/usr/include/linbox/algorithms/gauss.h is in liblinbox-dev 1.4.2-3.
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* Copyright (C) 1999 Jean-Guillaume Dumas
*
* Written by Jean-Guillaume Dumas <Jean-Guillaume.Dumas@imag.fr>
*
* -----------------------------------------------------------
* 2003-02-02 Bradford Hovinen <bghovinen@math.uwaterloo.ca>
*
* Ported to new matrix archetype; update interface to meet current
* standards. Rename gauss_foo as foo and gauss_Uin as upperin
*
* Move function definitions to gauss.inl
* -----------------------------------------------------------
*
*
* ========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========
*.
*/
// ========================================================================= //
// (C) The Linbox Group 1999
// Calcul de rang par la méthode de Gauss pivot par ligne, sur matrice creuse
// Time-stamp: <03 Nov 00 19:19:06 Jean-Guillaume.Dumas@imag.fr>
// ========================================================================= //
#ifndef __LINBOX_gauss_H
#define __LINBOX_gauss_H
#include "linbox/util/debug.h"
#include "linbox/util/commentator.h"
#include "linbox/field/archetype.h"
#include "linbox/field/gf2.h"
#include "linbox/matrix/sparse-matrix.h"
#include "linbox/matrix/archetype.h"
#include "linbox/solutions/methods.h"
/** @file algorithms/gauss.h
* @brief Gauss elimination and applications for sparse matrices.
* Rank, nullspace, solve...
* @warning this codes expects SparseSeq matrices
*/
namespace LinBox
{
/** \brief Repository of functions for rank by elimination on sparse matrices.
Several versions allow for adjustment of the pivoting strategy
and for choosing in-place elimination or for not modifying the input matrix.
Also an LU interface is offered.
*/
template <class _Field>
class GaussDomain {
public:
typedef _Field Field;
typedef typename Field::Element Element;
private:
const Field *_field;
public:
/** \brief The field parameter is the domain
* over which to perform computations
*/
GaussDomain (const Field &F) :
_field (&F)
{}
//Copy constructor
///
GaussDomain (const GaussDomain &Mat) :
_field (Mat._field)
{}
/** accessor for the field of computation
*/
const Field &field () const { return *_field; }
/** @name rank
Callers of the different rank routines\\
-/ The "in" suffix indicates in place computation\\
-/ Without Ni, Nj, the Matrix parameter must be a vector of sparse
row vectors, NOT storing any zero.\\
-/ Calls @link rankinLinearPivoting@endlink (by default) or @link rankinNoReordering@endlink
*/
//@{
///
template <class Matrix> unsigned long& rankin(unsigned long &rank,
Matrix &A,
SparseEliminationTraits::PivotStrategy reord = SparseEliminationTraits::PIVOT_LINEAR) const;
///
template <class Matrix> unsigned long& rankin(unsigned long &rank,
Matrix &A,
unsigned long Ni,
unsigned long Nj,
SparseEliminationTraits::PivotStrategy reord = SparseEliminationTraits::PIVOT_LINEAR) const;
///
template <class Matrix> unsigned long& rank(unsigned long &rank,
const Matrix &A,
SparseEliminationTraits::PivotStrategy reord = SparseEliminationTraits::PIVOT_LINEAR) const;
///
template <class Matrix> unsigned long& rank(unsigned long &rank,
const Matrix &A,
unsigned long Ni,
unsigned long Nj,
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 Matrix 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 Matrix> Element& detin(Element &determinant,
Matrix &A,
SparseEliminationTraits::PivotStrategy reord = SparseEliminationTraits::PIVOT_LINEAR) const;
///
template <class Matrix> Element& detin(Element &determinant,
Matrix &A,
unsigned long Ni,
unsigned long Nj,
SparseEliminationTraits::PivotStrategy reord = SparseEliminationTraits::PIVOT_LINEAR) const;
///
template <class Matrix> Element& det(Element &determinant,
const Matrix &A,
SparseEliminationTraits::PivotStrategy reord = SparseEliminationTraits::PIVOT_LINEAR) const;
///
template <class Matrix> Element& det(Element &determinant,
const Matrix &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 Matrix 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 Matrix, class Perm>
unsigned long& QLUPin(unsigned long &rank,
Element& determinant,
Perm &Q,
Matrix &L,
Matrix &U,
Perm &P,
unsigned long Ni,
unsigned long Nj) const;
template <class Matrix, class Perm>
unsigned long& DenseQLUPin(unsigned long &rank,
Element& determinant,
std::deque<std::pair<size_t,size_t> > &invQ,
Matrix &L,
Matrix &U,
Perm &P,
unsigned long Ni,
unsigned long Nj) const;
template <class Matrix, class Perm, class Vector1, class Vector2>
Vector1& solve(Vector1& x, Vector1& w, unsigned long rank, const Perm& Q, const Matrix& L, const Matrix& U, const Perm& P, const Vector2& b) const;
template <class Matrix, class Vector1, class Vector2>
Vector1& solvein(Vector1 &x,
Matrix &A,
const Vector2 &b) const;
template <class Matrix, class Vector1, class Vector2, class Random>
Vector1& solvein(Vector1 &x,
Matrix &A,
const Vector2 &b, Random& generator) const;
template <class Matrix, class Perm, class Block>
Block& nullspacebasis(Block& x,
unsigned long rank,
const Matrix& U,
const Perm& P) const ;
template <class Matrix, class Block>
Block& nullspacebasisin(Block& x, Matrix& A) const;
template <class Matrix, class Block>
Block& nullspacebasis(Block& x, const Matrix& A) const;
// Sparsest method
// erases elements while computing rank/det.
template <class Matrix>
unsigned long& InPlaceLinearPivoting(unsigned long &rank,
Element& determinant,
Matrix &A,
unsigned long Ni,
unsigned long Nj) const;
// Same as the latter but keeps trace
// of column permutations
// of remaining elements in the matrix
template <class Matrix,class Perm>
unsigned long& InPlaceLinearPivoting(unsigned long &rank,
Element& determinant,
Matrix &A,
Perm &P,
unsigned long Ni,
unsigned long Nj) const;
/** \brief Sparse Gaussian elimination without reordering.
Gaussian elimination is done on a copy of the matrix.
Using : SparseFindPivot
eliminate
Requirements : SLA is an array of sparse rows
WARNING : NOT IN PLACE, THERE IS A COPY.
Without reordering (Pivot is first non-zero in row)
*/
template <class Matrix>
unsigned long& NoReordering (unsigned long &rank, Element& determinant, Matrix &LigneA, unsigned long Ni, unsigned long Nj) const;
/** \brief Dense in place LU factorization without reordering
Using : FindPivot and LU
*/
template <class Matrix>
unsigned long &LUin (unsigned long &rank, Matrix &A) const;
/** \brief Dense in place Gaussian elimination without reordering
Using : FindPivot and LU
*/
template <class Matrix>
unsigned long &upperin (unsigned long &rank, Matrix &A) const;
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 eliminate (Element & headpivot,
Vector &lignecourante,
const Vector &lignepivot,
const unsigned long indcol,
const long indpermut,
const unsigned long npiv,
D &columns) const;
template <class Vector, class D>
void eliminate (Vector &lignecourante,
const Vector &lignepivot,
const unsigned long &indcol,
const long &indpermut,
D &columns) const;
template <class Vector>
void permute (Vector &lignecourante,
const unsigned long &indcol,
const long &indpermut) const;
//-----------------------------------------
// Sparse elimination using a pivot row :
// lc <-- lc - lc[k]/lp[0] * lp
// No density update
// Vector is a vector of Pair (lin_pair.h)
//-----------------------------------------
template <class Vector>
void eliminate (Vector &lignecourante,
const Vector &lignepivot,
const unsigned long &indcol,
const long &indpermut) const;
//-----------------------------------------
// Dense elimination using a pivot row :
// lc <-- lc - lc[k]/lp[0] * lp
// Computing only for k to n (and not 0 to n in LU)
//-----------------------------------------
template<class Vector>
void Upper (Vector &lignecur,
const Vector &lignepivot,
unsigned long indcol,
long indpermut) const;
//-----------------------------------------
// Dense elimination using a pivot row :
// lc <-- lc - lc[k]/lp[0] * lp
//-----------------------------------------
template <class Vector>
void LU (Vector &lignecur,
const Vector &lignepivot,
unsigned long indcol,
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 SparseFindPivot (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 SparseFindPivot (Vector &lignepivot, unsigned long &indcol, long &indpermut, Element& determinant) const;
//------------------------------------------
// Looking for a non-zero pivot in a row
// Dense search
//------------------------------------------
template <class Vector>
void FindPivot (Vector &lignepivot, unsigned long &k, long &indpermut) const;
template <class Matrix, class Perm>
unsigned long& SparseContinuation(unsigned long &rank,
Element& determinant,
std::deque<std::pair<size_t,size_t> > &invQ,
Matrix &L,
Matrix &U,
Perm &P,
unsigned long Ni,
unsigned long Nj) const;
template <class Matrix, class Perm, bool hasFFLAS>
struct Continuation {
unsigned long& operator()(
unsigned long &rank,
Element& determinant,
std::deque<std::pair<size_t,size_t> > &invQ,
Matrix &L,
Matrix &U,
Perm &P,
unsigned long Ni,
unsigned long Nj, bool) const;
};
};
} // namespace LinBox
#include "linbox/algorithms/gauss/gauss.inl"
#include "linbox/algorithms/gauss/gauss-pivot.inl"
#include "linbox/algorithms/gauss/gauss-elim.inl"
#include "linbox/algorithms/gauss/gauss-solve.inl"
#include "linbox/algorithms/gauss/gauss-nullspace.inl"
#include "linbox/algorithms/gauss/gauss-rank.inl"
#include "linbox/algorithms/gauss/gauss-det.inl"
#endif // __LINBOX_gauss_H
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// mode: C++
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