/usr/include/m4rie/ple.h is in libm4rie-dev 20150908-1.
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* \file ple.h
* \brief PLE decomposition: \f$ L \cdot E = P \cdot A\f$.
*
* \author Martin Albrecht <martinralbrecht@googlemail.com>
*/
#ifndef M4RIE_PLE_H
#define M4RIE_PLE_H
/******************************************************************************
*
* M4RIE: Linear Algebra over GF(2^e)
*
* Copyright (C) 2011 Martin Albrecht <martinralbrecht@googlemail.com>
*
* Distributed under the terms of the GNU General Public License (GEL)
* version 2 or higher.
*
* This code is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* The full text of the GPL is available at:
*
* http://www.gnu.org/licenses/
******************************************************************************/
#include <m4ri/m4ri.h>
#include <m4rie/mzed.h>
#include <m4rie/mzd_slice.h>
#include <m4rie/conversion.h>
/**
* \brief PLE decomposition: \f$ L \cdot E = P \cdot A \f$.
*
* Modifies A in place to store lower triangular L below (and on) the
* main diagonal and E -- an echelon form of A -- above the main
* diagonal (pivots are stored in Q). P and Q are updated with row and
* column permutations respectively.
*
* This function uses naive cubic PLE decomposition depending on the
* size of the underlying field.
*
* \param A Matrix
* \param P Permutation vector of length A->nrows
* \param Q Permutation vector of length A->ncols
*
* \ingroup PLE
*
* \sa mzed_ple_newton_john() mzed_ple()
*/
rci_t mzed_ple_naive(mzed_t *A, mzp_t *P, mzp_t *Q);
/**
* \brief PLE decomposition: \f$ L \cdot E = P \cdot A \f$.
*
* Modifies A in place to store lower triangular L below (and on) the
* main diagonal and E -- an echelon form of A -- above the main
* diagonal (pivots are stored in Q). P and Q are updated with row and
* column permutations respectively.
*
* This function uses either asymptotically fast PLE decomposition by
* reducing it to matrix multiplication or naive cubic PLE
* decomposition depending on the size of the underlying field. If
* asymptotically fast PLE decomposition is used, then the algorithm
* switches to mzed_ple_newton_john if e * ncols * nrows is <= cutoff
* where e is the exponent of the finite field.
*
* \param A Matrix
* \param P Permutation vector of length A->nrows
* \param Q Permutation vector of length A->ncols
* \param cutoff Integer
*
* \ingroup PLE
*
* \sa mzed_ple_naive() mzed_ple_newton_john() mzed_ple()
*/
rci_t _mzd_slice_ple(mzd_slice_t *A, mzp_t *P, mzp_t *Q, rci_t cutoff);
/**
* \brief PLE decomposition: \f$ L \cdot E = P \cdot A \f$.
*
* Modifies A in place to store lower triangular L below (and on) the
* main diagonal and E -- an echelon form of A -- above the main
* diagonal (pivots are stored in Q). P and Q are updated with row and
* column permutations respectively.
*
* This function implements asymptotically fast PLE decomposition by
* reducing it to matrix multiplication.
*
* \param A Matrix
* \param P Permutation vector of length A->nrows
* \param Q Permutation vector of length A->ncols
*
* \ingroup PLE
*
* \sa mzed_ple_naive() mzed_ple_newton_john() _mzd_slice_ple()
*/
static inline rci_t mzd_slice_ple(mzd_slice_t *A, mzp_t *P, mzp_t *Q) {
assert(P->length == A->nrows);
assert(Q->length == A->ncols);
return _mzd_slice_ple(A, P, Q, 0);
}
/**
* \brief PLUQ decomposition: \f$ L \cdot U \cdot Q = P \cdot A\f$.
*
* This function implements asymptotically fast PLE decomposition by
* reducing it to matrix multiplication. From PLE the PLUQ
* decomposition is then obtained.
*
* \param A Matrix
* \param P Permutation vector of length A->nrows
* \param Q Permutation vector of length A->ncols
* \param cutoff Crossover to base case if mzed_t::w * mzed_t::ncols * mzed_t::nrows < cutoff.
*
* \ingroup PLE
*/
rci_t _mzd_slice_pluq(mzd_slice_t *A, mzp_t *P, mzp_t *Q, rci_t cutoff);
/**
* \brief PLUQ decomposition: \f$ L \cdot U \cdot Q = P \cdot A\f$.
*
* This function implements asymptotically fast PLE decomposition by
* reducing it to matrix multiplication. From PLE the PLUQ
* decomposition is then obtained.
*
* \param A Matrix
* \param P Permutation vector of length A->nrows
* \param Q Permutation vector of length A->ncols
*
* \ingroup PLE
*/
static inline rci_t mzd_slice_pluq(mzd_slice_t *A, mzp_t *P, mzp_t *Q) {
assert(P->length == A->nrows);
assert(Q->length == A->ncols);
return _mzd_slice_pluq(A, P, Q, 0);
}
/**
* \brief PLE decomposition: \f$ L \cdot E = P \cdot A \f$.
*
* Modifies A in place to store lower triangular L below (and on) the
* main diagonal and E -- an echelon form of A -- above the main
* diagonal (pivots are stored in Q). P and Q are updated with row and
* column permutations respectively.
*
* This function uses either asymptotically fast PLE decomposition by
* reducing it to matrix multiplication or naive cubic PLE
* decomposition depending on the size of the underlying field. If
* asymptotically fast PLE decomposition is used, then the algorithm
* switches to mzed_ple_newton_john if e * ncols * nrows is <= cutoff
* where e is the exponent of the finite field.
*
* \param A Matrix
* \param P Permutation vector of length A->nrows
* \param Q Permutation vector of length A->ncols
* \param cutoff Integer >= 0
*
* \ingroup PLE
*
* \sa mzed_ple_naive() mzed_ple_newton_john() _mzed_ple()
*/
rci_t _mzed_ple(mzed_t *A, mzp_t *P, mzp_t *Q, rci_t cutoff);
/**
* Default crossover to PLE base case (Newton-John based).
*/
#define __M4RIE_PLE_CUTOFF (__M4RI_CPU_L2_CACHE<<2)
/**
* \brief PLE decomposition: \f$ L \cdot E = P \cdot A \f$.
*
* Modifies A in place to store lower triangular L below (and on) the
* main diagonal and E -- an echelon form of A -- above the main
* diagonal (pivots are stored in Q). P and Q are updated with row and
* column permutations respectively.
*
* This function uses either asymptotically fast PLE decomposition by
* reducing it to matrix multiplication or naive cubic PLE
* decomposition depending on the size of the underlying field.
*
* \param A Matrix
* \param P Permutation vector of length A->nrows
* \param Q Permutation vector of length A->ncols
*
* \ingroup PLE
*
* \sa mzed_ple_naive() mzed_ple_newton_john() _mzed_ple()
*
*/
static inline rci_t mzed_ple(mzed_t *A, mzp_t *P, mzp_t *Q) {
return _mzed_ple(A, P, Q, __M4RIE_PLE_CUTOFF);
}
#endif //M4RIE_PLE_H
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