Package gov.nih.mipav.model.algorithms

Class Hypergeometric

java.lang.Object
gov.nih.mipav.model.algorithms.Hypergeometric
public class Hypergeometric extends 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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  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    private double
    a
    Input parameter
    private double
    b
    Input parameter
    private double
    c
    Input argument
    static final int
    COMPLEX_VERSION
     
    private double[]
    imagResult
     
    private double
    imagZ
     
    static final 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 Details

    • REAL_VERSION

      public static final int REAL_VERSION
      See Also:

    • COMPLEX_VERSION

      public static final int COMPLEX_VERSION
      See Also:

    • 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 Details

    • 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 Details

    • finalize

      public void finalize() throws Throwable
      Cleanup memory.
      Overrides:
      finalize in class Object
      Throws:
      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 invalid input: '<'= 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[]