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