/usr/include/linbox/algorithms/lanczos.h is in liblinbox-dev 1.4.2-5build1.
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* Copyright (C) 2002 LinBox
*
* Written by Bradford Hovinen <hovinen@cis.udel.edu>
*
* ------------------------------------
*
*
* ========LICENCE========
* This file is part of the library LinBox.
*
* LinBox is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
* ========LICENCE========
*.
*/
#ifndef __LINBOX_lanczos_H
#define __LINBOX_lanczos_H
#include <vector>
#include <algorithm>
#include "linbox/blackbox/archetype.h"
#include "linbox/util/debug.h"
#include "linbox/vector/vector-domain.h"
#include "linbox/solutions/methods.h"
namespace LinBox
{
/**
\brief Solve a linear system using the conjugate Lanczos iteration.
*
* Lanczos system solver class.
* This class encapsulates the functionality required for solving a linear
* system through the conjugate Lanczos iteration
*/
template <class Field, class Vector>
class LanczosSolver {
public:
/** @brief Constructor
* @param F Field over which to operate
* @param traits @ref SolverTraits structure describing user
* options for the solver
*/
LanczosSolver (const Field &F, const LanczosTraits &traits) :
_traits (traits), _field (&F), _randiter (F), _VD (F)
{}
/** @brief Constructor with a random iterator
* @param F Field over which to operate
* @param traits @ref SolverTraits structure describing user
* options for the solver
* @param r Random iterator to use for randomization
*/
LanczosSolver (const Field &F, const LanczosTraits &traits, typename Field::RandIter r) :
_traits (traits), _field (&F), _randiter (r), _VD (F)
{}
/** Solve the linear system Ax = b.
*
* If the system is nonsingular, this method computes the unique
* solution to the system Ax = b. If the system is singular, it computes
* a random solution.
*
* If the matrix A is nonsymmetric, this method preconditions the matrix
* A with the preconditioner D_1 A^T D_2 A D_1, where D_1 and D_2 are
* random nonsingular diagonal matrices. If the matrix A is symmetric,
* this method preconditions the system with A D, where D is a random
* diagonal matrix.
*
* @param A Black box for the matrix A
* @param x Vector in which to store solution
* @param b Right-hand side of system
* @return Reference to solution vector
*/
template <class Blackbox>
Vector &solve (const Blackbox &A, Vector &x, const Vector &b);
inline const Field & field() const { return *_field; }
private:
// Run the Lanczos iteration and return the result. Return false
// if the method breaks down. Do not check that Ax = b in the end
template<class Blackbox>
bool iterate (const Blackbox &A, Vector &x, const Vector &b);
const LanczosTraits &_traits;
const Field *_field;
typename Field::RandIter _randiter;
VectorDomain<Field> _VD;
Vector _w[2], _Aw; // Temporaries used in the Lanczos iteration
};
}
#include "linbox/algorithms/lanczos.inl"
#endif // __LINBOX_lanczos_H
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