// 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 #include #include #include #include #include #include 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 Standard_Real theFTolerance, const Standard_Integer tehNbIterations = 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 Standard_Real theFTolerance, const Standard_Integer 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 Standard_Boolean IsSolutionReached (math_FunctionSetWithDerivatives& F); //! Returns true if the computations are successful, otherwise returns false. Standard_Boolean 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. Standard_Integer 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. Standard_Integer 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; Standard_Real TolF; math_IntegerVector Indx; math_Vector Scratch; math_Vector Sol; math_Vector DeltaX; math_Vector FValues; math_Matrix Jacobian; private: Standard_Boolean Done; Standard_Integer State; Standard_Integer Iter; Standard_Integer Itermax; }; #include #endif // _math_NewtonFunctionSetRoot_HeaderFile