class ROOT::Math::AdaptiveIntegratorMultiDim: public ROOT::Math::VirtualIntegratorMultiDim
class for adaptive quadrature integration in multi-dimensions using rectangular regions.
Algorithm from A.C. Genz, A.A. Malik, An adaptive algorithm for numerical integration over
an N-dimensional rectangular region, J. Comput. Appl. Math. 6 (1980) 295-302.
Converted/adapted by R.Brun to C++ from Fortran CERNLIB routine RADMUL (D120)
The new code features many changes compared to the Fortran version.
Control parameters are:
minpts: Minimum number of function evaluations requested. Must not exceed maxpts.
if minpts < 1 minpts is set to 2^n +2*n*(n+1) +1 where n is the function dimension
maxpts: Maximum number of function evaluations to be allowed.
maxpts >= 2^n +2*n*(n+1) +1
if maxpts<minpts, maxpts is set to 10*minpts
epstol, epsrel : Specified relative and absolute accuracy.
The integral will stop if the relative error is less than relative tolerance OR the
absolute error is less than the absolute tolerance
The class computes in addition to the integral of the function is the desired interval:
an estimation of the relative accuracy of the result.
number of function evaluations performed.
status code :
0 Normal exit. . At least minpts and at most maxpts calls to the function were performed.
1 maxpts is too small for the specified accuracy eps.
The result and relerr contain the values obtainable for the
specified value of maxpts.
3 n<2 or n>15
Method:
An integration rule of degree seven is used together with a certain
strategy of subdivision.
For a more detailed description of the method see References.
Notes:
1.Multi-dimensional integration is time-consuming. For each rectangular
subregion, the routine requires function evaluations.
Careful programming of the integrand might result in substantial saving
of time.
2.Numerical integration usually works best for smooth functions.
Some analysis or suitable transformations of the integral prior to
numerical work may contribute to numerical efficiency.
References:
1.A.C. Genz and A.A. Malik, Remarks on algorithm 006:
An adaptive algorithm for numerical integration over
an N-dimensional rectangular region, J. Comput. Appl. Math. 6 (1980) 295-302.
2.A. van Doren and L. de Ridder, An adaptive algorithm for numerical
integration over an n-dimensional cube, J.Comput. Appl. Math. 2 (1976) 207-217.
@ingroup Integration
Function Members (Methods)
public:
protected:
| double | DoIntegral(const double* xmin, const double* xmax, bool absVal = false) |
Data Members
private:
| double | fAbsTol | absolute tolerance |
| unsigned int | fDim | dimentionality of integrand |
| double | fError | integration error |
| const ROOT::Math::IMultiGenFunction* | fFun | pointer to integrand function |
| unsigned int | fMaxPts | maximum number of function evaluation requested |
| unsigned int | fMinPts | minimum number of function evaluation requested |
| int | fNEval | number of function evaluation |
| double | fRelError | Relative error |
| double | fRelTol | relative tolerance |
| double | fResult | last integration result |
| unsigned int | fSize | max size of working array (explode with dimension) |
| int | fStatus | status of algorithm (error if not zero) |
Class Charts
Function documentation
AdaptiveIntegratorMultiDim(double absTol = 1.0000000000000001E-9, double relTol = 1.0000000000000001E-9, unsigned int maxpts = 100000, unsigned int size = 0)
construct given optionally tolerance (absolute and relative), maximum number of function evaluation (maxpts) and
size of the working array.
The size of working array represents the number of sub-division used for calculating the integral.
Higher the dimension, larger sizes are required for getting the same accuracy.
The size must be larger than >= (2N + 3) * (1 + MAXPTS/(2**N + 2N(N + 1) + 1))/2). For smaller value passed, the
minimum allowed will be used
AdaptiveIntegratorMultiDim(const ROOT::Math::IMultiGenFunction& f, double absTol = 1.0000000000000001E-9, double relTol = 1.0000000000000001E-9, unsigned int maxcall = 100000, unsigned int size = 0)
Construct with a reference to the integrand function and given optionally
tolerance (absolute and relative), maximum number of function evaluation (maxpts) and
size of the working array.
double Integral(const double* xmin, const double* xmax)
evaluate the integral with the previously given function between xmin[] and xmax[]
return DoIntegral(const double* xmin, const double* xmax, bool absVal = false)
double Integral(const ROOT::Math::IMultiGenFunction& f, const double* xmin, const double* xmax)
evaluate the integral passing a new function
void SetFunction(const ROOT::Math::IMultiGenFunction& f)
set the integration function (must implement multi-dim function interface: IBaseFunctionMultiDim)
int NEval() const
return number of function evaluations in calculating the integral
{ return fNEval; }