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 // Created on: 1991-05-14
 // Created by: Laurent PAINNOT
 // Copyright (c) 1991-1999 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_NewtonFunctionSetRoot_HeaderFile
 #define _math_NewtonFunctionSetRoot_HeaderFile
 
 #include <Standard.hxx>
 #include <Standard_DefineAlloc.hxx>
 
 #include <Standard_Integer.hxx>
 #include <math_Vector.hxx>
 #include <math_IntegerVector.hxx>
 #include <math_Matrix.hxx>
 #include <Standard_OStream.hxx>
 class math_FunctionSetWithDerivatives;
 
 //! This class computes the root of a set of N functions of N variables,
 //! knowing an initial guess at the solution and using the
 //! Newton Raphson algorithm. Knowledge of all the partial
 //! derivatives (Jacobian) is required.
 class math_NewtonFunctionSetRoot
 {
 public:
   DEFINE_STANDARD_ALLOC
 
   //! Initialize correctly all the fields of this class.
   //! The range (1, F.NbVariables()) must be especially respected for
   //! all vectors and matrix declarations.
   Standard_EXPORT math_NewtonFunctionSetRoot(math_FunctionSetWithDerivatives& theFunction,
                                              const math_Vector&               theXTolerance,
                                              const double                     theFTolerance,
                                              const int theNbIterations = 100);
 
   //! This constructor should be used in a sub-class to initialize
   //! correctly all the fields of this class.
   //! The range (1, F.NbVariables()) must be especially respected for
   //! all vectors and matrix declarations.
   //! The method SetTolerance must be called before performing the algorithm.
   Standard_EXPORT math_NewtonFunctionSetRoot(math_FunctionSetWithDerivatives& theFunction,
                                              const double                     theFTolerance,
                                              const int theNbIterations = 100);
 
   //! Destructor
   Standard_EXPORT virtual ~math_NewtonFunctionSetRoot();
 
   //! Initializes the tolerance values for the unknowns.
   Standard_EXPORT void SetTolerance(const math_Vector& XTol);
 
   //! The Newton method is done to improve the root of the function
   //! from the initial guess point. The solution is found when:
   //! abs(Xj - Xj-1)(i) <= XTol(i) and abs(Fi) <= FTol for all i;
   Standard_EXPORT void Perform(math_FunctionSetWithDerivatives& theFunction,
                                const math_Vector&               theStartingPoint);
 
   //! The Newton method is done to improve the root of the function
   //! from the initial guess point. Bounds may be given, to constrain the solution.
   //! The solution is found when:
   //! abs(Xj - Xj-1)(i) <= XTol(i) and abs(Fi) <= FTol for all i;
   Standard_EXPORT void Perform(math_FunctionSetWithDerivatives& theFunction,
                                const math_Vector&               theStartingPoint,
                                const math_Vector&               theInfBound,
                                const math_Vector&               theSupBound);
 
   //! This method is called at the end of each iteration to check if the
   //! solution is found.
   //! Vectors DeltaX, Fvalues and Jacobian Matrix are consistent with the
   //! possible solution Vector Sol and can be inspected to decide whether
   //! the solution is reached or not.
   virtual bool IsSolutionReached(math_FunctionSetWithDerivatives& F);
 
   //! Returns true if the computations are successful, otherwise returns false.
   bool IsDone() const;
 
   //! Returns the value of the root of function F.
   //! Exceptions
   //! StdFail_NotDone if the algorithm fails (and IsDone returns false).
   const math_Vector& Root() const;
 
   //! outputs the root vector in Root.
   //! Exception NotDone is raised if the root was not found.
   //! Exception DimensionError is raised if the range of Root is
   //! not equal to the range of the StartingPoint.
   void Root(math_Vector& Root) const;
 
   //! Outputs the state number associated with the solution
   //! vector root.
   int StateNumber() const;
 
   //! Returns the matrix value of the derivative at the root.
   //! Exception NotDone is raised if the root was not found.
   const math_Matrix& Derivative() const;
 
   //! Outputs the matrix value of the derivative at the root in
   //! Der.
   //! Exception NotDone is raised if the root was not found.
   //! Exception DimensionError is raised if the range of Der is
   //! not equal to the range of the StartingPoint.
   void Derivative(math_Matrix& Der) const;
 
   //! Returns the vector value of the error done on the
   //! functions at the root.
   //! Exception NotDone is raised if the root was not found.
   const math_Vector& FunctionSetErrors() const;
 
   //! Outputs the vector value of the error done on the
   //! functions at the root in Err.
   //! Exception NotDone is raised if the root was not found.
   //! Exception DimensionError is raised if the range of Err is
   //! not equal to the range of the StartingPoint.
   void FunctionSetErrors(math_Vector& Err) const;
 
   //! Returns the number of iterations really done
   //! during the computation of the Root.
   //! Exception NotDone is raised if the root was not found.
   int NbIterations() const;
 
   //! Prints information on the current state of the object.
   //! Is used to redefine the operator <<.
   Standard_EXPORT void Dump(Standard_OStream& o) const;
 
 protected:
   math_Vector        TolX;
   double             TolF;
   math_IntegerVector Indx;
   math_Vector        Scratch;
   math_Vector        Sol;
   math_Vector        DeltaX;
   math_Vector        FValues;
   math_Matrix        Jacobian;
 
 private:
   bool Done;
   int  State;
   int  Iter;
   int  Itermax;
 };
 
 #include <math_NewtonFunctionSetRoot.lxx>
 
 #endif // _math_NewtonFunctionSetRoot_HeaderFile

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