WeightsGauss Routine

Summary

Gauss base points and weights.

Declaration

Procedure WeightsGauss(NumPoints: Integer; Points, Weights: TVec);

Description

Calculates base points and weight factors by using the so called Gauss algorithm given by Davis and Rabinowitz in 'Methods of Numerical Integration', page 365, Academic Press, 1975.

See Also
WeightsChebyshevGauss
WeightsNewtonCotes

Example 1

Use a ten point Gauss formula to evaluate six(x) on interval [0,PI]. For start use only one subsection.

    // 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 bpoints,weights: Vector;
      area: TSample;
    begin
      WeightsGauss(10,bpoints,weights);
      area := QuadGauss(IntFunc,0,PI,bpoints,weights,1);
    end;

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

    // Integrating function
    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)*Math.Exp(-x*x);
    }
    void __fastcall Example();
    {
      Vector bpoints, weights;
      WeightsGauss(10,bpoints,weights);
      double area = QuadGauss(IntFun,-0.5*PI,PI,bpoints,weights,64);
    }

    private double IntFun(TVec x, double[] c, object[] o)
    {
      double x = x[0];
      return System.Math.Sin(x)*System.Math.Exp(-x*x);
    }
    private void Example()
    {
      Vector bpoints = new Vector(0);
      Vector weights = new Vector(0);
      MtxIntDiff.WeightsGauss(10,bpoints,weights);
      double area = MtxIntDif.QuadGauss(IntFun,-0.5*System.Math.PI,System.Math.PI,bpoints,weights,64);
    }