/usr/include/m4ri/ple.h is in libm4ri-dev 20140914-2.
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* \file ple.h
*
* \brief PLE and PLUQ matrix decomposition routines.
*
* \author Clement Pernet <clement.pernet@gmail.com>
*
*/
#ifndef M4RI_PLUQ_H
#define M4RI_PLUQ_H
/*******************************************************************
*
* M4RI: Linear Algebra over GF(2)
*
* Copyright (C) 2008, 2009 Clement Pernet <clement.pernet@gmail.com>
*
* Distributed under the terms of the GNU General Public License (GPL)
* version 2 or higher.
*
* This code 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
* General Public License for more details.
*
* The full text of the GPL is available at:
*
* http://www.gnu.org/licenses/
*
********************************************************************/
#include <m4ri/mzd.h>
#include <m4ri/mzp.h>
/**
* Crossover point for PLUQ factorization.
*/
#define __M4RI_PLE_CUTOFF MIN(524288, __M4RI_CPU_L3_CACHE >> 3)
/**
* \brief 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.
*
* \param A Input m x n matrix
* \param P Output row permutation of length m
* \param Q Output column permutation matrix of length n
* \param cutoff Minimal dimension for Strassen recursion.
*
* \sa _mzd_pluq() _mzd_pluq_mmpf() mzd_echelonize_pluq()
*
* \return Rank of A.
*/
rci_t mzd_pluq(mzd_t *A, mzp_t *P, mzp_t *Q, const int cutoff);
/**
* \brief 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.
*
* \param A Input m x n matrix
* \param P Output row permutation of length m
* \param Q Output column permutation matrix of length n
* \param cutoff Minimal dimension for Strassen recursion.
*
* \sa _mzd_ple() _mzd_pluq() _mzd_pluq_mmpf() mzd_echelonize_pluq()
*
* \return Rank of A.
*/
rci_t mzd_ple(mzd_t *A, mzp_t *P, mzp_t *Q, const int cutoff);
/**
* \brief PLUQ matrix decomposition.
*
* See mzd_pluq() for details.
*
* \param A Input matrix
* \param P Output row mzp_t matrix
* \param Q Output column mzp_t matrix
* \param cutoff Minimal dimension for Strassen recursion.
*
* \sa mzd_pluq()
*
* \return Rank of A.
*/
rci_t _mzd_pluq(mzd_t *A, mzp_t *P, mzp_t *Q, const int cutoff);
/**
* \brief PLE matrix decomposition.
*
* See mzd_ple() for details.
*
* \param A Input matrix
* \param P Output row mzp_t matrix
* \param Qt Output column mzp_t matrix
* \param cutoff Minimal dimension for Strassen recursion.
*
* \sa mzd_ple()
*
* \return Rank of A.
*/
rci_t _mzd_ple(mzd_t *A, mzp_t *P, mzp_t *Qt, const int cutoff);
/**
* \brief PLUQ matrix decomposition (naive base case).
*
* See mzd_pluq() for details.
*
* \param A Input matrix
* \param P Output row mzp_t matrix
* \param Q Output column mzp_t matrix
*
* \sa mzd_pluq()
*
* \return Rank of A.
*/
rci_t _mzd_pluq_naive(mzd_t *A, mzp_t *P, mzp_t *Q);
/**
* \brief PLE matrix decomposition (naive base case).
*
* See mzd_ple() for details.
*
* \param A Input matrix
* \param P Output row mzp_t matrix
* \param Qt Output column mzp_t matrix
*
* \sa mzd_ple()
*
* \return Rank of A.
*/
rci_t _mzd_ple_naive(mzd_t *A, mzp_t *P, mzp_t *Qt);
#endif // M4RI_PLUQ_H
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