Copyright © 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg
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)
@@ -513,7 +513,7 @@Last revised: July 08, 2011 at 17:57:48 GMT |
+Last revised: July 09, 2011 at 16:25:51 GMT |
A B C D E F G H I K L M N P Q R S T U V W Z
betac
+ +betaf
binomial_coefficient
+ +brent_find_minima
+ +cdf
+ +changesign
checked_narrowing_cast
+ +chf
+ +comp_ellint_1
comp_ellint_2
+ +comp_ellint_2f
+ +comp_ellint_2l
+ +comp_ellint_3
+ +comp_ellint_3f
+ +comp_ellint_3l
+ +conf_hyperg
continued_fraction_a
+ +continued_fraction_b
+ +copysign
e
+ +ellint_1
ellint_rc
+ +ellint_rd
+ +ellint_rf
+ +ellint_rj
+ +epsilon
+ +erf
erfc_inv
+ +erff
erf_inv
+ +evaluate_even_polynomial
+ +evaluate_odd_polynomial
+ +evaluate_polynomial
+ +evaluate_rational
+ +exp2
e_float
+ +fdim
find_beta
+ +find_degrees_of_freedom
+ +find_location
+ +find_lower_bound_on_p
+ +find_non_centrality
+ +find_scale
+ +find_upper_bound_on_p
+ +float_advance
+ +float_distance
+ +float_next
+ +float_prior
+ +fma
gamma_p
+ +gamma_p_derivative
+ +gamma_p_inv
+ +gamma_p_inva
+ +gamma_q
+ +gamma_q_inv
+ +gamma_q_inva
+ +get_user_parameter_info
+ +halley_iterate
+ +hazard
+ +hermite
hermite_next
+ +hyperg
ibeta
+ +ibetac
+ +ibetac_inv
+ +ibetac_inva
+ +ibetac_invb
+ +ibeta_derivative
+ +ibeta_inv
+ +ibeta_inva
+ +ibeta_invb
+ +ilogb
infinity
+ +insert
+ +iround
+ +isfinite
isnormal
+itrunc
+ +kahan_sum_series
+ +kurtosis
+ +kurtosis_excess
+ +laguerre_next
+ +ldexp
+ +legendre
legendre_next
+ +legendre_p
+ +legendre_q
+ +lgamma
lltrunc
+ +log1p
ltrunc
+ +make_periodic_param
+ +make_policy
+ +make_power_param
+ +make_random_param
+ +mean
+ +median
+ +mode
+ +msg
+ +newton_raphson_iterate
+ +nextafter
norm
+ +quantile
+Some Miscellaneous Examples of the Normal (Gaussian) Distribution
r
+ +range
+ +relative_error
+ +remainder
round
RR
+ +scale
+schroeder_iterate
+ +shape
+ +sign
signbit
+skewness
+ +spherical_harmonic
+ +spherical_harmonic_i
+ +spherical_harmonic_r
+ +sph_bessel
standard_deviation
+ +sum_series
+ +t
+ +test
+ +tgamma
tgamma1pm1
+ +tgammaf
tgamma_delta_ratio
+ +tgamma_lower
+ +tgamma_ratio
+ +tol
+ +trunc
user_denorm_error
+ +user_domain_error
+ +user_evaluation_error
+ +user_indeterminate_result_error
+ +user_overflow_error
+ +user_pole_error
+ +user_rounding_error
+ +user_underflow_error
+ +value
+ +variance
+ +write_code
+ +write_csv
+ +|
- 17.89[2] +17.89[2]
(4.248e-005s) @@ -548,11 +548,11 @@ | ||||||||
|
- [1] + [1] Cephes gets stuck in an infinite loop while trying to execute our test cases. [2] + [2] The performance here is dominated by a few cases where the parameters grow very large: faster asymptotic expansions are available, but are of limited (or even frankly terrible) precision. The @@ -659,7 +659,7 @@
| - 67.66[1] +67.66[1]
(3.366e-004s) @@ -1088,7 +1088,7 @@
| - 3.60[2] +3.60[2]
(5.987e-007s) @@ -1317,7 +1317,7 @@
| - 43.43[3] +43.43[3]
(3.732e-004s) @@ -1387,7 +1387,7 @@
| - 393.90[4] +393.90[4]
(2.673e-002s) @@ -1523,7 +1523,7 @@
| - 1.00[5] +1.00[5]
(4.411e-004s) @@ -1809,28 +1809,28 @@ | |||
|
- [1] + [1] There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result. [2] + [2] This result is somewhat misleading: for small values of the parameters there is virtually no difference between the two libraries, but for large values the Boost implementation is much slower, albeit with much improved precision. [3] + [3] The R library appears to use a linear-search strategy, that can perform very badly in a small number of pathological cases, but may or may not be more efficient in "typical" cases [4] + [4] There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result. [5] + [5] There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result. @@ -1934,7 +1934,7 @@
| - 30.51[1] +30.51[1]
(3.616e-004s) @@ -2363,7 +2363,7 @@
| - 2.20[2] +2.20[2]
(3.522e-007s) @@ -2592,7 +2592,7 @@
| - 25.92[3] +25.92[3]
(4.407e-004s) @@ -2662,7 +2662,7 @@
| - 144.91[4] +144.91[4]
(3.214e-002s) @@ -2798,7 +2798,7 @@
| - 1.00[5] +1.00[5]
(5.916e-004s) @@ -3084,28 +3084,28 @@ | |||
|
- [1] + [1] There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result. [2] + [2] This result is somewhat misleading: for small values of the parameters there is virtually no difference between the two libraries, but for large values the Boost implementation is much slower, albeit with much improved precision. [3] + [3] The R library appears to use a linear-search strategy, that can perform very badly in a small number of pathological cases, but may or may not be more efficient in "typical" cases [4] + [4] There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result. [5] + [5] There are a small number of our test cases where the R library fails to converge on a result: these tend to dominate the performance result. diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html index 16e6e5672..95c862ee8 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html +++ b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html @@ -278,7 +278,7 @@ Π(n, φ+mπ, k) = Π(n, φ, k) + 2mΠ(n, k) ; n <= 1 - Π(n, φ+mπ, k) = Π(n, φ, k) ; n > 1 [1] + Π(n, φ+mπ, k) = Π(n, φ, k) ; n > 1 [1] are used to move φ to the range [0, π/2]. @@ -298,7 +298,7 @@ - [1] + [1] I haven't been able to find a literature reference for this relation, but it appears to be the convention used by Mathematica. Intuitively the first 2 * m * Π(n, k) terms cancel out as the diff --git a/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html b/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html index 7aa8d5589..1b3a19780 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html +++ b/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html @@ -247,7 +247,7 @@ a minimax rational approximation rescaled so that it is evaluated over [-1,1]. Note that while the rational approximation over [0,6] converges rapidly to the minimax solution it is rather ill-conditioned in practice. - Cody and Thacher [2] experienced the same issue and converted the polynomials into + Cody and Thacher [2] experienced the same issue and converted the polynomials into Chebeshev form to ensure stable computation. By experiment we found that the polynomials are just as stable in polynomial as Chebyshev form, provided they are computed over the interval [-1,1]. @@ -277,7 +277,7 @@ | ||||||||