Polynoms.PolyFit Method

Overload List

#	Signature	Description
1	void PolyFit(TVec XValues, TVec YValues, Int32 Degree, TVec Coeff, TMtx R, ref Int32 DegFreedom, ref Double L2R, TVec Weights)	Fits a polynomial to data.
2	void PolyFit(TVec XValues, TVec YValues, Int32 Degree, TVec Coeff, TVec Weights)	Fits a polynomial to data.

Overload 1: void PolyFit(TVec XValues, TVec YValues, Int32 Degree, TVec Coeff, TMtx R, ref Int32 DegFreedom, ref Double L2R, TVec Weights)

Fits a polynomial to data.

#	Name	Description
1	XValues	Defines x values in p=p(x).
2	YValues	Defines polynomial, evaluated at x i.e p(x).
3	Degree	Defines polynomial degree.
4	Weights	If not nil, defines fitting weights.
5	Coeff	Returns the coeficients of fitted polynomial.
6	R	Returns the Cholesky factor of the Vandermonde matrix.
7	DegFreedom	Returns the degree of freedom.
8	L2R	Returns the L2 norm of the residuals.

Result: stored in self (calling object)

Remarks:

The PolyFit procedure uses the least-squares method to find the fitted polynomial coefficients.

Examples

using Dew.Math;
using Dew.Math.Units;
using Dew.Math.Tee;

namespace Dew.Examples
{
    private void Example()
    {
        Vector X = new Vector(0);
        Vector Y = new Vector(0);
        Vector YCalc = new Vector(0);
        Vector Delta = new Vector(0);
        Vector Coeff = new Vector(0);
        Matrix R = new Matrix(0,0);
        int degF;
        double L2R;

        X.Ramp(100);
        y.Size(X);
        Y.RandomGauss(2.0,3.0);
        Polynoms.PolyFit(X,Y,3,Coeff,R, out degF, out L2R, null); //Fit
        Polynoms.PolyEval(X,Coeff,degF,L2R,YCalc,Delta); // Evaluate
        MtxVecTee.DrawIt(new Vector[] {Y,YCalc}, new string[] {"Original","Fit"},"Fit results",false);
    }
}

Overload 2: void PolyFit(TVec XValues, TVec YValues, Int32 Degree, TVec Coeff, TVec Weights)

Fits a polynomial to data.

#	Name	Type	Description
1	XValues	TVec	source TVec
2	YValues	TVec	source TVec
3	Degree	Int32
4	Coeff	TVec	source TVec
5	Weights	TVec	source TVec

Result: stored in self (calling object)

Remarks:

This overload does not return additional statistical parameters like Cholesky matrix or degrees of freedom.