Repository of functions for rank by elimination on sparse matrices. More...
#include <gauss.h>
Public Member Functions | |
| GaussDomain (const Field &F) | |
| The field parameter is the domain over which to perform computations. | |
| const Field & | field () |
| template<class Matrix > | |
| unsigned long & | InPlaceLinearPivoting (unsigned long &rank, Element &determinant, Matrix &A, unsigned long Ni, unsigned long Nj) |
| 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 & | NoReordering (unsigned long &rank, Element &determinant, Matrix &LigneA, unsigned long Ni, unsigned long Nj) |
| Sparse Gaussian elimination without reordering. | |
| template<class Matrix > | |
| unsigned long & | LUin (unsigned long &rank, Matrix &A) |
| Dense in place LU factorization without reordering. | |
| template<class Matrix > | |
| unsigned long & | upperin (unsigned long &rank, Matrix &A) |
| Dense in place Gaussian elimination without reordering. | |
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 rankinLinearPivoting (by default) or rankinNoReordering | |
| template<class Matrix > | |
| unsigned long & | rankin (unsigned long &rank, Matrix &A, SparseEliminationTraits::PivotStrategy reord=SparseEliminationTraits::PIVOT_LINEAR) |
| template<class Matrix > | |
| unsigned long & | rankin (unsigned long &rank, Matrix &A, unsigned long Ni, unsigned long Nj, SparseEliminationTraits::PivotStrategy reord=SparseEliminationTraits::PIVOT_LINEAR) |
| template<class Matrix > | |
| unsigned long & | rank (unsigned long &rank, const Matrix &A, SparseEliminationTraits::PivotStrategy reord=SparseEliminationTraits::PIVOT_LINEAR) |
| template<class Matrix > | |
| unsigned long & | rank (unsigned long &rank, const Matrix &A, unsigned long Ni, unsigned long Nj, SparseEliminationTraits::PivotStrategy reord=SparseEliminationTraits::PIVOT_LINEAR) |
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 LinearPivoting (by default) or NoReordering | |
| template<class Matrix > | |
| Element & | detin (Element &determinant, Matrix &A, SparseEliminationTraits::PivotStrategy reord=SparseEliminationTraits::PIVOT_LINEAR) |
| template<class Matrix > | |
| Element & | detin (Element &determinant, Matrix &A, unsigned long Ni, unsigned long Nj, SparseEliminationTraits::PivotStrategy reord=SparseEliminationTraits::PIVOT_LINEAR) |
| template<class Matrix > | |
| Element & | det (Element &determinant, const Matrix &A, SparseEliminationTraits::PivotStrategy reord=SparseEliminationTraits::PIVOT_LINEAR) |
| template<class Matrix > | |
| Element & | det (Element &determinant, const Matrix &A, unsigned long Ni, unsigned long Nj, SparseEliminationTraits::PivotStrategy reord=SparseEliminationTraits::PIVOT_LINEAR) |
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.
Member Function Documentation
| const Field& field | ( | ) | [inline] |
accessor for the field of computation
| unsigned long& InPlaceLinearPivoting | ( | unsigned long & | rank, |
| Element & | determinant, | ||
| Matrix & | A, | ||
| unsigned long | Ni, | ||
| unsigned long | Nj | ||
| ) |
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.
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
[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& NoReordering | ( | unsigned long & | rank, |
| Element & | determinant, | ||
| 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
The documentation for this class was generated from the following file:
- /build/buildd/linbox-1.1.6~rc0/linbox/algorithms/gauss.h
