// Copyright (c) 1995-1999 Matra Datavision
// Copyright (c) 1999-2014 OPEN CASCADE SAS
//
// This file is part of Open CASCADE Technology software library.
//
// This library is free software; you can redistribute it and/or modify it under
// the terms of the GNU Lesser General Public License version 2.1 as published
// by the Free Software Foundation, with special exception defined in the file
// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
// distribution for complete text of the license and disclaimer of any warranty.
//
// Alternatively, this file may be used under the terms of Open CASCADE
// commercial license or contractual agreement.

// lpa, le 11/09/91


// Application de la methode du gradient corrige pour minimiser 
// F  = somme(||C(ui, Poles(ui)) - ptli||2.
// La methode de gradient conjugue est programmee dans la bibliotheque 
// mathematique: math_BFGS.


#define No_Standard_RangeError
#define No_Standard_OutOfRange

#include <AppParCurves_Constraint.hxx>
#include <AppParCurves_ConstraintCouple.hxx>
#include <math_BFGS.hxx>
#include <StdFail_NotDone.hxx>
#include <AppParCurves_MultiPoint.hxx>
#include <gp_Pnt.hxx>
#include <gp_Pnt2d.hxx>
#include <gp_Vec.hxx>
#include <gp_Vec2d.hxx>
#include <TColgp_Array1OfPnt.hxx>
#include <TColgp_Array1OfPnt2d.hxx>
#include <TColgp_Array1OfVec.hxx>
#include <TColgp_Array1OfVec2d.hxx>

static AppParCurves_Constraint FirstConstraint
  (const Handle(AppParCurves_HArray1OfConstraintCouple)& TheConstraints,
   const Standard_Integer FirstPoint)
{
  Standard_Integer i, myindex;
  Standard_Integer low = TheConstraints->Lower(), upp= TheConstraints->Upper();
  AppParCurves_ConstraintCouple mycouple;
  AppParCurves_Constraint Cons = AppParCurves_NoConstraint;

  for (i = low; i <= upp; i++) {
    mycouple = TheConstraints->Value(i);
    Cons = mycouple.Constraint();
    myindex = mycouple.Index();
    if (myindex == FirstPoint) {
      break;
    }
  }
  return Cons;
}


static AppParCurves_Constraint LastConstraint
  (const Handle(AppParCurves_HArray1OfConstraintCouple)& TheConstraints,
   const Standard_Integer LastPoint)
{
  Standard_Integer i, myindex;
  Standard_Integer low = TheConstraints->Lower(), upp= TheConstraints->Upper();
  AppParCurves_ConstraintCouple mycouple;
  AppParCurves_Constraint Cons = AppParCurves_NoConstraint;

  for (i = low; i <= upp; i++) {
    mycouple = TheConstraints->Value(i);
    Cons = mycouple.Constraint();
    myindex = mycouple.Index();
    if (myindex == LastPoint) {
      break;
    }
  }
  return Cons;
}





AppParCurves_BSpGradient::
   AppParCurves_BSpGradient(const MultiLine& SSP,
         const Standard_Integer FirstPoint,
         const Standard_Integer LastPoint,
	 const Handle(AppParCurves_HArray1OfConstraintCouple)& TheConstraints,
         math_Vector& Parameters,
	 const TColStd_Array1OfReal& Knots,
	 const TColStd_Array1OfInteger& Mults,
         const Standard_Integer Deg,
	 const Standard_Real Tol3d,
	 const Standard_Real Tol2d,
	 const Standard_Integer NbIterations):
	 ParError(FirstPoint, LastPoint,0.0),
         mylambda1(0.0),
         mylambda2(0.0),
         myIsLambdaDefined(Standard_False)
{
  Perform(SSP, FirstPoint, LastPoint, TheConstraints, Parameters, 
	  Knots, Mults, Deg, Tol3d, Tol2d, NbIterations);
}


AppParCurves_BSpGradient::
   AppParCurves_BSpGradient(const MultiLine& SSP,
         const Standard_Integer FirstPoint,
         const Standard_Integer LastPoint,
	 const Handle(AppParCurves_HArray1OfConstraintCouple)& TheConstraints,
         math_Vector& Parameters,
	 const TColStd_Array1OfReal& Knots,
	 const TColStd_Array1OfInteger& Mults,
         const Standard_Integer Deg,
	 const Standard_Real Tol3d,
	 const Standard_Real Tol2d,
	 const Standard_Integer NbIterations,
	 const Standard_Real lambda1,
	 const Standard_Real lambda2):
	 ParError(FirstPoint, LastPoint,0.0),
         mylambda1(lambda1),
         mylambda2(lambda2),
         myIsLambdaDefined(Standard_True)
{
  Perform(SSP, FirstPoint, LastPoint, TheConstraints, Parameters, 
	  Knots, Mults, Deg, Tol3d, Tol2d, NbIterations);
}







void AppParCurves_BSpGradient::
  Perform(const MultiLine& SSP,
         const Standard_Integer FirstPoint,
         const Standard_Integer LastPoint,
	 const Handle(AppParCurves_HArray1OfConstraintCouple)& TheConstraints,
         math_Vector& Parameters,
	 const TColStd_Array1OfReal& Knots,
	 const TColStd_Array1OfInteger& Mults,
         const Standard_Integer Deg,
	 const Standard_Real Tol3d,
	 const Standard_Real Tol2d,
	 const Standard_Integer NbIterations)
{

//  Standard_Boolean grad = Standard_True;
  Standard_Integer i, j, k, i2, l;
  Standard_Real UF, DU, Fval = 0.0, FU, DFU;
  Standard_Integer nbP3d = ToolLine::NbP3d(SSP);
  Standard_Integer nbP2d = ToolLine::NbP2d(SSP);
  Standard_Integer mynbP3d=nbP3d, mynbP2d=nbP2d;
  Standard_Integer nbP = nbP3d + nbP2d;
//  gp_Pnt Pt, P1, P2;
  gp_Pnt Pt;
//  gp_Pnt2d Pt2d, P12d, P22d;
  gp_Pnt2d Pt2d;
//  gp_Vec V1, V2, MyV;
  gp_Vec V1, MyV;
//  gp_Vec2d V12d, V22d, MyV2d;
  gp_Vec2d V12d, MyV2d;
  Done = Standard_False;
  
  if (nbP3d == 0) mynbP3d = 1;
  if (nbP2d == 0) mynbP2d = 1;
  TColgp_Array1OfPnt TabP(1, mynbP3d);
  TColgp_Array1OfPnt2d TabP2d(1, mynbP2d);
  TColgp_Array1OfVec TabV(1, mynbP3d);
  TColgp_Array1OfVec2d TabV2d(1, mynbP2d);

  // Calcul de la fonction F= somme(||C(ui)-Ptli||2):
  // Appel a une fonction heritant de MultipleVarFunctionWithGradient
  // pour calculer F et grad_F.
  // ================================================================

  Standard_Integer nbpoles = -Deg -1;
  for (i = Mults.Lower() ;i <= Mults.Upper(); i++) {
    nbpoles += Mults(i);
  }

  TColgp_Array1OfPnt   TabPole(1, nbpoles);
  TColgp_Array1OfPnt2d TabPole2d(1, nbpoles);
  TColgp_Array1OfPnt    ThePoles(1, (nbpoles)*mynbP3d);
  TColgp_Array1OfPnt2d  ThePoles2d(1, (nbpoles)*mynbP2d);


  AppParCurves_Constraint 
    FirstCons = FirstConstraint(TheConstraints, FirstPoint), 
    LastCons  = LastConstraint(TheConstraints, LastPoint);


  AppParCurves_BSpParFunction MyF(SSP, FirstPoint,LastPoint, TheConstraints, 
				  Parameters, Knots, Mults, nbpoles);



  if (FirstCons >= AppParCurves_TangencyPoint ||
      LastCons >= AppParCurves_TangencyPoint) {

    if (!myIsLambdaDefined) {
      AppParCurves_BSpParLeastSquare thefitt(SSP, Knots, Mults, FirstPoint,
					     LastPoint, FirstCons, LastCons, 
					     Parameters, nbpoles);
      if (FirstCons >= AppParCurves_TangencyPoint) {
	mylambda1 = thefitt.FirstLambda();
	MyF.SetFirstLambda(mylambda1);
      }
      if (LastCons >= AppParCurves_TangencyPoint) {
	mylambda2 = thefitt.LastLambda();
	MyF.SetLastLambda(mylambda2);
      }
    }
    else {
      MyF.SetFirstLambda(mylambda1);
      MyF.SetLastLambda(mylambda2);
    }
  }


  MyF.Value(Parameters, Fval);
  MError3d = MyF.MaxError3d();
  MError2d = MyF.MaxError2d();
  SCU = MyF.CurveValue();

  if (MError3d > Tol3d || MError2d > Tol2d) {

    // Stockage des Poles des courbes pour projeter:
    // ============================================
    i2 = 0;
    for (k = 1; k <= nbP3d; k++) {
      SCU.Curve(k, TabPole);
      for (j=1; j<=nbpoles; j++) ThePoles(j+i2) = TabPole(j);
      i2 += nbpoles;
    }
    i2 = 0;
    for (k = 1; k <= nbP2d; k++) {
      SCU.Curve(nbP3d+k, TabPole2d);
      for (j=1; j<=nbpoles; j++) ThePoles2d(j+i2) = TabPole2d(j);
      i2 += nbpoles;
    }
    
    //  Une iteration rapide de projection est faite par la methode de 
    //  Rogers & Fog 89, methode equivalente a Hoschek 88 qui ne necessite pas
    //  le calcul de D2.
    
    const math_Matrix& A = MyF.FunctionMatrix();
    const math_Matrix& DA = MyF.DerivativeFunctionMatrix();
    const math_IntegerVector& Index = MyF.Index();
    Standard_Real aa, da, a, b, c, d , e , f, px, py, pz;
    Standard_Integer indexdeb, indexfin;

    for (j = FirstPoint+1; j <= LastPoint-1; j++) {
      
      UF = Parameters(j);
      if (nbP3d != 0 && nbP2d != 0) ToolLine::Value(SSP, j, TabP, TabP2d);
      else if (nbP2d != 0)          ToolLine::Value(SSP, j, TabP2d);
      else                          ToolLine::Value(SSP, j, TabP);
      
      FU = 0.0;
      DFU = 0.0;
      i2 = 0;
      
      indexdeb = Index(j) + 1;
      indexfin = indexdeb + Deg;

      for (k = 1; k <= nbP3d; k++) {
	a = b = c = d = e = f = 0.0;
	for (l = indexdeb; l <= indexfin; l++) {
	  Pt = ThePoles(l+i2); 
	  px = Pt.X(); py = Pt.Y(); pz = Pt.Z();
	  aa = A(j, l); da = DA(j, l);
	  a += aa* px; d += da* px;
	  b += aa* py; e += da* py;
	  c += aa* pz; f += da* pz;
	}
	Pt.SetCoord(a, b, c);
	V1.SetCoord(d, e, f);
	i2 += nbpoles;

	MyV = gp_Vec(Pt, TabP(k));
	FU += MyV*V1;
	DFU += V1.SquareMagnitude();
      }
      i2 = 0;
      for (k = 1; k <= nbP2d; k++) {
	a = b = d = e = 0.0;
	for (l = indexdeb; l <= indexfin; l++) {
	  Pt2d = ThePoles2d(l+i2); 
	  px = Pt2d.X(); py = Pt2d.Y();
	  aa = A(j, l); da = DA(j, l);
	  a += aa* px; d += da* px;
	  b += aa* py; e += da* py;
	}
	Pt2d.SetCoord(a, b);
	V12d.SetCoord(d, e);
	i2 += nbpoles;

	MyV2d = gp_Vec2d(Pt2d, TabP2d(k));
	FU += MyV2d*V12d;
	DFU += V12d.SquareMagnitude();
      }
      
      if (DFU >= RealEpsilon()) {
	DU = FU/DFU;
	DU = Sign(Min(5.e-02, Abs(DU)), DU);
	UF += DU;
	Parameters(j) = UF;
      }
    }
    
    MyF.Value(Parameters, Fval);
    MError3d = MyF.MaxError3d();
    MError2d = MyF.MaxError2d();
  }


  if (MError3d<= Tol3d && MError2d <= Tol2d) {
    Done = Standard_True;
  }
  else if (NbIterations != 0) {
    // NbIterations de gradient conjugue:
    // =================================
    Standard_Real Eps = 1.e-07;
    AppParCurves_BSpGradient_BFGS FResol(MyF, Parameters, Tol3d, 
					 Tol2d, Eps, NbIterations);
  }

  SCU = MyF.CurveValue();


  AvError = 0.;
  for (j = FirstPoint; j <= LastPoint; j++) {  
    Parameters(j) = MyF.NewParameters()(j);
    // Recherche des erreurs maxi et moyenne a un index donne:
    for (k = 1; k <= nbP; k++) {
      ParError(j) = Max(ParError(j), MyF.Error(j, k));
    }
    AvError += ParError(j);
  }
  AvError = AvError/(LastPoint-FirstPoint+1);


  MError3d = MyF.MaxError3d();
  MError2d = MyF.MaxError2d();
  if (MError3d <= Tol3d && MError2d <= Tol2d) {
    Done = Standard_True;
  }

}



AppParCurves_MultiBSpCurve AppParCurves_BSpGradient::Value() const {
  return SCU;
}


Standard_Boolean AppParCurves_BSpGradient::IsDone() const {
  return Done;
}


Standard_Real AppParCurves_BSpGradient::Error(const Standard_Integer Index) const {
  return ParError(Index);
}

Standard_Real AppParCurves_BSpGradient::AverageError() const {
  return AvError;
}

Standard_Real AppParCurves_BSpGradient::MaxError3d() const {
  return MError3d;
}

Standard_Real AppParCurves_BSpGradient::MaxError2d() const {
  return MError2d;
}