Complete and incomplete gamma function approximations. More...

#include <cmath>
#include "vnl/vnl_export.h"

Functions
VNL_EXPORT double	vnl_log_gamma (double x)
	Approximate log of gamma function. More...

double	vnl_gamma (double x)
	Approximate gamma function. More...

VNL_EXPORT double	vnl_gamma_p (double a, double x)
	Normalised Incomplete gamma function, P(a,x). More...

VNL_EXPORT double	vnl_gamma_q (double a, double x)
	Normalised Incomplete gamma function, Q(a,x). More...

double	vnl_cum_prob_chi2 (int n_dof, double chi2)
	P(chi<chi2). More...

VNL_EXPORT double	vnl_digamma (double x)
	approximate digamma function, dLog[gamma[z]]/dz. More...

Detailed Description

Complete and incomplete gamma function approximations.

Author: Tim Cootes

Definition in file vnl_gamma.h.

Function Documentation

◆ vnl_cum_prob_chi2()

double vnl_cum_prob_chi2	(	int	n_dof,
		double	chi2
	)

inline

P(chi<chi2).

Calculates the probability that a value generated at random from a chi-square distribution with given degrees of freedom is less than the value chi2

Parameters

n_dof	Number of degrees of freedom
chi2	Value of chi-squared

Definition at line 43 of file vnl_gamma.h.

◆ vnl_digamma()

VNL_EXPORT double vnl_digamma ( double x )

approximate digamma function, dLog[gamma[z]]/dz.

Analytic derivative of the Lanczos approximation. Error < 10^-11 1<z<20.

Definition at line 114 of file vnl_gamma.cxx.

◆ vnl_gamma()

double vnl_gamma ( double x )

inline

Approximate gamma function.

Uses 6 parameter Lanczos approximation as described by Toth (http://www.rskey.org/gamma.htm) Accurate to about one part in 3e-11.

Definition at line 25 of file vnl_gamma.h.

◆ vnl_gamma_p()

VNL_EXPORT double vnl_gamma_p	(	double	a,
		double	x
	)

Normalised Incomplete gamma function, P(a,x).

$P(a,x)=\frac{1}{\Gamma(a)}\int_0^x e^{-t}t^{a-1}dt$ Note the order of parameters - this is the normal maths order. MATLAB uses gammainc(x,a), ie the other way around

Definition at line 92 of file vnl_gamma.cxx.

◆ vnl_gamma_q()

VNL_EXPORT double vnl_gamma_q	(	double	a,
		double	x
	)

Normalised Incomplete gamma function, Q(a,x).

$Q(a,x)=\frac{1}{\Gamma(a)}\int_x^{\infty}e^{-t}t^{a-1}dt$

Definition at line 103 of file vnl_gamma.cxx.

◆ vnl_log_gamma()

VNL_EXPORT double vnl_log_gamma ( double x )

Approximate log of gamma function.