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20a218bbe1d8b4a78f819e396f8be615e6a38358
geant4/source/processes/hadronic/models/lend/src/ptwXY_integration.cc
T
Gabriele Cosmo fc6af9e721 Import Geant4 10.4.0 source tree
2017-12-08 12:52:30 +01:00

748 lines
27 KiB
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/*
# <<BEGIN-copyright>>
# <<END-copyright>>
*/
#include <cmath>
#include <float.h>
#include "ptwXY.h"
#include <nf_Legendre.h>
#include <nf_integration.h>
#if defined __cplusplus
#include "G4Log.hh"
#include "G4Pow.hh"
namespace GIDI {
using namespace GIDI;
#endif
typedef struct ptwXY_integrateWithFunctionInfo_s {
int degree;
ptwXY_createFromFunction_callback func;
void *argList;
ptwXY_interpolation interpolation;
double x1, x2, y1, y2;
} ptwXY_integrateWithFunctionInfo;
static nfu_status ptwXY_integrateWithFunction2( nf_Legendre_GaussianQuadrature_callback integrandFunction, void *argList, double x1,
double x2, double *integral );
static nfu_status ptwXY_integrateWithFunction3( double x, double *y, void *argList );
/*
************************************************************
*/
nfu_status ptwXY_f_integrate( ptwXY_interpolation interpolation, double x1, double y1, double x2, double y2, double *value ) {
nfu_status status = nfu_Okay;
double r;
*value = 0.;
switch( interpolation ) {
case ptwXY_interpolationLinLin : /* x linear, y linear */
*value = 0.5 * ( y1 + y2 ) * ( x2 - x1 );
break;
case ptwXY_interpolationLinLog : /* x linear, y log */
if( ( y1 <= 0. ) || ( y2 <= 0. ) ) {
status = nfu_badIntegrationInput; }
else {
r = y2 / y1;
if( std::fabs( r - 1. ) < 1e-4 ) {
r = r - 1.;
*value = y1 * ( x2 - x1 ) / ( 1. + r * ( -0.5 + r * ( 1. / 3. + r * ( -0.25 + .2 * r ) ) ) ); }
else {
*value = ( y2 - y1 ) * ( x2 - x1 ) / G4Log( r );
}
}
break;
case ptwXY_interpolationLogLin : /* x log, y linear */
if( ( x1 <= 0. ) || ( x2 <= 0. ) ) {
status = nfu_badIntegrationInput; }
else {
r = x2 / x1;
if( std::fabs( r - 1. ) < 1e-4 ) {
r = r - 1.;
r = r * ( -0.5 + r * ( 1. / 3. + r * ( -0.25 + .2 * r ) ) );
*value = x1 * ( y2 - y1 ) * r / ( 1. + r ) + y2 * ( x2 - x1 ); }
else {
*value = ( y1 - y2 ) * ( x2 - x1 ) / G4Log( r ) + x2 * y2 - x1 * y1;
}
}
break;
case ptwXY_interpolationLogLog : /* x log, y log */
if( ( x1 <= 0. ) || ( x2 <= 0. ) || ( y1 <= 0. ) || ( y2 <= 0. ) ) {
status = nfu_badIntegrationInput; }
else {
int i, n;
double a, z, lx, ly, s, f;
r = y2 / y1;
if( std::fabs( r - 1. ) < 1e-4 ) {
ly = ( y2 - y1 ) / y1;
ly = ly * ( 1. + ly * ( -0.5 + ly * ( 1. / 3. - 0.25 * ly ) ) ); }
else {
ly = G4Log( r );
}
r = x2 / x1;
if( std::fabs( r - 1. ) < 1e-4 ) {
lx = ( x2 - x1 ) / x1;
lx = lx * ( 1 + lx * ( -0.5 + lx * ( 1. / 3. - 0.25 * lx ) ) ); }
else {
lx = G4Log( r );
}
a = ly / lx;
if( std::fabs( r - 1. ) < 1e-3 ) {
z = ( x2 - x1 ) / x1;
n = (int) a;
if( n > 10 ) n = 12;
if( n < 4 ) n = 6;
a = a - n + 1;
f = n + 1.;
for( i = 0, s = 0.; i < n; i++, a++, f-- ) s = ( 1. + s ) * a * z / f;
*value = y1 * ( x2 - x1 ) * ( 1. + s ); }
else {
*value = y1 * x1 * ( G4Pow::GetInstance()->powA( r, a + 1. ) - 1. ) / ( a + 1. );
}
}
break;
case ptwXY_interpolationFlat : /* x ?, y flat */
*value = y1 * ( x2 - x1 );
break;
case ptwXY_interpolationOther :
status = nfu_otherInterpolation;
}
return( status );
}
/*
************************************************************
*/
double ptwXY_integrate( ptwXYPoints *ptwXY, double xMin, double xMax, nfu_status *status ) {
int64_t i, n = ptwXY->length;
double sum = 0., dSum, x, y, x1, x2, y1, y2, _sign = 1.;
ptwXYPoint *point;
if( ( *status = ptwXY->status ) != nfu_Okay ) return( 0. );
*status = nfu_otherInterpolation;
if( ptwXY->interpolation == ptwXY_interpolationOther ) return( 0. );
if( xMax < xMin ) {
x = xMin;
xMin = xMax;
xMax = x;
_sign = -1.;
}
if( n < 2 ) return( 0. );
if( ( *status = ptwXY_simpleCoalescePoints( ptwXY ) ) != nfu_Okay ) return( 0. );
for( i = 0, point = ptwXY->points; i < n; i++, point++ ) {
if( point->x >= xMin ) break;
}
if( i == n ) return( 0. );
x2 = point->x;
y2 = point->y;
if( i > 0 ) {
if( x2 > xMin ) {
x1 = point[-1].x;
y1 = point[-1].y;
if( ( *status = ptwXY_interpolatePoint( ptwXY->interpolation, xMin, &y, x1, y1, x2, y2 ) ) != nfu_Okay ) return( 0. );
if( x2 > xMax ) {
double yMax;
if( ( *status = ptwXY_interpolatePoint( ptwXY->interpolation, xMax, &yMax, x1, y1, x2, y2 ) ) != nfu_Okay ) return( 0. );
if( ( *status = ptwXY_f_integrate( ptwXY->interpolation, xMin, y, xMax, yMax, &sum ) ) != nfu_Okay ) return( 0. );
return( sum ); }
else {
if( ( *status = ptwXY_f_integrate( ptwXY->interpolation, xMin, y, x2, y2, &sum ) ) != nfu_Okay ) return( 0. );
}
}
}
i++;
point++;
for( ; i < n; i++, point++ ) {
x1 = x2;
y1 = y2;
x2 = point->x;
y2 = point->y;
if( x2 > xMax ) {
if( ( *status = ptwXY_interpolatePoint( ptwXY->interpolation, xMax, &y, x1, y1, x2, y2 ) ) != nfu_Okay ) return( 0. );
if( ( *status = ptwXY_f_integrate( ptwXY->interpolation, x1, y1, xMax, y, &dSum ) ) != nfu_Okay ) return( 0. );
sum += dSum;
break;
}
if( ( *status = ptwXY_f_integrate( ptwXY->interpolation, x1, y1, x2, y2, &dSum ) ) != nfu_Okay ) return( 0. );
sum += dSum;
}
return( _sign * sum );
}
/*
************************************************************
*/
double ptwXY_integrateDomain( ptwXYPoints *ptwXY, nfu_status *status ) {
if( ( *status = ptwXY->status ) != nfu_Okay ) return( 0. );
if( ptwXY->length > 0 ) return( ptwXY_integrate( ptwXY, ptwXY_getXMin( ptwXY ), ptwXY_getXMax( ptwXY ), status ) );
return( 0. );
}
/*
************************************************************
*/
nfu_status ptwXY_normalize( ptwXYPoints *ptwXY ) {
/*
* This function assumes ptwXY_integrateDomain checks status and coalesces the points.
*/
int64_t i;
nfu_status status;
double sum = ptwXY_integrateDomain( ptwXY, &status );
if( status != nfu_Okay ) return( status );
if( sum == 0. ) {
status = nfu_badNorm; }
else {
for( i = 0; i < ptwXY->length; i++ ) ptwXY->points[i].y /= sum;
}
return( status );
}
/*
************************************************************
*/
double ptwXY_integrateDomainWithWeight_x( ptwXYPoints *ptwXY, nfu_status *status ) {
if( ( *status = ptwXY->status ) != nfu_Okay ) return( 0. );
if( ptwXY->length < 2 ) return( 0. );
return( ptwXY_integrateWithWeight_x( ptwXY, ptwXY_getXMin( ptwXY ), ptwXY_getXMax( ptwXY ), status ) );
}
/*
************************************************************
*/
double ptwXY_integrateWithWeight_x( ptwXYPoints *ptwXY, double xMin, double xMax, nfu_status *status ) {
int64_t i, n = ptwXY->length;
double sum = 0., x, y, x1, x2, y1, y2, _sign = 1.;
ptwXYPoint *point;
if( ( *status = ptwXY->status ) != nfu_Okay ) return( 0. );
*status = nfu_unsupportedInterpolation;
if( ( ptwXY->interpolation != ptwXY_interpolationLinLin ) &&
( ptwXY->interpolation != ptwXY_interpolationFlat ) ) return( 0. );
if( n < 2 ) return( 0. );
if( xMax < xMin ) {
x = xMin;
xMin = xMax;
xMax = x;
_sign = -1.;
}
if( ( *status = ptwXY_simpleCoalescePoints( ptwXY ) ) != nfu_Okay ) return( 0. );
for( i = 0, point = ptwXY->points; i < n; ++i, ++point ) {
if( point->x >= xMin ) break;
}
if( i == n ) return( 0. );
x2 = point->x;
y2 = point->y;
if( i > 0 ) {
if( x2 > xMin ) {
if( ( *status = ptwXY_interpolatePoint( ptwXY->interpolation, xMin, &y, point[-1].x, point[-1].y, x2, y2 ) ) != nfu_Okay ) return( 0. );
x2 = xMin;
y2 = y;
--i;
--point;
}
}
++i;
++point;
for( ; i < n; ++i, ++point ) {
x1 = x2;
y1 = y2;
x2 = point->x;
y2 = point->y;
if( x2 > xMax ) {
if( ( *status = ptwXY_interpolatePoint( ptwXY->interpolation, xMax, &y, x1, y1, x2, y2 ) ) != nfu_Okay ) return( 0. );
x2 = xMax;
y2 = y;
}
switch( ptwXY->interpolation ) {
case ptwXY_interpolationFlat :
sum += ( x2 - x1 ) * y1 * 3 * ( x1 + x2 );
break;
case ptwXY_interpolationLinLin :
sum += ( x2 - x1 ) * ( y1 * ( 2 * x1 + x2 ) + y2 * ( x1 + 2 * x2 ) );
break;
default : /* Only to stop compilers from complaining. */
break;
}
if( x2 == xMax ) break;
}
return( _sign * sum / 6 );
}
/*
************************************************************
*/
double ptwXY_integrateDomainWithWeight_sqrt_x( ptwXYPoints *ptwXY, nfu_status *status ) {
if( ( *status = ptwXY->status ) != nfu_Okay ) return( 0. );
if( ptwXY->length < 2 ) return( 0. );
return( ptwXY_integrateWithWeight_sqrt_x( ptwXY, ptwXY_getXMin( ptwXY ), ptwXY_getXMax( ptwXY ), status ) );
}
/*
************************************************************
*/
double ptwXY_integrateWithWeight_sqrt_x( ptwXYPoints *ptwXY, double xMin, double xMax, nfu_status *status ) {
int64_t i, n = ptwXY->length;
double sum = 0., x, y, x1, x2, y1, y2, _sign = 1., sqrt_x1, sqrt_x2, inv_apb, c;
ptwXYPoint *point;
if( ( *status = ptwXY->status ) != nfu_Okay ) return( 0. );
*status = nfu_unsupportedInterpolation;
if( ( ptwXY->interpolation != ptwXY_interpolationLinLin ) &&
( ptwXY->interpolation != ptwXY_interpolationFlat ) ) return( 0. );
if( n < 2 ) return( 0. );
if( xMax < xMin ) {
x = xMin;
xMin = xMax;
xMax = x;
_sign = -1.;
}
if( ( *status = ptwXY_simpleCoalescePoints( ptwXY ) ) != nfu_Okay ) return( 0. );
for( i = 0, point = ptwXY->points; i < n; ++i, ++point ) {
if( point->x >= xMin ) break;
}
if( i == n ) return( 0. );
x2 = point->x;
y2 = point->y;
if( i > 0 ) {
if( x2 > xMin ) {
if( ( *status = ptwXY_interpolatePoint( ptwXY->interpolation, xMin, &y, point[-1].x, point[-1].y, x2, y2 ) ) != nfu_Okay ) return( 0. );
x2 = xMin;
y2 = y;
--i;
--point;
}
}
++i;
++point;
sqrt_x2 = std::sqrt( x2 );
for( ; i < n; ++i, ++point ) {
x1 = x2;
y1 = y2;
sqrt_x1 = sqrt_x2;
x2 = point->x;
y2 = point->y;
if( x2 > xMax ) {
if( ( *status = ptwXY_interpolatePoint( ptwXY->interpolation, xMax, &y, x1, y1, x2, y2 ) ) != nfu_Okay ) return( 0. );
x2 = xMax;
y2 = y;
}
sqrt_x2 = std::sqrt( x2 );
inv_apb = sqrt_x1 + sqrt_x2;
c = 2. * ( sqrt_x1 * sqrt_x2 + x1 + x2 );
switch( ptwXY->interpolation ) {
case ptwXY_interpolationFlat :
sum += ( sqrt_x2 - sqrt_x1 ) * y1 * 2.5 * c;
break;
case ptwXY_interpolationLinLin :
sum += ( sqrt_x2 - sqrt_x1 ) * ( y1 * ( c + x1 * ( 1. + sqrt_x2 / inv_apb ) ) + y2 * ( c + x2 * ( 1. + sqrt_x1 / inv_apb ) ) );
break;
default : /* Only to stop compilers from complaining. */
break;
}
if( x2 == xMax ) break;
}
return( 2. / 15. * _sign * sum );
}
/*
************************************************************
*/
ptwXPoints *ptwXY_groupOneFunction( ptwXYPoints *ptwXY, ptwXPoints *groupBoundaries, ptwXY_group_normType normType, ptwXPoints *ptwX_norm, nfu_status *status ) {
int64_t i, igs, ngs;
double x1, y1, x2, y2, y2p, xg1, xg2, sum;
ptwXYPoints *f;
ptwXPoints *groupedData = NULL;
if( ( *status = ptwXY_simpleCoalescePoints( ptwXY ) ) != nfu_Okay ) return( NULL );
if( ( *status = groupBoundaries->status ) != nfu_Okay ) return( NULL );
*status = nfu_otherInterpolation;
if( ptwXY->interpolation == ptwXY_interpolationOther ) return( NULL );
ngs = ptwX_length( groupBoundaries ) - 1;
if( normType == ptwXY_group_normType_norm ) {
if( ptwX_norm == NULL ) {
*status = nfu_badNorm;
return( NULL );
}
*status = ptwX_norm->status;
if( ptwX_norm->status != nfu_Okay ) return( NULL );
if( ptwX_length( ptwX_norm ) != ngs ) {
*status = nfu_badNorm;
return( NULL );
}
}
if( ( f = ptwXY_intersectionWith_ptwX( ptwXY, groupBoundaries, status ) ) == NULL ) return( NULL );
if( f->length == 0 ) return( ptwX_createLine( ngs, ngs, 0, 0, status ) );
if( ( groupedData = ptwX_new( ngs, status ) ) == NULL ) goto err;
xg1 = groupBoundaries->points[0];
x1 = f->points[0].x;
y1 = f->points[0].y;
for( igs = 0, i = 1; igs < ngs; igs++ ) {
xg2 = groupBoundaries->points[igs+1];
sum = 0;
if( xg2 > x1 ) {
for( ; i < f->length; i++, x1 = x2, y1 = y2 ) {
x2 = f->points[i].x;
if( x2 > xg2 ) break;
y2p = y2 = f->points[i].y;
if( f->interpolation == ptwXY_interpolationFlat ) y2p = y1;
sum += ( y1 + y2p ) * ( x2 - x1 );
}
}
if( sum != 0. ) {
if( normType == ptwXY_group_normType_dx ) {
sum /= ( xg2 - xg1 ); }
else if( normType == ptwXY_group_normType_norm ) {
if( ptwX_norm->points[igs] == 0. ) {
*status = nfu_divByZero;
goto err;
}
sum /= ptwX_norm->points[igs];
}
}
groupedData->points[igs] = 0.5 * sum;
groupedData->length++;
xg1 = xg2;
}
ptwXY_free( f );
return( groupedData );
err:
ptwXY_free( f );
if( groupedData != NULL ) ptwX_free( groupedData );
return( NULL );
}
/*
************************************************************
*/
ptwXPoints *ptwXY_groupTwoFunctions( ptwXYPoints *ptwXY1, ptwXYPoints *ptwXY2, ptwXPoints *groupBoundaries, ptwXY_group_normType normType,
ptwXPoints *ptwX_norm, nfu_status *status ) {
int64_t i, igs, ngs;
double x1, fy1, gy1, x2, fy2, gy2, fy2p, gy2p, xg1, xg2, sum;
ptwXYPoints *f = NULL, *ff, *g = NULL, *gg = NULL;
ptwXPoints *groupedData = NULL;
if( ( *status = ptwXY_simpleCoalescePoints( ptwXY1 ) ) != nfu_Okay ) return( NULL );
if( ( *status = ptwXY_simpleCoalescePoints( ptwXY2 ) ) != nfu_Okay ) return( NULL );
if( ( *status = groupBoundaries->status ) != nfu_Okay ) return( NULL );
*status = nfu_otherInterpolation;
if( ptwXY1->interpolation == ptwXY_interpolationOther ) return( NULL );
if( ptwXY2->interpolation == ptwXY_interpolationOther ) return( NULL );
ngs = ptwX_length( groupBoundaries ) - 1;
if( normType == ptwXY_group_normType_norm ) {
if( ptwX_norm == NULL ) {
*status = nfu_badNorm;
return( NULL );
}
if( ( *status = ptwX_norm->status ) != nfu_Okay ) return( NULL );
if( ptwX_length( ptwX_norm ) != ngs ) {
*status = nfu_badNorm;
return( NULL );
}
}
if( ( ff = ptwXY_intersectionWith_ptwX( ptwXY1, groupBoundaries, status ) ) == NULL ) return( NULL );
if( ( gg = ptwXY_intersectionWith_ptwX( ptwXY2, groupBoundaries, status ) ) == NULL ) goto err;
if( ( ff->length == 0 ) || ( gg->length == 0 ) ) {
ptwXY_free( ff );
ptwXY_free( gg );
return( ptwX_createLine( ngs, ngs, 0, 0, status ) );
}
if( ( *status = ptwXY_tweakDomainsToMutualify( ff, gg, 4, 0 ) ) != nfu_Okay ) goto err;
if( ( f = ptwXY_union( ff, gg, status, ptwXY_union_fill ) ) == NULL ) goto err;
if( ( g = ptwXY_union( gg, f, status, ptwXY_union_fill ) ) == NULL ) goto err;
if( ( groupedData = ptwX_new( ngs, status ) ) == NULL ) goto err;
xg1 = groupBoundaries->points[0];
x1 = f->points[0].x;
fy1 = f->points[0].y;
gy1 = g->points[0].y;
for( igs = 0, i = 1; igs < ngs; igs++ ) {
xg2 = groupBoundaries->points[igs+1];
sum = 0;
if( xg2 > x1 ) {
for( ; i < f->length; i++, x1 = x2, fy1 = fy2, gy1 = gy2 ) {
x2 = f->points[i].x;
if( x2 > xg2 ) break;
fy2p = fy2 = f->points[i].y;
if( f->interpolation == ptwXY_interpolationFlat ) fy2p = fy1;
gy2p = gy2 = g->points[i].y;
if( g->interpolation == ptwXY_interpolationFlat ) gy2p = gy1;
sum += ( ( fy1 + fy2p ) * ( gy1 + gy2p ) + fy1 * gy1 + fy2p * gy2p ) * ( x2 - x1 );
}
}
if( sum != 0. ) {
if( normType == ptwXY_group_normType_dx ) {
sum /= ( xg2 - xg1 ); }
else if( normType == ptwXY_group_normType_norm ) {
if( ptwX_norm->points[igs] == 0. ) {
*status = nfu_divByZero;
goto err;
}
sum /= ptwX_norm->points[igs];
}
}
groupedData->points[igs] = sum / 6.;
groupedData->length++;
xg1 = xg2;
}
ptwXY_free( f );
ptwXY_free( g );
ptwXY_free( ff );
ptwXY_free( gg );
return( groupedData );
err:
ptwXY_free( ff );
if( gg != NULL ) ptwXY_free( gg );
// Coverity #63063
if( f != NULL ) ptwXY_free( f );
if( g != NULL ) ptwXY_free( g );
if( groupedData != NULL ) ptwX_free( groupedData );
return( NULL );
}
/*
************************************************************
*/
ptwXPoints *ptwXY_groupThreeFunctions( ptwXYPoints *ptwXY1, ptwXYPoints *ptwXY2, ptwXYPoints *ptwXY3, ptwXPoints *groupBoundaries,
ptwXY_group_normType normType, ptwXPoints *ptwX_norm, nfu_status *status ) {
int64_t i, igs, ngs;
double x1, fy1, gy1, hy1, x2, fy2, gy2, hy2, fy2p, gy2p, hy2p, xg1, xg2, sum;
ptwXYPoints *f = NULL, *ff, *fff = NULL, *g = NULL, *gg = NULL, *h = NULL, *hh = NULL;
ptwXPoints *groupedData = NULL;
if( ( *status = ptwXY_simpleCoalescePoints( ptwXY1 ) ) != nfu_Okay ) return( NULL );
if( ( *status = ptwXY_simpleCoalescePoints( ptwXY2 ) ) != nfu_Okay ) return( NULL );
if( ( *status = ptwXY_simpleCoalescePoints( ptwXY3 ) ) != nfu_Okay ) return( NULL );
if( ( *status = groupBoundaries->status ) != nfu_Okay ) return( NULL );
*status = nfu_otherInterpolation;
if( ptwXY1->interpolation == ptwXY_interpolationOther ) return( NULL );
if( ptwXY2->interpolation == ptwXY_interpolationOther ) return( NULL );
if( ptwXY3->interpolation == ptwXY_interpolationOther ) return( NULL );
ngs = ptwX_length( groupBoundaries ) - 1;
if( normType == ptwXY_group_normType_norm ) {
if( ptwX_norm == NULL ) {
*status = nfu_badNorm;
return( NULL );
}
if( ( *status = ptwX_norm->status ) != nfu_Okay ) return( NULL );
if( ptwX_length( ptwX_norm ) != ngs ) {
*status = nfu_badNorm;
return( NULL );
}
}
if( ( ff = ptwXY_intersectionWith_ptwX( ptwXY1, groupBoundaries, status ) ) == NULL ) return( NULL );
if( ( gg = ptwXY_intersectionWith_ptwX( ptwXY2, groupBoundaries, status ) ) == NULL ) goto err;
if( ( hh = ptwXY_intersectionWith_ptwX( ptwXY3, groupBoundaries, status ) ) == NULL ) goto err;
if( ( ff->length == 0 ) || ( gg->length == 0 ) || ( hh->length == 0 ) ) return( ptwX_createLine( ngs, ngs, 0, 0, status ) );
if( ( *status = ptwXY_tweakDomainsToMutualify( ff, gg, 4, 0 ) ) != nfu_Okay ) goto err;
if( ( *status = ptwXY_tweakDomainsToMutualify( ff, hh, 4, 0 ) ) != nfu_Okay ) goto err;
if( ( *status = ptwXY_tweakDomainsToMutualify( gg, hh, 4, 0 ) ) != nfu_Okay ) goto err;
if( ( fff = ptwXY_union( ff, gg, status, ptwXY_union_fill ) ) == NULL ) goto err;
if( ( h = ptwXY_union( hh, fff, status, ptwXY_union_fill ) ) == NULL ) goto err;
if( ( f = ptwXY_union( fff, h, status, ptwXY_union_fill ) ) == NULL ) goto err;
if( ( g = ptwXY_union( gg, h, status, ptwXY_union_fill ) ) == NULL ) goto err;
if( ( groupedData = ptwX_new( ngs, status ) ) == NULL ) goto err;
xg1 = groupBoundaries->points[0];
x1 = f->points[0].x;
fy1 = f->points[0].y;
gy1 = g->points[0].y;
hy1 = h->points[0].y;
for( igs = 0, i = 1; igs < ngs; igs++ ) {
xg2 = groupBoundaries->points[igs+1];
sum = 0;
if( xg2 > x1 ) {
for( ; i < f->length; i++, x1 = x2, fy1 = fy2, gy1 = gy2, hy1 = hy2 ) {
x2 = f->points[i].x;
if( x2 > xg2 ) break;
fy2p = fy2 = f->points[i].y;
if( f->interpolation == ptwXY_interpolationFlat ) fy2p = fy1;
gy2p = gy2 = g->points[i].y;
if( g->interpolation == ptwXY_interpolationFlat ) gy2p = gy1;
hy2p = hy2 = h->points[i].y;
if( h->interpolation == ptwXY_interpolationFlat ) hy2p = hy1;
sum += ( ( fy1 + fy2p ) * ( gy1 + gy2p ) * ( hy1 + hy2p ) + 2 * fy1 * gy1 * hy1 + 2 * fy2p * gy2p * hy2p ) * ( x2 - x1 );
}
}
if( sum != 0. ) {
if( normType == ptwXY_group_normType_dx ) {
sum /= ( xg2 - xg1 ); }
else if( normType == ptwXY_group_normType_norm ) {
if( ptwX_norm->points[igs] == 0. ) {
*status = nfu_divByZero;
goto err;
}
sum /= ptwX_norm->points[igs];
}
}
groupedData->points[igs] = sum / 12.;
groupedData->length++;
xg1 = xg2;
}
ptwXY_free( f );
ptwXY_free( g );
ptwXY_free( h );
ptwXY_free( ff );
ptwXY_free( gg );
ptwXY_free( hh );
ptwXY_free( fff );
return( groupedData );
err:
ptwXY_free( ff );
if( fff != NULL ) ptwXY_free( fff );
if( gg != NULL ) ptwXY_free( gg );
if( hh != NULL ) ptwXY_free( hh );
if( f != NULL ) ptwXY_free( f );
if( g != NULL ) ptwXY_free( g );
if( h != NULL ) ptwXY_free( h );
if( groupedData != NULL ) ptwX_free( groupedData );
return( NULL );
}
/*
************************************************************
*/
ptwXPoints *ptwXY_runningIntegral( ptwXYPoints *ptwXY, nfu_status *status ) {
int i;
ptwXPoints *runningIntegral = NULL;
double integral = 0., sum;
if( ( *status = ptwXY_simpleCoalescePoints( ptwXY ) ) != nfu_Okay ) return( NULL );
if( ( runningIntegral = ptwX_new( ptwXY->length, status ) ) == NULL ) goto err;
if( ( *status = ptwX_setPointAtIndex( runningIntegral, 0, 0. ) ) != nfu_Okay ) goto err;
for( i = 1; i < ptwXY->length; i++ ) {
if( ( *status = ptwXY_f_integrate( ptwXY->interpolation, ptwXY->points[i-1].x, ptwXY->points[i-1].y,
ptwXY->points[i].x, ptwXY->points[i].y, &sum ) ) != nfu_Okay ) goto err;
integral += sum;
if( ( *status = ptwX_setPointAtIndex( runningIntegral, i, integral ) ) != nfu_Okay ) goto err;
}
return( runningIntegral );
err:
if( runningIntegral != NULL ) ptwX_free( runningIntegral );
return( NULL );
}
/*
************************************************************
*/
double ptwXY_integrateWithFunction( ptwXYPoints *ptwXY, ptwXY_createFromFunction_callback func, void *argList,
double xMin, double xMax, int degree, int recursionLimit, double tolerance, nfu_status *status ) {
int64_t i1, i2, n1 = ptwXY->length;
long evaluations;
double integral = 0., integral_, sign = -1., xa, xb;
ptwXY_integrateWithFunctionInfo integrateWithFunctionInfo;
ptwXYPoint *point;
if( ( *status = ptwXY->status ) != nfu_Okay ) return( 0. );
if( xMin == xMax ) return( 0. );
if( n1 < 2 ) return( 0. );
ptwXY_simpleCoalescePoints( ptwXY );
if( xMin > xMax ) {
sign = xMin;
xMin = xMax;
xMax = sign;
sign = -1.;
}
if( xMin >= ptwXY->points[n1-1].x ) return( 0. );
if( xMax <= ptwXY->points[0].x ) return( 0. );
for( i1 = 0; i1 < ( n1 - 1 ); i1++ ) {
if( ptwXY->points[i1+1].x > xMin ) break;
}
for( i2 = n1 - 1; i2 > i1; i2-- ) {
if( ptwXY->points[i2-1].x < xMax ) break;
}
point = &(ptwXY->points[i1]);
integrateWithFunctionInfo.degree = degree;
integrateWithFunctionInfo.func = func;
integrateWithFunctionInfo.argList = argList;
integrateWithFunctionInfo.interpolation = ptwXY->interpolation;
integrateWithFunctionInfo.x2 = point->x;
integrateWithFunctionInfo.y2 = point->y;
xa = xMin;
for( ; i1 < i2; i1++ ) {
integrateWithFunctionInfo.x1 = integrateWithFunctionInfo.x2;
integrateWithFunctionInfo.y1 = integrateWithFunctionInfo.y2;
++point;
integrateWithFunctionInfo.x2 = point->x;
integrateWithFunctionInfo.y2 = point->y;
xb = point->x;
if( xb > xMax ) xb = xMax;
*status = nf_GnG_adaptiveQuadrature( ptwXY_integrateWithFunction2, ptwXY_integrateWithFunction3, &integrateWithFunctionInfo,
xa, xb, recursionLimit, tolerance, &integral_, &evaluations );
if( *status != nfu_Okay ) return( 0. );
integral += integral_;
xa = xb;
}
return( integral );
}
/*
************************************************************
*/
static nfu_status ptwXY_integrateWithFunction2( nf_Legendre_GaussianQuadrature_callback integrandFunction, void *argList, double x1,
double x2, double *integral ) {
ptwXY_integrateWithFunctionInfo *integrateWithFunctionInfo = (ptwXY_integrateWithFunctionInfo *) argList;
nfu_status status;
status = nf_Legendre_GaussianQuadrature( integrateWithFunctionInfo->degree, x1, x2, integrandFunction, argList, integral );
return( status );
}
/*
************************************************************
*/
static nfu_status ptwXY_integrateWithFunction3( double x, double *y, void *argList ) {
double yf;
ptwXY_integrateWithFunctionInfo *integrateWithFunctionInfo = (ptwXY_integrateWithFunctionInfo *) argList;
nfu_status status;
if( ( status = ptwXY_interpolatePoint( integrateWithFunctionInfo->interpolation, x, &yf,
integrateWithFunctionInfo->x1, integrateWithFunctionInfo->y1,
integrateWithFunctionInfo->x2, integrateWithFunctionInfo->y2 ) ) == nfu_Okay ) {
status = integrateWithFunctionInfo->func( x, y, integrateWithFunctionInfo->argList );
*y *= yf;
}
return( status );
}
#if defined __cplusplus
}
#endif
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