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// File AppParCurves_Function.gxx
// Lpa, le 20/09/91


// Calcul de la valeur de F et grad_F, connaissant le parametrage.
// Cette fonction, appelee par le gradient conjugue, calcul F et 
// DF(ui, Poles(ui)) ce qui implique un calcul des nouveaux poles 
//  a chaque appel.

#define No_Standard_RangeError
#define No_Standard_OutOfRange



#include <AppParCurves_MultiCurve.hxx>
#include <AppParCurves_MultiPoint.hxx>
#include <TColStd_HArray1OfInteger.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 <AppParCurves_ConstraintCouple.hxx>

AppParCurves_Function::
  AppParCurves_Function(const MultiLine& SSP,
	 const Standard_Integer FirstPoint,
	 const Standard_Integer LastPoint,
	 const Handle(AppParCurves_HArray1OfConstraintCouple)& TheConstraints,
	 const math_Vector& Parameters,
	 const Standard_Integer Deg) :
         MyMultiLine(SSP),
         MyMultiCurve(Deg+1),          
         myParameters(Parameters.Lower(), Parameters.Upper()),
         ValGrad_F(FirstPoint, LastPoint),
         MyF(FirstPoint, LastPoint, 
	     1, ToolLine::NbP3d(SSP)+ToolLine::NbP2d(SSP), 0.0),
         PTLX(FirstPoint, LastPoint, 
	     1, ToolLine::NbP3d(SSP)+ToolLine::NbP2d(SSP), 0.0),
         PTLY(FirstPoint, LastPoint, 
	     1, ToolLine::NbP3d(SSP)+ToolLine::NbP2d(SSP), 0.0),
         PTLZ(FirstPoint, LastPoint, 
	     1, ToolLine::NbP3d(SSP)+ToolLine::NbP2d(SSP), 0.0),
         A(FirstPoint, LastPoint, 1, Deg+1),
         DA(FirstPoint, LastPoint, 1, Deg+1),
         MyLeastSquare(SSP, FirstPoint, LastPoint, 
		       FirstConstraint(TheConstraints, FirstPoint),
		       LastConstraint(TheConstraints, LastPoint), Deg+1)
{
  Standard_Integer i;
  for (i=Parameters.Lower(); i<=Parameters.Upper();i++)
    myParameters(i)=Parameters(i);
  FirstP = FirstPoint;
  LastP = LastPoint;
  myConstraints = TheConstraints;
  NbP = LastP-FirstP+1;
  Adeb = FirstP;
  Afin = LastP;
  Degre = Deg;
  Contraintes = Standard_False;
  Standard_Integer myindex;
  Standard_Integer low = TheConstraints->Lower(), upp= TheConstraints->Upper();
  AppParCurves_ConstraintCouple mycouple;
  AppParCurves_Constraint Cons;

  for (i = low; i <= upp; i++) {
    mycouple = TheConstraints->Value(i);
    Cons = mycouple.Constraint();
    myindex = mycouple.Index();
    if (myindex == FirstP) {
      if (Cons >= 1) Adeb = Adeb+1;
    }
    else if (myindex == LastP) {
      if (Cons >= 1) Afin = Afin-1;
    }
    else {
      if (Cons >= 1) Contraintes = Standard_True;
    }
  }

  Standard_Integer nb3d = ToolLine::NbP3d(SSP);
  Standard_Integer nb2d = ToolLine::NbP2d(SSP);
  Standard_Integer mynb3d= nb3d, mynb2d=nb2d;
  if (nb3d == 0) mynb3d = 1;
  if (nb2d == 0) mynb2d = 1;

  NbCu = nb3d+nb2d;
  tabdim = new TColStd_HArray1OfInteger(0, NbCu-1);

  if (Contraintes) {
    for (i = 1; i <= NbCu; i++) {
      if (i <= nb3d) tabdim->SetValue(i-1, 3);
      else tabdim->SetValue(i-1, 2);
    }

    TColgp_Array1OfPnt TabP(1, mynb3d);
    TColgp_Array1OfPnt2d TabP2d(1, mynb2d);
    
    for ( i = FirstP; i <= LastP; i++) {
      if (nb3d != 0 && nb2d != 0) ToolLine::Value(SSP, i, TabP, TabP2d);
      else if (nb3d != 0)         ToolLine::Value(SSP, i, TabP);
      else                        ToolLine::Value(SSP, i, TabP2d);
      for (Standard_Integer j = 1; j <= NbCu; j++) {
	if (tabdim->Value(j-1) == 3) {
	  TabP(j).Coord(PTLX(i, j), PTLY(i, j),PTLZ(i, j));
	}
	else {
	  TabP2d(j).Coord(PTLX(i, j), PTLY(i, j));
	}
      }
    }
  }
}


AppParCurves_Constraint AppParCurves_Function::FirstConstraint
  (const Handle(AppParCurves_HArray1OfConstraintCouple)& TheConstraints,
   const Standard_Integer FirstPoint) const
{
  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;
}


AppParCurves_Constraint AppParCurves_Function::LastConstraint
  (const Handle(AppParCurves_HArray1OfConstraintCouple)& TheConstraints,
   const Standard_Integer LastPoint) const
{
  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;
}




Standard_Boolean AppParCurves_Function::Value (const math_Vector& X, 
					       Standard_Real& F) {

  myParameters = X;

  // Resolution moindres carres:
  // ===========================
  MyLeastSquare.Perform(myParameters);
  if (!(MyLeastSquare.IsDone())) { 
    Done = Standard_False;
    return Standard_False;
  }
  if (!Contraintes) {
    MyLeastSquare.Error(FVal, ERR3d, ERR2d);
    F = FVal;
  }

  // Resolution avec contraintes:
  // ============================
  else { 
    Standard_Integer Npol = Degre+1;
//    Standard_Boolean Ext = Standard_True;
    Standard_Integer Ci, i, j, dimen;
    Standard_Real AA, BB, CC, AIJ, FX, FY, FZ, Fi;
    math_Vector PTCXCI(1, Npol), PTCYCI(1, Npol), PTCZCI(1, Npol);
    ERR3d = ERR2d = 0.0;
    
    MyMultiCurve = MyLeastSquare.BezierValue();

    A = MyLeastSquare.FunctionMatrix();
    ResolCons Resol(MyMultiLine, MyMultiCurve, FirstP, LastP, myConstraints,
		    A, MyLeastSquare.DerivativeFunctionMatrix());
    if (!Resol.IsDone()) {
      Done = Standard_False;
      return Standard_False;
    }

    // Calcul de F = Sum||C(ui)-Ptli||2  sur toutes les courbes :
    // ========================================================================
    FVal = 0.0;
    
    for (Ci = 1; Ci <= NbCu; Ci++) {
      dimen = tabdim->Value(Ci-1);
      for (j = 1; j <= Npol; j++) {
	if (dimen == 3){ 
	  MyMultiCurve.Value(j).Point(Ci).Coord(PTCXCI(j),PTCYCI(j),PTCZCI(j));
	}
	else{ 
	  MyMultiCurve.Value(j).Point2d(Ci).Coord(PTCXCI(j), PTCYCI(j));
	}
      }
      
      // Calcul de F:
      // ============
      for (i = Adeb; i <= Afin; i++) {
	AA = 0.0; BB = 0.0; CC = 0.0;
	for (j = 1; j <= Npol; j++) {
	  AIJ = A(i, j);
	  AA += AIJ*PTCXCI(j);
	  BB += AIJ*PTCYCI(j);
	  if (dimen == 3) { 
	    CC += AIJ*PTCZCI(j);
	  }
	}
	FX = AA-PTLX(i, Ci);
	FY = BB-PTLY(i, Ci);
	MyF(i,Ci) = FX*FX + FY*FY;
	if (dimen == 3) {
	  FZ = CC-PTLZ(i,Ci);
	  MyF(i, Ci) += FZ*FZ;
	  Fi = MyF(i, Ci);
	  if (Sqrt(Fi) > ERR3d) ERR3d = Sqrt(Fi);
	}
	else {
	  Fi = MyF(i, Ci);
	  if (Sqrt(Fi) > ERR2d) ERR2d = Sqrt(Fi);
	}
	FVal += Fi;
      }
    }
    F = FVal;
  }  
  return Standard_True;
}




void AppParCurves_Function::Perform(const math_Vector& X) {
  Standard_Integer j;

  myParameters = X;
  // Resolution moindres carres:
  // ===========================
  MyLeastSquare.Perform(myParameters);

  if (!(MyLeastSquare.IsDone())) { 
    Done = Standard_False;
    return;
  }

  for(j = myParameters.Lower(); j <= myParameters.Upper(); j++) {
    ValGrad_F(j) = 0.0;
  }

  if (!Contraintes) {
    MyLeastSquare.ErrorGradient(ValGrad_F, FVal, ERR3d, ERR2d);
  }
  else {
    Standard_Integer Pi, Ci, i, k, dimen;
    Standard_Integer  Npol = Degre+1;
    Standard_Real Scal, AA, BB, CC, DAA, DBB, DCC;
    Standard_Real FX, FY, FZ, AIJ, DAIJ, px, py, pz, Fi;
    AppParCurves_Constraint Cons=AppParCurves_NoConstraint;
    math_Matrix Grad_F(FirstP, LastP, 1, NbCu, 0.0);
    math_Vector PTCXCI(1, Npol), PTCYCI(1, Npol), PTCZCI(1, Npol);
    math_Vector PTCOXCI(1, Npol), PTCOYCI(1, Npol), PTCOZCI(1, Npol);
//    Standard_Boolean Ext = Standard_True;
    ERR3d = ERR2d = 0.0;

    math_Matrix PTCOX(1, Npol, 1, NbCu), PTCOY(1, Npol, 1, NbCu), 
                PTCOZ(1, Npol,1, NbCu);
    math_Matrix PTCX(1, Npol, 1, NbCu), PTCY(1, Npol, 1, NbCu), 
                PTCZ(1, Npol,1, NbCu);
    Standard_Integer Inc;

    MyMultiCurve = MyLeastSquare.BezierValue();

    for (Ci =1; Ci <= NbCu; Ci++) {
      dimen = tabdim->Value(Ci-1);
      for (j = 1; j <= Npol; j++) {
	if (dimen == 3){ 
	  MyMultiCurve.Value(j).Point(Ci).Coord(PTCOX(j, Ci),
						PTCOY(j, Ci),
						PTCOZ(j, Ci));
	}
	else{ 
	  MyMultiCurve.Value(j).Point2d(Ci).Coord(PTCOX(j, Ci), PTCOY(j, Ci));
	  PTCOZ(j, Ci) = 0.0;
	}
      }
    }

    A = MyLeastSquare.FunctionMatrix();
    DA = MyLeastSquare.DerivativeFunctionMatrix();
    
    // Resolution avec contraintes:
    // ============================
    
    ResolCons Resol(MyMultiLine, MyMultiCurve, FirstP, LastP, 
		    myConstraints, A, DA);
    if (!Resol.IsDone()) {
      Done = Standard_False;
      return;
    }
    
    
    // Calcul de F = Sum||C(ui)-Ptli||2 et du gradient non contraint de F pour
    // chaque point PointIndex.
    // ========================================================================
    FVal = 0.0;
    for(j = FirstP; j <= LastP; j++) {
      ValGrad_F(j) = 0.0;
    }

    math_Matrix TrA(A.LowerCol(), A.UpperCol(), A.LowerRow(), A.UpperRow());
    math_Matrix TrDA(DA.LowerCol(), DA.UpperCol(), DA.LowerRow(), DA.UpperRow());
    math_Matrix RESTM(A.LowerCol(), A.UpperCol(), A.LowerCol(), A.UpperCol());

    const math_Matrix& K = Resol.ConstraintMatrix();
    const math_Matrix& DK = Resol.ConstraintDerivative(MyMultiLine, X, Degre, DA);
    math_Matrix TK(K.LowerCol(), K.UpperCol(), K.LowerRow(), K.UpperRow());
    TK = K.Transposed();
    const math_Vector& Vardua = Resol.Duale();
    math_Matrix KK(K.LowerCol(), K.UpperCol(), Vardua.Lower(), Vardua.Upper());
    KK = (K.Transposed())*(Resol.InverseMatrix());
    math_Matrix DTK(DK.LowerCol(), DK.UpperCol(), DK.LowerRow(), DK.UpperRow());
    DTK = DK.Transposed();
    TrA = A.Transposed();
    TrDA = DA.Transposed();
    RESTM = ((A.Transposed()*A).Inverse());

    math_Vector DPTCO(1, K.ColNumber());
    math_Matrix DPTCO1(FirstP, LastP, 1, K.ColNumber());
    math_Vector DKPTC(1, K.RowNumber());




    FVal = 0.0;
    for (Ci = 1; Ci <= NbCu; Ci++) {
      dimen = tabdim->Value(Ci-1);
      for (j = 1; j <= Npol; j++) {
	if (dimen == 3){ 
	  MyMultiCurve.Value(j).Point(Ci).Coord(PTCX(j, Ci), 
						PTCY(j, Ci), 
						PTCZ(j, Ci));
	}
	else{ 
	  MyMultiCurve.Value(j).Point2d(Ci).Coord(PTCX(j, Ci), PTCY(j,Ci));
	  PTCZ(j, Ci) = 0.0;
	}
      }
    }

    
    // Calcul du gradient sans contraintes:
    // ====================================

    for (Ci = 1; Ci <= NbCu; Ci++) {
      dimen = tabdim->Value(Ci-1);
      for (i = Adeb; i <= Afin; i++) {
	AA = 0.0; BB = 0.0; CC = 0.0; DAA = 0.0; DBB = 0.0; DCC = 0.0;
	for (j = 1; j <= Npol; j++) {
	  AIJ = A(i, j); DAIJ = DA(i, j);
	  px = PTCX(j, Ci); py = PTCY(j, Ci);
	  AA += AIJ*px;  BB += AIJ*py;
	  DAA += DAIJ*px;  DBB += DAIJ*py;
	  if (dimen == 3) { 
	    pz = PTCZ(j, Ci);
	    CC += AIJ*pz;  DCC += DAIJ*pz;
	  }
	}
	FX = AA-PTLX(i, Ci);
	FY = BB-PTLY(i, Ci);
	MyF(i,Ci) = FX*FX + FY*FY;
	Grad_F(i, Ci) = 2.0*(DAA*FX + DBB*FY);
	if (dimen == 3) {
	  FZ = CC-PTLZ(i,Ci);
	  MyF(i, Ci) += FZ*FZ;
	  Grad_F(i, Ci) += 2.0*DCC*FZ;
	  Fi = MyF(i, Ci);
	  if (Sqrt(Fi) > ERR3d) ERR3d = Sqrt(Fi);
	}
	else {
	  Fi = MyF(i, Ci);
	  if (Sqrt(Fi) > ERR2d) ERR2d = Sqrt(Fi);
	}
	FVal += Fi;
	ValGrad_F(i) += Grad_F(i, Ci);
      }
    }


    // Calcul de DK*PTC:
    // =================
    for (i = 1; i <= K.RowNumber(); i++) {
      Inc = 0;
      for (Ci = 1; Ci <= NbCu; Ci++) {
	dimen = tabdim->Value(Ci-1);
	DKPTC(i) = 0.0;
	for (j = 1; j <= Npol; j++) {
	  DKPTC(i) += DK(i, j+Inc)*PTCX(j, Ci)+ DK(i, j+Inc+Npol)*PTCY(j, Ci);
	  if (dimen == 3) {
	    DKPTC(i) += DK(i, j+Inc+2*Npol)*PTCZ(j, Ci);
	  }
	}
	if (dimen == 3) Inc = Inc +3*Npol;
	else Inc = Inc +2*Npol;
      }
    }
    
    math_Vector DERR(DTK.LowerRow(), DTK.UpperRow());
    DERR = (DTK)*Vardua-KK* ((DKPTC) + K*(DTK)*Vardua);

    // rajout du gradient avec contraintes:
    // ====================================
    // dPTCO1/duk = [d(TA)/duk*[A*PTCO-PTL] + TA*dA/duk*PTCO]


    Inc = 0;

    math_Vector Errx(A.LowerRow(), A.UpperRow());
    math_Vector Erry(A.LowerRow(), A.UpperRow());
    math_Vector Errz(A.LowerRow(), A.UpperRow());
    math_Vector Scalx(DA.LowerRow(), DA.UpperRow());
    math_Vector Scaly(DA.LowerRow(), DA.UpperRow());
    math_Vector Scalz(DA.LowerRow(), DA.UpperRow());
    math_Vector Erruzax(PTCXCI.Lower(), PTCXCI.Upper());
    math_Vector Erruzay(PTCYCI.Lower(), PTCYCI.Upper());
    math_Vector Erruzaz(PTCZCI.Lower(), PTCZCI.Upper());
    math_Vector TrDAPI(TrDA.LowerRow(), TrDA.UpperRow());
    math_Vector TrAPI(TrA.LowerRow(), TrA.UpperRow());

    for (Ci = 1; Ci <= NbCu; Ci++) {
      dimen = tabdim->Value(Ci-1);
      PTCOXCI = PTCOX.Col(Ci);
      PTCOYCI = PTCOY.Col(Ci);
      PTCOZCI = PTCOZ.Col(Ci);
      PTCXCI = PTCX.Col(Ci);
      PTCYCI = PTCY.Col(Ci);
      PTCZCI = PTCZ.Col(Ci);


      Errx = (A*PTCOXCI - PTLX.Col(Ci));
      Erry = (A*PTCOYCI - PTLY.Col(Ci));
      Errz = (A*PTCOZCI - PTLZ.Col(Ci));
      Scalx = (DA*PTCOXCI);   // Scal = DA * PTCO
      Scaly = (DA*PTCOYCI);
      Scalz = (DA*PTCOZCI);
      Erruzax = (PTCXCI - PTCOXCI);
      Erruzay = (PTCYCI - PTCOYCI);
      Erruzaz = (PTCZCI - PTCOZCI);
      
      for (Pi = FirstP; Pi <= LastP; Pi++) {
	TrDAPI = (TrDA.Col(Pi));
	TrAPI = (TrA.Col(Pi));
	Standard_Real Taa = TrAPI*A.Row(Pi);
	Scal = 0.0;
	for (j = 1; j <= Npol; j++) {
	  DPTCO1(Pi, j + Inc) = (TrDAPI*Errx(Pi)+TrAPI*Scalx(Pi))(j);
	  DPTCO1(Pi, j + Inc+ Npol) = (TrDAPI*Erry(Pi)+TrAPI*Scaly(Pi))(j);
	  Scal += DPTCO1(Pi, j+Inc)* Taa*Erruzax(j) + DPTCO1(Pi, j+Inc+Npol)*Taa*Erruzay(j);
	  if (dimen == 3) {
	    DPTCO1(Pi, j + Inc+ 2*Npol) = (TrDAPI*Errz(Pi)+TrAPI*Scalz(Pi))(j);
	    Scal += DPTCO1(Pi, j+Inc+2*Npol)*Taa*Erruzaz(j);
	  }
	}
	ValGrad_F(Pi) = ValGrad_F(Pi) - 2*Scal;
      }
      if (dimen == 3) Inc = Inc + 3*Npol;
      else Inc = Inc +2*Npol;
    }


    // on calcule DPTCO = - RESTM * DPTCO1:
    
    // Calcul de DPTCO/duk:
    // dPTCO/duk = -Inv(T(A)*A)*[d(TA)/duk*[A*PTCO-PTL] + TA*dA/duk*PTCO]

    Standard_Integer low=myConstraints->Lower(), upp=myConstraints->Upper();
    Inc = 0;
    for (Pi = FirstP; Pi <= LastP; Pi++) {
      for (i = low; i <= upp; i++) {
	if (myConstraints->Value(i).Index() == Pi) {
	  Cons = myConstraints->Value(i).Constraint();
	  break;
	}
      }
      if (Cons >= 1) {
	Inc = 0;
	for (Ci = 1; Ci <= NbCu; Ci++) {
	  dimen = tabdim->Value(Ci-1);
	  for (j = 1; j <= Npol; j++) {
	    DPTCO(j+Inc) = 0.0;
	    DPTCO(j+Inc+Npol) = 0.0;
	    if (dimen == 3) DPTCO(j+Inc+2*Npol) = 0.0;
	    for (k = 1; k <= Npol; k++) {
	      DPTCO(j+Inc) = DPTCO(j+Inc) -RESTM(j, k) * DPTCO1(Pi, j+Inc);
	      DPTCO(j+Inc+Npol)=DPTCO(j+Inc+Npol)-RESTM(j, k)*DPTCO1(Pi,j+Inc+Npol);
	      if (dimen == 3) {
		DPTCO(j+Inc+2*Npol) = DPTCO(j+Inc+2*Npol) 
		  -RESTM(j, k) * DPTCO1(Pi, j+Inc+2*Npol);
	      }
	    }
	  }
	  if (dimen == 3) Inc += 3*Npol;
	  else Inc += 2*Npol;
	}
	
	DERR = DERR-KK*K*DPTCO;
	
	Inc = 0;
	for (Ci = 1; Ci <= NbCu; Ci++) {
	  dimen = tabdim->Value(Ci-1);
	  PTCOXCI = PTCOX.Col(Ci);
	  PTCOYCI = PTCOY.Col(Ci);
	  PTCOZCI = PTCOZ.Col(Ci);
	  PTCXCI = PTCX.Col(Ci);
	  PTCYCI = PTCY.Col(Ci);
	  PTCZCI = PTCZ.Col(Ci);
	  Erruzax = (PTCXCI - PTCOXCI);
	  Erruzay = (PTCYCI - PTCOYCI);
	  Erruzaz = (PTCZCI - PTCOZCI);
	  Scal = 0.0;
	  
	  for (j = 1; j <= Npol ; j++) {
	    Scal = (A(Pi, j)*Erruzax(j)) * (A(Pi, j)*DERR(j+Inc)) + 
	      (A(Pi, j)*Erruzay(j)) * (A(Pi, j)*DERR(j+Inc+Npol));
	    if (dimen == 3) {
	      Scal += (A(Pi, j)*Erruzax(j)) * (A(Pi, j)*DERR(j+Inc+2*Npol)); 
	    }
	  }
	  
	  ValGrad_F(Pi) = ValGrad_F(Pi) + 2*Scal;
	  if (dimen == 3) Inc = Inc +3*Npol;
	  else Inc = Inc + 2*Npol;
	}
      }
    }
    
  }
}


Standard_Integer AppParCurves_Function::NbVariables() const{ 
  return NbP;
}


Standard_Boolean AppParCurves_Function::Gradient (const math_Vector& X,
						  math_Vector& G) {

  Perform(X);
  G = ValGrad_F;

  return Standard_True;
}


Standard_Boolean AppParCurves_Function::Values (const math_Vector& X, 
						Standard_Real& F, 
						math_Vector& G) {


  Perform(X);
  F = FVal;
  G = ValGrad_F;
  return Standard_True;
}


const AppParCurves_MultiCurve& AppParCurves_Function::CurveValue() {
  if (!Contraintes)  MyMultiCurve = MyLeastSquare.BezierValue();
  return MyMultiCurve;
}


Standard_Real AppParCurves_Function::Error(const Standard_Integer IPoint,
				     const Standard_Integer CurveIndex) const {
  return Sqrt(MyF(IPoint, CurveIndex));
}

Standard_Real AppParCurves_Function::MaxError3d() const
{
  return ERR3d;
}

Standard_Real AppParCurves_Function::MaxError2d() const
{
  return ERR2d;
}



const math_Vector& AppParCurves_Function::NewParameters() const
{
  return myParameters;
}