ECCE @ EIC Software
 All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Friends Macros Groups Pages
nf_GnG_adaptiveQuadrature.cc
Go to the documentation of this file. Or view the newest version in sPHENIX GitHub for file nf_GnG_adaptiveQuadrature.cc
1 /*
2 # <<BEGIN-copyright>>
3 # <<END-copyright>>
4 */
5 
6 #include <float.h>
7 
8 #include "nf_integration.h"
9 
10 #if defined __cplusplus
11 namespace GIDI {
12 using namespace GIDI;
13 #endif
14 
18  void *argList;
20  double estimate;
21  int evaluations, maxDepth, maxDepthReached;
23 
24 static double initialPoints[] = { 0.2311, 0.4860, 0.6068, 0.8913, 0.9501 };
25 static int numberOfInitialPoints = sizeof( initialPoints ) / sizeof( initialPoints[0] );
26 
27 static double nf_GnG_adaptiveQuadrature2( nf_GnG_adaptiveQuadrature_info *adaptiveQuadrature_info, double currentIntrgral, double x1, double x2, int depth );
28 /*
29 ============================================================
30 */
32  void *argList, double x1, double x2, int maxDepth, double tolerance, double *integral, long *evaluations ) {
33 /*
34 * See W. Gander and W. Gautschi, "Adaptive quadrature--revisited", BIT 40 (2000), 84-101.
35 */
36  int i1;
37  double estimate = 0., y1, integral_, coarse;
38  nfu_status status = nfu_Okay;
39  nf_GnG_adaptiveQuadrature_info adaptiveQuadrature_info = { nfu_Okay, integrandFunction, argList, quadratureFunction, 0., 0, maxDepth, 0 };
40 
41  *integral = 0.;
42  *evaluations = 0;
43  if( x1 == x2 ) return( nfu_Okay );
44 
45  if( tolerance < 10 * DBL_EPSILON ) tolerance = 10 * DBL_EPSILON;
47 
48  for( i1 = 0; i1 < numberOfInitialPoints; i1++ ) {
49  if( ( status = integrandFunction( x1 + ( x2 - x1 ) * initialPoints[i1], &y1, argList ) ) != nfu_Okay ) return( status );
50  estimate += y1;
51  }
52  if( ( status = quadratureFunction( integrandFunction, argList, x1, x2, &integral_ ) ) != nfu_Okay ) return( status );
53  estimate = 0.5 * ( estimate * ( x2 - x1 ) / numberOfInitialPoints + integral_ );
54  if( estimate == 0. ) estimate = x2 - x1;
55  adaptiveQuadrature_info.estimate = tolerance * estimate / DBL_EPSILON;
56 
57  if( ( status = quadratureFunction( integrandFunction, argList, x1, x2, &coarse ) ) != nfu_Okay ) return( status );
58  integral_ = nf_GnG_adaptiveQuadrature2( &adaptiveQuadrature_info, coarse, x1, x2, 0 );
59 
60  for( i1 = 0; i1 < 2; i1++ ) { /* Estimate may be off by more than a factor of 10. Iterate at most 2 times. */
61  if( integral_ == 0. ) break;
62  y1 = integral_ / estimate;
63  if( ( y1 > 0.1 ) && ( y1 < 10. ) ) break;
64 
65  estimate = integral_;
66  adaptiveQuadrature_info.estimate = tolerance * integral_ / DBL_EPSILON;
67  *evaluations += adaptiveQuadrature_info.evaluations;
68  adaptiveQuadrature_info.evaluations = 0;
69  integral_ = nf_GnG_adaptiveQuadrature2( &adaptiveQuadrature_info, integral_, x1, x2, 0 );
70  }
71 
72  *evaluations += adaptiveQuadrature_info.evaluations;
73  if( adaptiveQuadrature_info.status == nfu_Okay ) *integral = integral_;
74  return( adaptiveQuadrature_info.status );
75 }
76 /*
77 ============================================================
78 */
79 static double nf_GnG_adaptiveQuadrature2( nf_GnG_adaptiveQuadrature_info *adaptiveQuadrature_info, double coarse, double x1, double x2, int depth ) {
80 
81  double xm, intregral1, intregral2, fine, extrapolate;
82 
83  if( adaptiveQuadrature_info->status != nfu_Okay ) return( 0. );
84  if( x1 == x2 ) return( 0. );
85 
86  adaptiveQuadrature_info->evaluations++;
87  depth++;
88  if( depth > adaptiveQuadrature_info->maxDepthReached ) adaptiveQuadrature_info->maxDepthReached = depth;
89 
90  xm = 0.5 * ( x1 + x2 );
91  if( ( adaptiveQuadrature_info->status = adaptiveQuadrature_info->quadratureFunction( adaptiveQuadrature_info->integrandFunction,
92  adaptiveQuadrature_info->argList, x1, xm, &intregral1 ) ) != nfu_Okay ) return( 0. );
93  if( ( adaptiveQuadrature_info->status = adaptiveQuadrature_info->quadratureFunction( adaptiveQuadrature_info->integrandFunction,
94  adaptiveQuadrature_info->argList, xm, x2, &intregral2 ) ) != nfu_Okay ) return( 0. );
95  fine = intregral1 + intregral2;
96  extrapolate = ( 16. * fine - coarse ) / 15.;
97  if( extrapolate != 0 ) {
98  if( adaptiveQuadrature_info->estimate + ( extrapolate - fine ) == adaptiveQuadrature_info->estimate ) return( fine );
99  }
100  if( depth > adaptiveQuadrature_info->maxDepth ) return( fine );
101  return( nf_GnG_adaptiveQuadrature2( adaptiveQuadrature_info, intregral1, x1, xm, depth ) +
102  nf_GnG_adaptiveQuadrature2( adaptiveQuadrature_info, intregral2, xm, x2, depth ) );
103 }
104 
105 #if defined __cplusplus
106 }
107 #endif