Package gov.nih.mipav.model.algorithms

Class Hypergeometric

java.lang.Object

gov.nih.mipav.model.algorithms.Hypergeometric

public class Hypergeometric
extends java.lang.Object

The function 2F1(a,b,c,x) is the hypergeometric function or Gauss's hypergeometric function.

The Pochhammer(a,b) = Gamma(a+b)/Gamma(a) 2F1(a,b,c,x) = sum from k = 0 to infinity of Poch(a,k)*Poch(b,k)*z**k/(k! * Poch(c,k))

It is the solution of the hypergeometric differential equation: z(1-z)y" + [c-(a+b+1)z]y' - aby = 0

The FORTRAN code this class is based upon is from Computation of Special Functions by Shanjie Zhang and Jianming Jin and copyright 1996 John Wiley & Sons, Inc.

From the diskette that the FORTRAN code came on:

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 these  programs  are  free  of  error,  or are consistent with any 
 particular  standard  of  merchantability,  or that they will meet 
 your requirements for any particular application.  They should not 
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 the programs in such a manner, it is at your own risk. The authors 
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Field Summary

Fields

Modifier and Type	Field	Description
private double	a	Input parameter
private double	b	Input parameter
private double	c	Input argument
static int	COMPLEX_VERSION
private double[]	imagResult
private double	imagZ
static int	REAL_VERSION
private double[]	realResult	outputted result
private double	realZ	Input argument
private double[]	result	Outputted result
private int	version	Tells whether real number or complex number version
private double	x	Input argument

Constructor Summary

Constructors

Constructor	Description
Hypergeometric()
Hypergeometric(double a, double b, double c, double x, double[] result)
Hypergeometric(double a, double b, double c, double realZ, double imagZ, double[] realResult, double[] imagResult)

Method Summary

Modifier and Type	Method	Description
private void	complexArgument()	This is a port of subroutine HYGFZ from Computation of Special Functions by Shanjie Zhang and Jianming Jin, pp. 380-385.
void	finalize()	Cleanup memory.
private void	realArgument()	This is a port of subroutine HYGFX from Computation of Special Functions by Shanjie Zhang and Jianming Jin, pp. 376-379.
void	run()
void	testcomplexArgument()
void	testrealArgument()
private double	zabs(double zr, double zi)	zabs computes the absolute value or magnitude of a double precision complex variable zr + j*zi.
private void	zdiv(double ar, double ai, double br, double bi, double[] cr, double[] ci)	complex divide c = a/b.
private void	zexp(double ar, double ai, double[] br, double[] bi)	complex exponential function b = exp(a).
private void	zlog(double ar, double ai, double[] br, double[] bi, int[] ierr)	complex logarithm b = clog(a).
private void	zmlt(double ar, double ai, double br, double bi, double[] cr, double[] ci)	complex multiply c = a * b.
private void	zpow(double zr, double zi, double a, double[] br, double[] bi, int[] ierr)	b = z**a = exp(a*log(z))
private void	zshch(double zr, double zi, double[] cshr, double[] cshi, double[] cchr, double[] cchi)	zshch computes the complex hyperbolic functions csh = sinh(x+i*y) and cch = cosh(x+i*y).
private void	zsqrt(double ar, double ai, double[] br, double[] bi)	complex square root b = csqrt(a).

Methods inherited from class java.lang.Object

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

Field Detail

REAL_VERSION

public static final int REAL_VERSION

See Also:

Constant Field Values

COMPLEX_VERSION

public static final int COMPLEX_VERSION

See Also:

Constant Field Values

version

private int version

Tells whether real number or complex number version

a

private double a

Input parameter

b

private double b

Input parameter

c

private double c

Input argument

result

private double[] result

Outputted result

x

private double x

Input argument

realZ

private double realZ

Input argument

imagZ

private double imagZ

realResult

private double[] realResult

outputted result

imagResult

private double[] imagResult

Constructor Detail

Hypergeometric

public Hypergeometric()

Hypergeometric

public Hypergeometric(double a,
                      double b,
                      double c,
                      double x,
                      double[] result)

Parameters:

a - input parameter

b - input parameter

c - input parameter c must not equal 0, -1, -2, ...

x - input argument

result - outputted result

Hypergeometric

public Hypergeometric(double a,
                      double b,
                      double c,
                      double realZ,
                      double imagZ,
                      double[] realResult,
                      double[] imagResult)

Parameters:

a - input real parameter

b - input real parameter

c - input real parameter c must not equal 0, -1, -2, ...

realZ - input real part of argument

imagZ - input imaginary part of argument

realResult - real part of outputted result

imagResult - imaginary part of outputted result

Method Detail

finalize

public void finalize()
              throws java.lang.Throwable

Cleanup memory.

Overrides:

finalize in class java.lang.Object

Throws:

java.lang.Throwable - DOCUMENT ME!

run

public void run()

testrealArgument

public void testrealArgument()

testcomplexArgument

public void testcomplexArgument()

realArgument

private void realArgument()

This is a port of subroutine HYGFX from Computation of Special Functions by Shanjie Zhang and Jianming Jin, pp. 376-379. c != 0, -1, -2 x <= 1

complexArgument

private void complexArgument()

This is a port of subroutine HYGFZ from Computation of Special Functions by Shanjie Zhang and Jianming Jin, pp. 380-385.

zpow

private void zpow(double zr,
                  double zi,
                  double a,
                  double[] br,
                  double[] bi,
                  int[] ierr)

b = z**a = exp(a*log(z))

Parameters:

zr -

zi -

a -

br -

bi -

ierr -

zabs

private double zabs(double zr,
                    double zi)

zabs computes the absolute value or magnitude of a double precision complex variable zr + j*zi.

Parameters:

zr - double

zi - double

Returns:

double

zdiv

private void zdiv(double ar,
                  double ai,
                  double br,
                  double bi,
                  double[] cr,
                  double[] ci)

complex divide c = a/b.

Parameters:

ar - double

ai - double

br - double

bi - double

cr - double[]

ci - double[]

zexp

private void zexp(double ar,
                  double ai,
                  double[] br,
                  double[] bi)

complex exponential function b = exp(a).

Parameters:

ar - double

ai - double

br - double[]

bi - double[]

zlog

private void zlog(double ar,
                  double ai,
                  double[] br,
                  double[] bi,
                  int[] ierr)

complex logarithm b = clog(a).

Parameters:

ar - double

ai - double

br - double[]

bi - double[]

ierr - int[] ierr = 0, normal return ierr = 1, z = cmplx(0.0, 0.0)

zmlt

private void zmlt(double ar,
                  double ai,
                  double br,
                  double bi,
                  double[] cr,
                  double[] ci)

complex multiply c = a * b.

Parameters:

ar - double

ai - double

br - double

bi - double

cr - double[]

ci - double[]

zshch

private void zshch(double zr,
                   double zi,
                   double[] cshr,
                   double[] cshi,
                   double[] cchr,
                   double[] cchi)

zshch computes the complex hyperbolic functions csh = sinh(x+i*y) and cch = cosh(x+i*y).

Parameters:

zr - double

zi - double

cshr - double[]

cshi - double[]

cchr - double[]

cchi - double[]

zsqrt

private void zsqrt(double ar,
                   double ai,
                   double[] br,
                   double[] bi)

complex square root b = csqrt(a).

Parameters:

ar - double

ai - double

br - double[]

bi - double[]