Example 1

     function Banana(Pars: TVec; const Consts: Array of TSample;const PConsts: Array of Pointer): TSample;
     begin
      Result := 100*Sqr(Pars[1]-Sqr(Pars[0]))+Sqr(1-Pars[0]);
     end;

     procedure GradHessBanana(Fun: TRealFunction; Pars: TVec; const Consts: Array of TSample;const ObjConsts: Array of TObject; Grad: TVec; Hess: TMtx);
     begin
	    Grad.Values[0] := -400*(Pars[1]-Sqr(Pars[0]))*Pars[0]-2*(1-Pars[0]);
	    Grad.Values[1] := 200*(Pars[1]-Sqr(Pars[0]));
	    Hess.Values[0,0] := -400*Pars[1]+1200*Sqr(Pars[0])+2;
	    Hess.Values[0,1] := -400*Pars[0];
	    Hess.Values[1,0] := -400*Pars[0];
	    Hess.Values[1,1] := 200;
     end;

     procedure TForm1.FormCreate(Sender: TObject);
     begin
      MtxOptim.VariableParameters.SetIt(false,[2,-1]);
      MtxOptim.RealFunction := Banana;
      MtxOptim.OptimizationMethod := optMarquardt;
      // use exact gradient and Hessian matrix calculation
      // NOTE : set MtxOptim.GradHessProcedure to nil if you want to use numeric gradient and Hessian matrix approximation
      MtxOptim.GradHessProcedure := GradHessBanana;
      MtxOptim.Recalculate;
     end;

    #include "MtxVecCpp.h" //MtxVecCPP.cpp must be included in the project
    #include "Math387.hpp"
    #include "Optimization.hpp"
    #include "MtxIntDiff.hpp"
    #include "MtxVecTools.hpp"

    // Objective function
    double __fastcall Banana(TVec * Parameters, const double * Constants, const int Constants_Size,
     System::TObject* const * ObjConst, const int ObjConst_Size)
    {
      return 100.0*IntPower(Parameters[1]-IntPower(Parameters[0],2),2)+IntPower(1.0-Parameters[0],2);
    }

    // Analytical gradient and Hessian matrix of the objective function
    void __fastcall BananaGradHess(TRealFunction Fun, TVec * Parameters, const double * Consts, const int Consts_Size,
	    System::TObject* const * ObjConst, const int ObjConst_Size, TVec* Grad, TMtx* Hess)
    {
      double* Pars = Parameters->PValues(0); //get pointer to the first element

      Grad->Values[0] = -400*(Pars[1]-IntPower(Pars[0],2))*Pars[0] - 2*(1-Pars[0]);
      Grad->Values[1] = 200*(Pars[1]-IntPower(Pars[0],2));
      Hess->Values1D[0] = -400*Pars[1]+1200*IntPower(Pars[0],2)+2;
      Hess->Values1D[1] = -400*Pars[0];
      Hess->Values1D[2] = -400*Pars[0];
      Hess->Values1D[3] = 200;
    }

    void __fastcall TForm1::FormCreate(TObject *Sender)
    {
      MtxOptim->VariableParameters->SetIt(false,OPENARRAY(TSample,(2,-1)));
      MtxOptim->RealFunction = Banana;
      MtxOptim.OptimizationMethod = optBFGS;
      // use exact gradient vector calculation
      // NOTE : set MtxOptim.GradProcedure to NULL if you
	    //        want to use internal numeric gradient calculation
      MtxOptim->GradHessProcedure = GradHessBanana;
      MtxOptim->Recalculate();

    }