FracFit Routine

Summary

Fits rational fraction equation to data.

Declaration

Procedure FracFit(B: TVec; X, Y: TVec; DegNom, DegDenom: Integer; Constant: boolean = false; Weights: TVec = nil);

Parameter	Description
X	Vector of independent variable.
Y	Vector of dependent variable.
DegNom	Nominator degree.
DegDenom	Denominator degree.
Constant	If false, B[0] i.e. constant term in nominator is set to 0.0.
Weights	Weights (optional). Weights are used only if they are set.
B	Returns regression coefficients for rational function.

Description

The routine fits equations to data by minimizing the sum of squared residuals. The observed values obey the following equation:

where n and d are nominator and denominator polynomial degrees.

See Also
FracEval

Example 1

In the following example we generate some data. Then we fit power function to this data and retreive it's regression coefficients.

  Uses MathExpr, MtxVecTee, Series, RegModels;
  procedure Example(Series1: TLineSeries);
  var Y,YHat,B,X: Vector;
  begin
    X.Size(100);
    Y.Size(X);
    X.Ramp(-5,0.05); // X = (-5, -4.95, ...-0.05)
    Y.RandGauss(3.5,0.12); // populate sample data
    FracFit(B,X,Y,2,4); // calculate coefficients, no constant term
    // evaluate y by using calculated coefficients
    FracEval(B.Values,X,YHat,2);
    DrawValues(X,Y,Series1); // draw original data
    DrawValues(X,YHat,Series2); // draw fitted data
  end;

  #include "MtxVecCpp.h"
  #include "Math387.hpp"
  #include "RegModels.hpp"
  #include "MtxVecTee.hpp"
  void __fastcall Example(TLineSeries* Series1, TLineSeries* Series2);
  {
    Vector X,Y;
    Vector B, YHat;
    X->Size(100,false);
    Y->Size(X);
    X->Ramp(-5.0, 0.05); // x= -5, -4.95, ...-0.05
    Y->RandGauss(3.5, 0.12); // sample data
    FracFit(B,X,Y,2,4); // calculate coefficients
    // evaluate y by using calculated coefficients
    LineEval(B->Values,X, YHat,2,false,NULL);
    DrawValues(X,Y,Series1,false); // draw original data
    DrawValues(X,YHat,Series2,false); // draw fitted data
  }

  using Dew.Math;
  using Dew.Stats.Units;
  namespace Dew.Examples
  {
    private void Example(Steema.TeeChart.Styles.Line line1,
      Steema.TeeChart.Styles.Line line2)
    {
      Vector X = new Vector(100);
      Vector Y = new Vector(100);
      Vector B = new Vector(0);
      Vector YHat = new Vector(0);
      X.Ramp(-5.0, 0.05); // x= -5.0, -4.95, ... -0.05
      Y.RandGauss(3.5, 0.12); // sample data
      // calculate coefficients
      RegModels.FracFit(B,X,Y,2,4,false,null);
      // evaluate y by using calculated coefficients
      RegModels.FracEval(B.Values,X, YHat,2);
      MtxVecTee.DrawValues(X,Y,line1,false);
      MtxVecTee.DrawValues(X,YHat,line2,false);
    }
  }