public class Gamma
extends java.lang.Object
Modifier and Type | Field and Description |
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static double |
GAMMA
|
Modifier and Type | Method and Description |
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static double |
digamma(double x)
Computes the digamma function of x.
|
static double |
logGamma(double x)
Returns the natural logarithm of the gamma function Γ(x).
|
static double |
regularizedGammaP(double a,
double x)
Returns the regularized gamma function P(a, x).
|
static double |
regularizedGammaP(double a,
double x,
double epsilon,
int maxIterations)
Returns the regularized gamma function P(a, x).
|
static double |
regularizedGammaQ(double a,
double x)
Returns the regularized gamma function Q(a, x) = 1 - P(a, x).
|
static double |
regularizedGammaQ(double a,
double x,
double epsilon,
int maxIterations)
Returns the regularized gamma function Q(a, x) = 1 - P(a, x).
|
static double |
trigamma(double x)
Computes the trigamma function of x.
|
public static final double GAMMA
public static double logGamma(double x)
x
- Value.public static double regularizedGammaP(double a, double x)
a
- Parameter.x
- Value.MaxCountExceededException
- if the algorithm fails to converge.public static double regularizedGammaP(double a, double x, double epsilon, int maxIterations)
a
- the a parameter.x
- the value.epsilon
- When the absolute value of the nth item in the
series is less than epsilon the approximation ceases to calculate
further elements in the series.maxIterations
- Maximum number of "iterations" to complete.MaxCountExceededException
- if the algorithm fails to converge.public static double regularizedGammaQ(double a, double x)
a
- the a parameter.x
- the value.MaxCountExceededException
- if the algorithm fails to converge.public static double regularizedGammaQ(double a, double x, double epsilon, int maxIterations)
a
- the a parameter.x
- the value.epsilon
- When the absolute value of the nth item in the
series is less than epsilon the approximation ceases to calculate
further elements in the series.maxIterations
- Maximum number of "iterations" to complete.MaxCountExceededException
- if the algorithm fails to converge.public static double digamma(double x)
Computes the digamma function of x.
This is an independently written implementation of the algorithm described in Jose Bernardo, Algorithm AS 103: Psi (Digamma) Function, Applied Statistics, 1976.
Some of the constants have been changed to increase accuracy at the moderate expense of run-time. The result should be accurate to within 10^-8 absolute tolerance for x >= 10^-5 and within 10^-8 relative tolerance for x > 0.
Performance for large negative values of x will be quite expensive (proportional to |x|). Accuracy for negative values of x should be about 10^-8 absolute for results less than 10^5 and 10^-8 relative for results larger than that.
x
- Argument.public static double trigamma(double x)
x
- Argument.digamma(double)