TMtxMultiNonLinReg Class

Performs multiple-nonlinear regression.

Pascal

TMtxMultiNonLinReg = class(TMtxComponent);

File

StatTools

Description

How to use TMtxMultiNonLinReg component?

Drop a TMtxMultiNonLinReg component on the form.
Define X the vector of independent variables.
Define Y the vector of dependent variables. Make sure that X and Y have the same length.
Define initial estimates for B regression parameters.
(Optionaly) define Weights. If you'll use weights, set UseWeights property to true.
Define regression function.
(Optionally) define the derivative procedure. If you don't define derivative procedure then the numeric approximation will be used to calculate the derivative at specific point.
Define the optimization method. Depending on your function different methods will give better/worse results.
(Optionally) define desired tolerance for result.
Define the maximum number of steps for optimization method. Internal optimization method will stop when number of iterations exceeds MaxIter or internal minimum precision is within Tolerance.
Verbose property, if assigned, stores Fun, evaluated at each iteration step. Optionally, you can also assign TOptControl object to the Verbose property. This allows the optimization procedure to be interrupted from another thread and optionally also allows logging and iteration count monitoring.

Results:

B : Regression coefficients estimates.
YCalc : Fitted Y values.

The component internally performs vectorized optimization process. It can also be used to speed-up nonlinear regression with only one independent variable by 10-20x.

Example

In the following example we use the TMtxMultiNonLinReg component to fit generated data to non-linear function B[0]/Power((1.0 + Exp(B[1]-B[2]*X)),1/B[3]). In this example exact derivate procedure is not used - algorithm uses numerical derivatives:

// regress function
procedure Rat43(const B: TVec; const X: TVecList; const y: TVec);
begin
    // Rat43 := B[0] / Power((1.0 + Exp(B[1]-B[2]*X)),1/B[3]);

    y.Mul(x[0], -B[2]);
    y.Add(B[1]);
    y.Exp();
    y.Add(1);
    y.Power(1/B[3]);
    y.DivideBy(B[0]);
end;

procedure TfrmNonLinTest.FormCreate(Sender: TObject);
var MtxNonLinReg: TMtxMultiNonLinReg;
begin
  MtxNonLinReg := TMtxMultiNonLinReg.Create;
  try
    // Load data - independent variable
    MtxNonLinReg.X.Add(); //add one variable
    MtxNonLinReg.X[0].SetIt(false,[9.000, 14.000, 21.000, 28.000,
                                42.000, 57.000, 63.000, 70.000,
                                79.000]);
    // Load data - dependent variable
    MtxNonLinReg.Y.SetIt(false,[8.930, 10.800, 18.590, 22.330,
                                39.350, 56.110, 61.730, 64.620,
                                67.080]);
    // Initial estimates for regression coefficients
    MtxNonLinReg.b.SetIt(false,[100,10,1,1]);
    // setup optimization parameters
    MtxNonLinReg.Tolerance := 1.0e-6; // 6 digits should do the trick
    MtxNonLinReg.GradTolerance := 1.0e-3 // 3 digits
    MtxNonLinReg.MaxIterations := 400;
    MtxNonLinReg.RegressFunction := Rat43; // regression function
    // Marquardt method
    MtxNonLinReg.OptMethod := optMarquardt;
    MtxNonLinReg.Recalc;
    // MtxNinLinReg.b now stores calculated regression parameter estimates
  finally
    MtxNonLinReg.Free;
  end;
end;

    #include "MtxExpr.hpp"
#include "StatTools.hpp"
#include "Math387.hpp"

void __fastcall Rat43(TVec* const b, TVecList* const x, TVec * const y)
{
    double* B = b->PValues1D(0);

//      return B[0] / Power((1.0 + Exp(b[1]-b[2]*x)),1/b[3]);

    y->Mul((*x)[0], -B[2]);
    y->Add(B[1]);
    y->Exp();
    y->Add(1);
    y->Power(1/B[3]);
    y->DivideBy(B[0]);
}

void __fastcall Example()
{
  TMtxMultiNonLinReg *nlr = new TMtxMultiNonLinReg(NULL);
  try
  {
      const int xLen = 9;
      double xData[xLen] = {9.000, 14.000, 21.000, 28.000, 42.000, 57.000, 63.000, 70.000, 79.000};

      const int yLen = 9;
      double yData[yLen] = {8.930, 10.800, 18.590, 22.330, 39.350, 56.110, 61.730, 64.620, 67.080};

      // Load data - independent variable
      nlr->X->Add(); //add one variable
      (*(nlr->X))[0]->SetIt(false, xData, xLen - 1);

      // Load data - dependent variable
      nlr->Y->SetIt(false, yData, yLen - 1);

      // Initial estimates for regression coefficients
      nlr->B->SetIt(false,OPENARRAY(double,(100,10,1,1)));

      // setup optimization parameters
      nlr->Tolerance = 1.0e-6; // 6 digits should do the trick
      nlr->GradTolerance = 1.0e-5; // 5 digits
      nlr->MaxIteration = 400;
      nlr->RegressFunction = Rat43; // regression function

      // Marquardt method
      nlr->OptMethod = optMarquardt;
      nlr->Recalc();

      // MtxNonLinReg->B now stores calculated regression parameter estimates
  }
  __finally
  {
      nlr->Free();
  }
}

TMtxMultiNonLinReg Fields, TMtxMultiNonLinReg Methods, TMtxMultiNonLinReg Properties, TMtxMultiNonLinReg Members, StatTools, Classes, Example

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