nf_integration.h File Reference

#include <nf_utilities.h>
#include <nf_Legendre.h>

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Macros
#define	nf_GnG_adaptiveQuadrature_MaxMaxDepth   20

Typedefs
typedef nfu_status(*	nf_GnG_adaptiveQuadrature_callback )(nf_Legendre_GaussianQuadrature_callback integrandFunction, void *argList, double x1, double x2, double *integral)

Functions
nfu_status	nf_GnG_adaptiveQuadrature (nf_GnG_adaptiveQuadrature_callback quadratureFunction, nf_Legendre_GaussianQuadrature_callback integrandFunction, void *argList, double x1, double x2, int maxDepth, double tolerance, double *integral, long *evaluations)

Macro Definition Documentation

#define nf_GnG_adaptiveQuadrature_MaxMaxDepth   20

Definition at line 17 of file nf_integration.h.

Typedef Documentation

typedef nfu_status(* nf_GnG_adaptiveQuadrature_callback)(nf_Legendre_GaussianQuadrature_callback integrandFunction, void *argList, double x1, double x2, double *integral)

Definition at line 19 of file nf_integration.h.

Function Documentation

nfu_status nf_GnG_adaptiveQuadrature	(	nf_GnG_adaptiveQuadrature_callback	quadratureFunction,
		nf_Legendre_GaussianQuadrature_callback	integrandFunction,
		void *	argList,
		double	x1,
		double	x2,
		int	maxDepth,
		double	tolerance,
		double *	integral,
		long *	evaluations
	)

Definition at line 31 of file nf_GnG_adaptiveQuadrature.cc.

                                                                                                               {
/*
*   See W. Gander and W. Gautschi, "Adaptive quadrature--revisited", BIT 40 (2000), 84-101.
*/
    int i1;
    double estimate = 0., y1, integral_, coarse;
    nfu_status status = nfu_Okay;
    nf_GnG_adaptiveQuadrature_info adaptiveQuadrature_info = { nfu_Okay, integrandFunction, argList, quadratureFunction, 0., 0, maxDepth, 0 };

    *integral = 0.;
    *evaluations = 0;
    if( x1 == x2 ) return( nfu_Okay );

    if( tolerance < 10 * DBL_EPSILON ) tolerance = 10 * DBL_EPSILON;
    if( maxDepth > nf_GnG_adaptiveQuadrature_MaxMaxDepth ) maxDepth = nf_GnG_adaptiveQuadrature_MaxMaxDepth;

    for( i1 = 0; i1 < numberOfInitialPoints; i1++ ) {
        if( ( status = integrandFunction( x1 + ( x2 - x1 ) * initialPoints[i1], &y1, argList ) ) != nfu_Okay ) return( status );
        estimate += y1;
    }
    if( ( status = quadratureFunction( integrandFunction, argList, x1, x2, &integral_ ) ) != nfu_Okay ) return( status );
    estimate = 0.5 * ( estimate * ( x2 - x1 ) / numberOfInitialPoints + integral_ );
    if( estimate == 0. ) estimate = x2 - x1;
    adaptiveQuadrature_info.estimate = tolerance * estimate / DBL_EPSILON;

    if( ( status = quadratureFunction( integrandFunction, argList, x1, x2, &coarse ) ) != nfu_Okay ) return( status );
    integral_ = nf_GnG_adaptiveQuadrature2( &adaptiveQuadrature_info, coarse, x1, x2, 0 );

    for( i1 = 0; i1 < 2; i1++ ) {       /* Estimate may be off by more than a factor of 10. Iterate at most 2 times. */
        if( integral_ == 0. ) break;
        y1 = integral_ / estimate;
        if( ( y1 > 0.1 ) && ( y1 < 10. ) ) break;

        estimate = integral_;
        adaptiveQuadrature_info.estimate = tolerance * integral_ / DBL_EPSILON;
        *evaluations += adaptiveQuadrature_info.evaluations;
        adaptiveQuadrature_info.evaluations = 0;
        integral_ = nf_GnG_adaptiveQuadrature2( &adaptiveQuadrature_info, integral_, x1, x2, 0 );
    }

    *evaluations += adaptiveQuadrature_info.evaluations;
    if( adaptiveQuadrature_info.status == nfu_Okay ) *integral = integral_;
    return( adaptiveQuadrature_info.status );
}

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