Library for doing Number Theory by
Victor Shoup].
@@ -223,7 +223,7 @@ Victor Shoup].
Unfortunately `NTL::RR` doesn't quite satisfy our conceptual requirements,
so there is a very thin wrapper class `boost::math::ntl::RR` defined in
[@../../../../../boost/math/bindings/rr.hpp boost/math/bindings/rr.hpp] that you
[@../../../../boost/math/bindings/rr.hpp boost/math/bindings/rr.hpp] that you
should use in place of `NTL::RR`. The class is intended to be a drop-in
replacement for the "real" NTL::RR that adds some syntactic sugar to keep
this library happy, plus some of the standard library functions not implemented
@@ -235,7 +235,7 @@ up to approximately 3e-113. This therefore sets the upper limit for accuracy
to the majority of functions defined this library when used with `NTL::RR`.
There is a concept checking test program for NTL support
[@../../../../../libs/math/test/ntl_concept_check.cpp here].
[@../../../../libs/math/test/ntl_concept_check.cpp here].
[endsect] [/section:use_ntl Using With NTL - a High-Precision Floating-Point Library]
@@ -255,7 +255,7 @@ you will need to override the default `boost::multiprecision::et_on` with
[expression_template_1]
A full example code is at [@../../../example/test_cpp_float_close_fraction.cpp test_cpp_float_close_fraction.cpp]
A full example code is at [@../../example/test_cpp_float_close_fraction.cpp test_cpp_float_close_fraction.cpp]
[endsect] [/section:using_test Using without expression templates for Boost.Test and others]
@@ -269,7 +269,7 @@ any type /RealType/ that meets the conceptual requirements given below. All
the built-in floating-point types will meet these requirements.
User-defined types that meet the requirements can also be used.
For example, with [link math_toolkit.using_udt.high_precision.use_ntl a thin wrapper class]
For example, with [link math_toolkit.high_precision.use_ntl a thin wrapper class]
one of the types provided with [@http://shoup.net/ntl/ NTL (RR)] can be used.
But now that __multiprecision library is available,
this has become the reference real number type.
@@ -357,7 +357,7 @@ synthesised from the others, and so no explicit specialisation is required.
# 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 boost/math/bindings/rr.hpp]
[@../../../../boost/math/bindings/rr.hpp boost/math/bindings/rr.hpp]
for an example where the precision does vary at runtime).
# The functions `digits`, `max_value` and `min_value`, all get synthesised
automatically from `std::numeric_limits`. However, if `numeric_limits`
@@ -365,7 +365,7 @@ is not specialised for type RealType, then you will get a compiler error
when code tries to use these functions, /unless/ you explicitly specialise them.
For example if the precision of RealType varies at runtime, then
`numeric_limits` support may not be appropriate, see
[@../../../../../boost/math/bindings/rr.hpp boost/math/bindings/rr.hpp] for examples.
[@../../../../boost/math/bindings/rr.hpp boost/math/bindings/rr.hpp] for examples.
[warning
If `std::numeric_limits<>` is *not specialized*
@@ -436,15 +436,15 @@ argument-dependent-lookup can take place.
In addition, for efficient and accurate results, a __lanczos is highly desirable.
You may be able to adapt an existing approximation from
[@../../../../../boost/math/special_functions/lanczos.hpp
[@../../../../boost/math/special_functions/lanczos.hpp
boost/math/special_functions/lanczos.hpp] or
[@../../../../../boost/math/bindings/detail/big_lanczos.hpp
[@../../../../boost/math/bindings/detail/big_lanczos.hpp
boost/math/bindings/detail/big_lanczos.hpp]:
in the former case you will need change
static_cast's to lexical_cast's, and the constants to /strings/
(in order to ensure the coefficients aren't truncated to long double)
and then specialise `lanczos_traits` for type T. Otherwise you may have to hack
[@../../../tools/lanczos_generator.cpp
[@../../tools/lanczos_generator.cpp
libs/math/tools/lanczos_generator.cpp] to find a suitable
approximation for your RealType. The code will still compile if you don't do
this, but both accuracy and efficiency will be greatly compromised in any
@@ -459,8 +459,8 @@ requirements, and encapsulates a statistical distribution.
Please note that this documentation should not be used as a substitute
for the
[link math_toolkit.dist.dist_ref reference documentation], and
[link math_toolkit.dist.stat_tut tutorial] of the statistical
[link math_toolkit.dist_ref reference documentation], and
[link math_toolkit.stat_tut tutorial] of the statistical
distributions.
In the following table, /d/ is an object of type `DistributionType`,
@@ -543,7 +543,7 @@ been brought into the current scope with a using declaration.
[h6 Testing the real concept]
There is a test program
[@../../../test/std_real_concept_check.cpp libs/math/test/std_real_concept_check.cpp]
[@../../test/std_real_concept_check.cpp libs/math/test/std_real_concept_check.cpp]
that instantiates every template in this library with type
`std_real_concept` to verify its usage of standard library functions.
@@ -558,7 +558,7 @@ that instantiates every template in this library with type
}}} // namespaces
`real_concept` is an archetype for
[link math_toolkit.using_udt.concepts user defined real types],
[link math_toolkit.concepts user defined real types],
it declares its standard library functions in its own
namespace: these will only be found if they are called unqualified
allowing argument dependent lookup to locate them. In addition
@@ -566,11 +566,11 @@ this type is useable at runtime:
this allows code that would not otherwise be exercised by the built-in
floating point types to be tested. There is no std::numeric_limits<>
support for this type, since numeric_limits is not a conceptual requirement
for [link math_toolkit.using_udt.concepts RealType]s.
for [link math_toolkit.concepts RealType]s.
NTL RR is an example of a type meeting the requirements that this type
models, but note that use of a thin wrapper class is required: refer to
[linkmath_toolkit.using_udt.high_precision.use_ntl "Using With NTL - a High-Precision Floating-Point Library"].
[link math_toolkit.high_precision.use_ntl "Using With NTL - a High-Precision Floating-Point Library"].
There is no specific test case for type `real_concept`, instead, since this
type is usable at runtime, each individual test case as well as testing
@@ -595,23 +595,23 @@ Distribution Concept models statistical distributions.
}}} // namespaces
The class template `distribution_archetype` is a model of the
[link math_toolkit.using_udt.dist_concept Distribution concept].
[link math_toolkit.dist_concept Distribution concept].
The class template `DistributionConcept` is a
[@../../../../../libs/concept_check/index.html concept checking class]
[@../../../../libs/concept_check/index.html concept checking class]
for distribution types.
[h6 Testing the distribution concept]
The test program
[@../../../test/compile_test/distribution_concept_check.cpp distribution_concept_check.cpp]
[@../../test/compile_test/distribution_concept_check.cpp distribution_concept_check.cpp]
is responsible for using `DistributionConcept` to verify that all the
distributions in this library conform to the
[link math_toolkit.using_udt.dist_concept Distribution concept].
[link math_toolkit.dist_concept Distribution concept].
The class template `DistributionConcept` verifies the existence
(but not proper function) of the non-member accessors
required by the [link math_toolkit.using_udt.dist_concept Distribution concept].
required by the [link math_toolkit.dist_concept Distribution concept].
These are checked by calls like
v = pdf(dist, x); // (Result v is ignored).

22
doc/sf_and_dist/constants.qbk → doc/constants/constants.qbk
View File

@@ -1,6 +1,8 @@
[section:constants Mathematical Constants]
[section:intro Introduction]
[mathpart constants..Mathematical Constants]
[section:constants_intro Introduction]
Boost.Math provides a collection of mathematical constants.
@@ -8,7 +10,7 @@ Boost.Math provides a collection of 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 [link math_toolkit.constants.tutorial.non_templ use in non-template code]!)
(If that's all you want, jump direct to [link math_toolkit.tutorial.non_templ 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.
@@ -19,7 +21,7 @@ chosen floating-point type
* Less risk of inaccurate result from functions pow, trig and log at [@http://en.wikipedia.org/wiki/Corner_case corner cases].
* Less risk of [@http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html cancellation error].
* Portable - as possible between different systems using different floating-point precisions:
see [link math_toolkit.constants.tutorial.templ use in template code].
see [link math_toolkit.tutorial.templ use in template code].
* Tested - by comparison with other published sources, or separately computed at long double precision.
* Faster - can avoid (re-)calculation at runtime.
* If the value returned is a builtin type then it's returned by value as a `constexpr` (C++11 feature, if available).
@@ -64,9 +66,9 @@ we could have written instead:
Likewise, constants that are suitable for use at `long double` precision
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].
You can see the full list of available constants at [link math_toolkit.constants].
Some examples of using constants are at [@../../../example/constants_eg1.cpp constants_eg1].
Some examples of using constants are at [@../../example/constants_eg1.cpp constants_eg1].
[endsect]
@@ -491,7 +493,7 @@ The result of an expanded macro for Pi is shown below.
[endsect] [/section:new_const Defining New Constants]
[section:FAQ FAQs]
[section:constants_faq FAQs]
[h4 Why are ['these] Constants Chosen?]
It is, of course, impossible to please everyone with a list like this.
@@ -579,7 +581,7 @@ to diverge wildly because internal comparisons just fail.
[h4 What is the Internal Format of the constants, and why?]
See [link math_toolkit.constants.tutorial tutorial] above for normal use,
See [link math_toolkit.tutorial tutorial] above for normal use,
but this FAQ explains the internal details used for the constants.
Constants are stored as 100 decimal digit values.
@@ -605,7 +607,7 @@ So, for example, a constant like pi is internally defined as
In this case the significand is 109 decimal digits, ensuring 100 decimal digits are exact, and exponent is zero.
See [link math_toolkit.constants.new_const defining new constants] to calculate new constants.
See [link math_toolkit.new_const defining new constants] to calculate new constants.
A macro definition like this can be pasted into user code where convenient,
or into `boost/math/constants.hpp` if it is to be added to the Boost.Math library.
@@ -729,7 +731,7 @@ Some physical constants may be available in Boost.Units.
[endsect] [/section:FAQ FAQ]
[endsect] [/section:constants Mathematical Constants]
[endmathpart] [/section:constants Mathematical Constants]
[/
Copyright 2012 John Maddock and Paul A. Bristow.

0
doc/sf_and_dist/pp_pi.hpp → doc/constants/pp_pi.hpp
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6
doc/sf_and_dist/background.qbk → doc/distributions/background.qbk
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@@ -62,12 +62,12 @@ the requested coverage will be present in the tails.
This behaviour can be changed so that the quantile functions are rounded
differently, or even return a real-valued result using
[link math_toolkit.policy.pol_overview Policies]. It is strongly
[link math_toolkit.pol_overview Policies]. It is strongly
recommended that you read the tutorial
[link math_toolkit.policy.pol_tutorial.understand_dis_quant
[link math_toolkit.pol_tutorial.understand_dis_quant
Understanding Quantiles of Discrete Distributions] before
using the quantile function on a discrete distribution. The
[link math_toolkit.policy.pol_ref.discrete_quant_ref reference docs]
[link math_toolkit.pol_ref.discrete_quant_ref reference docs]
describe how to change the rounding policy
for these distributions.
]

2
doc/sf_and_dist/distributions/bernoulli.qbk → doc/distributions/bernoulli.qbk
View File

@@ -61,7 +61,7 @@ Returns the /success_fraction/ parameter of this distribution.
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions]
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions]
that are generic to all distributions are supported: __usual_accessors.
The domain of the random variable is 0 and 1,

6
doc/sf_and_dist/distributions/beta.qbk → doc/distributions/beta.qbk
View File

@@ -180,7 +180,7 @@ Returns the value of [beta][space] that gives:
[h4 Non-member Accessor Functions]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions]
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions]
that are generic to all distributions are supported: __usual_accessors.
The formulae for calculating these are shown in the table below, and at
@@ -217,8 +217,8 @@ with its p parameter set to x.
[h4 Accuracy]
This distribution is implemented using the
[link math_toolkit.special.sf_beta.beta_function beta functions] __beta and
[link math_toolkit.special.sf_beta.ibeta_function incomplete beta functions] __ibeta and __ibetac;
[link math_toolkit.sf_beta.beta_function beta functions] __beta and
[link math_toolkit.sf_beta.ibeta_function incomplete beta functions] __ibeta and __ibetac;
please refer to these functions for information on accuracy.
[h4 Implementation]

14
doc/sf_and_dist/distributions/binomial.qbk → doc/distributions/binomial.qbk
View File

@@ -133,7 +133,7 @@ want to be 95% sure that the true value is [*greater than] some value,
p``[sub min]`` = binomial_distribution<RealType>::find_lower_bound_on_p(
n, k, 0.05);
[link math_toolkit.dist.stat_tut.weg.binom_eg.binom_conf See worked example.]
[link math_toolkit.stat_tut.weg.binom_eg.binom_conf See worked example.]
There are currently two possible values available for the /method/
optional parameter: /clopper_pearson_exact_interval/
@@ -213,7 +213,7 @@ want to be 95% sure that the true value is [*less than] some value,
p``[sub max]`` = binomial_distribution<RealType>::find_upper_bound_on_p(
n, k, 0.05);
[link math_toolkit.dist.stat_tut.weg.binom_eg.binom_conf See worked example.]
[link math_toolkit.stat_tut.weg.binom_eg.binom_conf See worked example.]
[note
In order to obtain a two sided bound on the success fraction, you
@@ -227,7 +227,7 @@ then you pass [alpha]/2 to these functions.
So for example a two sided 95% confidence interval would be obtained
by passing [alpha] = 0.025 to each of the functions.
[link math_toolkit.dist.stat_tut.weg.binom_eg.binom_conf See worked example.]
[link math_toolkit.stat_tut.weg.binom_eg.binom_conf See worked example.]
]
@@ -280,11 +280,11 @@ Returns the largest number of trials we can conduct and still be 95% certain
of not observing any events that occur with one in a million frequency.
This is typically used in failure analysis.
[link math_toolkit.dist.stat_tut.weg.binom_eg.binom_size_eg See Worked Example.]
[link math_toolkit.stat_tut.weg.binom_eg.binom_size_eg See Worked Example.]
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions]
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions]
that are generic to all distributions are supported: __usual_accessors.
The domain for the random variable /k/ is `0 <= k <= N`, otherwise a
@@ -328,7 +328,7 @@ the context of this distribution:
[h4 Examples]
Various [link math_toolkit.dist.stat_tut.weg.binom_eg worked examples]
Various [link math_toolkit.stat_tut.weg.binom_eg worked examples]
are available illustrating the use of the binomial distribution.
[h4 Accuracy]
@@ -374,7 +374,7 @@ There are also various special cases: refer to the code for details. ]]
[[quantile][Since the cdf is non-linear in variate /k/ none of the inverse
incomplete beta functions can be used here. Instead the quantile
is found numerically using a derivative free method
([link math_toolkit.toolkit.internals1.roots2 TOMS Algorithm 748]).]]
([link math_toolkit.internals1.roots2 TOMS Algorithm 748]).]]
[[quantile from the complement][Found numerically as above.]]
[[mean][ `p * n` ]]
[[variance][ `p * n * (1-p)` ]]

12
doc/sf_and_dist/distributions/binomial_example.qbk → doc/distributions/binomial_example.qbk
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@@ -4,10 +4,10 @@ See also the reference documentation for the __binomial_distrib.
[section:binomial_coinflip_example Binomial Coin-Flipping Example]
[import ../../../example/binomial_coinflip_example.cpp]
[import ../../example/binomial_coinflip_example.cpp]
[binomial_coinflip_example1]
See [@../../../example/binomial_coinflip_example.cpp binomial_coinflip_example.cpp]
See [@../../example/binomial_coinflip_example.cpp binomial_coinflip_example.cpp]
for full source code, the program output looks like this:
[binomial_coinflip_example_output]
@@ -16,12 +16,12 @@ for full source code, the program output looks like this:
[section:binomial_quiz_example Binomial Quiz Example]
[import ../../../example/binomial_quiz_example.cpp]
[import ../../example/binomial_quiz_example.cpp]
[binomial_quiz_example1]
[binomial_quiz_example2]
[discrete_quantile_real]
See [@../../../example/binomial_quiz_example.cpp binomial_quiz_example.cpp]
See [@../../example/binomial_quiz_example.cpp binomial_quiz_example.cpp]
for full source code and output.
[endsect] [/section:binomial_coinflip_quiz Binomial Coin-Flipping example]
@@ -39,7 +39,7 @@ were observed. The static member functions
`binomial_distribution<>::find_upper_bound_on_p` allow you to calculate
the confidence intervals for your estimate of the occurrence frequency.
The sample program [@../../../example/binomial_confidence_limits.cpp
The sample program [@../../example/binomial_confidence_limits.cpp
binomial_confidence_limits.cpp] illustrates their use. It begins by defining
a procedure that will print a table of confidence limits for various degrees
of certainty:
@@ -222,7 +222,7 @@ can be used to estimate the maximum number of "uses" of that component for some
acceptable risk level /alpha/.
The example program
[@../../../example/binomial_sample_sizes.cpp binomial_sample_sizes.cpp]
[@../../example/binomial_sample_sizes.cpp binomial_sample_sizes.cpp]
demonstrates its usage. It centres on a routine that prints out
a table of maximum sample sizes for various probability thresholds:

0
doc/sf_and_dist/distributions/c_sharp.qbk → doc/distributions/c_sharp.qbk
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4
doc/sf_and_dist/distributions/cauchy.qbk → doc/distributions/cauchy.qbk
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@@ -72,12 +72,12 @@ Returns the scale parameter of the distribution.
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions]
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions]
that are generic to all distributions are supported: __usual_accessors.
Note however that the Cauchy distribution does not have a mean,
standard deviation, etc. See __math_undefined
[/link math_toolkit.policy.pol_ref.assert_undefined mathematically undefined function]
[/link math_toolkit.pol_ref.assert_undefined mathematically undefined function]
to control whether these should fail to compile with a BOOST_STATIC_ASSERTION_FAILURE,
which is the default.

6
doc/sf_and_dist/distributions/chi_squared.qbk → doc/distributions/chi_squared.qbk
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@@ -102,7 +102,7 @@ See also section on Sample sizes required in
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions]
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions]
that are generic to all distributions are supported: __usual_accessors.
(We have followed the usual restriction of the mode to degrees of freedom >= 2,
@@ -114,13 +114,13 @@ The domain of the random variable is \[0, +[infin]\].
[h4 Examples]
Various [link math_toolkit.dist.stat_tut.weg.cs_eg worked examples]
Various [link math_toolkit.stat_tut.weg.cs_eg worked examples]
are available illustrating the use of the Chi Squared Distribution.
[h4 Accuracy]
The Chi-Squared distribution is implemented in terms of the
[link math_toolkit.special.sf_gamma.igamma incomplete gamma functions]:
[link math_toolkit.sf_gamma.igamma incomplete gamma functions]:
please refer to the accuracy data for those functions.
[h4 Implementation]

8
doc/sf_and_dist/distributions/chi_squared_examples.qbk → doc/distributions/chi_squared_examples.qbk
View File

@@ -9,7 +9,7 @@ For this situation the Chi Squared distribution can be used to calculate
confidence intervals for the standard deviation.
The full example code & sample output is in
[@../../../example/chi_square_std_dev_test.cpp chi_square_std_deviation_test.cpp].
[@../../example/chi_square_std_dev_test.cpp chi_square_std_deviation_test.cpp].
We'll begin by defining the procedure that will calculate and print out the
confidence intervals:
@@ -178,7 +178,7 @@ situations where we wish to compare the standard deviation of a new
process to an established one.
The code for this example is contained in
[@../../../example/chi_square_std_dev_test.cpp chi_square_std_dev_test.cpp], and
[@../../example/chi_square_std_dev_test.cpp chi_square_std_dev_test.cpp], and
we'll begin by defining the procedure that will print out the test
statistics:
@@ -364,7 +364,7 @@ Suppose we conduct a Chi Squared test for standard deviation and the result
is borderline, a legitimate question to ask is "How large would the sample size
have to be in order to produce a definitive result?"
The class template [link math_toolkit.dist.dist_ref.dists.chi_squared_dist
The class template [link math_toolkit.dist_ref.dists.chi_squared_dist
chi_squared_distribution] has a static method
`find_degrees_of_freedom` that will calculate this value for
some acceptable risk of type I failure /alpha/, type II failure
@@ -372,7 +372,7 @@ some acceptable risk of type I failure /alpha/, type II failure
note that the method used works on variance, and not standard deviation
as is usual for the Chi Squared Test.
The code for this example is located in [@../../../example/chi_square_std_dev_test.cpp
The code for this example is located in [@../../example/chi_square_std_dev_test.cpp
chi_square_std_dev_test.cpp].
We begin by defining a procedure to print out the sample sizes required

2
doc/sf_and_dist/dist_algorithms.qbk → doc/distributions/dist_algorithms.qbk
View File

@@ -65,7 +65,7 @@ Probability arguments must be [0, 1], otherwise __domain_error is called.
If the choice of arguments would give a negative scale, __domain_error is called, unless the policy is to ignore, when the negative (impossible) value of scale is returned.
[link math_toolkit.dist.stat_tut.weg.find_eg Find Mean and standard deviation examples]
[link math_toolkit.stat_tut.weg.find_eg Find Mean and standard deviation examples]
gives simple examples of use of both find_scale and find_location, and a longer example finding means and standard deviations of normally distributed weights to meet a specification.
[endsect] [/section:dist_algorithms dist_algorithms]

66
doc/sf_and_dist/dist_reference.qbk → doc/distributions/dist_reference.qbk
View File

@@ -1,40 +1,40 @@
[section:dist_ref Statistical Distributions Reference]
[include distributions/non_members.qbk]
[include non_members.qbk]
[section:dists Distributions]
[include distributions/bernoulli.qbk]
[include distributions/beta.qbk]
[include distributions/binomial.qbk]
[include distributions/cauchy.qbk]
[include distributions/chi_squared.qbk]
[include distributions/exponential.qbk]
[include distributions/extreme_value.qbk]
[include distributions/fisher.qbk]
[include distributions/gamma.qbk]
[include distributions/geometric.qbk]
[include distributions/hypergeometric.qbk]
[include distributions/inverse_chi_squared.qbk]
[include distributions/inverse_gamma.qbk]
[include distributions/inverse_gaussian.qbk]
[include distributions/laplace.qbk]
[include distributions/logistic.qbk]
[include distributions/lognormal.qbk]
[include distributions/negative_binomial.qbk]
[include distributions/nc_beta.qbk]
[include distributions/nc_chi_squared.qbk]
[include distributions/nc_f.qbk]
[include distributions/nc_t.qbk]
[include distributions/normal.qbk]
[include distributions/pareto.qbk]
[include distributions/poisson.qbk]
[include distributions/rayleigh.qbk]
[include distributions/skew_normal.qbk]
[include distributions/students_t.qbk]
[include distributions/triangular.qbk]
[include distributions/uniform.qbk]
[include distributions/weibull.qbk]
[include bernoulli.qbk]
[include beta.qbk]
[include binomial.qbk]
[include cauchy.qbk]
[include chi_squared.qbk]
[include exponential.qbk]
[include extreme_value.qbk]
[include fisher.qbk]
[include gamma.qbk]
[include geometric.qbk]
[include hypergeometric.qbk]
[include inverse_chi_squared.qbk]
[include inverse_gamma.qbk]
[include inverse_gaussian.qbk]
[include laplace.qbk]
[include logistic.qbk]
[include lognormal.qbk]
[include negative_binomial.qbk]
[include nc_beta.qbk]
[include nc_chi_squared.qbk]
[include nc_f.qbk]
[include nc_t.qbk]
[include normal.qbk]
[include pareto.qbk]
[include poisson.qbk]
[include rayleigh.qbk]
[include skew_normal.qbk]
[include students_t.qbk]
[include triangular.qbk]
[include uniform.qbk]
[include weibull.qbk]
[endsect][/section:dists Distributions]
@@ -110,7 +110,7 @@ package could be added reasonably easily, for example:
InputIterator b,
typename std::iterator_traits<InputIterator>::value_type expected_mean);
Returns the probability that the data in the sequence [a,b) has the mean
Returns the probability that the data in the sequence \[a,b) has the mean
/expected_mean/.
[h4 Integration With Statistical Accumulators]

67
doc/sf_and_dist/dist_tutorial.qbk → doc/distributions/dist_tutorial.qbk
View File

@@ -1,10 +1,10 @@
[/ 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]]
[def __F_distrib [link math_toolkit.dist.dist_ref.dists.f_dist Fisher F Distribution]]
[def __students_t_distrib [link math_toolkit.dist.dist_ref.dists.students_t_dist Students t Distribution]]
[def __binomial_distrib [link math_toolkit.dist_ref.dists.binomial_dist Binomial Distribution]]
[def __chi_squared_distrib [link math_toolkit.dist_ref.dists.chi_squared_dist Chi Squared Distribution]]
[def __normal_distrib [link math_toolkit.dist_ref.dists.normal_dist Normal Distribution]]
[def __F_distrib [link math_toolkit.dist_ref.dists.f_dist Fisher F Distribution]]
[def __students_t_distrib [link math_toolkit.dist_ref.dists.students_t_dist Students t Distribution]]
[def __handbook [@http://www.itl.nist.gov/div898/handbook/
NIST/SEMATECH e-Handbook of Statistical Methods.]]
@@ -21,11 +21,11 @@ provides a few worked examples of applying the library to statistical tests.
All the code in this library is inside namespace boost::math.
In order to use a distribution /my_distribution/ you will need to include
either the header <boost/math/distributions/my_distribution.hpp> or
either the header <boost/math/my_distribution.hpp> or
the "include all the distributions" header: <boost/math/distributions.hpp>.
For example, to use the Students-t distribution include either
<boost/math/distributions/students_t.hpp> or
<boost/math/students_t.hpp> or
<boost/math/distributions.hpp>
You also need to bring distribution names into scope,
@@ -41,14 +41,14 @@ or specific `using` declarations like `using boost::math::normal;` (*recommende
Each kind of distribution in this library is a class type - an object.
[link math_toolkit.policy Policies] provide fine-grained control
[link policy Policies] provide fine-grained control
of the behaviour of these classes, allowing the user to customise
behaviour such as how errors are handled, or how the quantiles
of discrete distribtions behave.
[tip If you are familiar with statistics libraries using functions,
and 'Distributions as Objects' seem alien, see
[link math_toolkit.dist.stat_tut.weg.nag_library the comparison to
[link math_toolkit.stat_tut.weg.nag_library the comparison to
other statistics libraries.]
] [/tip]
@@ -216,7 +216,7 @@ Mathematically, the functions may make sense with an (+ or -) infinite value,
but except for a few special cases (in the Normal and Cauchy distributions)
this implementation limits random variates to finite values from the `max`
to `min` for the `RealType`.
(See [link math_toolkit.backgrounders.implementation.handling_of_floating_point_infinity
(See [link math_toolkit.sf_implementation.handling_of_floating_point_infin
Handling of Floating-Point Infinity] for rationale).
@@ -250,12 +250,12 @@ the requested coverage will be present in the tails.
This behaviour can be changed so that the quantile functions are rounded
differently, or return a real-valued result using
[link math_toolkit.policy.pol_overview Policies]. It is strongly
[link math_toolkit.pol_overview Policies]. It is strongly
recommended that you read the tutorial
[link math_toolkit.policy.pol_tutorial.understand_dis_quant
[link math_toolkit.pol_tutorial.understand_dis_quant
Understanding Quantiles of Discrete Distributions] before
using the quantile function on a discrete distribtion. The
[link math_toolkit.policy.pol_ref.discrete_quant_ref reference docs]
[link math_toolkit.pol_ref.discrete_quant_ref reference docs]
describe how to change the rounding policy
for these distributions.
@@ -269,7 +269,6 @@ degrees of freedom do have a genuine meaning.
[endsect] [/ section:generic Generic operations common to all distributions are non-member functions]
[#complements]
[section:complements Complements are supported too - and when to use them]
Often you don't want the value of the CDF, but its complement, which is
@@ -429,22 +428,22 @@ Now that you have the basics, the next section looks at some worked examples.
[endsect] [/section:overview Overview]
[section:weg Worked Examples]
[include distributions/distribution_construction.qbk]
[include distributions/students_t_examples.qbk]
[include distributions/chi_squared_examples.qbk]
[include distributions/f_dist_example.qbk]
[include distributions/binomial_example.qbk]
[include distributions/geometric_example.qbk]
[include distributions/negative_binomial_example.qbk]
[include distributions/normal_example.qbk]
[/include distributions/inverse_gamma_example.qbk]
[/include distributions/inverse_gaussian_example.qbk]
[include distributions/inverse_chi_squared_eg.qbk]
[include distributions/nc_chi_squared_example.qbk]
[include distributions/error_handling_example.qbk]
[include distributions/find_location_and_scale.qbk]
[include distributions/nag_library.qbk]
[include distributions/c_sharp.qbk]
[include distribution_construction.qbk]
[include students_t_examples.qbk]
[include chi_squared_examples.qbk]
[include f_dist_example.qbk]
[include binomial_example.qbk]
[include geometric_example.qbk]
[include negative_binomial_example.qbk]
[include normal_example.qbk]
[/include inverse_gamma_example.qbk]
[/include inverse_gaussian_example.qbk]
[include inverse_chi_squared_eg.qbk]
[include nc_chi_squared_example.qbk]
[include error_handling_example.qbk]
[include find_location_and_scale.qbk]
[include nag_library.qbk]
[include c_sharp.qbk]
[endsect] [/section:weg Worked Examples]
[include background.qbk]
@@ -458,11 +457,3 @@ Now that you have the basics, the next section looks at some worked examples.
http://www.boost.org/LICENSE_1_0.txt).
]

4
doc/sf_and_dist/distributions/distribution_construction.qbk → doc/distributions/distribution_construction.qbk
View File

@@ -1,10 +1,10 @@
[section:dist_construct_eg Distribution Construction Examples]
[import ../../../example/distribution_construction.cpp]
[import ../../example/distribution_construction.cpp]
[distribution_construction_1]
[distribution_construction_2]
See [@../../../example/distribution_construction.cpp distribution_construction.cpp] for full source code.
See [@../../example/distribution_construction.cpp distribution_construction.cpp] for full source code.
[endsect] [/section:dist_construct_eg Distribution Construction Examples]

4
doc/sf_and_dist/distributions/error_handling_example.qbk → doc/distributions/error_handling_example.qbk
View File

@@ -1,6 +1,6 @@
[section:error_eg Error Handling Example]
See [link math_toolkit.main_overview.error_handling error handling documentation]
See [link math_toolkit.error_handling error handling documentation]
for a detailed explanation of the mechanism of handling errors,
including the common "bad" arguments to distributions and functions,
and how to use __policy_section to control it.
@@ -12,7 +12,7 @@ an appropriate value returned, usually a NaN (domain errors
pole errors or internal errors), or infinity (from overflow),
you need to change the policy.
[import ../../../example/error_handling_example.cpp]
[import ../../example/error_handling_example.cpp]
[error_handling_example]

2
doc/sf_and_dist/distributions/exponential.qbk → doc/distributions/exponential.qbk
View File

@@ -52,7 +52,7 @@ Accessor function returns the lambda parameter of the distribution.
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions]
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions]
that are generic to all distributions are supported: __usual_accessors.
The domain of the random variable is \[0, +[infin]\].

2
doc/sf_and_dist/distributions/extreme_value.qbk → doc/distributions/extreme_value.qbk
View File

@@ -76,7 +76,7 @@ Returns the scale parameter of the distribution.
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions]
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions]
that are generic to all distributions are supported: __usual_accessors.
The domain of the random parameter is \[-[infin], +[infin]\].

2
doc/sf_and_dist/distributions/f_dist_example.qbk → doc/distributions/f_dist_example.qbk
View File

@@ -13,7 +13,7 @@ The data for this case study were collected by Said Jahanmir of the
NIST Ceramics Division in 1996 in connection with a NIST/industry
ceramics consortium for strength optimization of ceramic strength.
The example program is [@../../../example/f_test.cpp f_test.cpp],
The example program is [@../../example/f_test.cpp f_test.cpp],
program output has been deliberately made as similar as possible
to the DATAPLOT output in the corresponding
[@http://www.itl.nist.gov/div898/handbook/eda/section3/eda359.htm

12
doc/sf_and_dist/distributions/find_location_and_scale.qbk → doc/distributions/find_location_and_scale.qbk
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@@ -1,28 +1,28 @@
[section:find_eg Find Location and Scale Examples]
[section:find_location_eg Find Location (Mean) Example]
[import ../../../example/find_location_example.cpp]
[import ../../example/find_location_example.cpp]
[find_location1]
[find_location2]
See [@../../../example/find_location_example.cpp find_location_example.cpp]
See [@../../example/find_location_example.cpp find_location_example.cpp]
for full source code: the program output looks like this:
[find_location_example_output]
[endsect] [/section:find_location_eg Find Location (Mean) Example]
[section:find_scale_eg Find Scale (Standard Deviation) Example]
[import ../../../example/find_scale_example.cpp]
[import ../../example/find_scale_example.cpp]
[find_scale1]
[find_scale2]
See [@../../../example/find_scale_example.cpp find_scale_example.cpp]
See [@../../example/find_scale_example.cpp find_scale_example.cpp]
for full source code: the program output looks like this:
[find_scale_example_output]
[endsect] [/section:find_scale_eg Scale (Standard Deviation) Example]
[section:find_mean_and_sd_eg Find mean and standard deviation example]
[import ../../../example/find_mean_and_sd_normal.cpp]
[import ../../example/find_mean_and_sd_normal.cpp]
[normal_std]
[normal_find_location_and_scale_eg]
See [@../../../example/find_mean_and_sd_normal.cpp find_mean_and_sd_normal.cpp]
See [@../../example/find_mean_and_sd_normal.cpp find_mean_and_sd_normal.cpp]
for full source code & appended program output.
[endsect] [/find_mean_and_sd_eg Find mean and standard deviation example]

8
doc/sf_and_dist/distributions/fisher.qbk → doc/distributions/fisher.qbk
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@@ -64,21 +64,21 @@ Returns the denominator degrees of freedom parameter of the distribution.
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions]
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions]
that are generic to all distributions are supported: __usual_accessors.
The domain of the random variable is \[0, +[infin]\].
[h4 Examples]
Various [link math_toolkit.dist.stat_tut.weg.f_eg worked examples] are
Various [link math_toolkit.stat_tut.weg.f_eg worked examples] are
available illustrating the use of the F Distribution.
[h4 Accuracy]
The normal distribution is implemented in terms of the
[link math_toolkit.special.sf_beta.ibeta_function incomplete beta function]
and its [link math_toolkit.special.sf_beta.ibeta_inv_function inverses],
[link math_toolkit.sf_beta.ibeta_function incomplete beta function]
and its [link math_toolkit.sf_beta.ibeta_inv_function inverses],
refer to those functions for accuracy data.
[h4 Implementation]

2
doc/sf_and_dist/distributions/gamma.qbk → doc/distributions/gamma.qbk
View File

@@ -94,7 +94,7 @@ Returns the /scale/ parameter of this distribution.
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions] that are generic to all
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions] that are generic to all
distributions are supported: __usual_accessors.
The domain of the random variable is \[0,+[infin]\].

8
doc/sf_and_dist/distributions/geometric.qbk → doc/distributions/geometric.qbk
View File

@@ -161,7 +161,7 @@ want to be 95% sure that the true value is [*greater than] some value,
p``[sub min]`` = geometric_distribution<RealType>::
find_lower_bound_on_p(failures, 0.05);
[link math_toolkit.dist.stat_tut.weg.neg_binom_eg.neg_binom_conf See negative_binomial confidence interval example.]
[link math_toolkit.stat_tut.weg.neg_binom_eg.neg_binom_conf See negative_binomial confidence interval example.]
This function uses the Clopper-Pearson method of computing the lower bound on the
success fraction, whilst many texts refer to this method as giving an "exact"
@@ -195,7 +195,7 @@ want to be 95% sure that the true value is [*less than] some value,
p``[sub max]`` = geometric_distribution<RealType>::find_upper_bound_on_p(
k, 0.05);
[link math_toolkit.dist.stat_tut.weg.neg_binom_eg.neg_binom_conf See negative binomial confidence interval example.]
[link math_toolkit.stat_tut.weg.neg_binom_eg.neg_binom_conf See negative binomial confidence interval example.]
This function uses the Clopper-Pearson method of computing the lower bound on the
success fraction, whilst many texts refer to this method as giving an "exact"
@@ -230,7 +230,7 @@ For example:
Returns the smallest number of trials we must conduct to be 95% (1-0.05) sure
of seeing 10 failures that occur with frequency one half.
[link math_toolkit.dist.stat_tut.weg.neg_binom_eg.neg_binom_size_eg Worked Example.]
[link math_toolkit.stat_tut.weg.neg_binom_eg.neg_binom_size_eg Worked Example.]
This function uses numeric inversion of the geometric distribution
to obtain the result: another interpretation of the result is that it finds
@@ -267,7 +267,7 @@ of observing more than k failures.
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions]
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions]
that are generic to all distributions are supported: __usual_accessors.
However it's worth taking a moment to define what these actually mean in

6
doc/sf_and_dist/distributions/geometric_example.qbk → doc/distributions/geometric_example.qbk
View File

@@ -1,13 +1,13 @@
[section:geometric_eg Geometric Distribution Examples]
[import ../../../example/geometric_examples.cpp]
[import ../../example/geometric_examples.cpp]
[geometric_eg1_1]
[geometric_eg1_2]
See full source C++ of this example at
[@../../../example/geometric_examples.cpp geometric_examples.cpp]
[@../../example/geometric_examples.cpp geometric_examples.cpp]
[link math_toolkit.dist.stat_tut.weg.neg_binom_eg.neg_binom_conf See negative_binomial confidence interval example.]
[link math_toolkit.stat_tut.weg.neg_binom_eg.neg_binom_conf See negative_binomial confidence interval example.]
[endsect] [/section:geometric_eg Geometric Distribution Examples]

8
doc/sf_and_dist/distributions/hypergeometric.qbk → doc/distributions/hypergeometric.qbk
View File

@@ -75,7 +75,7 @@ Returns the number of objects /n/ which are sampled from the population /N/.
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions]
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions]
that are generic to all distributions are supported: __usual_accessors.
The domain of the random variable is the unsigned integers in the range
@@ -93,12 +93,12 @@ the requested coverage will be present in the tails.
This behaviour can be changed so that the quantile functions are rounded
differently using
[link math_toolkit.policy.pol_overview Policies]. It is strongly
[link math_toolkit.pol_overview Policies]. It is strongly
recommended that you read the tutorial
[link math_toolkit.policy.pol_tutorial.understand_dis_quant
[link math_toolkit.pol_tutorial.understand_dis_quant
Understanding Quantiles of Discrete Distributions] before
using the quantile function on the Hypergeometric distribution. The
[link math_toolkit.policy.pol_ref.discrete_quant_ref reference docs]
[link math_toolkit.pol_ref.discrete_quant_ref reference docs]
describe how to change the rounding policy
for these distributions.

2
doc/sf_and_dist/distributions/inverse_chi_squared.qbk → doc/distributions/inverse_chi_squared.qbk
View File

@@ -118,7 +118,7 @@ Returns the scale [xi] parameter of this distribution.
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions] that are generic to all
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions] that are generic to all
distributions are supported: __usual_accessors.
The domain of the random variate is \[0,+[infin]\].

4
doc/sf_and_dist/distributions/inverse_chi_squared_eg.qbk → doc/distributions/inverse_chi_squared_eg.qbk
View File

@@ -1,7 +1,7 @@
[section:inverse_chi_squared_eg Inverse Chi-Squared Distribution Bayes Example]
[import ../../../example/inverse_chi_squared_bayes_eg.cpp]
[import ../../example/inverse_chi_squared_bayes_eg.cpp]
[inverse_chi_squared_bayes_eg_1]
[inverse_chi_squared_bayes_eg_output_1]
[inverse_chi_squared_bayes_eg_2]
@@ -19,7 +19,7 @@ A full sample output is:
(See also the reference documentation for the __inverse_chi_squared_distrib.)
See the full source C++ of this example at
[@../../../example/inverse_chi_squared_bayes_eg.cpp]
[@../../example/inverse_chi_squared_bayes_eg.cpp]
[endsect] [/section:inverse_chi_squared_eg Inverse Chi-Squared Distribution Bayes Example]

2
doc/sf_and_dist/distributions/inverse_gamma.qbk → doc/distributions/inverse_gamma.qbk
View File

@@ -81,7 +81,7 @@ Returns the [beta] scale parameter of this inverse gamma distribution.
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions] that are generic to all
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions] that are generic to all
distributions are supported: __usual_accessors.
The domain of the random variate is \[0,+[infin]\].

0
doc/sf_and_dist/distributions/inverse_gamma_example.qbk → doc/distributions/inverse_gamma_example.qbk
View File

2
doc/sf_and_dist/distributions/inverse_gaussian.qbk → doc/distributions/inverse_gaussian.qbk
View File

@@ -108,7 +108,7 @@ Returns the scale [lambda] parameter of this distribution.
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions] that are generic to all
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions] that are generic to all
distributions are supported: __usual_accessors.
The domain of the random variate is \[0,+[infin]).

2
doc/sf_and_dist/distributions/laplace.qbk → doc/distributions/laplace.qbk
View File

@@ -72,7 +72,7 @@ Returns the /scale/ parameter of this distribution.
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions] that are generic to all
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions] that are generic to all
distributions are supported: __usual_accessors.
The domain of the random variable is \[-[infin],+[infin]\].

2
doc/sf_and_dist/distributions/logistic.qbk → doc/distributions/logistic.qbk
View File

@@ -55,7 +55,7 @@ Returns the scale of this distribution.
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions]
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions]
that are generic to all distributions are supported: __usual_accessors.
The domain of the random variable is \[-\[max_value\], +\[min_value\]\].

4
doc/sf_and_dist/distributions/lognormal.qbk → doc/distributions/lognormal.qbk
View File

@@ -75,7 +75,7 @@ Returns the /scale/ parameter of this distribution.
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions] that are generic to all
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions] that are generic to all
distributions are supported: __usual_accessors.
The domain of the random variable is \[0,+[infin]\].
@@ -84,7 +84,7 @@ The domain of the random variable is \[0,+[infin]\].
The lognormal distribution is implemented in terms of the
standard library log and exp functions, plus the
[link math_toolkit.special.sf_erf.error_function error function],
[link math_toolkit.sf_erf.error_function error function],
and as such should have very low error rates.
[h4 Implementation]

2
doc/sf_and_dist/distributions/nag_library.qbk → doc/distributions/nag_library.qbk
View File

@@ -47,7 +47,7 @@ and values can be output thus:
`pdf(dist, k)` is equivalent to NAG library `peqk`, point probability of == k
See [@../../../example/binomial_example_nag.cpp binomial_example_nag.cpp] for details.
See [@../../example/binomial_example_nag.cpp binomial_example_nag.cpp] for details.
[endsect] [/section:nag_library Comparison with C, R, FORTRAN-style Free Functions]

4
doc/sf_and_dist/distributions/nc_beta.qbk → doc/distributions/nc_beta.qbk
View File

@@ -79,7 +79,7 @@ Returns the parameter /lambda/ from which this object was constructed.
[h4 Non-member Accessors]
Most of the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions]
Most of the [link math_toolkit.dist_ref.nmp usual non-member accessor functions]
are supported: __cdf, __pdf, __quantile, __mean, __variance, __sd,
__median, __mode, __hazard, __chf, __range and __support.
@@ -195,7 +195,7 @@ and the relation:
[equation nc_beta_ref1]
Quantiles are computed using a specially modified version of
[link math_toolkit.toolkit.internals1.roots2 bracket_and_solve_root],
[link math_toolkit.internals1.roots2 bracket_and_solve_root],
starting the search for the root at the mean of the distribution.
(A Cornish-Fisher type expansion was also tried, but while this gets
quite close to the root in many cases, when it is wrong it tends to

4
doc/sf_and_dist/distributions/nc_chi_squared.qbk → doc/distributions/nc_chi_squared.qbk
View File

@@ -115,7 +115,7 @@ this function returns the non centrality parameter /lambda/ such that:
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions]
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions]
that are generic to all distributions are supported: __usual_accessors.
The domain of the random variable is \[0, +[infin]\].
@@ -123,7 +123,7 @@ The domain of the random variable is \[0, +[infin]\].
[h4 Examples]
There is a
[link math_toolkit.dist.stat_tut.weg.nccs_eg worked example]
[link math_toolkit.stat_tut.weg.nccs_eg worked example]
for the noncentral chi-squared distribution.
[h4 Accuracy]

2
doc/sf_and_dist/distributions/nc_chi_squared_example.qbk → doc/distributions/nc_chi_squared_example.qbk
View File

@@ -5,7 +5,7 @@
[section:nccs_power_eg Tables of the power function of the chi[super 2] test.]
[/chi super 2 failed to show the chi in pdf why??? (OK in html) so use words.]
[import ../../../example/nc_chi_sq_example.cpp]
[import ../../example/nc_chi_sq_example.cpp]
[nccs_eg]
[endsect] [/nccs_power_eg Tables of the power function of the chi-squared [chi][super 2] test.]

2
doc/sf_and_dist/distributions/nc_f.qbk → doc/distributions/nc_f.qbk
View File

@@ -76,7 +76,7 @@ Returns the non-centrality parameter /lambda/ from which this object was constru
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions]
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions]
that are generic to all distributions are supported: __usual_accessors.
The domain of the random variable is \[0, +[infin]\].

4
doc/sf_and_dist/distributions/nc_t.qbk → doc/distributions/nc_t.qbk
View File

@@ -69,7 +69,7 @@ Returns the non-centrality parameter /delta/ from which this object was construc
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions]
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions]
that are generic to all distributions are supported: __usual_accessors.
The domain of the random variable is \[-[infin], +[infin]\].
@@ -194,7 +194,7 @@ t-Distribution". C. van Eeden. International Statistical Review, 29, 4-31.
N. Balkrishnan. 1995. John Wiley and Sons New York.
The quantile is calculated via the usual
[link math_toolkit.toolkit.internals1.roots2
[link math_toolkit.internals1.roots2
derivative-free root-finding techniques],
with the initial guess taken as the quantile of a normal approximation
to the noncentral T.

8
doc/sf_and_dist/distributions/negative_binomial.qbk → doc/distributions/negative_binomial.qbk
View File

@@ -156,7 +156,7 @@ want to be 95% sure that the true value is [*greater than] some value,
p``[sub min]`` = negative_binomial_distribution<RealType>::find_lower_bound_on_p(
failures, successes, 0.05);
[link math_toolkit.dist.stat_tut.weg.neg_binom_eg.neg_binom_conf See negative binomial confidence interval example.]
[link math_toolkit.stat_tut.weg.neg_binom_eg.neg_binom_conf See negative binomial confidence interval example.]
This function uses the Clopper-Pearson method of computing the lower bound on the
success fraction, whilst many texts refer to this method as giving an "exact"
@@ -192,7 +192,7 @@ want to be 95% sure that the true value is [*less than] some value,
p``[sub max]`` = negative_binomial_distribution<RealType>::find_upper_bound_on_p(
r, k, 0.05);
[link math_toolkit.dist.stat_tut.weg.neg_binom_eg.neg_binom_conf See negative binomial confidence interval example.]
[link math_toolkit.stat_tut.weg.neg_binom_eg.neg_binom_conf See negative binomial confidence interval example.]
This function uses the Clopper-Pearson method of computing the lower bound on the
success fraction, whilst many texts refer to this method as giving an "exact"
@@ -227,7 +227,7 @@ For example:
Returns the smallest number of trials we must conduct to be 95% sure
of seeing 10 failures that occur with frequency one half.
[link math_toolkit.dist.stat_tut.weg.neg_binom_eg.neg_binom_size_eg Worked Example.]
[link math_toolkit.stat_tut.weg.neg_binom_eg.neg_binom_size_eg Worked Example.]
This function uses numeric inversion of the negative binomial distribution
to obtain the result: another interpretation of the result, is that it finds
@@ -264,7 +264,7 @@ of observing more than k failures.
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions]
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions]
that are generic to all distributions are supported: __usual_accessors.
However it's worth taking a moment to define what these actually mean in

14
doc/sf_and_dist/distributions/negative_binomial_example.qbk → doc/distributions/negative_binomial_example.qbk
View File

@@ -20,10 +20,10 @@ and how many successes were observed. The static member functions
`negative_binomial_distribution<>::find_upper_bound_on_p`
allow you to calculate the confidence intervals for your estimate of the success fraction.
The sample program [@../../../example/neg_binom_confidence_limits.cpp
The sample program [@../../example/neg_binom_confidence_limits.cpp
neg_binom_confidence_limits.cpp] illustrates their use.
[import ../../../example/neg_binom_confidence_limits.cpp]
[import ../../example/neg_binom_confidence_limits.cpp]
[neg_binomial_confidence_limits]
Let's see some sample output for a 1 in 10
@@ -95,10 +95,10 @@ can be used to estimate the minimum number of trials required to be P% sure
of observing the desired number of failures.
The example program
[@../../../example/neg_binomial_sample_sizes.cpp neg_binomial_sample_sizes.cpp]
[@../../example/neg_binomial_sample_sizes.cpp neg_binomial_sample_sizes.cpp]
demonstrates its usage.
[import ../../../example/neg_binomial_sample_sizes.cpp]
[import ../../example/neg_binomial_sample_sizes.cpp]
[neg_binomial_sample_sizes]
[note Since we're calculating the /minimum/ number of trials required,
@@ -165,10 +165,10 @@ So now 103 trials are required to observe at least 5 failures with
[section:negative_binomial_example1 Negative Binomial Sales Quota Example.]
This example program
[@../../../example/negative_binomial_example1.cpp negative_binomial_example1.cpp (full source code)]
[@../../example/negative_binomial_example1.cpp negative_binomial_example1.cpp (full source code)]
demonstrates a simple use to find the probability of meeting a sales quota.
[import ../../../example/negative_binomial_example1.cpp]
[import ../../example/negative_binomial_example1.cpp]
[negative_binomial_eg1_1]
[negative_binomial_eg1_2]
@@ -176,7 +176,7 @@ demonstrates a simple use to find the probability of meeting a sales quota.
[section:negative_binomial_example2 Negative Binomial Table Printing Example.]
Example program showing output of a table of values of cdf and pdf for various k failures.
[import ../../../example/negative_binomial_example2.cpp]
[import ../../example/negative_binomial_example2.cpp]
[neg_binomial_example2]
[neg_binomial_example2_1]
[endsect] [/section:negative_binomial_example1 Negative Binomial example 2.]

114
doc/sf_and_dist/distributions/non_members.qbk → doc/distributions/non_members.qbk
View File

@@ -4,61 +4,61 @@ Properties that are common to all distributions are accessed via non-member
getter functions: non-membership allows more of these functions to be added over time,
as the need arises. Unfortunately the literature uses many different and
confusing names to refer to a rather small number of actual concepts; refer
to the [link concept_index concept index] to find the property you
to the [link math_toolkit.dist_ref.nmp.concept_index concept index] to find the property you
want by the name you are most familiar with.
Or use the [link function_index function index]
Or use the [link math_toolkit.dist_ref.nmp.function_index function index]
to go straight to the function you want if you already know its name.
[h4 [#function_index]Function Index]
[h4:function_index Function Index]
* [link math.dist.cdf cdf].
* [link math.dist.ccdf cdf complement].
* [link math.dist.chf chf].
* [link math.dist.hazard hazard].
* __cdf.
* __ccdf.
* __chf.
* __hazard.
* __kurtosis.
* __kurtosis_excess
* __mean.
* [link math.dist.median median].
* __median.
* __mode.
* [link math.dist.pdf pdf].
* [link math.dist.range range].
* [link math.dist.quantile quantile].
* [link math.dist.quantile_c quantile from the complement].
* __pdf.
* __range.
* __quantile.
* __quantile_c.
* __skewness.
* [link math.dist.sd standard_deviation].
* [link math.dist.support support].
* __sd.
* __support.
* __variance.
[h4 [#concept_index]Conceptual Index]
[h4:concept_index Conceptual Index]
* __ccdf.
* __cdf.
* __chf.
* [link cdf_inv Inverse Cumulative Distribution Function].
* [link survival_inv Inverse Survival Function].
* [link math_toolkit.dist_ref.nmp.cdf_inv Inverse Cumulative Distribution Function].
* [link math_toolkit.dist_ref.nmp.survival_inv Inverse Survival Function].
* __hazard
* [link lower_critical Lower Critical Value].
* [link math_toolkit.dist_ref.nmp.lower_critical Lower Critical Value].
* __kurtosis.
* __kurtosis_excess
* __mean.
* [link math.dist.median median].
* __median.
* __mode.
* [link cdfPQ P].
* [link percent Percent Point Function].
* [link math_toolkit.dist_ref.nmp.cdfPQ P].
* [link math_toolkit.dist_ref.nmp.percent Percent Point Function].
* __pdf.
* [link pmf Probability Mass Function].
* [link math.dist.range range].
* [link cdfPQ Q].
* [link math_toolkit.dist_ref.nmp.pmf Probability Mass Function].
* __range.
* [link math_toolkit.dist_ref.nmp.cdfPQ Q].
* __quantile.
* [link math.dist.quantile_c Quantile from the complement of the probability].
* [link math_toolkit.dist_ref.nmp.quantile_c Quantile from the complement of the probability].
* __skewness.
* __sd
* [link survival Survival Function].
* [link math.dist.support support].
* [link upper_critical Upper Critical Value].
* [link math_toolkit.dist_ref.nmp.survival Survival Function].
* [link math_toolkit.dist_ref.nmp.support support].
* [link math_toolkit.dist_ref.nmp.upper_critical Upper Critical Value].
* __variance.
[h4 [#math.dist.cdf]Cumulative Distribution Function]
[h4:cdf Cumulative Distribution Function]
template <class RealType, class ``__Policy``>
RealType cdf(const ``['Distribution-Type]``<RealType, ``__Policy``>& dist, const RealType& x);
@@ -75,7 +75,7 @@ normal distribution:
[$../graphs/cdf.png]
[h4 [#math.dist.ccdf]Complement of the Cumulative Distribution Function]
[h4:ccdf Complement of the Cumulative Distribution Function]
template <class Distribution, class RealType>
RealType cdf(const ``['Unspecified-Complement-Type]``<Distribution, RealType>& comp);
@@ -105,7 +105,7 @@ normal distribution:
See __why_complements for why the complement is useful and when it should be used.
[h4 [#math.dist.hazard]Hazard Function]
[h4:hazard Hazard Function]
template <class RealType, class ``__Policy``>
RealType hazard(const ``['Distribution-Type]``<RealType, ``__Policy``>& dist, const RealType& x);
@@ -121,7 +121,7 @@ the defined range for the distribution.
Some authors refer to this as the conditional failure
density function rather than the hazard function.]
[h4 [#math.dist.chf]Cumulative Hazard Function]
[h4:chf Cumulative Hazard Function]
template <class RealType, class ``__Policy``>
RealType chf(const ``['Distribution-Type]``<RealType, ``__Policy``>& dist, const RealType& x);
@@ -136,7 +136,7 @@ the defined range for the distribution.
[caution
Some authors refer to this as simply the "Hazard Function".]
[h4 [#math.dist.mean]mean]
[h4:mean mean]
template<class RealType, class ``__Policy``>
RealType mean(const ``['Distribution-Type]``<RealType, ``__Policy``>& dist);
@@ -146,14 +146,14 @@ Returns the mean of the distribution /dist/.
This function may return a __domain_error if the distribution does not have
a defined mean (for example the Cauchy distribution).
[h4 [#math.dist.median]median]
[h4:median median]
template<class RealType, class ``__Policy``>
RealType median(const ``['Distribution-Type]``<RealType, ``__Policy``>& dist);
Returns the median of the distribution /dist/.
[h4 [#math.dist.mode]mode]
[h4:mode mode]
template<class RealType, ``__Policy``>
RealType mode(const ``['Distribution-Type]``<RealType, ``__Policy``>& dist);
@@ -163,7 +163,7 @@ Returns the mode of the distribution /dist/.
This function may return a __domain_error if the distribution does not have
a defined mode.
[h4 [#math.dist.pdf]Probability Density Function]
[h4:pdf Probability Density Function]
template <class RealType, class ``__Policy``>
RealType pdf(const ``['Distribution-Type]``<RealType, ``__Policy``>& dist, const RealType& x);
@@ -184,14 +184,14 @@ For example, for a standard normal distribution the pdf looks like this:
[$../graphs/pdf.png]
[h4 [#math.dist.range]Range]
[h4:range Range]
template<class RealType, class ``__Policy``>
std::pair<RealType, RealType> range(const ``['Distribution-Type]``<RealType, ``__Policy``>& dist);
Returns the valid range of the random variable over distribution /dist/.
[h4 [#math.dist.quantile]Quantile]
[h4:quantile Quantile]
template <class RealType, class ``__Policy``>
RealType quantile(const ``['Distribution-Type]``<RealType, ``__Policy``>& dist, const RealType& p);
@@ -211,8 +211,8 @@ distribution:
[$../graphs/quantile.png]
[h4 [#math.dist.quantile_c]Quantile from the complement of the probability.]
[link complements complements]
[h4:quantile_c Quantile from the complement of the probability.]
See also [link math_toolkit.stat_tut.overview.complements complements].
template <class Distribution, class RealType>
@@ -246,7 +246,7 @@ distribution:
[$../graphs/survival_inv.png]
[h4 [#math.dist.sd]Standard Deviation]
[h4:sd Standard Deviation]
template <class RealType, class ``__Policy``>
RealType standard_deviation(const ``['Distribution-Type]``<RealType, ``__Policy``>& dist);
@@ -256,7 +256,7 @@ Returns the standard deviation of distribution /dist/.
This function may return a __domain_error if the distribution does not have
a defined standard deviation.
[h4 [#math.dist.support]support]
[h4:support support]
template<class RealType, class ``__Policy``>
std::pair<RealType, RealType> support(const ``['Distribution-Type]``<RealType, ``__Policy``>& dist);
@@ -270,7 +270,7 @@ Non-mathematicians might say it means the 'interesting' smallest range
of random variate x that has the cdf going from zero to unity.
Outside are uninteresting zones where the pdf is zero, and the cdf zero or unity.
[h4 [#math.dist.variance]Variance]
[h4:variance Variance]
template <class RealType, class ``__Policy``>
RealType variance(const ``['Distribution-Type]``<RealType, ``__Policy``>& dist);
@@ -280,7 +280,7 @@ Returns the variance of the distribution /dist/.
This function may return a __domain_error if the distribution does not have
a defined variance.
[h4 [#math.dist.skewness]Skewness]
[h4:skewness Skewness]
template <class RealType, class ``__Policy``>
RealType skewness(const ``['Distribution-Type]``<RealType, ``__Policy``>& dist);
@@ -290,7 +290,7 @@ Returns the skewness of the distribution /dist/.
This function may return a __domain_error if the distribution does not have
a defined skewness.
[h4 [#math.dist.kurtosis]Kurtosis]
[h4:kurtosis Kurtosis]
template <class RealType, class ``__Policy``>
RealType kurtosis(const ``['Distribution-Type]``<RealType, ``__Policy``>& dist);
@@ -322,7 +322,7 @@ a defined kurtosis.
'Proper' kurtosis can have a value from zero to + infinity.
[h4 [#math.dist.kurtosis_excess]Kurtosis excess]
[h4:kurtosis_excess Kurtosis excess]
template <class RealType, ``__Policy``>
RealType kurtosis_excess(const ``['Distribution-Type]``<RealType, ``__Policy``>& dist);
@@ -347,50 +347,50 @@ Kurtosis excess can have a value from -2 to + infinity.
The kurtosis excess of a normal distribution is zero.
[h4 [#cdfPQ]P and Q]
[h4:cdfPQ P and Q]
The terms P and Q are sometimes used to refer to the __cdf
and its [link math.dist.ccdf complement] respectively.
and its [link math_toolkit.dist_ref.nmp.ccdf complement] respectively.
Lowercase p and q are sometimes used to refer to the values returned
by these functions.
[h4 [#percent]Percent Point Function or Percentile]
[h4:percent Percent Point Function or Percentile]
The percent point function, also known as the percentile, is the same as
the __quantile.
[h4 [#cdf_inv]Inverse CDF Function.]
[h4:cdf_inv Inverse CDF Function.]
The inverse of the cumulative distribution function, is the same as the
__quantile.
[h4 [#survival_inv]Inverse Survival Function.]
[h4:survival_inv Inverse Survival Function.]
The inverse of the survival function, is the same as computing the
[link math.dist.quantile_c quantile
[link math_toolkit.dist_ref.nmp.quantile_c quantile
from the complement of the probability].
[h4 [#pmf]Probability Mass Function]
[h4:pmf Probability Mass Function]
The Probability Mass Function is the same as the __pdf.
The term Mass Function is usually applied to discrete distributions,
while the term __pdf applies to continuous distributions.
[h4 [#lower_critical]Lower Critical Value.]
[h4:lower_critical Lower Critical Value.]
The lower critical value calculates the value of the random variable
given the area under the left tail of the distribution.
It is equivalent to calculating the __quantile.
[h4 [#upper_critical]Upper Critical Value.]
[h4: upper_critical Upper Critical Value.]
The upper critical value calculates the value of the random variable
given the area under the right tail of the distribution. It is equivalent to
calculating the [link math.dist.quantile_c quantile from the complement of the
calculating the [link math_toolkit.dist_ref.nmp.quantile_c quantile from the complement of the
probability].
[h4 [#survival]Survival Function]
[h4:survival Survival Function]
Refer to the __ccdf.

4
doc/sf_and_dist/distributions/normal.qbk → doc/distributions/normal.qbk
View File

@@ -74,7 +74,7 @@ allowing the functions find_location and find_scale to be used generically).
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions] that are generic to all
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions] that are generic to all
distributions are supported: __usual_accessors.
The domain of the random variable is \[-[max_value], +[min_value]\].
@@ -86,7 +86,7 @@ if RealType permits.
[h4 Accuracy]
The normal distribution is implemented in terms of the
[link math_toolkit.special.sf_erf.error_function error function],
[link math_toolkit.sf_erf.error_function error function],
and as such should have very low error rates.
[h4 Implementation]

4
doc/sf_and_dist/distributions/normal_example.qbk → doc/distributions/normal_example.qbk
View File

@@ -4,10 +4,10 @@
[section:normal_misc Some Miscellaneous Examples of the Normal (Gaussian) Distribution]
The sample program [@../../../example/normal_misc_examples.cpp
The sample program [@../../example/normal_misc_examples.cpp
normal_misc_examples.cpp] illustrates their use.
[import ../../../example/normal_misc_examples.cpp]
[import ../../example/normal_misc_examples.cpp]
[h4 Traditional Tables]
[normal_basic1]

2
doc/sf_and_dist/distributions/pareto.qbk → doc/distributions/pareto.qbk
View File

@@ -70,7 +70,7 @@ Returns the /shape/ parameter of this distribution.
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions] that are generic to all
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions] that are generic to all
distributions are supported: __usual_accessors.
The supported domain of the random variable is \[scale, [infin]\].

2
doc/sf_and_dist/distributions/poisson.qbk → doc/distributions/poisson.qbk
View File

@@ -57,7 +57,7 @@ Returns the /mean/ of this distribution.
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions] that are generic to all
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions] that are generic to all
distributions are supported: __usual_accessors.
The domain of the random variable is \[0, [infin]\].

2
doc/sf_and_dist/distributions/rayleigh.qbk → doc/distributions/rayleigh.qbk
View File

@@ -72,7 +72,7 @@ Returns the /sigma/ parameter of this distribution.
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions] that are generic to all
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions] that are generic to all
distributions are supported: __usual_accessors.
The domain of the random variable is \[0, max_value\].

4
doc/sf_and_dist/distributions/skew_normal.qbk → doc/distributions/skew_normal.qbk
View File

@@ -112,7 +112,7 @@ by Adelchi Azzalini (2005-11-2).
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions]
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions]
that are generic to all distributions are supported: __usual_accessors.
The domain of the random variable is ['-[max_value], +[min_value]].
@@ -145,7 +145,7 @@ __Mathematica was also used to generate some more accurate spot test data.
The skew_normal distribution with shape = zero is implemented as a special case,
equivalent to the normal distribution in terms of the
[link math_toolkit.special.sf_erf.error_function error function],
[link math_toolkit.sf_erf.error_function error function],
and therefore should have excellent accuracy.
The PDF and mean, variance, skewness and kurtosis are also accurately evaluated using

8
doc/sf_and_dist/distributions/students_t.qbk → doc/distributions/students_t.qbk
View File

@@ -105,21 +105,21 @@ NIST Engineering Statistics Handbook].
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions] that are generic to all
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions] that are generic to all
distributions are supported: __usual_accessors.
The domain of the random variable is \[-[infin], +[infin]\].
[h4 Examples]
Various [link math_toolkit.dist.stat_tut.weg.st_eg worked examples] are available illustrating the use of the Student's t
Various [link math_toolkit.stat_tut.weg.st_eg worked examples] are available illustrating the use of the Student's t
distribution.
[h4 Accuracy]
The normal distribution is implemented in terms of the
[link math_toolkit.special.sf_beta.ibeta_function incomplete beta function]
and [link math_toolkit.special.sf_beta.ibeta_inv_function its inverses],
[link math_toolkit.sf_beta.ibeta_function incomplete beta function]
and [link math_toolkit.sf_beta.ibeta_inv_function its inverses],
refer to accuracy data on those functions for more information.
[h4 Implementation]

14
doc/sf_and_dist/distributions/students_t_examples.qbk → doc/distributions/students_t_examples.qbk
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@@ -47,7 +47,7 @@ From the formula, it should be clear that:
* The width increases as the ['significance level decreases] (0.5 towards 0.00000...01 - stronger).
The following example code is taken from the example program
[@../../../example/students_t_single_sample.cpp students_t_single_sample.cpp].
[@../../example/students_t_single_sample.cpp students_t_single_sample.cpp].
We'll begin by defining a procedure to calculate intervals for
various confidence levels; the procedure will print these out
@@ -202,7 +202,7 @@ Of course, the assignment of "true" to one mean may be quite arbitrary,
often this is simply a "traditional" method of measurement.
The following example code is taken from the example program
[@../../../example/students_t_single_sample.cpp students_t_single_sample.cpp].
[@../../example/students_t_single_sample.cpp students_t_single_sample.cpp].
We'll begin by defining a procedure to determine which of the
possible hypothesis are rejected or not-rejected
@@ -407,7 +407,7 @@ The parameter estimators of the students_t_distribution class
can provide this information.
This section is based on the example code in
[@../../../example/students_t_single_sample.cpp students_t_single_sample.cpp]
[@../../example/students_t_single_sample.cpp students_t_single_sample.cpp]
and we begin by defining a procedure that will print out a table of
estimated sample sizes for various confidence levels:
@@ -535,7 +535,7 @@ Car Mileage sample data] from the
miles per gallon of US cars with miles per gallon of Japanese cars.
The sample code is in
[@../../../example/students_t_two_samples.cpp students_t_two_samples.cpp].
[@../../example/students_t_two_samples.cpp students_t_two_samples.cpp].
There are two ways in which this test can be conducted: we can assume
that the true standard deviations of the two samples are equal or not.
@@ -759,13 +759,13 @@ we used in the single sample cases previously discussed.
That means we can:
* [link math_toolkit.dist.stat_tut.weg.st_eg.tut_mean_intervals Calculate confidence intervals of the mean].
* [link math_toolkit.stat_tut.weg.st_eg.tut_mean_intervals 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.
* [link math_toolkit.dist.stat_tut.weg.st_eg.tut_mean_test Test whether the true mean is zero]. If the
* [link math_toolkit.stat_tut.weg.st_eg.tut_mean_test 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.
* [link math_toolkit.dist.stat_tut.weg.st_eg.tut_mean_size Calculate how many pairs of readings we would need
* [link math_toolkit.stat_tut.weg.st_eg.tut_mean_size Calculate how many pairs of readings we would need
in order to obtain a significant result].
[endsect]

10
doc/sf_and_dist/distributions/triangular.qbk → doc/distributions/triangular.qbk
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@@ -102,7 +102,7 @@ Returns the /upper/ parameter of this distribution (default+1).
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions] that are generic to all
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions] that are generic to all
distributions are supported: __usual_accessors.
The domain of the random variable is \lower\ to \upper\,
@@ -134,12 +134,12 @@ x = c ; for p == p0
x = b - sqrt((b-a)(b-c)q) ; for p > p0
(See [@../../../../../boost/math/distributions/triangular.hpp /boost/math/distributions/triangular.hpp] for details.)]]
[[quantile from the complement][As quantile (See [@../../../../../boost/math/distributions/triangular.hpp /boost/math/distributions/triangular.hpp] for details.)]]
(See [@../../../../boost/math/distributions/triangular.hpp /boost/math/distributions/triangular.hpp] for details.)]]
[[quantile from the complement][As quantile (See [@../../../../boost/math/distributions/triangular.hpp /boost/math/distributions/triangular.hpp] for details.)]]
[[mean][(a + b + 3) \/ 3 ]]
[[variance][(a[super 2]+b[super 2]+c[super 2] - ab - ac - bc)\/18]]
[[mode][c]]
[[skewness][(See [@../../../../../boost/math/distributions/triangular.hpp /boost/math/distributions/triangular.hpp] for details). ]]
[[skewness][(See [@../../../../boost/math/distributions/triangular.hpp /boost/math/distributions/triangular.hpp] for details). ]]
[[kurtosis][12\/5]]
[[kurtosis excess][-3\/5]]
]
@@ -151,7 +151,7 @@ Some 'known good' test values were obtained from
* [@http://en.wikipedia.org/wiki/Triangular_distribution Wikpedia triangular distribution]
* [@http://mathworld.wolfram.com/TriangularDistribution.html Weisstein, Eric W. "Triangular Distribution." From MathWorld--A Wolfram Web Resource.]
* Evans, M.; Hastings, N.; and Peacock, B. "Triangular Distribution." Ch. 40 in Statistical Distributions, 3rd ed. New York: Wiley, pp. 187-188, 2000, ISBN - 0471371246]
* Evans, M.; Hastings, N.; and Peacock, B. "Triangular Distribution." Ch. 40 in Statistical Distributions, 3rd ed. New York: Wiley, pp. 187-188, 2000, ISBN - 0471371246.
* [@http://www.brighton-webs.co.uk/distributions/triangular.asp Brighton Webs Ltd. BW D-Calc 1.0 Distribution Calculator]
* [@http://www.worldscibooks.com/mathematics/etextbook/5720/5720_chap1.pdf The Triangular Distribution including its history.]
* [@http://www.measurement.sk/2002/S1/Wimmer2.pdf Gejza Wimmer, Viktor Witkovsky and Tomas Duby,

2
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@@ -87,7 +87,7 @@ Returns the /upper/ parameter of this distribution.
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions]
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions]
that are generic to all distributions are supported: __usual_accessors.
The domain of the random variable is any finite value,

2
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@@ -84,7 +84,7 @@ Returns the /scale/ parameter of this distribution.
[h4 Non-member Accessors]
All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions] that are generic to all
All the [link math_toolkit.dist_ref.nmp usual non-member accessor functions] that are generic to all
distributions are supported: __usual_accessors.
The domain of the random variable is \[0, [infin]\].

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