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1// @(#)root/mathcore:$Id$
2// Author: M. Slawinska 08/2007
3
4/**********************************************************************
5 * *
6 * Copyright (c) 2007 , LCG ROOT MathLib Team *
7 * *
8 * *
9 **********************************************************************/
10
12
13
16
17#include "Math/IFunctionfwd.h"
18
20
21namespace ROOT {
22namespace Math {
23
25 \ingroup Integration
26
28Algorithm from A.C. Genz, A.A. Malik, An adaptive algorithm for numerical integration over
29an N-dimensional rectangular region, J. Comput. Appl. Math. 6 (1980) 295-302.
30
32The new code features many changes compared to the Fortran version.
33
34Control parameters are:
35
36 - \f$minpts \f$: Minimum number of function evaluations requested. Must not exceed maxpts.
37 if minpts < 1 minpts is set to \f$2^n +2n(n+1) +1 \f$ where n is the function dimension
38 - \f$maxpts \f$: Maximum number of function evaluations to be allowed.
39 \f$maxpts >= 2^n +2n(n+1) +1 \f$
40 if \f$maxpts<minpts \f$, \f$maxpts \f$ is set to \f$10minpts \f$
41 - \f$epstol \f$, \f$epsrel \f$ : Specified relative and absolute accuracy.
42
43The integral will stop if the relative error is less than relative tolerance OR the
44absolute error is less than the absolute tolerance
45
46The class computes in addition to the integral of the function in the desired interval:
47
48 - an estimation of the relative accuracy of the result.
49 - number of function evaluations performed.
50 - status code:
51 0. Normal exit. . At least minpts and at most maxpts calls to the function were performed.
52 1. maxpts is too small for the specified accuracy eps.
53 The result and relerr contain the values obtainable for the
54 specified value of maxpts.
55 2. size is too small for the specified number MAXPTS of function evaluations.
56 3. n<2 or n>15
57
58### Method:
59
60An integration rule of degree seven is used together with a certain
61strategy of subdivision.
62For a more detailed description of the method see References.
63
64### Notes:
65
66 1..Multi-dimensional integration is time-consuming. For each rectangular
67 subregion, the routine requires function evaluations.
68 Careful programming of the integrand might result in substantial saving
69 of time.
70 2..Numerical integration usually works best for smooth functions.
71 Some analysis or suitable transformations of the integral prior to
72 numerical work may contribute to numerical efficiency.
73
74### References:
75
76 1. A.C. Genz and A.A. Malik, Remarks on algorithm 006:
77 An adaptive algorithm for numerical integration over
78 an N-dimensional rectangular region, J. Comput. Appl. Math. 6 (1980) 295-302.
79 2. A. van Doren and L. de Ridder, An adaptive algorithm for numerical
80 integration over an n-dimensional cube, J.Comput. Appl. Math. 2 (1976) 207-217.
81
82*/
83
85
86public:
87
88 /**
89 Construct given optionally tolerance (absolute and relative), maximum number of function evaluation (maxpts) and
90 size of the working array.
91 The integration will stop when the absolute error is less than the absolute tolerance OR when the relative error is less
92 than the relative tolerance. The absolute tolerance by default is not used (it is equal to zero).
93 The size of working array represents the number of sub-division used for calculating the integral.
94 Higher the dimension, larger sizes are required for getting the same accuracy.
95 The size must be larger than
96 \f$(2n + 3) (1 + maxpts/(2^n + 2n(n + 1) + 1))/2) \f$.
97 For smaller value passed, the minimum allowed will be used
98 */
99 explicit
100 AdaptiveIntegratorMultiDim(double absTol = 0.0, double relTol = 1E-9, unsigned int maxpts = 100000, unsigned int size = 0);
101
102 /**
103 Construct with a reference to the integrand function and given optionally
104 tolerance (absolute and relative), maximum number of function evaluation (maxpts) and
105 size of the working array.
106 */
107 explicit
108 AdaptiveIntegratorMultiDim(const IMultiGenFunction &f, double absTol = 0.0, double relTol = 1E-9, unsigned int maxcall = 100000, unsigned int size = 0);
109
110 /**
111 destructor (no operations)
112 */
114
115
116 /**
117 evaluate the integral with the previously given function between xmin[] and xmax[]
118 */
119 double Integral(const double* xmin, const double * xmax) {
120 return DoIntegral(xmin,xmax, false);
121 }
122
123
124 /// evaluate the integral passing a new function
125 double Integral(const IMultiGenFunction &f, const double* xmin, const double * xmax);
126
127 /// set the integration function (must implement multi-dim function interface: IBaseFunctionMultiDim)
128 void SetFunction(const IMultiGenFunction &f);
129
130 /// return result of integration
131 double Result() const { return fResult; }
132
133 /// return integration error
134 double Error() const { return fError; }
135
136 /// return relative error
137 double RelError() const { return fRelError; }
138
139 /// return status of integration
140 /// - status = 0 successful integration
141 /// - status = 1
142 /// MAXPTS is too small for the specified accuracy EPS.
143 /// The result contain the values
144 /// obtainable for the specified value of MAXPTS.
145 /// - status = 2
146 /// size is too small for the specified number MAXPTS of function evaluations.
147 /// - status = 3
148 /// wrong dimension , N<2 or N > 15. Returned result and error are zero
149 int Status() const { return fStatus; }
150
151 /// return number of function evaluations in calculating the integral
152 int NEval() const { return fNEval; }
153
154 /// set relative tolerance
155 void SetRelTolerance(double relTol);
156
157 /// set absolute tolerance
158 void SetAbsTolerance(double absTol);
159
160 ///set workspace size
161 void SetSize(unsigned int size) { fSize = size; }
162
163 ///set min points
164 void SetMinPts(unsigned int n) { fMinPts = n; }
165
166 ///set max points
167 void SetMaxPts(unsigned int n) { fMaxPts = n; }
168
169 /// set the options
171
172 /// get the option used for the integration
174
175protected:
176
177 // internal function to compute the integral (if absVal is true compute abs value of function integral
178 double DoIntegral(const double* xmin, const double * xmax, bool absVal = false);
179
180 private:
181
182 unsigned int fDim; // dimensionality of integrand
183 unsigned int fMinPts; // minimum number of function evaluation requested
184 unsigned int fMaxPts; // maximum number of function evaluation requested
185 unsigned int fSize; // max size of working array (explode with dimension)
186 double fAbsTol; // absolute tolerance
187 double fRelTol; // relative tolerance
188
189 double fResult; // last integration result
190 double fError; // integration error
191 double fRelError; // Relative error
192 int fNEval; // number of function evaluation
193 int fStatus; // status of algorithm (error if not zero)
194
195 const IMultiGenFunction* fFun; // pointer to integrand function
196
197};
198
199}//namespace Math
200}//namespace ROOT
201
#define f(i)
Definition RSha256.hxx:104
float xmin
float xmax
void SetOptions(const ROOT::Math::IntegratorMultiDimOptions &opt)
set the options
void SetAbsTolerance(double absTol)
set absolute tolerance
double Result() const
return result of integration
int Status() const
return status of integration
double DoIntegral(const double *xmin, const double *xmax, bool absVal=false)
void SetSize(unsigned int size)
set workspace size
int NEval() const
return number of function evaluations in calculating the integral
destructor (no operations)
void SetMaxPts(unsigned int n)
set max points
void SetFunction(const IMultiGenFunction &f)
set the integration function (must implement multi-dim function interface: IBaseFunctionMultiDim)
double Error() const
return integration error
ROOT::Math::IntegratorMultiDimOptions Options() const
get the option used for the integration
void SetRelTolerance(double relTol)
set relative tolerance
double RelError() const
return relative error
double Integral(const double *xmin, const double *xmax)
evaluate the integral with the previously given function between xmin[] and xmax[]
void SetMinPts(unsigned int n)
set min points
Documentation for the abstract class IBaseFunctionMultiDim.
Definition IFunction.h:62
Numerical multi dimensional integration options.
Interface (abstract) class for multi numerical integration It must be implemented by the concrete Int...
const Int_t n
Definition legend1.C:16
Namespace for new Math classes and functions.
tbb::task_arena is an alias of tbb::interface7::task_arena, which doesn't allow to forward declare tb...