/usr/include/linbox/algorithms/gauss-gf2.h is in liblinbox-dev 1.4.2-5build1.
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* Copyright (C) 2009 The LinBox group
* Written by JG Dumas
*
* Time-stamp: <23 Mar 12 17:28:19 Jean-Guillaume.Dumas@imag.fr>
*
*
* ========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========
*.
*
* SparseSeqMatrix is container< container< size_t > >
* as e.g. linbox/blackbox/zo-gf2.h
*/
#ifndef __LINBOX_gauss_gf2_H
#define __LINBOX_gauss_gf2_H
#include "linbox/util/debug.h"
#include "linbox/util/commentator.h"
#include "linbox/field/gf2.h"
#include "linbox/vector/vector-domain.h"
#include "linbox/algorithms/gauss.h"
#include "linbox/blackbox/zo-gf2.h"
/** @file algorithms/gauss-gf2.h
* @brief Gauss elimination and applications for sparse matrices on \f$F_2\f$.
* Rank, nullspace, solve...
*/
namespace LinBox
{
template <>
class GaussDomain<GF2> {
public:
typedef GF2 Field;
typedef Field::Element Element;
// Preferred Matrix type
typedef ZeroOne<GF2> Matrix;
public:
/** \brief The field parameter is the domain over which to perform computations.
*/
GaussDomain (const Field &) {}
//Copy constructor
///
GaussDomain (const GaussDomain &) {}
/** accessor for the field of computation.
*/
const Field &field () const { return *(new GF2()); }
/** @name rank
Callers of the different rank routines
@li The "in" suffix indicates in place computation
@li Without Ni, Nj, the SparseSeqMatrix parameter must be a vector of sparse
row vectors, NOT storing any zero.
@li Calls @link rankinLinearPivoting@endlink (by default) or @link rankinNoReordering@endlink
*/
//@{
///
///
template <class SparseSeqMatrix> unsigned long& rankin(unsigned long &Rank,
SparseSeqMatrix &A,
unsigned long Ni,
unsigned long Nj,
SparseEliminationTraits::PivotStrategy reord = SparseEliminationTraits::PIVOT_LINEAR) const ;
///
template <class SparseSeqMatrix> unsigned long& rankin(unsigned long &Rank,
SparseSeqMatrix &A,
SparseEliminationTraits::PivotStrategy reord = SparseEliminationTraits::PIVOT_LINEAR) const;
///
template <class SparseSeqMatrix> unsigned long& rank(unsigned long &rk,
const SparseSeqMatrix &A,
unsigned long Ni,
unsigned long Nj,
SparseEliminationTraits::PivotStrategy reord = SparseEliminationTraits::PIVOT_LINEAR) const ;
///
template <class SparseSeqMatrix> unsigned long& rank(unsigned long &rk,
const SparseSeqMatrix &A,
SparseEliminationTraits::PivotStrategy reord = SparseEliminationTraits::PIVOT_LINEAR) const ;
//@}
/** @name det
Callers of the different determinant routines\\
-/ The "in" suffix indicates in place computation\\
-/ Without Ni, Nj, the SparseSeqMatrix parameter must be a vector of sparse
row vectors, NOT storing any zero.\\
-/ Calls @link LinearPivoting@endlink (by default) or @link NoReordering@endlink
*/
//@{
///
template <class SparseSeqMatrix> Element& detin(Element &determinant,
SparseSeqMatrix &A,
SparseEliminationTraits::PivotStrategy reord = SparseEliminationTraits::PIVOT_LINEAR) const;
///
template <class SparseSeqMatrix> Element& detin(Element &determinant,
SparseSeqMatrix &A,
unsigned long Ni,
unsigned long Nj,
SparseEliminationTraits::PivotStrategy reord = SparseEliminationTraits::PIVOT_LINEAR) const;
///
template <class SparseSeqMatrix> Element& det(Element &determinant,
const SparseSeqMatrix &A,
SparseEliminationTraits::PivotStrategy reord = SparseEliminationTraits::PIVOT_LINEAR) const;
///
template <class SparseSeqMatrix> Element& det(Element &determinant,
const SparseSeqMatrix &A,
unsigned long Ni,
unsigned long Nj,
SparseEliminationTraits::PivotStrategy reord = SparseEliminationTraits::PIVOT_LINEAR) const;
//@}
/** \brief Sparse in place Gaussian elimination with reordering to reduce fill-in.
* pivots are chosen in sparsest column of sparsest row.
* This runs in linear overhead.
* It is similar in spirit but different from Markovitz' approach.
*
* \pre Using : SparseFindPivot(..., density) for sparsest column, and
* eliminate (..., density)
*
* The SparseSeqMatrix parameter must meet the LinBox sparse matrix interface.
* [check details].
* The computedet indicates whether the algorithm must compute the determionant as it goes
*
* @bib
* - Jean-Guillaume Dumas and Gilles Villard,
* <i>Computing the rank of sparse matrices over finite fields.</i>
* In Ganzha et~al. CASC'2002, pages 47--62.
*/
template <class SparseSeqMatrix, class Perm>
unsigned long& QLUPin(unsigned long &Rank,
Element& determinant,
Perm &Q,
SparseSeqMatrix &L,
SparseSeqMatrix &U,
Perm &P,
unsigned long Ni,
unsigned long Nj) const;
template <class SparseSeqMatrix, class Perm, class Vector1, class Vector2>
Vector1& solve(Vector1& x, Vector1& w, unsigned long Rank, const Perm& Q, const SparseSeqMatrix& L, const SparseSeqMatrix& U, const Perm& P, const Vector2& b) const;
template <class SparseSeqMatrix, class Vector1, class Vector2>
Vector1& solvein(Vector1& x,
SparseSeqMatrix &A,
const Vector2& b) const;
template <class SparseSeqMatrix, class Vector1, class Vector2, class Random>
Vector1& solvein(Vector1& x,
SparseSeqMatrix &A,
const Vector2& b, Random& generator) const;
template <class SparseSeqMatrix, class Perm>
unsigned long& InPlaceLinearPivoting(unsigned long &Rank,
Element& determinant,
SparseSeqMatrix &A,
Perm &P,
unsigned long Ni,
unsigned long Nj) const;
template <class SparseSeqMatrix>
unsigned long& NoReordering (unsigned long & Rank, Element& , SparseSeqMatrix &, unsigned long , unsigned long ) const
{
std::cerr << "Sparse elimination over GF2 without reordering not implemented" << std::endl;
return Rank;
}
protected:
//-----------------------------------------
// Sparse elimination using a pivot row :
// lc <-- lc - lc[k]/lp[0] * lp
// D is the number of elements per column
// it is updated and used for reordering
// Vector is a vector of Pair (lin_pair.h)
//-----------------------------------------
template <class Vector, class D>
void eliminateBinary (Element & headpivot,
Vector &lignecourante,
const Vector &lignepivot,
const unsigned long indcol,
const long indpermut,
const unsigned long npiv,
D &columns) const;
template <class Vector>
void permuteBinary (Vector &lignecourante,
const unsigned long &indcol,
const long &indpermut) const;
//------------------------------------------
// Looking for a non-zero pivot in a row
// Using the column density for reordering
// Pivot is chosen as to :
// 1. Row density is minimum
// 2. Column density is minimum for this row
//------------------------------------------
template <class Vector, class D>
void SparseFindPivotBinary (Vector &lignepivot, unsigned long &indcol, long &indpermut, D &columns, Element& determinant) const;
//------------------------------------------
// Looking for a non-zero pivot in a row
// No reordering
//------------------------------------------
template <class Vector>
void SparseFindPivotBinary (Vector &lignepivot, unsigned long &indcol, long &indpermut, Element& determinant) const;
};
} // namespace LinBox
#include "linbox/algorithms/gauss/gauss-gf2.inl"
#include "linbox/algorithms/gauss/gauss-pivot-gf2.inl"
#include "linbox/algorithms/gauss/gauss-elim-gf2.inl"
#include "linbox/algorithms/gauss/gauss-rank-gf2.inl"
#include "linbox/algorithms/gauss/gauss-solve-gf2.inl"
#endif // __LINBOX_gauss_gf2_H
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