fr.cnes.sirius.patrius.math.special

Class Beta

java.lang.Object

fr.cnes.sirius.patrius.math.special.Beta

public final class Beta
extends Object

This is a utility class that provides computation methods related to the Beta family of functions.

Implementation of logBeta(double, double) is based on the algorithms described in

• Didonato and Morris (1986), Computation of the Incomplete Gamma Function Ratios and their Inverse, TOMS 12(4), 377-393,
• Didonato and Morris (1992), Algorithm 708: Significant Digit Computation of the Incomplete Beta Function Ratios, TOMS 18(3), 360-373,

and implemented in the NSWC Library of Mathematical Functions, available here. This library is "approved for public release", and the Copyright guidance indicates that unless otherwise stated in the code, all FORTRAN functions in this library are license free. Since no such notice appears in the code these functions can safely be ported to Commons-Math.

Version:

$Id: Beta.java 18108 2017-10-04 06:45:27Z bignon $

Method Summary

Modifier and Type	Method and Description
static double	logBeta(double p, double q) Returns the value of log B(p, q) for 0 ≤ x ≤ 1 and p, q > 0.
protected static double	logGammaMinusLogGammaSum(double a, double b) Returns the value of log[Γ(b) / Γ(a + b)] for a ≥ 0 and b ≥ 10.
protected static double	logGammaSum(double a, double b) Returns the value of log Γ(a + b) for 1 ≤ a, b ≤ 2.
static double	regularizedBeta(double x, double a, double b) Returns the regularized beta function I(x, a, b).
static double	regularizedBeta(double x, double a, double b, double epsilon) Returns the regularized beta function I(x, a, b).
static double	regularizedBeta(double x, double a, double b, double epsilon, int maxIterations) Returns the regularized beta function I(x, a, b).
static double	regularizedBeta(double x, double a, double b, int maxIterations) Returns the regularized beta function I(x, a, b).
protected static double	sumDeltaMinusDeltaSum(double p, double q) Returns the value of Δ(p) + Δ(q) - Δ(p + q), with p, q ≥ 10.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

regularizedBeta

public static double regularizedBeta(double x,
                                     double a,
                                     double b)

Returns the regularized beta function I(x, a, b).

Parameters:

x - Value.

a - Parameter a.

b - Parameter b.

Returns:

the regularized beta function I(x, a, b).

Throws:

MaxCountExceededException - if the algorithm fails to converge.

regularizedBeta

public static double regularizedBeta(double x,
                                     double a,
                                     double b,
                                     double epsilon)

Returns the regularized beta function I(x, a, b).

Parameters:

x - Value.

a - Parameter a.

b - Parameter b.

epsilon - When the absolute value of the nth item in the series is less than epsilon the approximation ceases to calculate further elements in the series.

Returns:

the regularized beta function I(x, a, b)

Throws:

MaxCountExceededException - if the algorithm fails to converge.

regularizedBeta

public static double regularizedBeta(double x,
                                     double a,
                                     double b,
                                     int maxIterations)

Returns the regularized beta function I(x, a, b).

Parameters:

x - the value.

a - Parameter a.

b - Parameter b.

maxIterations - Maximum number of "iterations" to complete.

Returns:

the regularized beta function I(x, a, b)

Throws:

MaxCountExceededException - if the algorithm fails to converge.

regularizedBeta

public static double regularizedBeta(double x,
                                     double a,
                                     double b,
                                     double epsilon,
                                     int maxIterations)

Returns the regularized beta function I(x, a, b). The implementation of this method is based on:

• Regularized Beta Function.
• Regularized Beta Function.

Parameters:

x - the value.

a - Parameter a.

b - Parameter b.

epsilon - When the absolute value of the nth item in the series is less than epsilon the approximation ceases to calculate further elements in the series.

maxIterations - Maximum number of "iterations" to complete.

Returns:

the regularized beta function I(x, a, b)

Throws:

MaxCountExceededException - if the algorithm fails to converge.

logGammaSum

protected static double logGammaSum(double a,
                                    double b)

Returns the value of log Γ(a + b) for 1 ≤ a, b ≤ 2. Based on the NSWC Library of Mathematics Subroutines double precision implementation, DGSMLN.

Parameters:

a - First argument.

b - Second argument.

Returns:

the value of log(Gamma(a + b)).

Throws:

OutOfRangeException - if a or b is lower than 1.0 or greater than 2.0.

logGammaMinusLogGammaSum

protected static double logGammaMinusLogGammaSum(double a,
                                                 double b)

Returns the value of log[Γ(b) / Γ(a + b)] for a ≥ 0 and b ≥ 10. Based on the NSWC Library of Mathematics Subroutines double precision implementation, DLGDIV.

Parameters:

a - First argument.

b - Second argument.

Returns:

the value of log(Gamma(b) / Gamma(a + b)).

Throws:

NumberIsTooSmallException - if a < 0.0 or b < 10.0.

sumDeltaMinusDeltaSum

protected static double sumDeltaMinusDeltaSum(double p,
                                              double q)

Returns the value of Δ(p) + Δ(q) - Δ(p + q), with p, q ≥ 10. Based on the NSWC Library of Mathematics Subroutines double precision implementation, DBCORR.

Parameters:

p - First argument.

q - Second argument.

Returns:

the value of Delta(p) + Delta(q) - Delta(p + q).

Throws:

NumberIsTooSmallException - if p < 10.0 or q < 10.0.

logBeta

public static double logBeta(double p,
                             double q)

Returns the value of log B(p, q) for 0 ≤ x ≤ 1 and p, q > 0. Based on the NSWC Library of Mathematics Subroutines implementation, DBETLN.

Parameters:

p - First argument.

q - Second argument.

Returns:

the value of log(Beta(p, q)), NaN if p <= 0 or q <= 0.