Author: celestin
Date: Tue Oct 2 05:00:41 2012
New Revision: 1392739
URL: http://svn.apache.org/viewvc?rev=1392739&view=rev
Log:
User's guide for special functions now reports accuracy of
Gamma.logGamma(double).
Modified:
commons/proper/math/trunk/src/site/apt/userguide/special.apt
Modified: commons/proper/math/trunk/src/site/apt/userguide/special.apt
URL:
http://svn.apache.org/viewvc/commons/proper/math/trunk/src/site/apt/userguide/special.apt?rev=1392739&r1=1392738&r2=1392739&view=diff
==============================================================================
--- commons/proper/math/trunk/src/site/apt/userguide/special.apt (original)
+++ commons/proper/math/trunk/src/site/apt/userguide/special.apt Tue Oct 2
05:00:41 2012
@@ -39,16 +39,35 @@
* 5.3 Gamma functions
- {{{../apidocs/org/apache/commons/math3/special/Gamma.html}Gamma}} contains
- several useful functions involving the Gamma Function.
+ Class {{{../apidocs/org/apache/commons/math3/special/Gamma.html}<<<Gamma>>>}}
+ contains several useful functions involving the Gamma Function.
-*-------------------+-------------------+---------------------------------------------------------------------------------------------------------------+
-|| Function || Method || Reference
|
-*-------------------+-------------------+---------------------------------------------------------------------------------------------------------------+
-| Log Gamma | logGamma | See
{{{http://mathworld.wolfram.com/GammaFunction.html}Gamma Function}} from
MathWorld |
-*-------------------+-------------------+---------------------------------------------------------------------------------------------------------------+
-| Regularized Gamma | regularizedGammaP | See
{{{http://mathworld.wolfram.com/RegularizedGammaFunction.html}Regularized Gamma
Function}} from MathWorld |
-*-------------------+-------------------+---------------------------------------------------------------------------------------------------------------+
+** 5.3.1 Log Gamma
+
+ <<<Gamma.logGamma(x)>>> computes the natural logarithm of the Gamma function,
+ log \u0393(x), for x > 0
+ (see {{{http://mathworld.wolfram.com/LogGammaFunction.html}MathWorld}},
+ {{{http://dlmf.nist.gov/5}DLMF}}). The accuracy of the Commons-Math
+ implementation is assessed by comparaison with high precision values computed
+ with the {{{http://maxima.sourceforge.net/}Maxima}} Computer Algebra System.
+
+*---------------------------------------------+---------------------------------------+-----------------+----------------+
+|| Interval || Values tested
|| Average error || Maximum error |
+*---------------------------------------------+---------------------------------------+-----------------+----------------+
+| (0.0, 8.0] | <<<k / 1024, k = 1, ...,
8192>>> | 0.32 ulps | 4.0 ulps |
+*---------------------------------------------+---------------------------------------+-----------------+----------------+
+| (8.0, 1024.0] | <<<k / 8, k = 65, ..., 8192>>>
| 0.43 ulps | 3.0 ulps |
+*---------------------------------------------+---------------------------------------+-----------------+----------------+
+| (1024.0, 8192.0] | <<<k, k = 1025, 8192>>>
| 0.53 ulps | 3.0 ulps |
+*---------------------------------------------+---------------------------------------+-----------------+----------------+
+| [8933.439345993791, 1.75555970201398e+305] | <<<2**(k / 8), k = 105, ...,
8112>>> | 0.35 ulps | 2.0 ulps |
+*---------------------------------------------+---------------------------------------+-----------------+----------------+
+
+** 5.3.2 Regularized Gamma
+
+ <<<Gamma.regularizedGammaP(a, x)>>> computes the value of the regularized
+ Gamma function, P(a, x)
+ (see
{{{http://mathworld.wolfram.com/RegularizedGammaFunction.html}MathWorld}}).
* 5.4 Beta funtions
