GaussDomain Class Template Reference

#include <gauss.h>

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Detailed Description

template<class _Field>
class LinBox::GaussDomain< _Field >

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.

Public Types
typedef _Field	Field
typedef Field::Element	Element
Public Member Functions
	GaussDomain (const Field &F)
	The field parameter is the domain over which to perform computations.
	GaussDomain (const GaussDomain &M)
const Field &	field ()
template<class Matrix> unsigned long &	rankinLinearPivoting (unsigned long &rank, Matrix &A, unsigned long Ni, unsigned long Nj, bool storrows=false)
	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.
template<class Matrix> unsigned long &	rankinNoReordering (unsigned long &rank, Matrix &LigneA, unsigned long Ni, unsigned long Nj)
	Sparse Gaussian elimination without reordering. Gaussian elimination is done on a copy of the matrix. Using : SparseFindPivot eliminate.
template<class Matrix> unsigned long &	LUin (unsigned long &rank, Matrix &A)
	Dense in place LU factorization without reordering Using : FindPivot and LU.
template<class Matrix> unsigned long &	upperin (unsigned long &rank, Matrix &A)
	Dense in place Gaussian elimination without reordering Using : FindPivot and LU.
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.\ -/ Calls rankinLinearPivoting (by default) or rankinNoReordering
template<class Matrix> unsigned long &	rankin (unsigned long &rank, Matrix &A, SparseEliminationTraits::PivotStrategy reord=SparseEliminationTraits::PIVOT_LINEAR, bool storrows=false)
template<class Matrix> unsigned long &	rankin (unsigned long &rank, Matrix &A, unsigned long Ni, unsigned long Nj, SparseEliminationTraits::PivotStrategy reord=SparseEliminationTraits::PIVOT_LINEAR, bool storrows=false)
template<class Matrix> unsigned long &	rank (unsigned long &rank, const Matrix &A, SparseEliminationTraits::PivotStrategy reord=SparseEliminationTraits::PIVOT_LINEAR, bool storrows=false)
template<class Matrix> unsigned long &	rank (unsigned long &rank, const Matrix &A, unsigned long Ni, unsigned long Nj, SparseEliminationTraits::PivotStrategy reord=SparseEliminationTraits::PIVOT_LINEAR, bool storrows=false)
Protected Member Functions
template<class Vector, class D> void	eliminate (Vector &lignecourante, const Vector &lignepivot, const unsigned long &indcol, const unsigned long &indpermut, D &columns)
template<class Vector> void	eliminate (Vector &lignecourante, const Vector &lignepivot, const unsigned long &indcol, const unsigned long &indpermut)
template<class Vector> void	Upper (Vector &lignecur, const Vector &lignepivot, unsigned long indcol, unsigned long indpermut)
template<class Vector> void	LU (Vector &lignecur, const Vector &lignepivot, unsigned long indcol, unsigned long indpermut)
template<class Vector, class D> void	SparseFindPivot (Vector &lignepivot, unsigned long &indcol, unsigned long &indpermut, D &columns)
template<class Vector> void	SparseFindPivot (Vector &lignepivot, unsigned long &indcol, unsigned long &indpermut)
template<class Vector> void	FindPivot (Vector &lignepivot, unsigned long &k, unsigned long &indpermut)

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Member Typedef Documentation

typedef _Field Field

typedef Field::Element Element

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Constructor & Destructor Documentation

GaussDomain (  const Field &  F  )  [inline]

The field parameter is the domain over which to perform computations.

GaussDomain (  const GaussDomain< _Field > &  M  )  [inline]

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Member Function Documentation

const Field& field (   )  [inline]

accessor for the field of computation

unsigned long& rankin (  unsigned long &  rank, Matrix &  A, SparseEliminationTraits::PivotStrategy  reord = SparseEliminationTraits::PIVOT_LINEAR, bool  storrows = false )

unsigned long& rankin (  unsigned long &  rank, Matrix &  A, unsigned long  Ni, unsigned long  Nj, SparseEliminationTraits::PivotStrategy  reord = SparseEliminationTraits::PIVOT_LINEAR, bool  storrows = false )

unsigned long& rank (  unsigned long &  rank, const Matrix &  A, SparseEliminationTraits::PivotStrategy  reord = SparseEliminationTraits::PIVOT_LINEAR, bool  storrows = false )

unsigned long& rank (  unsigned long &  rank, const Matrix &  A, unsigned long  Ni, unsigned long  Nj, SparseEliminationTraits::PivotStrategy  reord = SparseEliminationTraits::PIVOT_LINEAR, bool  storrows = false )

unsigned long& rankinLinearPivoting (  unsigned long &  rank, Matrix &  A, unsigned long  Ni, unsigned long  Nj, bool  storrows = false )

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. {verbatim} Using : SparseFindPivot(..., density) for sparsest column, and eliminate (..., density) {verbatim} The Matrix parameter must meet the LinBox sparse matrix interface. [check details]. The storrows indicates whether the algorithm must keep already computed rows. [Jean-Guillaume Dumas and Gilles Villard, Computing the rank of sparse matrices over finite fields. In Ganzha et~al. CASC'2002, pages 47--62.]

unsigned long& rankinNoReordering (  unsigned long &  rank, Matrix &  LigneA, unsigned long  Ni, unsigned long  Nj )

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)

unsigned long& LUin (  unsigned long &  rank, Matrix &  A )

Dense in place LU factorization without reordering Using : FindPivot and LU.

unsigned long& upperin (  unsigned long &  rank, Matrix &  A )

Dense in place Gaussian elimination without reordering Using : FindPivot and LU.

void eliminate (  Vector &  lignecourante, const Vector &  lignepivot, const unsigned long &  indcol, const unsigned long &  indpermut, D &  columns )  [protected]

void eliminate (  Vector &  lignecourante, const Vector &  lignepivot, const unsigned long &  indcol, const unsigned long &  indpermut )  [protected]

void Upper (  Vector &  lignecur, const Vector &  lignepivot, unsigned long  indcol, unsigned long  indpermut )  [protected]

void LU (  Vector &  lignecur, const Vector &  lignepivot, unsigned long  indcol, unsigned long  indpermut )  [protected]

void SparseFindPivot (  Vector &  lignepivot, unsigned long &  indcol, unsigned long &  indpermut, D &  columns )  [protected]

void SparseFindPivot (  Vector &  lignepivot, unsigned long &  indcol, unsigned long &  indpermut )  [protected]

void FindPivot (  Vector &  lignepivot, unsigned long &  k, unsigned long &  indpermut )  [protected]

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