ple.h File Reference

PLE and PLUQ matrix decomposition routines. More...

#include <m4ri/mzd.h>
#include <m4ri/mzp.h>

Go to the source code of this file.

Macros
#define	__M4RI_PLE_CUTOFF   MIN(524288, __M4RI_CPU_L3_CACHE >> 3)

Functions
rci_t	mzd_pluq (mzd_t *A, mzp_t *P, mzp_t *Q, const int cutoff)
	PLUQ matrix decomposition. More...
rci_t	mzd_ple (mzd_t *A, mzp_t *P, mzp_t *Q, const int cutoff)
	PLE matrix decomposition. More...
rci_t	_mzd_pluq (mzd_t *A, mzp_t *P, mzp_t *Q, const int cutoff)
	PLUQ matrix decomposition. More...
rci_t	_mzd_ple (mzd_t *A, mzp_t *P, mzp_t *Qt, const int cutoff)
	PLE matrix decomposition. More...
rci_t	_mzd_pluq_naive (mzd_t *A, mzp_t *P, mzp_t *Q)
	PLUQ matrix decomposition (naive base case). More...
rci_t	_mzd_ple_naive (mzd_t *A, mzp_t *P, mzp_t *Qt)
	PLE matrix decomposition (naive base case). More...

Detailed Description

PLE and PLUQ matrix decomposition routines.

Author

Clement Pernet cleme.nosp@m.nt.p.nosp@m.ernet.nosp@m.@gma.nosp@m.il.co.nosp@m.m

Macro Definition Documentation

#define __M4RI_PLE_CUTOFF   MIN(524288, __M4RI_CPU_L3_CACHE >> 3)

Crossover point for PLUQ factorization.

Function Documentation

rci_t _mzd_ple	(	mzd_t *	A,
		mzp_t *	P,
		mzp_t *	Qt,
		const int	cutoff
	)

PLE matrix decomposition.

See mzd_ple() for details.

Parameters

A	Input matrix
P	Output row mzp_t matrix
Qt	Output column mzp_t matrix
cutoff	Minimal dimension for Strassen recursion.

See also

mzd_ple()

Returns

Rank of A.

rci_t _mzd_ple_naive	(	mzd_t *	A,
		mzp_t *	P,
		mzp_t *	Qt
	)

PLE matrix decomposition (naive base case).

See mzd_ple() for details.

Parameters

A	Input matrix
P	Output row mzp_t matrix
Qt	Output column mzp_t matrix

See also

mzd_ple()

Returns

Rank of A.

rci_t _mzd_pluq	(	mzd_t *	A,
		mzp_t *	P,
		mzp_t *	Q,
		const int	cutoff
	)

PLUQ matrix decomposition.

See mzd_pluq() for details.

Parameters

A	Input matrix
P	Output row mzp_t matrix
Q	Output column mzp_t matrix
cutoff	Minimal dimension for Strassen recursion.

See also

mzd_pluq()

Returns

Rank of A.

rci_t _mzd_pluq_naive	(	mzd_t *	A,
		mzp_t *	P,
		mzp_t *	Q
	)

PLUQ matrix decomposition (naive base case).

See mzd_pluq() for details.

Parameters

A	Input matrix
P	Output row mzp_t matrix
Q	Output column mzp_t matrix

See also

mzd_pluq()

Returns

Rank of A.

rci_t mzd_ple	(	mzd_t *	A,
		mzp_t *	P,
		mzp_t *	Q,
		const int	cutoff
	)

PLE matrix decomposition.

Computes the PLE matrix decomposition using a block recursive algorithm.

Returns (P,L,S,Q) satisfying PLE = 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.

P and Q must be preallocated but they don't have to be identity permutations. If cutoff is zero a value is chosen automatically. It is recommended to set cutoff to zero for most applications.

This is the wrapper function including bounds checks. See _mzd_ple() for implementation details.

Parameters

A	Input m x n matrix
P	Output row permutation of length m
Q	Output column permutation matrix of length n
cutoff	Minimal dimension for Strassen recursion.

See also

_mzd_ple() _mzd_pluq() _mzd_pluq_mmpf() mzd_echelonize_pluq()

Returns

Rank of A.

rci_t mzd_pluq	(	mzd_t *	A,
		mzp_t *	P,
		mzp_t *	Q,
		const int	cutoff
	)

PLUQ matrix decomposition.

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.

P and Q must be preallocated but they don't have to be identity permutations. If cutoff is zero a value is chosen automatically. It is recommended to set cutoff to zero for most applications.

The row echelon form (not reduced) can be read from the upper triangular matrix U. See mzd_echelonize_pluq() for details.

This is the wrapper function including bounds checks. See _mzd_pluq() for implementation details.

Parameters

A	Input m x n matrix
P	Output row permutation of length m
Q	Output column permutation matrix of length n
cutoff	Minimal dimension for Strassen recursion.

See also

_mzd_pluq() _mzd_pluq_mmpf() mzd_echelonize_pluq()

Returns

Rank of A.

Examples:

testsuite/test_ple.c.