Package etomica.math

Class SpecialFunctions

java.lang.Object

etomica.math.SpecialFunctions

public final class SpecialFunctions
extends java.lang.Object

Static-method library of various functions

Field Summary

Fields

Modifier and Type	Field	Description
protected static double	lastLPX
protected static double[]	lp
protected static int	maxLPN

Method Summary

Modifier and Type	Method	Description
static double	besselI(double order, double x)	The modified Bessel function of the first kind, I Reference: http://mathworld.wolfram.com/ModifiedBesselFunctionoftheFirstKind.html
static double	besselJ(double order, double x)	The unmodified Bessel function of the first kind, J.
static double	calcLegendrePolynomial(int n, double x)	Calculates Pn(x), Legendre polynomial of order n for the given input value.
static double	confluentHypergeometric1F1(double a, double c, double xin)	The confluent hypergeometric function, usually given the symbol 1F1.
static double	erfc(double x)	Complementary error function, computed using the approximant 7.1.26 of Abramowitz & Stegun.
static long	factorial(int n)	The factorial function, n! Will overflow with any input value greater than 20.
static double	gamma(double x)	Returns the value of the gamma function of x.
static double	lnFactorial(int n)	The log of the factorial function, ln(n!).
static double	lnGamma(double x)	Returns the ln(gamma), the natural logarithm of the gamma function.
static void	main(java.lang.String[] args)

Methods inherited from class java.lang.Object

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

Field Detail

lp

protected static double[] lp

lastLPX

protected static double lastLPX

maxLPN

protected static int maxLPN

Method Detail

erfc

public static double erfc(double x)

Complementary error function, computed using the approximant 7.1.26 of Abramowitz & Stegun. Absolute accuracy to within ~10^-7. If more precision is required, consider using Erf.erfc(double), which is more accurate but substantially slower (~10x - 100x) than the method given here.

Parameters:

x - argument to function, may take values from Double.NEGATIVE_INFINITY to Double.POSITIVE_INFINITY.

Returns:

value of complementary error function.

factorial

public static long factorial(int n)

The factorial function, n! Will overflow with any input value greater than 20.

Parameters:

n - an integer greater than or equal to 0

Returns:

the factorial of n

Throws:

java.lang.IllegalArgumentException - if n < 0

lnFactorial

public static double lnFactorial(int n)

The log of the factorial function, ln(n!). Will not overflow even if n! would be large.

Parameters:

n - an integer greater than or equal to 0

Returns:

the natural logarithm of the factorial of n.

Throws:

java.lang.IllegalArgumentException - if n < 0

lnGamma

public static double lnGamma(double x)

Returns the ln(gamma), the natural logarithm of the gamma function. Lanczos approximation, with precision ~15 digits coefficients from GSL (GNU Scientific Library) with g=7

Parameters:

x - a real number. If x is a non-positive integer (or if gamma(x) is negative), then NaN is returned.

Returns:

the natural logarithm of the gamma function of x.

gamma

public static double gamma(double x)

Returns the value of the gamma function of x.

Parameters:

x - a real number.

Returns:

the gamma function of x. If x is a non-positive integer, then NaN is returned.

confluentHypergeometric1F1

public static double confluentHypergeometric1F1(double a,
                                                double c,
                                                double xin)

The confluent hypergeometric function, usually given the symbol 1F1. For information about the function and use of parameters consult the link: http://mathworld.wolfram.com/ConfluentHypergeometricFunctionoftheFirstKind.html

calcLegendrePolynomial

public static double calcLegendrePolynomial(int n,
                                            double x)

Calculates Pn(x), Legendre polynomial of order n for the given input value. The method method makes use of recursion to calculate the return value, so calling the method for all n in a sequence should not be much more expensive than the call for the highest order.

Parameters:

n - order of the polynomial; must be non-negative.

x - argument of the polynomial.

Throws:

java.lang.IllegalArgumentException - if n < 0.

besselI

public static double besselI(double order,
                             double x)

The modified Bessel function of the first kind, I Reference: http://mathworld.wolfram.com/ModifiedBesselFunctionoftheFirstKind.html

Parameters:

order - of the Bessel function

x - the argument of the Bessel function

Returns:

modified Bessel function of the first kind, to machine precision.

besselJ

public static double besselJ(double order,
                             double x)

The unmodified Bessel function of the first kind, J. https://en.wikipedia.org/wiki/Bessel_function#Bessel_functions_of_the_first_kind:_J.CE.B1

Parameters:

order - of the Bessel function

x - the argument of the Bessel function

Returns:

unmodified Bessel function of the first kind, to the precision of 1E-13.

main

public static void main(java.lang.String[] args)