SciLib.Math
Class SpecFunc

java.lang.Object
  SciLib.Math.SpecFunc

public final class SpecFunc
extends java.lang.Object

This class contains some methods to construct numerical data.

Constructor Summary

SpecFunc()

Method Summary

static double	Bess0(double x, int n) The modified zeroth Bessl function
static double	beta(double z, double w) Compute the beta function at point z, w
static double	betainc(double a, double b, double x) Compute the incomplete beta function betainc(a,b,x) betainc(a,b,x) = 1/beta(a,b) * integral from 0 to x of t^(a-1)(1-t)^(b-1) dt
static double	bico(int n, int k) Compute the binomial coefficient
static double	diric(double x, int n) Compute Dirichlet(x,n)
static double	erf(double x) Compute the error function erf(x) erf(x) = 2/sqrt(pi) * integral from 0 to x of exp(-t^2)dt
static double	erfc(double x) Compute the error function erfc(x) erfx(x) = 2/sqrt(pi) * integral from x to inf of exp(-t^2)dt
static double	expi(double x) Compute the exponent integral function expi(n,x) = integral from -inf to x of exp(t)/t dt
static double	expint(int n, double x) Compute the exponent integral function expint(n,x) = integral from 1 to inf of exp(-x*t)/t^n dt
static double	factln(int n) Compute the logarithm of n!
static double	gamma(double x) Compute the logarithm of the gamma function at a point x gamma(x) = integral from 0 to inf of t^(x-1)exp(-t)dt
static double	gammaln(double x) Compute the logarithm of the gamma function at a point x gamma(x) = integral from 0 to inf of t^(x-1)exp(-t)dt
static double	gammap(double a, double x) Compute the gamma incomplete function P(a,x) gammap(a,x) = 1/gamma(a) * integral from 0 to x of t^(a-1)exp(-t)dt
static double	gammaq(double a, double x) Compute the gamma incomplete function Q(a,x) = 1 - P(a,x)

Methods inherited from class java.lang.Object

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

Constructor Detail

SpecFunc

public SpecFunc()

Method Detail

gamma

public static double gamma(double x)

Compute the logarithm of the gamma function at a point x gamma(x) = integral from 0 to inf of t^(x-1)exp(-t)dt

Parameters:

x - A double value. If x is an integer n gamma(n + 1) = n!

Returns:

A double value

gammaln

public static double gammaln(double x)

Compute the logarithm of the gamma function at a point x gamma(x) = integral from 0 to inf of t^(x-1)exp(-t)dt

Parameters:

x - A double value. If x is an integer n gamma(n + 1) = n!

Returns:

A double value

factln

public static double factln(int n)

Compute the logarithm of n!

Parameters:

n - An integer value

Returns:

A double value

bico

public static double bico(int n,
                          int k)

Compute the binomial coefficient

Parameters:

n - An integer value, n > 0.

k - An integer value, 0<= k <= n.

Returns:

An integer value, n!/k!(n-k)!

gammap

public static double gammap(double a,
                            double x)

Compute the gamma incomplete function P(a,x) gammap(a,x) = 1/gamma(a) * integral from 0 to x of t^(a-1)exp(-t)dt

Parameters:

a - A double value, a > 0.

x - A double value, x >= 0.

Returns:

A double value.

gammaq

public static double gammaq(double a,
                            double x)

Compute the gamma incomplete function Q(a,x) = 1 - P(a,x)

Parameters:

a - A double value, a > 0.

x - A double value, x >= 0.

Returns:

A double value.

erf

public static double erf(double x)

Compute the error function erf(x) erf(x) = 2/sqrt(pi) * integral from 0 to x of exp(-t^2)dt

Parameters:

x - A double value, x >= 0.

Returns:

A double value.

erfc

public static double erfc(double x)

Compute the error function erfc(x) erfx(x) = 2/sqrt(pi) * integral from x to inf of exp(-t^2)dt

Parameters:

x - A double value, x >= 0.

Returns:

A double value.

beta

public static double beta(double z,
                          double w)

Compute the beta function at point z, w

Parameters:

z - A double value.

w - A double value.

Returns:

A double value.

betainc

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

Compute the incomplete beta function betainc(a,b,x) betainc(a,b,x) = 1/beta(a,b) * integral from 0 to x of t^(a-1)(1-t)^(b-1) dt

Parameters:

a - A double value, a > 0.

b - A double value, b > 0.

x - A double value, 0 <= x <= 1.

Returns:

A double value.

expint

public static double expint(int n,
                            double x)

Compute the exponent integral function expint(n,x) = integral from 1 to inf of exp(-x*t)/t^n dt

Parameters:

n - An integer value, n >= 0.

x - A double value, x > 0.

Returns:

A double value.

expi

public static double expi(double x)

Compute the exponent integral function expi(n,x) = integral from -inf to x of exp(t)/t dt

Parameters:

x - A double value, x > 0.

Returns:

A double value.

diric

public static double diric(double x,
                           int n)

Compute Dirichlet(x,n)

Parameters:

x - A double value

n - An integer

Returns:

A double value

Bess0

public static double Bess0(double x,
                           int n)

The modified zeroth Bessl function

Parameters:

x - A double value

n - An integer

Returns:

A double value