Package etomica.spin.heisenberg

Class FunctionCosIntegral

java.lang.Object

etomica.spin.heisenberg.FunctionCosIntegral

public class FunctionCosIntegral
extends java.lang.Object

Constructor Summary

Constructors

Constructor	Description
FunctionCosIntegral()

Method Summary

Modifier and Type	Method	Description
static double	cos2cosInt(double x, double b)	Integral of cos(t)^2 Exp(b cos(t)) for t from 0 to x.
static double	coscosInt(double x, double b)	Integral of cos(t) Exp(b cos(t)) for t from 0 to x, accurate to within 0.01% for all b > 0 and -2Pi < x < 2Pi.
static double	cosInt(double x, double b)	Integral of Exp(b cos(t)) for t from 0 to x, accurate to within 0.01% for all b > 0 and -2Pi < x < 2Pi.
static double[]	getValue(double x, double b, double theta0)	thetaDot for mean-field mapping of XY model, calculation of correlation function via 2nd free-energy derivative
static void	main(java.lang.String[] args)
static double	sincoscosInt(double x, double b)	Integral of sin(t) cos(t) Exp(b cos(t)) for t from 0 to x, accurate to within 0.01% for all b > 0 and -2Pi < x < 2Pi.
static double	sincosInt(double x, double b)	Integral of sin(t) Exp(b cos(t)) for t from 0 to x, accurate to within 0.01% for all b > 0 and -2Pi < x < 2Pi.

Methods inherited from class java.lang.Object

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

Constructor Detail

FunctionCosIntegral

public FunctionCosIntegral()

Method Detail

getValue

public static double[] getValue(double x,
                                double b,
                                double theta0)

thetaDot for mean-field mapping of XY model, calculation of correlation function via 2nd free-energy derivative

Returns:

thetaDot, with components for derivative with respect to field in x and y directions, respectively

cosInt

public static double cosInt(double x,
                            double b)

Integral of Exp(b cos(t)) for t from 0 to x, accurate to within 0.01% for all b > 0 and -2Pi < x < 2Pi.

sincosInt

public static double sincosInt(double x,
                               double b)

Integral of sin(t) Exp(b cos(t)) for t from 0 to x, accurate to within 0.01% for all b > 0 and -2Pi < x < 2Pi.

sincoscosInt

public static double sincoscosInt(double x,
                                  double b)

Integral of sin(t) cos(t) Exp(b cos(t)) for t from 0 to x, accurate to within 0.01% for all b > 0 and -2Pi < x < 2Pi.

coscosInt

public static double coscosInt(double x,
                               double b)

Integral of cos(t) Exp(b cos(t)) for t from 0 to x, accurate to within 0.01% for all b > 0 and -2Pi < x < 2Pi.

cos2cosInt

public static double cos2cosInt(double x,
                                double b)

Integral of cos(t)^2 Exp(b cos(t)) for t from 0 to x. Evaluates via integration by parts using cosInt and coscosInt. Accurate to within 0.015% for b > 0 and x between 0 and 2pi.

main

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