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 // Created on: 2014-01-20
 // Created by: Alexaner Malyshev
 // Copyright (c) 2014-2015 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_GlobOptMin_HeaderFile
 #define _math_GlobOptMin_HeaderFile
 
 #include <gp_Pnt.hxx>
 #include <NCollection_CellFilter.hxx>
 #include <math_MultipleVarFunction.hxx>
 #include <NCollection_Sequence.hxx>
 
 //! This class represents Evtushenko's algorithm of global optimization based on non-uniform mesh.
 //! Article: Yu. Evtushenko. Numerical methods for finding global extreme (case of a non-uniform mesh).
 //! U.S.S.R. Comput. Maths. Math. Phys., Vol. 11, N 6, pp. 38-54.
 //!
 //! This method performs search on non-uniform mesh. The search space is a box in R^n space.
 //! The default behavior is to find all minimums in that box. Computation of maximums is not supported.
 //!
 //! The search box can be split into smaller boxes by discontinuity criteria.
 //! This functionality is covered by SetGlobalParams and SetLocalParams API.
 //!
 //! It is possible to set continuity of the local boxes.
 //! Such option can forcibly change local extrema search.
 //! In other words if theFunc can be casted to the function with Hessian but, continuity is set to 1
 //! Gradient based local optimization method will be used, not Hessian based method.
 //! This functionality is covered by SetContinuity and GetContinuity API.
 //!
 //! It is possible to freeze Lipschitz const to avoid internal modifications on it.
 //! This functionality is covered by SetLipConstState and GetLipConstState API.
 //!
 //! It is possible to perform single solution search.
 //! This functionality is covered by first parameter in Perform method.
 //!
 //! It is possible to set / get minimal value of the functional.
 //! It works well together with single solution search.
 //! This functionality is covered by SetFunctionalMinimalValue and GetFunctionalMinimalValue API.
 class math_GlobOptMin
 {
 public:
 
   //! Constructor. Perform method is not called from it.
   //! @param theFunc - objective functional.
   //! @param theLowerBorder - lower corner of the search box.
   //! @param theUpperBorder - upper corner of the search box.
   //! @param theC - Lipschitz constant.
   //! @param theDiscretizationTol - parameter space discretization tolerance.
   //! @param theSameTol - functional value space indifference tolerance.
   Standard_EXPORT math_GlobOptMin(math_MultipleVarFunction* theFunc,
                                  const math_Vector& theLowerBorder,
                                  const math_Vector& theUpperBorder,
                                  const Standard_Real theC = 9,
                                  const Standard_Real theDiscretizationTol = 1.0e-2,
                                  const Standard_Real theSameTol = 1.0e-7);
 
   //! @param theFunc - objective functional.
   //! @param theLowerBorder - lower corner of the search box.
   //! @param theUpperBorder - upper corner of the search box.
   //! @param theC - Lipschitz constant.
   //! @param theDiscretizationTol - parameter space discretization tolerance.
   //! @param theSameTol - functional value space indifference tolerance.
   Standard_EXPORT void SetGlobalParams(math_MultipleVarFunction* theFunc,
                                        const math_Vector& theLowerBorder,
                                        const math_Vector& theUpperBorder,
                                        const Standard_Real theC = 9,
                                        const Standard_Real theDiscretizationTol = 1.0e-2,
                                        const Standard_Real theSameTol = 1.0e-7);
 
   //! Method to reduce bounding box. Perform will use this box.
   //! @param theLocalA - lower corner of the local box.
   //! @param theLocalB - upper corner of the local box.
   Standard_EXPORT void SetLocalParams(const math_Vector& theLocalA,
                                       const math_Vector& theLocalB);
 
   //! Method to set tolerances.
   //! @param theDiscretizationTol - parameter space discretization tolerance.
   //! @param theSameTol - functional value space indifference tolerance.
   Standard_EXPORT void SetTol(const Standard_Real theDiscretizationTol,
                               const Standard_Real theSameTol);
 
   //! Method to get tolerances.
   //! @param theDiscretizationTol - parameter space discretization tolerance.
   //! @param theSameTol - functional value space indifference tolerance.
   Standard_EXPORT void GetTol(Standard_Real& theDiscretizationTol,
                               Standard_Real& theSameTol);
 
   //! @param isFindSingleSolution - defines whether to find single solution or all solutions.
   Standard_EXPORT void Perform(const Standard_Boolean isFindSingleSolution = Standard_False);
 
   //! Return solution theIndex, 1 <= theIndex <= NbExtrema.
   Standard_EXPORT void Points(const Standard_Integer theIndex, math_Vector& theSol);
 
   //! Set / Get continuity of local borders splits (0 ~ C0, 1 ~ C1, 2 ~ C2).
   inline void SetContinuity(const Standard_Integer theCont) { myCont = theCont; }
   inline Standard_Integer GetContinuity() const {return myCont; }
 
     //! Set / Get functional minimal value.
   inline void SetFunctionalMinimalValue(const Standard_Real theMinimalValue)
   { myFunctionalMinimalValue = theMinimalValue; }
   inline Standard_Real GetFunctionalMinimalValue() const {return myFunctionalMinimalValue;}
 
   //! Set / Get Lipchitz constant modification state. 
   //! True means that the constant is locked and unlocked otherwise.
   inline void SetLipConstState(const Standard_Boolean theFlag) {myIsConstLocked = theFlag; }
   inline Standard_Boolean GetLipConstState() const { return myIsConstLocked; }
 
   //! Return computation state of the algorithm.
   inline Standard_Boolean isDone() const {return myDone; }
 
   //! Get best functional value.
   inline Standard_Real GetF() const {return myF;}
 
   //! Return count of global extremas.
   inline Standard_Integer NbExtrema() const {return mySolCount;}
 
 private:
 
   //! Class for duplicate fast search. For internal usage only.
   class NCollection_CellFilter_Inspector
   {
   public:
 
     //! Points and target type
     typedef math_Vector Point;
     typedef math_Vector Target;
 
     NCollection_CellFilter_Inspector(const Standard_Integer theDim,
                                      const Standard_Real theTol)
       : myCurrent(1, theDim)
     {
       myTol = theTol * theTol;
       myIsFind = Standard_False;
       Dimension = theDim;
     }
 
     //! Access to coordinate.
     static Standard_Real Coord (int i, const Point &thePnt)
     {
       return thePnt(i + 1);
     }
 
     //! Auxiliary method to shift point by each coordinate on given value;
     //! useful for preparing a points range for Inspect with tolerance.
     void Shift (const Point& thePnt,
                 const NCollection_Array1<Standard_Real> &theTol,
                 Point& theLowPnt,
                 Point& theUppPnt) const
     {
       for(Standard_Integer anIdx = 1; anIdx <= Dimension; anIdx++)
       {
         theLowPnt(anIdx) = thePnt(anIdx) - theTol(anIdx - 1);
         theUppPnt(anIdx) = thePnt(anIdx) + theTol(anIdx - 1);
       }
     }
 
     void ClearFind()
     {
       myIsFind = Standard_False;
     }
 
     Standard_Boolean isFind()
     {
       return myIsFind;
     }
 
     //! Set current point to search for coincidence
     void SetCurrent (const math_Vector& theCurPnt)
     { 
       myCurrent = theCurPnt;
     }
 
     //! Implementation of inspection method
     NCollection_CellFilter_Action Inspect (const Target& theObject)
     {
       Standard_Real aSqDist = (myCurrent - theObject).Norm2();
 
       if(aSqDist < myTol)
       {
         myIsFind = Standard_True;
       }
 
       return CellFilter_Keep;
     }
 
   private:
     Standard_Real myTol;
     math_Vector myCurrent;
     Standard_Boolean myIsFind;
     Standard_Integer Dimension;
   };
 
 
   // Compute cell size.
   void initCellSize();
 
   // Compute initial solution
   void ComputeInitSol();
 
   math_GlobOptMin & operator = (const math_GlobOptMin & theOther);
 
   Standard_Boolean computeLocalExtremum(const math_Vector& thePnt, Standard_Real& theVal, math_Vector& theOutPnt);
 
   void computeGlobalExtremum(Standard_Integer theIndex);
 
   //! Check possibility to stop computations.
   //! Find single solution + in neighborhood of best possible solution.
   Standard_Boolean CheckFunctionalStopCriteria();
 
   //! Computes starting value / approximation:
   //! myF - initial best value.
   //! myY - initial best point.
   //! myC - approximation of Lipschitz constant.
   //! to improve convergence speed.
   void computeInitialValues();
 
   //! Check that myA <= thePnt <= myB
   Standard_Boolean isInside(const math_Vector& thePnt);
 
   //! Check presence of thePnt in GlobOpt sequence.
   Standard_Boolean isStored(const math_Vector &thePnt);
 
   //! Check and add candidate point into solutions.
   //! @param thePnt   Candidate point.
   //! @param theValue Function value in the candidate point.
   void checkAddCandidate(const math_Vector&  thePnt,
                          const Standard_Real theValue);
 
 
   // Input.
   math_MultipleVarFunction* myFunc;
   Standard_Integer myN;
   math_Vector myA; // Left border on current C2 interval.
   math_Vector myB; // Right border on current C2 interval.
   math_Vector myGlobA; // Global left border.
   math_Vector myGlobB; // Global right border.
   Standard_Real myTol; // Discretization tolerance, default 1.0e-2.
   Standard_Real mySameTol; // points with ||p1 - p2|| < mySameTol is equal,
                            // function values |val1 - val2| * 0.01 < mySameTol is equal,
                            // default value is 1.0e-7.
   Standard_Real myC; //Lipchitz constant, default 9
   Standard_Real myInitC; // Lipchitz constant initial value.
   Standard_Boolean myIsFindSingleSolution; // Default value is false.
   Standard_Real myFunctionalMinimalValue; // Default value is -Precision::Infinite
   Standard_Boolean myIsConstLocked;  // Is constant locked for modifications.
 
   // Output.
   Standard_Boolean myDone;
   NCollection_Sequence<Standard_Real> myY;// Current solutions.
   Standard_Integer mySolCount; // Count of solutions.
 
   // Algorithm data.
   Standard_Real myZ;
   Standard_Real myE1; // Border coefficient.
   Standard_Real myE2; // Minimum step size.
   Standard_Real myE3; // Local extrema starting parameter.
 
   math_Vector myX; // Current modified solution.
   math_Vector myTmp; // Current modified solution.
   math_Vector myV; // Steps array.
   math_Vector myMaxV; // Max Steps array.
   Standard_Real myLastStep; // Last step.
 
   NCollection_Array1<Standard_Real> myCellSize;
   Standard_Integer myMinCellFilterSol;
   Standard_Boolean isFirstCellFilterInvoke;
   NCollection_CellFilter<NCollection_CellFilter_Inspector> myFilter;
 
   // Continuity of local borders.
   Standard_Integer myCont;
 
   Standard_Real myF; // Current value of Global optimum.
 };
 
 #endif

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