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com.hartmath.expression
Class HDoubleSpecial
java.lang.Objectcom.hartmath.expression.HDoubleSpecial
- public class HDoubleSpecial
- extends java.lang.Object
The special function math library. This class cannot be subclassed or instantiated because all methods are static.
- Version:
- 1.0
| Field Summary | |
private static double[] |
ai02cs
|
private static double[] |
ai0cs
|
private static double[] |
ai12cs
|
private static double[] |
ai1cs
|
private static double[] |
aifcs
|
private static double[] |
aigcs
|
private static double[] |
aipcs
|
private static double[] |
am21cs
|
private static double[] |
am22cs
|
private static double[] |
ath1cs
|
private static double[] |
ath2cs
|
private static double[] |
bi0cs
|
private static double[] |
bi1cs
|
private static double[] |
bj0cs
|
private static double[] |
bj1cs
|
private static double[] |
bm0cs
|
private static double[] |
bm1cs
|
private static double[] |
bth0cs
|
private static double[] |
bth1cs
|
private static double[] |
by0cs
|
private static double[] |
by1cs
|
private static double |
logBetaCache_p
|
private static double |
logBetaCache_q
|
private static double |
logBetaCache_res
|
private static double |
logGamma_xBig
The largest argument for which logGamma(x) is representable in the machine. |
private static double |
logGammaCache_res
|
private static double |
logGammaCache_x
|
private static double |
LOGSQRT2PI
|
private static int |
MAX_ITERATIONS
|
private static double |
PRECISION
|
| Constructor Summary | |
private |
HDoubleSpecial()
Class Constructor. |
| Method Summary | |
static double |
airy(double x)
Airy function. |
private static double[] |
airyModPhase(double x)
Airy modulus and phase. |
static double |
besselFirstOne(double x)
Bessel function of first kind, order one. |
static double |
besselFirstZero(double x)
Bessel function of first kind, order zero. |
static double |
besselSecondOne(double x)
Bessel function of second kind, order one. |
static double |
besselSecondZero(double x)
Bessel function of second kind, order zero. |
static double |
beta(double p,
double q)
Beta function. |
private static double |
betaFraction(double x,
double p,
double q)
Evaluates of continued fraction part of incomplete beta function. |
static double |
chebyshev(double x,
double[] series)
Evaluates a Chebyshev series. |
static double |
complementaryError(double x)
Complementary error function. |
static double |
error(double x)
Error function. |
private static double |
expAiry(double x)
Exponential scaled Airy function. |
private static double |
expModBesselFirstOne(double x)
Exponential scaled modified Bessel function of first kind, order one. |
private static double |
expModBesselFirstZero(double x)
Exponential scaled modified Bessel function of first kind, order zero. |
static java.lang.String |
format(double d)
This method formats a floating point number to a minimum of 12 characters, six decimal places, in decimal format, right aligned, without + signs on positive numbers. |
static java.lang.String |
format(double d,
int width)
This method formats a floating point number to specified width, six decimal places, in decimal format, right aligned, without + signs on positive numbers. |
static java.lang.String |
format(double d,
int width,
int precision)
This method formats a floating point number to specified width, number of decimal places, in decimal format, right aligned, without + signs on positive numbers. |
static java.lang.String |
format(double d,
int width,
int precision,
boolean exponential)
This method formats a floating point number to specified width, number of decimal places, in exponential or decimal format, right aligned, without + signs on positive numbers. |
static java.lang.String |
format(double d,
int width,
int precision,
boolean exponential,
boolean alignLeft)
This method formats a floating point number to a specified width, number of decimal places, in exponential or decimal format, aligned left or right, without + signs on positive numbers. |
static java.lang.String |
format(double d,
int width,
int precision,
boolean exponential,
boolean alignLeft,
boolean usePlus)
This method formats a floating point number to a specified width, number of decimal places, in exponential or decimal format, aligned left or right, with or without + signs on positive numbers. |
static java.lang.String |
format(double d,
int width,
int precision,
boolean exponential,
boolean alignLeft,
boolean usePlus,
char pad)
This method formats a floating point number to a specified width, number of decimal places, in exponential or decimal format, aligned left or right, with or without + signs on positive numbers, and with a user-specified padding character used to fill out the number to the specified width. |
static double |
gamma(double x)
Gamma function. |
private static double |
gammaFraction(double a,
double x)
|
private static double |
gammaSeriesExpansion(double a,
double x)
|
static double |
incompleteBeta(double x,
double p,
double q)
Incomplete beta function. |
static double |
incompleteGamma(double a,
double x)
Incomplete gamma function. |
static double |
logBeta(double p,
double q)
The natural logarithm of the beta function. |
static double |
logGamma(double x)
The natural logarithm of the gamma function. |
static double |
modBesselFirstOne(double x)
Modified Bessel function of first kind, order one. |
static double |
modBesselFirstZero(double x)
Modified Bessel function of first kind, order zero. |
| Methods inherited from class java.lang.Object |
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
| Field Detail |
ai0cs
private static final double[] ai0cs
ai02cs
private static final double[] ai02cs
ai1cs
private static final double[] ai1cs
ai12cs
private static final double[] ai12cs
aifcs
private static final double[] aifcs
aigcs
private static final double[] aigcs
aipcs
private static final double[] aipcs
am21cs
private static final double[] am21cs
ath1cs
private static final double[] ath1cs
am22cs
private static final double[] am22cs
ath2cs
private static final double[] ath2cs
bi0cs
private static final double[] bi0cs
bj0cs
private static final double[] bj0cs
bm0cs
private static final double[] bm0cs
bth0cs
private static final double[] bth0cs
by0cs
private static final double[] by0cs
bi1cs
private static final double[] bi1cs
bj1cs
private static final double[] bj1cs
bm1cs
private static final double[] bm1cs
bth1cs
private static final double[] bth1cs
by1cs
private static final double[] by1cs
LOGSQRT2PI
private static final double LOGSQRT2PI
logGamma_xBig
private static final double logGamma_xBig
- The largest argument for which logGamma(x) is representable in the machine.
- See Also:
- Constant Field Values
logGammaCache_res
private static double logGammaCache_res
logGammaCache_x
private static double logGammaCache_x
MAX_ITERATIONS
private static final int MAX_ITERATIONS
- See Also:
- Constant Field Values
PRECISION
private static final double PRECISION
- See Also:
- Constant Field Values
logBetaCache_res
private static double logBetaCache_res
logBetaCache_p
private static double logBetaCache_p
logBetaCache_q
private static double logBetaCache_q
| Constructor Detail |
HDoubleSpecial
private HDoubleSpecial()
- Class Constructor.
| Method Detail |
chebyshev
public static double chebyshev(double x,
double[] series)
- Evaluates a Chebyshev series.
airy
public static double airy(double x)
- Airy function.
Based on the NETLIB Fortran function ai written by W. Fullerton.
airyModPhase
private static double[] airyModPhase(double x)
- Airy modulus and phase.
Based on the NETLIB Fortran subroutine r9aimp written by W. Fullerton.
expAiry
private static double expAiry(double x)
- Exponential scaled Airy function.
Based on the NETLIB Fortran function aie written by W. Fullerton.
besselFirstZero
public static double besselFirstZero(double x)
- Bessel function of first kind, order zero.
Based on the NETLIB Fortran function besj0 written by W. Fullerton.
modBesselFirstZero
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.
expModBesselFirstZero
private static double expModBesselFirstZero(double x)
- Exponential scaled modified Bessel function of first kind, order zero.
Based on the NETLIB Fortran function besi0e written by W. Fullerton.
besselFirstOne
public static double besselFirstOne(double x)
- Bessel function of first kind, order one.
Based on the NETLIB Fortran function besj1 written by W. Fullerton.
modBesselFirstOne
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.
expModBesselFirstOne
private static double expModBesselFirstOne(double x)
- Exponential scaled modified Bessel function of first kind, order one.
Based on the NETLIB Fortran function besi1e written by W. Fullerton.
besselSecondZero
public static double besselSecondZero(double x)
- Bessel function of second kind, order zero.
Based on the NETLIB Fortran function besy0 written by W. Fullerton.
besselSecondOne
public static double besselSecondOne(double x)
- Bessel function of second kind, order one.
Based on the NETLIB Fortran function besy1 written by W. Fullerton.
gamma
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:
- "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.
- 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.
logGamma
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:
- W. J. Cody and K. E. Hillstrom, 'Chebyshev Approximations for the Natural Logarithm of the Gamma Function,' Math. Comp. 21, 1967, pp. 198-203.
- K. E. Hillstrom, ANL/AMD Program ANLC366S, DGAMMA/DLGAMA, May, 1969.
- 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.
incompleteGamma
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).
gammaSeriesExpansion
private static double gammaSeriesExpansion(double a,
double x)
gammaFraction
private static double gammaFraction(double a,
double x)
beta
public static double beta(double p,
double q)
- Beta function.
logBeta
public static double logBeta(double p,
double q)
- The natural logarithm of the beta function.
incompleteBeta
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).
betaFraction
private static double betaFraction(double x,
double p,
double q)
- Evaluates of continued fraction part of incomplete beta function.
Based on an idea from Numerical Recipes (W.H. Press et al, 1992).
error
public static double error(double x)
- Error function.
Based on C-code for the error function developed at Sun Microsystems.
complementaryError
public static double complementaryError(double x)
- Complementary error function.
Based on C-code for the error function developed at Sun Microsystems.
format
public static java.lang.String format(double d)
- This method formats a floating point number to a minimum of 12 characters,
six decimal places, in decimal format,
right aligned, without +
signs on positive numbers. Spaces
fill out the number to the specified width.
format
public static java.lang.String format(double d, int width)
- This method formats a floating point number to specified width,
six decimal places, in decimal format,
right aligned, without +
signs on positive numbers. Spaces
fill out the number to the specified width.
format
public static java.lang.String format(double d, int width, int precision)
- This method formats a floating point number to specified width,
number of decimal places, in decimal format,
right aligned, without +
signs on positive numbers. Spaces
fill out the number to the specified width.
format
public static java.lang.String format(double d, int width, int precision, boolean exponential)
- This method formats a floating point number to specified width,
number of decimal places, in exponential or decimal format,
right aligned, without +
signs on positive numbers. Spaces
fill out the number to the specified width.
format
public static java.lang.String format(double d, int width, int precision, boolean exponential, boolean alignLeft)
- This method formats a floating point number to a specified width,
number of decimal places, in exponential or decimal format,
aligned left or right, without +
signs on positive numbers. Spaces
fill out the number to the specified width.
format
public static java.lang.String format(double d, int width, int precision, boolean exponential, boolean alignLeft, boolean usePlus)
- This method formats a floating point number to a specified width,
number of decimal places, in exponential or decimal format,
aligned left or right, with or without +
signs on positive numbers. Spaces
fill out the number to the specified width.
format
public static java.lang.String format(double d, int width, int precision, boolean exponential, boolean alignLeft, boolean usePlus, char pad)
- This method formats a floating point number to a specified width,
number of decimal places, in exponential or decimal format,
aligned left or right, with or without +
signs on positive numbers, and with a user-specified padding
character used to fill out the number to the specified width.
|
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| Home >> All >> com >> hartmath >> [ expression overview ] | PREV CLASS NEXT CLASS | ||||||||
|
SUMMARY: JAVADOC | SOURCE | DOWNLOAD | NESTED | FIELD | CONSTR | METHOD |
DETAIL: FIELD | CONSTR | METHOD | ||||||||