// Copyright (c) 1997-1999 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.

//#ifndef OCCT_DEBUG
#define No_Standard_RangeError
#define No_Standard_OutOfRange
#define No_Standard_DimensionError

//#endif

#include <math_BFGS.hxx>
#include <math_BracketMinimum.hxx>
#include <math_BrentMinimum.hxx>
#include <math_FunctionWithDerivative.hxx>
#include <math_Matrix.hxx>
#include <math_MultipleVarFunctionWithGradient.hxx>
#include <Precision.hxx>

// l'utilisation de math_BrentMinumim pur trouver un minimum dans une direction
// donnee n'est pas du tout optimale. voir peut etre interpolation cubique
// classique et aussi essayer "recherche unidimensionnelle economique"
// PROGRAMMATION MATHEMATIQUE (theorie et algorithmes) tome1 page 82.

// Target function for 1D problem, point and direction are known.
class DirFunction : public math_FunctionWithDerivative
{

  math_Vector *P0;
  math_Vector *Dir;
  math_Vector *P;
  math_Vector *G;
  math_MultipleVarFunctionWithGradient *F;

public:

  //! Ctor.
  DirFunction(math_Vector& V1,
              math_Vector& V2,
              math_Vector& V3,
              math_Vector& V4,
              math_MultipleVarFunctionWithGradient& f)
  : P0(&V1),
    Dir(&V2),
    P(&V3),
    G(&V4),
    F(&f)
  {}

  //! Sets point and direction.
  void Initialize(const math_Vector& p0,
                  const math_Vector& dir) const
  {
    *P0 = p0;
    *Dir = dir;
  }

  void TheGradient(math_Vector& Grad)
  {
    Grad = *G;
  }

  virtual Standard_Boolean Value(const Standard_Real x,
                                 Standard_Real&      fval)
  {
    *P = *Dir;
    P->Multiply(x);
    P->Add(*P0);
    fval = 0.;
    return F->Value(*P, fval);
  }

  virtual Standard_Boolean Values(const Standard_Real x,
                                  Standard_Real&      fval,
                                  Standard_Real&      D)
  {
    *P = *Dir;
    P->Multiply(x);
    P->Add(*P0);
    fval = D = 0.;
    if (F->Values(*P, fval, *G))
    {
      D = (*G).Multiplied(*Dir);
      return Standard_True;
    }

    return Standard_False;
  }
  virtual Standard_Boolean Derivative(const Standard_Real x,
                                      Standard_Real&      D)
  {
    *P = *Dir;
    P->Multiply(x);
    P->Add(*P0);
    Standard_Real fval;
    D = 0.;
    if (F->Values(*P, fval, *G))
    {
      D = (*G).Multiplied(*Dir);
      return Standard_True;
    }

    return Standard_False;
  }


};

//=============================================================================
//function : ComputeInitScale
//purpose  : Compute the appropriate initial value of scale factor to apply
//           to the direction to approach to the minimum of the function
//=============================================================================
static Standard_Boolean ComputeInitScale(const Standard_Real theF0,
                                         const math_Vector&  theDir,
                                         const math_Vector&  theGr,
                                         Standard_Real&      theScale)
{
  const Standard_Real dy1 = theGr * theDir;
  if (Abs(dy1) < RealSmall())
    return Standard_False;

  const Standard_Real aHnr1 = theDir.Norm2();
  const Standard_Real alfa = 0.7*(-theF0) / dy1;
  theScale = 0.015 / Sqrt(aHnr1);
  if (theScale > alfa)
    theScale = alfa;

  return Standard_True;
}

//=============================================================================
//function : ComputeMinMaxScale
//purpose  : For a given point and direction, and bounding box,
//           find min and max scale factors with which the point reaches borders
//           if we apply translation Point+Dir*Scale.
//return   : True if found, False if point is out of bounds.
//=============================================================================
static Standard_Boolean ComputeMinMaxScale(const math_Vector& thePoint,
                                           const math_Vector& theDir,
                                           const math_Vector& theLeft,
                                           const math_Vector& theRight,
                                           Standard_Real&     theMinScale,
                                           Standard_Real&     theMaxScale)
{
  for (Standard_Integer anIdx = 1; anIdx <= theLeft.Upper(); anIdx++)
  {
    const Standard_Real aLeft = theLeft(anIdx) - thePoint(anIdx);
    const Standard_Real aRight = theRight(anIdx) - thePoint(anIdx);
    if (Abs(theDir(anIdx)) > RealSmall())
    {
      // Use PConfusion to get off a little from the bounds to prevent
      // possible refuse in Value function.
      const Standard_Real aLScale = (aLeft + Precision::PConfusion()) / theDir(anIdx);
      const Standard_Real aRScale = (aRight - Precision::PConfusion()) / theDir(anIdx);
      if (Abs(aLeft) < Precision::PConfusion())
      {
        // Point is on the left border.
        theMaxScale = Min(theMaxScale, Max(0., aRScale));
        theMinScale = Max(theMinScale, Min(0., aRScale));
      }
      else if (Abs(aRight) < Precision::PConfusion())
      {
        // Point is on the right border.
        theMaxScale = Min(theMaxScale, Max(0., aLScale));
        theMinScale = Max(theMinScale, Min(0., aLScale));
      }
      else if (aLeft * aRight < 0)
      {
        // Point is inside allowed range.
        theMaxScale = Min(theMaxScale, Max(aLScale, aRScale));
        theMinScale = Max(theMinScale, Min(aLScale, aRScale));
      }
      else
        // point is out of bounds
        return Standard_False;
    }
    else
    {
      // Direction is parallel to the border.
      // Check that the point is not out of bounds
      if (aLeft  >  Precision::PConfusion() ||
          aRight < -Precision::PConfusion())
      {
        return Standard_False;
      }
    }
  }
  return Standard_True;
}

//=============================================================================
//function : MinimizeDirection
//purpose  : Solves 1D minimization problem when point and directions
//           are known.
//=============================================================================
static Standard_Boolean MinimizeDirection(math_Vector&       P,
                                          Standard_Real      F0,
                                          math_Vector&       Gr,
                                          math_Vector&       Dir,
                                          Standard_Real&     Result,
                                          DirFunction&       F,
                                          Standard_Boolean   isBounds,
                                          const math_Vector& theLeft,
                                          const math_Vector& theRight)
{
  Standard_Real lambda;
  if (!ComputeInitScale(F0, Dir, Gr, lambda))
    return Standard_False;

  // by default the scaling range is unlimited
  Standard_Real aMinLambda = -Precision::Infinite();
  Standard_Real aMaxLambda = Precision::Infinite();
  if (isBounds)
  {
    // limit the scaling range taking into account the bounds
    if (!ComputeMinMaxScale(P, Dir, theLeft, theRight, aMinLambda, aMaxLambda))
      return Standard_False;

    if (aMinLambda > -Precision::PConfusion() && aMaxLambda < Precision::PConfusion())
    {
      // Point is on the border and the direction shows outside.
      // Make direction to go along the border
      for (Standard_Integer anIdx = 1; anIdx <= theLeft.Upper(); anIdx++)
      {
        if ((Abs(P(anIdx) - theRight(anIdx)) < Precision::PConfusion() && Dir(anIdx) > 0.0) ||
            (Abs(P(anIdx) - theLeft(anIdx))  < Precision::PConfusion() && Dir(anIdx) < 0.0))
        {
          Dir(anIdx) = 0.0;
        }
      }

      // re-compute scale values with new direction
      if (!ComputeInitScale(F0, Dir, Gr, lambda))
        return Standard_False;
      if (!ComputeMinMaxScale(P, Dir, theLeft, theRight, aMinLambda, aMaxLambda))
        return Standard_False;
    }
    lambda = Min(lambda, aMaxLambda);
    lambda = Max(lambda, aMinLambda);
  }

  F.Initialize(P, Dir);
  Standard_Real F1;
  if (!F.Value(lambda, F1))
    return Standard_False;

  math_BracketMinimum Bracket(0.0, lambda);
  if (isBounds)
    Bracket.SetLimits(aMinLambda, aMaxLambda);
  Bracket.SetFA(F0);
  Bracket.SetFB(F1);
  Bracket.Perform(F);
  if (Bracket.IsDone())
  {
    // find minimum inside the bracket
    Standard_Real ax, xx, bx, Fax, Fxx, Fbx;
    Bracket.Values(ax, xx, bx);
    Bracket.FunctionValues(Fax, Fxx, Fbx);

    Standard_Integer niter = 100;
    Standard_Real tol = 1.e-03;
    math_BrentMinimum Sol(tol, Fxx, niter, 1.e-08);
    Sol.Perform(F, ax, xx, bx);
    if (Sol.IsDone())
    {
      Standard_Real Scale = Sol.Location();
      Result = Sol.Minimum();
      Dir.Multiply(Scale);
      P.Add(Dir);
      return Standard_True;
    }
  }
  else if (isBounds)
  {
    // Bracket definition is failure. If the bounds are defined then
    // set current point to intersection with bounds
    Standard_Real aFMin, aFMax;
    if (!F.Value(aMinLambda, aFMin))
      return Standard_False;
    if (!F.Value(aMaxLambda, aFMax))
      return Standard_False;
    Standard_Real aBestLambda;
    if (aFMin < aFMax)
    {
      aBestLambda = aMinLambda;
      Result = aFMin;
    }
    else
    {
      aBestLambda = aMaxLambda;
      Result = aFMax;
    }
    Dir.Multiply(aBestLambda);
    P.Add(Dir);
    return Standard_True;
  }
  return Standard_False;
}

//=============================================================================
//function : Perform
//purpose  : Performs minimization problem using BFGS method.
//=============================================================================
void  math_BFGS::Perform(math_MultipleVarFunctionWithGradient& F,
                         const math_Vector&                    StartingPoint)
{
  const Standard_Integer n = TheLocation.Length();
  Standard_Boolean Good = Standard_True;
  Standard_Integer j, i;
  Standard_Real fae, fad, fac;

  math_Vector xi(1, n), dg(1, n), hdg(1, n);
  math_Matrix hessin(1, n, 1, n);
  hessin.Init(0.0);

  math_Vector Temp1(1, n);
  math_Vector Temp2(1, n);
  math_Vector Temp3(1, n);
  math_Vector Temp4(1, n);
  DirFunction F_Dir(Temp1, Temp2, Temp3, Temp4, F);

  TheLocation = StartingPoint;
  Good = F.Values(TheLocation, PreviousMinimum, TheGradient);
  if (!Good)
  {
    Done = Standard_False;
    TheStatus = math_FunctionError;
    return;
  }
  for (i = 1; i <= n; i++)
  {
    hessin(i, i) = 1.0;
    xi(i) = -TheGradient(i);
  }


  for (nbiter = 1; nbiter <= Itermax; nbiter++)
  {
    TheMinimum = PreviousMinimum;
    const Standard_Boolean IsGood = MinimizeDirection(TheLocation, TheMinimum, TheGradient,
                                                      xi, TheMinimum, F_Dir, myIsBoundsDefined,
                                                      myLeft, myRight);

    if (IsSolutionReached(F))
    {
      Done = Standard_True;
      TheStatus = math_OK;
      return;
    }

    if (!IsGood)
    {
      Done = Standard_False;
      TheStatus = math_DirectionSearchError;
      return;
    }
    PreviousMinimum = TheMinimum;

    dg = TheGradient;

    Good = F.Values(TheLocation, TheMinimum, TheGradient);
    if (!Good)
    {
      Done = Standard_False;
      TheStatus = math_FunctionError;
      return;
    }

    for (i = 1; i <= n; i++)
      dg(i) = TheGradient(i) - dg(i);

    for (i = 1; i <= n; i++)
    {
      hdg(i) = 0.0;
      for (j = 1; j <= n; j++)
        hdg(i) += hessin(i, j) * dg(j);
    }

    fac = fae = 0.0;
    for (i = 1; i <= n; i++)
    {
      fac += dg(i) * xi(i);
      fae += dg(i) * hdg(i);
    }
    fac = 1.0 / fac;
    fad = 1.0 / fae;

    for (i = 1; i <= n; i++)
      dg(i) = fac * xi(i) - fad * hdg(i);

    for (i = 1; i <= n; i++)
    {
      for (j = 1; j <= n; j++)
        hessin(i, j) += fac * xi(i) * xi(j) - fad * hdg(i) * hdg(j) + fae * dg(i) * dg(j);
    }

    for (i = 1; i <= n; i++)
    {
      xi(i) = 0.0;
      for (j = 1; j <= n; j++)
        xi(i) -= hessin(i, j) * TheGradient(j);
    }
  }
  Done = Standard_False;
  TheStatus = math_TooManyIterations;
  return;
}

//=============================================================================
//function : IsSolutionReached
//purpose  : Checks whether solution reached or not.
//=============================================================================
Standard_Boolean math_BFGS::IsSolutionReached(math_MultipleVarFunctionWithGradient&) const
{

  return 2.0 * fabs(TheMinimum - PreviousMinimum) <=
    XTol * (fabs(TheMinimum) + fabs(PreviousMinimum) + EPSZ);
}

//=============================================================================
//function : math_BFGS
//purpose  : Constructor.
//=============================================================================
math_BFGS::math_BFGS(const Standard_Integer     NbVariables,
                     const Standard_Real        Tolerance,
                     const Standard_Integer     NbIterations,
                     const Standard_Real        ZEPS)
: TheStatus(math_OK),
  TheLocation(1, NbVariables),
  TheGradient(1, NbVariables),
  PreviousMinimum(0.),
  TheMinimum(0.),
  XTol(Tolerance),
  EPSZ(ZEPS),
  nbiter(0),
  myIsBoundsDefined(Standard_False),
  myLeft(1, NbVariables, 0.0),
  myRight(1, NbVariables, 0.0),
  Done(Standard_False),
  Itermax(NbIterations)
{
}

//=============================================================================
//function : ~math_BFGS
//purpose  : Destructor.
//=============================================================================
math_BFGS::~math_BFGS()
{
}

//=============================================================================
//function : Dump
//purpose  : Prints dump.
//=============================================================================
void math_BFGS::Dump(Standard_OStream& o) const
{

  o << "math_BFGS resolution: ";
  if (Done)
  {
    o << " Status = Done \n";
    o << " Location Vector = " << Location() << "\n";
    o << " Minimum value = " << Minimum() << "\n";
    o << " Number of iterations = " << NbIterations() << "\n";
  }
  else
    o << " Status = not Done because " << (Standard_Integer)TheStatus << "\n";
}

//=============================================================================
//function : SetBoundary
//purpose  : Set boundaries for conditional optimization
//=============================================================================
void math_BFGS::SetBoundary(const math_Vector& theLeftBorder,
                            const math_Vector& theRightBorder)
{
  myLeft = theLeftBorder;
  myRight = theRightBorder;
  myIsBoundsDefined = Standard_True;
}