smile.math.special

Class Gamma

java.lang.Object

smile.math.special.Gamma

public class Gamma
extends Object

The gamma, digamma, and incomplete gamma functions.

Author:

Haifeng Li

Constructor Summary

Constructors

Constructor and Description
Gamma()

Method Summary

Modifier and Type	Method and Description
static double	digamma(double x) The digamma function is defined as the logarithmic derivative of the gamma function.
static double	gamma(double x) Gamma function.
static double	inverseRegularizedIncompleteGamma(double a, double p) The inverse of regularized incomplete gamma function.
static double	logGamma(double x) log of the Gamma function.
static double	regularizedIncompleteGamma(double s, double x) Regularized Incomplete Gamma Function P(s,x) = ∫0x e-t t(s-1) dt
static double	regularizedUpperIncompleteGamma(double s, double x) Regularized Upper/Complementary Incomplete Gamma Function Q(s,x) = 1 - P(s,x) = 1 - ∫0x e-t t(s-1) dt

Methods inherited from class java.lang.Object

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

Constructor Detail

Gamma

public Gamma()

Method Detail

gamma

public static double gamma(double x)

Gamma function. Lanczos approximation (6 terms).

logGamma

public static double logGamma(double x)

log of the Gamma function. Lanczos approximation (6 terms)

regularizedIncompleteGamma

public static double regularizedIncompleteGamma(double s,
                                                double x)

Regularized Incomplete Gamma Function P(s,x) = ∫₀^x e^-t t^(s-1) dt

regularizedUpperIncompleteGamma

public static double regularizedUpperIncompleteGamma(double s,
                                                     double x)

Regularized Upper/Complementary Incomplete Gamma Function Q(s,x) = 1 - P(s,x) = 1 - ∫₀^x e^-t t^(s-1) dt

digamma

public static double digamma(double x)

The digamma function is defined as the logarithmic derivative of the gamma function.

inverseRegularizedIncompleteGamma

public static double inverseRegularizedIncompleteGamma(double a,
                                                       double p)

The inverse of regularized incomplete gamma function.