194 lines
4.0 KiB
C++
194 lines
4.0 KiB
C++
/* Translated into C++ by SciPy developers in 2024.
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* Original header with Copyright information appears below.
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*/
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/* chdtr.c
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*
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* Chi-square distribution
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*
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*
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*
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* SYNOPSIS:
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*
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* double df, x, y, chdtr();
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*
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* y = chdtr( df, x );
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*
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*
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*
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* DESCRIPTION:
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*
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* Returns the area under the left hand tail (from 0 to x)
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* of the Chi square probability density function with
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* v degrees of freedom.
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*
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*
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* inf.
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* -
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* 1 | | v/2-1 -t/2
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* P( x | v ) = ----------- | t e dt
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* v/2 - | |
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* 2 | (v/2) -
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* x
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*
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* where x is the Chi-square variable.
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*
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* The incomplete Gamma integral is used, according to the
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* formula
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*
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* y = chdtr( v, x ) = igam( v/2.0, x/2.0 ).
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*
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*
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* The arguments must both be positive.
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*
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*
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*
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* ACCURACY:
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*
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* See igam().
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*
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* ERROR MESSAGES:
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*
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* message condition value returned
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* chdtr domain x < 0 or v < 1 0.0
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*/
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/* chdtrc()
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*
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* Complemented Chi-square distribution
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*
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*
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*
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* SYNOPSIS:
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*
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* double v, x, y, chdtrc();
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*
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* y = chdtrc( v, x );
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*
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*
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*
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* DESCRIPTION:
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*
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* Returns the area under the right hand tail (from x to
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* infinity) of the Chi square probability density function
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* with v degrees of freedom:
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*
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*
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* inf.
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* -
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* 1 | | v/2-1 -t/2
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* P( x | v ) = ----------- | t e dt
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* v/2 - | |
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* 2 | (v/2) -
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* x
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*
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* where x is the Chi-square variable.
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*
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* The incomplete Gamma integral is used, according to the
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* formula
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*
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* y = chdtr( v, x ) = igamc( v/2.0, x/2.0 ).
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*
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*
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* The arguments must both be positive.
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*
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*
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*
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* ACCURACY:
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*
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* See igamc().
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*
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* ERROR MESSAGES:
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*
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* message condition value returned
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* chdtrc domain x < 0 or v < 1 0.0
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*/
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/* chdtri()
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*
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* Inverse of complemented Chi-square distribution
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*
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*
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*
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* SYNOPSIS:
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*
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* double df, x, y, chdtri();
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*
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* x = chdtri( df, y );
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*
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*
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*
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*
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* DESCRIPTION:
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*
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* Finds the Chi-square argument x such that the integral
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* from x to infinity of the Chi-square density is equal
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* to the given cumulative probability y.
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*
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* This is accomplished using the inverse Gamma integral
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* function and the relation
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*
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* x/2 = igamci( df/2, y );
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*
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*
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*
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*
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* ACCURACY:
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*
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* See igami.c.
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*
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* ERROR MESSAGES:
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*
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* message condition value returned
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* chdtri domain y < 0 or y > 1 0.0
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* v < 1
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*
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*/
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/* chdtr() */
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/*
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* Cephes Math Library Release 2.0: April, 1987
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* Copyright 1984, 1987 by Stephen L. Moshier
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* Direct inquiries to 30 Frost Street, Cambridge, MA 02140
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*/
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#pragma once
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#include "../config.h"
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#include "../error.h"
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#include "igam.h"
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#include "igami.h"
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namespace xsf {
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namespace cephes {
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XSF_HOST_DEVICE inline double chdtrc(double df, double x) {
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if (x < 0.0)
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return 1.0; /* modified by T. Oliphant */
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return (igamc(df / 2.0, x / 2.0));
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}
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XSF_HOST_DEVICE inline double chdtr(double df, double x) {
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if ((x < 0.0)) { /* || (df < 1.0) ) */
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set_error("chdtr", SF_ERROR_DOMAIN, NULL);
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return (std::numeric_limits<double>::quiet_NaN());
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}
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return (igam(df / 2.0, x / 2.0));
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}
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XSF_HOST_DEVICE double chdtri(double df, double y) {
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double x;
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if ((y < 0.0) || (y > 1.0)) { /* || (df < 1.0) ) */
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set_error("chdtri", SF_ERROR_DOMAIN, NULL);
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return (std::numeric_limits<double>::quiet_NaN());
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}
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x = igamci(0.5 * df, y);
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return (2.0 * x);
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}
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} // namespace cephes
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} // namespace xsf
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