All Packages  Class Hierarchy  This Package  Previous  Next  Index

Class JSci.maths.SpecialMath

java.lang.Object
   |
   +----JSci.maths.AbstractMath
           |
           +----JSci.maths.SpecialMath

public final class SpecialMath

extends AbstractMath

implements NumericalConstants

airy(double)

Airy function.

besselFirstOne(double)

Bessel function of first kind, order one.

besselFirstZero(double)

Bessel function of first kind, order zero.

besselSecondOne(double)

Bessel function of second kind, order one.

besselSecondZero(double)

Bessel function of second kind, order zero.

beta(double, double)

Beta function.

chebyshev(double, double[])

Evaluates a Chebyshev series.

complementaryError(double)

Complementary error function.

error(double)

Error function.

gamma(double)

Gamma function.

incompleteBeta(double, double, double)

Incomplete beta function.

incompleteGamma(double, double)

Incomplete gamma function.

logBeta(double, double)

The natural logarithm of the beta function.

logGamma(double)

The natural logarithm of the gamma function.

modBesselFirstOne(double)

Modified Bessel function of first kind, order one.

modBesselFirstZero(double)

Modified Bessel function of first kind, order zero.

 public static double chebyshev(double x,
                                double series[])

Evaluates a Chebyshev series.

Parameters:

x - value at which to evaluate series

series - the coefficients of the series

 public static double airy(double x)

Airy function. Based on the NETLIB Fortran function ai written by W. Fullerton.

 public static double besselFirstZero(double x)

Bessel function of first kind, order zero. Based on the NETLIB Fortran function besj0 written by W. Fullerton.

 public static double modBesselFirstZero(double x)

Modified Bessel function of first kind, order zero. Based on the NETLIB Fortran function besi0 written by W. Fullerton.

 public static double besselFirstOne(double x)

Bessel function of first kind, order one. Based on the NETLIB Fortran function besj1 written by W. Fullerton.

 public static double modBesselFirstOne(double x)

Modified Bessel function of first kind, order one. Based on the NETLIB Fortran function besi1 written by W. Fullerton.

 public static double besselSecondZero(double x)

Bessel function of second kind, order zero. Based on the NETLIB Fortran function besy0 written by W. Fullerton.

 public static double besselSecondOne(double x)

Bessel function of second kind, order one. Based on the NETLIB Fortran function besy1 written by W. Fullerton.

 public static double gamma(double x)

Gamma function. Based on public domain NETLIB (Fortran) code by W. J. Cody and L. Stoltz
Applied Mathematics Division
Argonne National Laboratory
Argonne, IL 60439

References:

1. "An Overview of Software Development for Special Functions", W. J. Cody, Lecture Notes in Mathematics, 506, Numerical Analysis Dundee, 1975, G. A. Watson (ed.), Springer Verlag, Berlin, 1976.
2. Computer Approximations, Hart, Et. Al., Wiley and sons, New York, 1968.

From the original documentation:

This routine calculates the GAMMA function for a real argument X. Computation is based on an algorithm outlined in reference 1. The program uses rational functions that approximate the GAMMA function to at least 20 significant decimal digits. Coefficients for the approximation over the interval (1,2) are unpublished. Those for the approximation for X .GE. 12 are from reference 2. The accuracy achieved depends on the arithmetic system, the compiler, the intrinsic functions, and proper selection of the machine-dependent constants.

Error returns:
The program returns the value XINF for singularities or when overflow would occur. The computation is believed to be free of underflow and overflow.

Returns:

Double.MAX_VALUE if overflow would occur, i.e. if abs(x) > 171.624

 public static double logGamma(double x)

The natural logarithm of the gamma function. Based on public domain NETLIB (Fortran) code by W. J. Cody and L. Stoltz
Applied Mathematics Division
Argonne National Laboratory
Argonne, IL 60439

References:

1. W. J. Cody and K. E. Hillstrom, 'Chebyshev Approximations for the Natural Logarithm of the Gamma Function,' Math. Comp. 21, 1967, pp. 198-203.
2. K. E. Hillstrom, ANL/AMD Program ANLC366S, DGAMMA/DLGAMA, May, 1969.
3. Hart, Et. Al., Computer Approximations, Wiley and sons, New York, 1968.

From the original documentation:

This routine calculates the LOG(GAMMA) function for a positive real argument X. Computation is based on an algorithm outlined in references 1 and 2. The program uses rational functions that theoretically approximate LOG(GAMMA) to at least 18 significant decimal digits. The approximation for X > 12 is from reference 3, while approximations for X < 12.0 are similar to those in reference 1, but are unpublished. The accuracy achieved depends on the arithmetic system, the compiler, the intrinsic functions, and proper selection of the machine-dependent constants.

Error returns:
The program returns the value XINF for X .LE. 0.0 or when overflow would occur. The computation is believed to be free of underflow and overflow.

Returns:

Double.MAX_VALUE for x < 0.0 or when overflow would occur, i.e. x > 2.55E305

 public static double incompleteGamma(double a,
                                      double x)

Incomplete gamma function. The computation is based on approximations presented in Numerical Recipes, Chapter 6.2 (W.H. Press et al, 1992).

Parameters:

a - require a>=0

x - require x>=0

Returns:

0 if x<0, a<=0 or a>2.55E305 to avoid errors and over/underflow

 public static double beta(double p,
                           double q)

Beta function.

Parameters:

p - require p>0

q - require q>0

Returns:

0 if p<=0, q<=0 or p+q>2.55E305 to avoid errors and over/underflow

 public static double logBeta(double p,
                              double q)

The natural logarithm of the beta function.

Parameters:

p - require p>0

q - require q>0

Returns:

0 if p<=0, q<=0 or p+q>2.55E305 to avoid errors and over/underflow

 public static double incompleteBeta(double x,
                                     double p,
                                     double q)

Incomplete beta function. The computation is based on formulas from Numerical Recipes, Chapter 6.4 (W.H. Press et al, 1992).

Parameters:

x - require 0<=x<=1

p - require p>0

q - require q>0

Returns:

0 if x<0, p<=0, q<=0 or p+q>2.55E305 and 1 if x>1 to avoid errors and over/underflow

 public static double error(double x)

Error function. Based on C-code for the error function developed at Sun Microsystems.

 public static double complementaryError(double x)

Complementary error function. Based on C-code for the error function developed at Sun Microsystems.

All Packages  Class Hierarchy  This Package  Previous  Next  Index