OCCT

// Created on: 1996-02-28
// Created by: Philippe MANGIN
// Copyright (c) 1996-1999 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 _math_NewtonMinimum_HeaderFile
#define _math_NewtonMinimum_HeaderFile

#include <Standard.hxx>
#include <Standard_DefineAlloc.hxx>

#include <Precision.hxx>
#include <math_Status.hxx>
#include <math_Vector.hxx>
#include <math_Matrix.hxx>
#include <Standard_Integer.hxx>
#include <Standard_OStream.hxx>
class math_MultipleVarFunctionWithHessian;

class math_NewtonMinimum
{
public:
  DEFINE_STANDARD_ALLOC

  //! The tolerance required on the solution is given by Tolerance.
  //! Iteration are stopped if (!WithSingularity) and H(F(Xi)) is not definite
  //! positive (if the smaller eigenvalue of H < Convexity)
  //! or IsConverged() returns True for 2 successives Iterations.
  //! Warning: This constructor does not perform computation.
  Standard_EXPORT math_NewtonMinimum(const math_MultipleVarFunctionWithHessian& theFunction,
                                     const double theTolerance       = Precision::Confusion(),
                                     const int    theNbIterations    = 40,
                                     const double theConvexity       = 1.0e-6,
                                     const bool   theWithSingularity = true);

  //! Search the solution.
  Standard_EXPORT void Perform(math_MultipleVarFunctionWithHessian& theFunction,
                               const math_Vector&                   theStartingPoint);

  //! Destructor
  Standard_EXPORT virtual ~math_NewtonMinimum();

  //! This method is called at the end of each iteration to check the convergence:
  //! || Xi+1 - Xi || < Tolerance or || F(Xi+1) - F(Xi)|| < Tolerance * || F(Xi) ||
  //! It can be redefined in a sub-class to implement a specific test.
  virtual bool IsConverged() const;

  //! Tests if an error has occurred.
  bool IsDone() const;

  //! Tests if the Function is convexe during optimization.
  bool IsConvex() const;

  //! returns the location vector of the minimum.
  //! Exception NotDone is raised if an error has occurred.
  const math_Vector& Location() const;

  //! outputs the location vector of the minimum in Loc.
  //! Exception NotDone is raised if an error has occurred.
  //! Exception DimensionError is raised if the range of Loc is not
  //! equal to the range of the StartingPoint.
  void Location(math_Vector& Loc) const;

  //! Set boundaries.
  Standard_EXPORT void SetBoundary(const math_Vector& theLeftBorder,
                                   const math_Vector& theRightBorder);

  //! returns the value of the minimum.
  //! Exception NotDone is raised if the minimum was not found.
  double Minimum() const;

  //! returns the gradient vector at the minimum.
  //! Exception NotDone is raised if an error has occurred.
  //! The minimum was not found.
  const math_Vector& Gradient() const;

  //! outputs the gradient vector at the minimum in Grad.
  //! Exception NotDone is raised if the minimum was not found.
  //! Exception DimensionError is raised if the range of Grad is not
  //! equal to the range of the StartingPoint.
  void Gradient(math_Vector& Grad) const;

  //! returns the number of iterations really done in the
  //! calculation of the minimum.
  //! The exception NotDone is raised if an error has occurred.
  int NbIterations() const;

  //! Returns the Status of computation.
  //! The exception NotDone is raised if an error has occurred.
  math_Status GetStatus() const;

  //! Prints on the stream o information on the current state
  //! of the object.
  //! Is used to redefine the operator <<.
  Standard_EXPORT void Dump(Standard_OStream& o) const;

protected:
  math_Status TheStatus;
  math_Vector TheLocation;
  math_Vector TheGradient;
  math_Vector TheStep;
  math_Matrix TheHessian;
  double      PreviousMinimum;
  double      TheMinimum;
  double      MinEigenValue;
  double      XTol;
  double      CTol;
  int         nbiter;
  bool        NoConvexTreatement;
  bool        Convex;
  bool        myIsBoundsDefined;
  math_Vector myLeft;
  math_Vector myRight;

private:
  bool Done;
  int  Itermax;
};

#include <math_NewtonMinimum.lxx>

#endif // _math_NewtonMinimum_HeaderFile