MtxIntDiff.QuadGauss Method

Overload List

#	Signature	Description
1	Double QuadGauss(TRealFunction Fun, Double lb, Double ub, ref TIntStopReason StopReason, TMtxFloatPrecision FloatPrecision, TQuadMethod QMethod, Double Tolerance, Int32 MaxIter)	Integration by using Gauss quadrature algorithm with no additional parameters for Fun.
2	Double QuadGauss(TRealFunction Fun, Double lb, Double ub, TVec BasePoints, TVec Weights, Int32 Parts)	Numerical integration by using regular Gaussian quadrature scheme.
3	Double QuadGauss(TRealFunction Fun, Double lb, Double ub, TVec Constants, Object[] ObjConst, ref TIntStopReason StopReason, TMtxFloatPrecision FloatPrecision, TQuadMethod QMethod, Double Tolerance, Int32 MaxIter)	Evaluate the numerical integral between lower and upper bound using Gauss quadrature algorithm.
4	Double QuadGauss(TRealFunction Fun, Double lb, Double ub, TVec Constants, Object[] ObjConst, TVec BasePoints, TVec Weights, Int32 Parts)	Numerical integration by using regular Gaussian quadrature scheme (Fun defined only with double(s)).

Overload 1: Double QuadGauss(TRealFunction Fun, Double lb, Double ub, ref TIntStopReason StopReason, TMtxFloatPrecision FloatPrecision, TQuadMethod QMethod, Double Tolerance, Int32 MaxIter)

Integration by using Gauss quadrature algorithm with no additional parameters for Fun.

#	Name	Type	Description
1	Fun	TRealFunction
2	lb	Double	scalar
3	ub	Double	scalar
4	StopReason	TIntStopReason (ref)
5	FloatPrecision	TMtxFloatPrecision
6	QMethod	TQuadMethod
7	Tolerance	Double	scalar
8	MaxIter	Int32

Returns: Double - the numerical approximate on integral of function Fun between limits lb and ub.

Remarks:

This version calculates base points and weights on the fly.

Note
Use this overload if integrating function is defined only by double parameter(s).

Examples

private double IntFun(TVec x, TVec c, params object[] o)
{
    double x = x[0];
    return System.Math.Sin(x)*System.Math.Exp(-x*x);
}
private void Example()
{
    TIntStopReason sr;
    double area = MtxIntDif.QuadGauss(IntFun,-0.5*System.Math.PI, System.Math.PI, out sr, 1.0e-4, 8);
}

Overload 2: Double QuadGauss(TRealFunction Fun, Double lb, Double ub, TVec BasePoints, TVec Weights, Int32 Parts)

Numerical integration by using regular Gaussian quadrature scheme.

#	Name	Type	Description
1	Fun	TRealFunction
2	lb	Double	scalar
3	ub	Double	scalar
4	BasePoints	TVec	source TVec
5	Weights	TVec	source TVec
6	Parts	Int32

Returns: Double - the numerical approximate on integral of function Fun between limits lb and ub.

Remarks:

Check the following link to learn more about this algorithm

Examples

private double IntFun(TVec x, TVec c, params 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);
}

Overload 3: Double QuadGauss(TRealFunction Fun, Double lb, Double ub, TVec Constants, Object[] ObjConst, ref TIntStopReason StopReason, TMtxFloatPrecision FloatPrecision, TQuadMethod QMethod, Double Tolerance, Int32 MaxIter)

Evaluate the numerical integral between lower and upper bound using Gauss quadrature algorithm.

#	Name	Type	Description
1	Fun	TRealFunction
2	lb	Double	scalar
3	ub	Double	scalar
4	Constants	TVec	source TVec
5	ObjConst	Object[]
6	StopReason	TIntStopReason (ref)
7	FloatPrecision	TMtxFloatPrecision
8	QMethod	TQuadMethod
9	Tolerance	Double	scalar
10	MaxIter	Int32

Returns: Double - the numerical approximate on integral of function Fun between limits lb and ub.

Remarks:

This version calculates base points and weights on the fly.

See Also: MtxIntDiff.Romberg

Overload 4: Double QuadGauss(TRealFunction Fun, Double lb, Double ub, TVec Constants, Object[] ObjConst, TVec BasePoints, TVec Weights, Int32 Parts)

Numerical integration by using regular Gaussian quadrature scheme (Fun defined only with double(s)).

#	Name	Type	Description
1	Fun	TRealFunction
2	lb	Double	scalar
3	ub	Double	scalar
4	Constants	TVec	source TVec
5	ObjConst	Object[]
6	BasePoints	TVec	source TVec
7	Weights	TVec	source TVec
8	Parts	Int32

Returns: Double