pls_mmpf.h File Reference

PLS and PLUQ factorization using Gray codes. More...

#include "packedmatrix.h"
#include "permutation.h"

Go to the source code of this file.

Functions
size_t	_mzd_pls_mmpf (mzd_t *A, mzp_t *P, mzp_t *Q, int k)
	PLS matrix decomposition of A using Gray codes.
size_t	_mzd_pluq_mmpf (mzd_t *A, mzp_t *P, mzp_t *Q, int k)
	PLUQ matrix decomposition of A using Gray codes.
size_t	_mzd_pls_submatrix (mzd_t *A, size_t start_row, size_t stop_row, size_t start_col, int k, mzp_t *P, mzp_t *Q, size_t *done, size_t *done_row)
	PLS matrix decomposition of a submatrix for up to k columns starting at (r,c).

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Detailed Description

PLS and PLUQ factorization using Gray codes.

Author:

Martin Albrecht <M.R.Albrecht@rhul.ac.uk>

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Function Documentation

size_t _mzd_pls_mmpf	(	mzd_t *	A,
		mzp_t *	P,
		mzp_t *	Q,
		int	k
	)

PLS matrix decomposition of A using Gray codes.

Returns (P,L,S,Q) satisfying PLS = A where P is a permutation matrix of dimension m x m, L is m x r unit lower triangular and S is an r x n matrix which is upper triangular except that its columns are permuted, that is S = UQ for U r x n upper triangular and Q is a n x n permutation matrix. The matrix L and S are stored in place over A.

Parameters:

A	Matrix.
P	Preallocated row permutation.
Q	Preallocated column permutation.
k	Size of Gray code tables.

Ignores offset atrtribute of packedmatrix.

Returns:

Rank of A.

size_t _mzd_pls_submatrix	(	mzd_t *	A,
		size_t	start_row,
		size_t	stop_row,
		size_t	start_col,
		int	k,
		mzp_t *	P,
		mzp_t *	Q,
		size_t *	done,
		size_t *	done_row
	)

PLS matrix decomposition of a submatrix for up to k columns starting at (r,c).

Updates P and Q and modifies A in place. The buffer done afterwards holds how far a particular row was already eliminated.

Parameters:

A	Matrix.
start_row	Row Offset.
stop_row	Up to which row the matrix should be processed (exclusive).
start_col	Column Offset.
k	Size of Gray code tables.
P	Preallocated row permutation.
Q	Preallocated column permutation.
done	Preallocated temporary buffer.
done_row	Stores the last row which is already reduced processed after function execution.

Return values:

kbar	Maximum k for which a pivot could be found.

size_t _mzd_pluq_mmpf	(	mzd_t *	A,
		mzp_t *	P,
		mzp_t *	Q,
		int	k
	)

PLUQ matrix decomposition of A using Gray codes.

Returns (P,L,U,Q) satisfying PLUQ = A where P and Q are two permutation matrices, of dimension respectively m x m and n x n, L is m x r unit lower triangular and U is r x n upper triangular.

Parameters:

A	Matrix.
P	Preallocated row permutation.
Q	Preallocated column permutation.
k	Size of Gray code tables.

Ignores offset atrtribute of packedmatrix.

Returns:

Rank of A.

Examples:

testsuite/bench_elimination.c.