org.mariuszgromada.math.mxparser.mathcollection

Class SpecialFunctions

java.lang.Object

org.mariuszgromada.math.mxparser.mathcollection.SpecialFunctions

public final class SpecialFunctions
extends Object

SpecialFunctions - special (non-elementary functions).

Version:

4.2.0

Author:

Mariusz Gromada
mariuszgromada.org@gmail.com
MathSpace.pl
MathParser.org - mXparser project page
mXparser on GitHub
mXparser on SourceForge
mXparser on Bitbucket
mXparser on CodePlex
Janet Sudoku - project web page
Janet Sudoku on GitHub
Janet Sudoku on CodePlex
Janet Sudoku on SourceForge
Janet Sudoku on BitBucket

Constructor Summary

Constructors

Constructor and Description
SpecialFunctions()

Method Summary

Modifier and Type	Method and Description
static double	beta(double x, double y) Beta special function
static double	diGamma(double x) Digamma function as the logarithmic derivative of the Gamma special function
static double	erf(double x) Calculates the error function
static double	erfc(double x) Calculates the complementary error function.
static double	erfcInv(double z) Calculates the complementary inverse error function evaluated at x.
static double	erfInv(double x) Calculates the inverse error function evaluated at x.
static double	exponentialIntegralEi(double x) Exponential integral function Ei(x)
static double	gamma(double x) Real valued Gamma function
static double	incompleteBeta(double a, double b, double x) Log Incomplete Beta special function
static double	incompleteGammaLower(double s, double x) Incomplete lower gamma function
static double	incompleteGammaUpper(double s, double x) Incomplete upper gamma function
static double	lambertW(double x, double branch) Real-valued Lambert-W function approximation.
static double	lanchosGamma(double x) Gamma function implementation based on Lanchos approximation algorithm
static double	logarithmicIntegralLi(double x) Logarithmic integral function li(x)
static double	logBeta(double x, double y) Log Beta special function
static double	logGamma(double x) Real valued log gamma function.
static double	offsetLogarithmicIntegralLi(double x) Offset logarithmic integral function Li(x)
static double	regularizedBeta(double a, double b, double x) Regularized incomplete Beta special function
static double	regularizedGammaLowerP(double s, double x) Regularized lower gamma function 'P'
static double	regularizedGammaUpperQ(double s, double x) Regularized upper gamma function 'Q'
static double	sgnGamma(double x) Signum from the real valued gamma function.

Methods inherited from class java.lang.Object

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

Constructor Detail

SpecialFunctions

public SpecialFunctions()

Method Detail

exponentialIntegralEi

public static double exponentialIntegralEi(double x)

Exponential integral function Ei(x)

Parameters:

x - Point at which function will be evaluated.

Returns:

Exponential integral function Ei(x)

logarithmicIntegralLi

public static final double logarithmicIntegralLi(double x)

Logarithmic integral function li(x)

Parameters:

x - Point at which function will be evaluated.

Returns:

Logarithmic integral function li(x)

offsetLogarithmicIntegralLi

public static final double offsetLogarithmicIntegralLi(double x)

Offset logarithmic integral function Li(x)

Parameters:

x - Point at which function will be evaluated.

Returns:

Offset logarithmic integral function Li(x)

erf

public static final double erf(double x)

Calculates the error function

Parameters:

x - Point at which function will be evaluated.

Returns:

Error function erf(x)

erfc

public static final double erfc(double x)

Calculates the complementary error function.

Parameters:

x - Point at which function will be evaluated.

Returns:

Complementary error function erfc(x)

erfInv

public static final double erfInv(double x)

Calculates the inverse error function evaluated at x.

Parameters:

x - Point at which function will be evaluated.

Returns:

Inverse error function erfInv(x)

erfcInv

public static final double erfcInv(double z)

Calculates the complementary inverse error function evaluated at x.

Parameters:

z - Point at which function will be evaluated.

Returns:

Inverse of complementary inverse error function erfcInv(x)

gamma

public static final double gamma(double x)

Real valued Gamma function

Parameters:

x - Argument value

Returns:

Returns gamma function value.

lanchosGamma

public static final double lanchosGamma(double x)

Gamma function implementation based on Lanchos approximation algorithm

Parameters:

x - Function parameter

Returns:

Gamma function value (Lanchos approx).

logGamma

public static double logGamma(double x)

Real valued log gamma function.

Parameters:

x - Argument value

Returns:

Returns log value from gamma function.

sgnGamma

public static final double sgnGamma(double x)

Signum from the real valued gamma function.

Parameters:

x - Argument value

Returns:

Returns signum of the gamma(x)

regularizedGammaLowerP

public static final double regularizedGammaLowerP(double s,
                                                  double x)

Regularized lower gamma function 'P'

Parameters:

s - Argument value

x - Argument value

Returns:

Value of the regularized lower gamma function 'P'.

incompleteGammaLower

public static final double incompleteGammaLower(double s,
                                                double x)

Incomplete lower gamma function

Parameters:

s - Argument value

x - Argument value

Returns:

Value of the incomplete lower gamma function.

regularizedGammaUpperQ

public static final double regularizedGammaUpperQ(double s,
                                                  double x)

Regularized upper gamma function 'Q'

Parameters:

s - Argument value

x - Argument value

Returns:

Value of the regularized upper gamma function 'Q'.

incompleteGammaUpper

public static final double incompleteGammaUpper(double s,
                                                double x)

Incomplete upper gamma function

Parameters:

s - Argument value

x - Argument value

Returns:

Value of the incomplete upper gamma function.

diGamma

public static final double diGamma(double x)

Digamma function as the logarithmic derivative of the Gamma special function

Parameters:

x - Argument value

Returns:

Approximated value of the digamma function.

logBeta

public static double logBeta(double x,
                             double y)

Log Beta special function

Parameters:

x - Argument value

y - Argument value

Returns:

Return logBeta special function (for positive x and positive y)

beta

public static double beta(double x,
                          double y)

Beta special function

Parameters:

x - Argument value

y - Argument value

Returns:

Return Beta special function (for positive x and positive y)

incompleteBeta

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

Log Incomplete Beta special function

Parameters:

a - Argument value

b - Argument value

x - Argument value

Returns:

Return incomplete Beta special function for positive a and positive b and x between 0 and 1

regularizedBeta

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

Regularized incomplete Beta special function

Parameters:

a - Argument value

b - Argument value

x - Argument value

Returns:

Return incomplete Beta special function for positive a and positive b and x between 0 and 1

lambertW

public static final double lambertW(double x,
                                    double branch)

Real-valued Lambert-W function approximation.

Parameters:

x - Point at which function will be approximated

branch - Branch id, 0 for principal branch, -1 for the other branch

Returns:

Principal branch for x greater or equal than -1/e, otherwise Double.NaN. Minus 1 branch for x greater or equal than -1/e and lower than 0, otherwise Double.NaN.