Package gov.nih.mipav.model.algorithms

Class 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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    • 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

      All Methods Instance Methods Concrete Methods 
      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

      • 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

        • 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[]