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 // Created on: 1991-08-22
 // 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_Uzawa_HeaderFile
 #define _math_Uzawa_HeaderFile
 
 #include <Standard.hxx>
 #include <Standard_DefineAlloc.hxx>
 
 #include <math_Vector.hxx>
 #include <math_Matrix.hxx>
 #include <Standard_Integer.hxx>
 #include <Standard_OStream.hxx>
 
 //! This class implements a system resolution C*X = B with
 //! an approach solution X0. There are no conditions on the
 //! number of equations. The algorithm used is the Uzawa
 //! algorithm. It is possible to have equal or inequal (<)
 //! equations to solve. The resolution is done with a
 //! minimization of Norm(X-X0).
 //! If there are only equal equations, the resolution is directly
 //! done and is similar to Gauss resolution with an optimisation
 //! because the matrix is a symmetric matrix.
 //! (The resolution is done with Crout algorithm)
 class math_Uzawa
 {
 public:
   DEFINE_STANDARD_ALLOC
 
   //! Given an input matrix Cont, two input vectors Secont
   //! and StartingPoint, it solves Cont*X = Secont (only
   //! = equations) with a minimization of Norme(X-X0).
   //! The maximum iterations number allowed is fixed to
   //! NbIterations.
   //! The tolerance EpsLic is fixed for the dual variable
   //! convergence. The tolerance EpsLix is used for the
   //! convergence of X.
   //! Exception ConstructionError is raised if the line number
   //! of Cont is different from the length of Secont.
   Standard_EXPORT math_Uzawa(const math_Matrix& Cont,
                              const math_Vector& Secont,
                              const math_Vector& StartingPoint,
                              const double       EpsLix       = 1.0e-06,
                              const double       EpsLic       = 1.0e-06,
                              const int          NbIterations = 500);
 
   //! Given an input matrix Cont, two input vectors Secont
   //! and StartingPoint, it solves Cont*X = Secont (the Nce
   //! first equations are equal equations and the Nci last
   //! equations are inequalities <) with a minimization
   //! of Norme(X-X0).
   //! The maximum iterations number allowed is fixed to
   //! NbIterations.
   //! The tolerance EpsLic is fixed for the dual variable
   //! convergence. The tolerance EpsLix is used for the
   //! convergence of X.
   //! There are no conditions on Nce and Nci.
   //! Exception ConstructionError is raised if the line number
   //! of Cont is different from the length of Secont and from
   //! Nce + Nci.
   Standard_EXPORT math_Uzawa(const math_Matrix& Cont,
                              const math_Vector& Secont,
                              const math_Vector& StartingPoint,
                              const int          Nci,
                              const int          Nce,
                              const double       EpsLix       = 1.0e-06,
                              const double       EpsLic       = 1.0e-06,
                              const int          NbIterations = 500);
 
   //! Returns true if the computations are successful, otherwise returns false.
   bool IsDone() const;
 
   //! Returns the vector solution of the system above.
   //! An exception is raised if NotDone.
   const math_Vector& Value() const;
 
   //! Returns the initial error Cont*StartingPoint-Secont.
   //! An exception is raised if NotDone.
   const math_Vector& InitialError() const;
 
   //! returns the duale variables V of the systeme.
   Standard_EXPORT void Duale(math_Vector& V) const;
 
   //! Returns the difference between X solution and the
   //! StartingPoint.
   //! An exception is raised if NotDone.
   const math_Vector& Error() const;
 
   //! returns the number of iterations really done.
   //! An exception is raised if NotDone.
   int NbIterations() const;
 
   //! returns the inverse matrix of (C * Transposed(C)).
   //! This result is needed for the computation of the gradient
   //! when approximating a curve.
   const math_Matrix& InverseCont() const;
 
   //! Prints information on the current state of the object.
   Standard_EXPORT void Dump(Standard_OStream& o) const;
 
 protected:
   //! Is used internally by the two constructors above.
   Standard_EXPORT void Perform(const math_Matrix& Cont,
                                const math_Vector& Secont,
                                const math_Vector& StartingPoint,
                                const int          Nci,
                                const int          Nce,
                                const double       EpsLix       = 1.0e-06,
                                const double       EpsLic       = 1.0e-06,
                                const int          NbIterations = 500);
 
 private:
   math_Vector Resul;
   math_Vector Erruza;
   math_Vector Errinit;
   math_Vector Vardua;
   math_Matrix CTCinv;
   int         NbIter;
   bool        Done;
 };
 
 #include <math_Uzawa.lxx>
 
 #endif // _math_Uzawa_HeaderFile

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