MathTL: numerics/eigenvalues.h Source File

00001 // -*- c++ -*-
00002 
00003 // +--------------------------------------------------------------------+
00004 // | This file is part of MathTL - the Mathematical Template Library    |
00005 // |                                                                    |
00006 // | Copyright (c) 2002-2009                                            |
00007 // | Thorsten Raasch, Manuel Werner                                     |
00008 // +--------------------------------------------------------------------+
00009 
00010 #ifndef _MATHTL_EIGENVALUES_H
00011 #define _MATHTL_EIGENVALUES_H
00012 
00013 // A small collection of iterative algorithms to compute
00014 // eigenvalues of a square matrix A
00015 
00016 // VECTOR: arbitrary vector class, should implement the operators +, -, * (scalar mult.)
00017 // MATRIX: matrix class, we only require a routine APPLY(const VECTOR&, VECTOR&)
00018 // PREC:   preconditioner, we again require APPLY(const VECTOR&, VECTOR&)
00019 
00020 namespace MathTL
00021 {
00023 
00031   template <class VECTOR, class MATRIX>
00032   double PowerIteration(const MATRIX& A, VECTOR& xk,
00033                         const double tol, const unsigned int maxit, unsigned int &iterations);
00034   
00036 
00045   template <class VECTOR, class MATRIX>
00046   double InversePowerIteration(const MATRIX& A, VECTOR& xk,
00047                                const double tol, const unsigned int maxit, unsigned int &iterations);
00048 
00050 
00060   template <class VECTOR, class MATRIX>
00061   double InversePowerIteration(const MATRIX& A, VECTOR& xk, const double lambda,
00062                                const double tol, const unsigned int maxit, unsigned int &iterations);
00063 
00068   template <class MATRIX>
00069   void LanczosIteration(const MATRIX& A, const double tol,
00070                         double& lambdamin, double& lambdamax,
00071                         const unsigned int maxit, unsigned int &iterations);
00072 
00074 
00080   template <class VECTOR, class MATRIX, class MATRIX2>
00081   void SymmEigenvalues(const MATRIX& A, VECTOR& evals, MATRIX2& evecs);
00082 
00084   template <class MATRIX>
00085   double CondSymm(const MATRIX& A,
00086                   double tol = 1e-6, unsigned int maxit = 100);
00087 
00089   template <class MATRIX>
00090   double CondNonSymm(const MATRIX &A,
00091                      double tol = 1e-6, unsigned int maxit = 100);
00092 }
00093 
00094 #include "numerics/eigenvalues.cpp"
00095 
00096 
00097 #endif