```// @(#)root/mathcore:\$Id\$
// Author: M. Slawinska   08/2007

/**********************************************************************
*                                                                    *
* Copyright (c) 2007 , LCG ROOT MathLib Team                         *
*                                                                    *
*                                                                    *
**********************************************************************/

#ifndef ROOT_Math_IFunctionfwd
#include "Math/IFunctionfwd.h"
#endif

#include "Math/VirtualIntegrator.h"

namespace ROOT {
namespace Math {

//__________________________________________________________________________________________
/**
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.

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

*/

class AdaptiveIntegratorMultiDim : public VirtualIntegratorMultiDim {

public:

/**
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
*/
explicit
AdaptiveIntegratorMultiDim(double absTol = 1.E-9, double relTol = 1E-9, unsigned int maxpts = 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.
*/
explicit
AdaptiveIntegratorMultiDim(const IMultiGenFunction &f, double absTol = 1.E-9, double relTol = 1E-9,  unsigned int maxcall = 100000, unsigned int size = 0);

/**
destructor (no operations)
*/

/**
evaluate the integral with the previously given function between xmin[] and xmax[]
*/
double Integral(const double* xmin, const double * xmax) {
return DoIntegral(xmin,xmax, false);
}

/// evaluate the integral passing a new function
double Integral(const IMultiGenFunction &f, const double* xmin, const double * xmax);

/// set the integration function (must implement multi-dim function interface: IBaseFunctionMultiDim)
void SetFunction(const IMultiGenFunction &f);

/// return result of integration
double Result() const { return fResult; }

/// return integration error
double Error() const { return fError; }

/// return relative error
double RelError() const { return fRelError; }

/// return status of integration
int Status() const { return fStatus; }

/// return number of function evaluations in calculating the integral
int NEval() const { return fNEval; }

/// set relative tolerance
void SetRelTolerance(double relTol);

/// set absolute tolerance
void SetAbsTolerance(double absTol);

///set workspace size
void SetSize(unsigned int size) { fSize = size; }

///set min points
void SetMinPts(unsigned int n) { fMinPts = n; }

///set max points
void SetMaxPts(unsigned int n) { fMaxPts = n; }

/// set the options
void SetOptions(const ROOT::Math::IntegratorMultiDimOptions & opt);

///  get the option used for the integration
ROOT::Math::IntegratorMultiDimOptions Options() const;

protected:

// internal function to compute the integral (if absVal is true compute abs value of function integral
double DoIntegral(const double* xmin, const double * xmax, bool absVal = false);

private:

unsigned int fDim;     // dimentionality of integrand
unsigned int fMinPts;    // minimum number of function evaluation requested
unsigned int fMaxPts;    // maximum number of function evaluation requested
unsigned int fSize;    // max size of working array (explode with dimension)
double fAbsTol;        // absolute tolerance
double fRelTol;        // relative tolerance

double fResult;        // last integration result
double fError;         // integration error
double fRelError;      // Relative error
int    fNEval;        // number of function evaluation
int fStatus;   // status of algorithm (error if not zero)

const IMultiGenFunction* fFun;   // pointer to integrand function

};

}//namespace Math
}//namespace ROOT

```