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// ============================================================================
// == ==
// == AMDiS - Adaptive multidimensional simulations ==
// == ==
Thomas Witkowski
committed
// == http://www.amdis-fem.org ==
// == ==
// ============================================================================
Thomas Witkowski
committed
//
// Software License for AMDiS
//
// Copyright (c) 2010 Dresden University of Technology
// All rights reserved.
// Authors: Simon Vey, Thomas Witkowski et al.
//
// This file is part of AMDiS
//
// See also license.opensource.txt in the distribution.
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/** \file Cholesky.h */
#ifndef CHOLESKY_H
#define CHOLESKY_H
#include "FixVec.h"
using namespace std;
using namespace AMDiS;
/**
* \ingroup Solvers
*
* \brief
* Solves a symmetric positive definite system using Cholesky decomposition.
* Returns true if the matrix in (numerically) positive definite.
*/
class Cholesky
{
public:
/** \brief
* Computes the Cholesky factor of a positive definite matrix A.
* On input, only the upper triangle of A need be given; it is not modified.
* The Cholesky factor is returned in the lower triangle of A, except for its
* diagonal elements which are returned in P.
*/
static bool factorization(Matrix<double> *A, Vector<double> *p);
/** \brief
* Solves system A*X=B, where A is a positive definite matrix.
* If P=NULL; A is assumed to be positive definite, and a Cholesky
* decomposition is computed using the previous routine.
* If P is given, A and P are assumed to be already given as the output of
* the previous routine.
*/
static bool solve(Matrix<double> *A, Vector<double> *b, Vector<double> *x,
Vector<double> *p = NULL);
static bool solve(Matrix<double> *A, Vector<WorldVector<double> > *b,
Vector<WorldVector<double> > *x,
Vector<double> *p = NULL);
};
#endif