Polynoms.PolyFit Function

Fits a polynomial to data.

Pascal

procedure PolyFit(XValues: TVec; YValues: TVec; Degree: Integer; Coeff: TVec; R: TMtx; out DegFreedom: Integer; out L2R: double; Weights: TVec = nil); overload;

File

Polynoms

Parameters

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

Description

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

Example

uses MtxExpr, Math387, MtxVec, MtxVecTee, Polynoms; procedure TForm1.Button1Click(Sender: TObject); var X,Y,YCalc,Delta,Coeff: Vector; R: Matrix; DegF: Integer; L2R : double; begin X.Size(100,false); Y.Size(X); X.Ramp; Y.RandGauss(2,3); PolyFit(X,Y,3,Coeff,R,DegF,L2R); //Fit PolyEval(X,Coeff,R,DegF,L2R,YCalc,Delta); // evaluate DrawIt([Y,YCalc],['Original','Polyfit']); end;

#include "MtxExpr.hpp" #include "Polynoms.hpp" #include "MtxVecTee.hpp" void __fastcall TForm1::BitBtn1Click(TObject *Sender) { Vector X,Y,YCalc,Delta,Coeff; Matrix R; int DegF; double L2R; X = Ramp(100); Y.Size(100); Y.RandGauss(2,3); PolyFit(X,Y,3,Coeff,R,DegF,L2R); //Fit PolyEval(X,Coeff,R,DegF,L2R,YCalc,Delta); // evaluate DrawIt(OPENARRAY(TVec*,(Y,YCalc)),OPENARRAY(AnsiString,("Original","Polyfit"))); }

Polynoms, Functions, Example

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