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ROOT::Math::AdaptiveIntegratorMultiDim Class Reference

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.

Definition at line 89 of file AdaptiveIntegratorMultiDim.h.

Public Member Functions

 AdaptiveIntegratorMultiDim (double absTol=0.0, double relTol=1E-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. More...
 
 AdaptiveIntegratorMultiDim (const IMultiGenFunction &f, double absTol=0.0, double relTol=1E-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. More...
 
virtual ~AdaptiveIntegratorMultiDim ()
 destructor (no operations) More...
 
double Integral (const double *xmin, const double *xmax)
 evaluate the integral with the previously given function between xmin[] and xmax[] More...
 
double Integral (const IMultiGenFunction &f, const double *xmin, const double *xmax)
 evaluate the integral passing a new function More...
 
void SetFunction (const IMultiGenFunction &f)
 set the integration function (must implement multi-dim function interface: IBaseFunctionMultiDim) More...
 
double Result () const
 return result of integration More...
 
double Error () const
 return integration error More...
 
double RelError () const
 return relative error More...
 
int Status () const
 return status of integration More...
 
int NEval () const
 return number of function evaluations in calculating the integral More...
 
void SetRelTolerance (double relTol)
 set relative tolerance More...
 
void SetAbsTolerance (double absTol)
 set absolute tolerance More...
 
void SetSize (unsigned int size)
 set workspace size More...
 
void SetMinPts (unsigned int n)
 set min points More...
 
void SetMaxPts (unsigned int n)
 set max points More...
 
void SetOptions (const ROOT::Math::IntegratorMultiDimOptions &opt)
 set the options More...
 
ROOT::Math::IntegratorMultiDimOptions Options () const
 get the option used for the integration More...
 
- Public Member Functions inherited from ROOT::Math::VirtualIntegratorMultiDim
virtual ~VirtualIntegratorMultiDim ()
 destructor: no operation More...
 
virtual ROOT::Math::IntegrationMultiDim::Type Type () const
 
- Public Member Functions inherited from ROOT::Math::VirtualIntegrator
virtual ~VirtualIntegrator ()
 

Protected Member Functions

double DoIntegral (const double *xmin, const double *xmax, bool absVal=false)
 

Private Attributes

unsigned int fDim
 
unsigned int fMinPts
 
unsigned int fMaxPts
 
unsigned int fSize
 
double fAbsTol
 
double fRelTol
 
double fResult
 
double fError
 
double fRelError
 
int fNEval
 
int fStatus
 
const IMultiGenFunctionfFun
 

#include <Math/AdaptiveIntegratorMultiDim.h>

+ Inheritance diagram for ROOT::Math::AdaptiveIntegratorMultiDim:
+ Collaboration diagram for ROOT::Math::AdaptiveIntegratorMultiDim:

Constructor & Destructor Documentation

ROOT::Math::AdaptiveIntegratorMultiDim::AdaptiveIntegratorMultiDim ( double  absTol = 0.0,
double  relTol = 1E-9,
unsigned int  maxpts = 100000,
unsigned int  size = 0 
)
explicit

construct given optionally tolerance (absolute and relative), maximum number of function evaluation (maxpts) and size of the working array.

The integration will stop when the absolute error is less than the absolute tolerance OR when the relative error is less than the relative tolerance. The absolute tolerance by defult is not used (it is equal to zero). 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

Definition at line 17 of file AdaptiveIntegratorMultiDim.cxx.

ROOT::Math::AdaptiveIntegratorMultiDim::AdaptiveIntegratorMultiDim ( const IMultiGenFunction f,
double  absTol = 0.0,
double  relTol = 1E-9,
unsigned int  maxcall = 100000,
unsigned int  size = 0 
)
explicit

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.

Definition at line 37 of file AdaptiveIntegratorMultiDim.cxx.

virtual ROOT::Math::AdaptiveIntegratorMultiDim::~AdaptiveIntegratorMultiDim ( )
inlinevirtual

destructor (no operations)

Definition at line 117 of file AdaptiveIntegratorMultiDim.h.

Member Function Documentation

double ROOT::Math::AdaptiveIntegratorMultiDim::DoIntegral ( const double xmin,
const double xmax,
bool  absVal = false 
)
protected

Definition at line 76 of file AdaptiveIntegratorMultiDim.cxx.

Referenced by Integral().

double ROOT::Math::AdaptiveIntegratorMultiDim::Error ( ) const
inlinevirtual

return integration error

Implements ROOT::Math::VirtualIntegrator.

Definition at line 138 of file AdaptiveIntegratorMultiDim.h.

Referenced by DoIntegral(), and integral_num().

double ROOT::Math::AdaptiveIntegratorMultiDim::Integral ( const double xmin,
const double xmax 
)
inlinevirtual

evaluate the integral with the previously given function between xmin[] and xmax[]

Implements ROOT::Math::VirtualIntegratorMultiDim.

Definition at line 123 of file AdaptiveIntegratorMultiDim.h.

Referenced by RooAdaptiveIntegratorND::integral(), Integral(), integral_num(), and TF1::IntegralMultiple().

double ROOT::Math::AdaptiveIntegratorMultiDim::Integral ( const IMultiGenFunction f,
const double xmin,
const double xmax 
)

evaluate the integral passing a new function

Definition at line 385 of file AdaptiveIntegratorMultiDim.cxx.

int ROOT::Math::AdaptiveIntegratorMultiDim::NEval ( ) const
inlinevirtual

return number of function evaluations in calculating the integral

Reimplemented from ROOT::Math::VirtualIntegrator.

Definition at line 147 of file AdaptiveIntegratorMultiDim.h.

Referenced by integral_num(), and TF1::IntegralMultiple().

ROOT::Math::IntegratorMultiDimOptions ROOT::Math::AdaptiveIntegratorMultiDim::Options ( ) const
virtual

get the option used for the integration

Implements ROOT::Math::VirtualIntegratorMultiDim.

Definition at line 393 of file AdaptiveIntegratorMultiDim.cxx.

double ROOT::Math::AdaptiveIntegratorMultiDim::RelError ( ) const
inline

return relative error

Definition at line 141 of file AdaptiveIntegratorMultiDim.h.

Referenced by RooAdaptiveIntegratorND::integral(), and TF1::IntegralMultiple().

double ROOT::Math::AdaptiveIntegratorMultiDim::Result ( ) const
inlinevirtual

return result of integration

Implements ROOT::Math::VirtualIntegrator.

Definition at line 135 of file AdaptiveIntegratorMultiDim.h.

Referenced by integral_num().

void ROOT::Math::AdaptiveIntegratorMultiDim::SetAbsTolerance ( double  absTol)
virtual

set absolute tolerance

Implements ROOT::Math::VirtualIntegrator.

Definition at line 73 of file AdaptiveIntegratorMultiDim.cxx.

Referenced by SetOptions().

void ROOT::Math::AdaptiveIntegratorMultiDim::SetFunction ( const IMultiGenFunction f)
virtual

set the integration function (must implement multi-dim function interface: IBaseFunctionMultiDim)

Implements ROOT::Math::VirtualIntegratorMultiDim.

Definition at line 63 of file AdaptiveIntegratorMultiDim.cxx.

Referenced by integral_num(), and RooAdaptiveIntegratorND::RooAdaptiveIntegratorND().

void ROOT::Math::AdaptiveIntegratorMultiDim::SetMaxPts ( unsigned int  n)
inline

set max points

Definition at line 162 of file AdaptiveIntegratorMultiDim.h.

Referenced by SetOptions().

void ROOT::Math::AdaptiveIntegratorMultiDim::SetMinPts ( unsigned int  n)
inline

set min points

Definition at line 159 of file AdaptiveIntegratorMultiDim.h.

void ROOT::Math::AdaptiveIntegratorMultiDim::SetOptions ( const ROOT::Math::IntegratorMultiDimOptions opt)
virtual

set the options

Reimplemented from ROOT::Math::VirtualIntegratorMultiDim.

Definition at line 404 of file AdaptiveIntegratorMultiDim.cxx.

void ROOT::Math::AdaptiveIntegratorMultiDim::SetRelTolerance ( double  relTol)
virtual

set relative tolerance

Implements ROOT::Math::VirtualIntegrator.

Definition at line 70 of file AdaptiveIntegratorMultiDim.cxx.

Referenced by SetOptions().

void ROOT::Math::AdaptiveIntegratorMultiDim::SetSize ( unsigned int  size)
inline

set workspace size

Definition at line 156 of file AdaptiveIntegratorMultiDim.h.

Referenced by SetOptions().

int ROOT::Math::AdaptiveIntegratorMultiDim::Status ( ) const
inlinevirtual

return status of integration

Implements ROOT::Math::VirtualIntegrator.

Definition at line 144 of file AdaptiveIntegratorMultiDim.h.

Referenced by RooAdaptiveIntegratorND::integral(), and TF1::IntegralMultiple().

Member Data Documentation

double ROOT::Math::AdaptiveIntegratorMultiDim::fAbsTol
private
unsigned int ROOT::Math::AdaptiveIntegratorMultiDim::fDim
private

Definition at line 177 of file AdaptiveIntegratorMultiDim.h.

Referenced by DoIntegral(), and SetFunction().

double ROOT::Math::AdaptiveIntegratorMultiDim::fError
private

Definition at line 185 of file AdaptiveIntegratorMultiDim.h.

Referenced by DoIntegral(), and Error().

const IMultiGenFunction* ROOT::Math::AdaptiveIntegratorMultiDim::fFun
private

Definition at line 190 of file AdaptiveIntegratorMultiDim.h.

Referenced by DoIntegral(), Integral(), and SetFunction().

unsigned int ROOT::Math::AdaptiveIntegratorMultiDim::fMaxPts
private
unsigned int ROOT::Math::AdaptiveIntegratorMultiDim::fMinPts
private

Definition at line 178 of file AdaptiveIntegratorMultiDim.h.

Referenced by DoIntegral(), and SetMinPts().

int ROOT::Math::AdaptiveIntegratorMultiDim::fNEval
private

Definition at line 187 of file AdaptiveIntegratorMultiDim.h.

Referenced by DoIntegral(), and NEval().

double ROOT::Math::AdaptiveIntegratorMultiDim::fRelError
private

Definition at line 186 of file AdaptiveIntegratorMultiDim.h.

Referenced by DoIntegral(), and RelError().

double ROOT::Math::AdaptiveIntegratorMultiDim::fRelTol
private
double ROOT::Math::AdaptiveIntegratorMultiDim::fResult
private

Definition at line 184 of file AdaptiveIntegratorMultiDim.h.

Referenced by DoIntegral(), and Result().

unsigned int ROOT::Math::AdaptiveIntegratorMultiDim::fSize
private
int ROOT::Math::AdaptiveIntegratorMultiDim::fStatus
private

Definition at line 188 of file AdaptiveIntegratorMultiDim.h.

Referenced by DoIntegral(), and Status().


The documentation for this class was generated from the following files: