MonteCarlo Routine

Summary

Numerical integration by Monte Carlo method.

Declaration

Function MonteCarlo(Fun: TRealFunction; lb, ub: TSample; const Constants: array of TSample; const ObjConst: array of TObject; N: Integer = 65536): TSample;

Parameter	Description
Fun	Integrating function.
lb	Lower bound.
ub	Upper bound.
N	Number of random points in [lb,ub] interval (see comments above).

Description

Performs a numerical integration of function of single variable by using Monte Carlo method.

See Also
QuadGauss

Example 1

Evaluate fuction Sin(x) on interval [0,PI] by using Monte Carlo algorithm.

    // Integrating function
    function IntFunc(Parameters: TVec; Const Constants: Array of TSample; Const ObjConst: Array of TObject): TSample;
    var x: TSample;
    begin
      x := Parameters[0];
      Result := Sin(x);
    end;
    // Integrate
    procedure DoIntegrate;
    var area: TSample;
    begin
      area := MonteCarlo(IntFunc,0,PI,16,[],[],65536); // 2^16 random points in [0,PI] interval
    end;

    #include "MtxVecCpp.h"
    #include "Math387.hpp"
    #include "MtxIntDiff.hpp"

    double __fastcall IntFun(TVec * Parameters, const double * Constants, const int Constants_Size,
     System::TObject* const * ObjConst, const int ObjConst_Size)
    {
      double x = (*Parameters)[0];
      return Math.Sin(x);
    }
    void __fastcall Example();
    {
      double area = MonteCarlo(IntFun,0.0,PI,NULL,NULL,65536); // 2^16 random points in [0,PI] interval
    }

    private double IntFun(TVec x, double[] c, object[] o)
    {
      double x = x[0];
      return System.Math.Sin(x);
    }
    private void Example()
    {
      TIntStopReason sr;
      double area = MtxIntDif.MonteCarlo(IntFun,0.0,System.Math.PI,null,null,65536);
    }