Uses MtxExp, Math387, Regress, Optimization, MtxVecTee;
// function definition
procedure Eckerle4(const B: TVec; const X: TVecList; const Y: TVec);
begin
    //= B[0]/B[1] * Exp(-0.5*Sqr((X-B[2])/B[1]));

    y.Normalize(X[0], B[2], B[1]);
    y.Sqr;
    y.Scale(-0.5);
    y.Exp;
    y.Scale(B[0]/B[1]);
end;
procedure Example;
var x0,y,b,yhat: Vector;
  StopReason: TOptStopReason;
  x: TVecList;
begin
  x := TVecList.Create;
  x.Add; //add

  x[0].SetIt(false,[400.0, 405.0, 410.0, 415.0,
                 420.0, 425.0, 430.0, 435.0,
                 436.5, 438.0, 439.5, 441.0,
                 442.5, 444.0, 445.5, 447.0,
                 448.5, 450.0, 451.5, 453.0,
                 454.5, 456.0, 457.5, 459.0,
                 460.5, 462.0, 463.5, 465.0,
                 470.0, 475.0, 480.0, 485.0,
                 490.0, 495.0, 500.0]);

  y.SetIt(false,[0.0001575, 0.0001699, 0.0002350, 0.0003102,
                 0.0004917, 0.0008710, 0.0017418, 0.0046400,
                 0.0065895, 0.0097302, 0.0149002, 0.0237310,
                 0.0401683, 0.0712559, 0.1264458, 0.2073413,
                 0.2902366, 0.3445623, 0.3698049, 0.3668534,
                 0.3106727, 0.2078154, 0.1164354, 0.0616764,
                 0.0337200, 0.0194023, 0.0117831, 0.0074357,
                 0.0022732, 0.0008800, 0.0004579, 0.0002345,
                 0.0001586, 0.0001143, 0.0000710]);

  b.SetIt(false,[1.0, 10.0, 500.0]); // initial estimates
  NLinRegress(x,y,Eckerle4,nil,b,optMarquardt, StopReason,
              nil,yhat,false,300,1e-8,1e-10);

  DrawValues(x[0],y,Series1,false); // draw data
  DrawValues(x[0],yhat,Series2,false); // draw fitted values

  x.Free;
end;

#include "MtxExpr.hpp"
#include "Regress.hpp"
#include "MtxVecTee.hpp"

void __fastcall Eckerle4(TVec* const b, TVecList* const x, TVec * const y)
{
    double* B = b->PValues1D(0);

    //      double a = (x-B[2])/B[1]);
    //      return B[0]/B[1] * Exp(-0.5*a*a);

    y->Normalize((*x)[0], B[2], B[1]);
    y->Sqr();
    y->Scale(-0.5);
    y->Exp();
    y->Scale(B[0]/B[1]);
}

void __fastcall Test(TLineSeries * series1, TLineSeries * series2)
{
    sVector y,b,yhat;
    TOptStopReason StopReason;

    TVecList *x = new TVecList();
    x->Add();

    const int xLen = 35;
    double xData[xLen] = {400.0, 405.0, 410.0, 415.0,
                         420.0, 425.0, 430.0, 435.0,
                         436.5, 438.0, 439.5, 441.0,
                         442.5, 444.0, 445.5, 447.0,
                         448.5, 450.0, 451.5, 453.0,
                         454.5, 456.0, 457.5, 459.0,
                         460.5, 462.0, 463.5, 465.0,
                         470.0, 475.0, 480.0, 485.0,
                         490.0, 495.0, 500.0};

    (*x)[0]->SetIt(false, xData, xLen-1);

    const int yLen = 35;
    double yData[yLen] = {0.0001575, 0.0001699, 0.0002350, 0.0003102,
                         0.0004917, 0.0008710, 0.0017418, 0.0046400,
                         0.0065895, 0.0097302, 0.0149002, 0.0237310,
                         0.0401683, 0.0712559, 0.1264458, 0.2073413,
                         0.2902366, 0.3445623, 0.3698049, 0.3668534,
                         0.3106727, 0.2078154, 0.1164354, 0.0616764,
                         0.0337200, 0.0194023, 0.0117831, 0.0074357,
                         0.0022732, 0.0008800, 0.0004579, 0.0002345,
                                 0.0001586, 0.0001143, 0.0000710};

    y.SetIt(false, yData, yLen-1);

    b.SetIt(false,OPENARRAY(double,(1.0, 10.0, 500.0))); // initial estimates

    NLinRegress(x,y,Eckerle4,NULL,b,optMarquardt, StopReason, NULL, yhat, false, 300, 1e-8, 1e-10);

    DrawValues((*x)[0], y, series1, false); // draw data
    DrawValues((*x)[0], yhat, series2, false); // draw fitted values
}