143 lines
5.0 KiB
C
143 lines
5.0 KiB
C
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/**
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* \file solve.h
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*
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* \brief System solving with matrix routines.
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*
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* \author Jean-Guillaume Dumas <Jean-Guillaume.Dumas@imag.fr>
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*
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*/
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#ifndef M4RI_SOLVE_H
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#define M4RI_SOLVE_H
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/*******************************************************************
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*
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* M4RI: Linear Algebra over GF(2)
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*
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* Copyright (C) 2008 Jean-Guillaume.Dumas@imag.fr
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*
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* Distributed under the terms of the GNU General Public License (GPL)
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*
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* This code is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* The full text of the GPL is available at:
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*
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* http://www.gnu.org/licenses/
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*
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********************************************************************/
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#include <m4ri/mzp.h>
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#include <m4ri/mzd.h>
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/**
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* \brief Solves A X = B with A and B matrices.
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*
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* The solution X is stored inplace on B.
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*
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* \param A Input matrix (overwritten).
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* \param B Input matrix, being overwritten by the solution matrix X
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* \param cutoff Minimal dimension for Strassen recursion (default: 0).
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* \param inconsistency_check decide wether or not to perform a check
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* for incosistency (faster without but output not defined if
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* system is not consistent).
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* \return 0 if a solution was found, -1 otherwise
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*/
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int mzd_solve_left(mzd_t *A, mzd_t *B, int const cutoff, int const inconsistency_check);
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/**
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* \brief Solves (P L U Q) X = B
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*
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* A is an input matrix supposed to store both:
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* \li an upper right triangular matrix U
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* \li a lower left unitary triangular matrix L.
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*
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* The solution X is stored inplace on B
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*
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* This version assumes that the matrices are at an even position on
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* the m4ri_radix grid and that their dimension is a multiple of m4ri_radix.
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*
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* \param A Input upper/lower triangular matrices.
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* \param rank is rank of A.
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* \param P Input row permutation matrix.
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* \param Q Input column permutation matrix.
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* \param B Input matrix, being overwritten by the solution matrix X.
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* \param cutoff Minimal dimension for Strassen recursion (default: 0).
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* \param inconsistency_check decide whether or not to perform a check
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* for incosistency (faster without but output not defined if
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* system is not consistent). \return 0 if a solution was
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* found, -1 otherwise
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* \return 0 if a solution was found, -1 otherwise
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*/
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int mzd_pluq_solve_left (mzd_t const *A, rci_t rank,
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mzp_t const *P, mzp_t const *Q,
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mzd_t *B, int const cutoff, int const inconsistency_check);
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/**
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* \brief Solves (P L U Q) X = B
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*
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* A is an input matrix supposed to store both:
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* \li an upper right triangular matrix U
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* \li a lower left unitary triangular matrix L.
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* The solution X is stored inplace on B.
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*
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* This version assumes that the matrices are at an even position on
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* the m4ri_radix grid and that their dimension is a multiple of m4ri_radix.
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*
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* \param A Input upper/lower triangular matrices.
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* \param rank is rank of A.
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* \param P Input row permutation matrix.
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* \param Q Input column permutation matrix.
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* \param B Input matrix, being overwritten by the solution matrix X.
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* \param cutoff Minimal dimension for Strassen recursion (default: 0).
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* \param inconsistency_check decide whether or not to perform a check
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* for incosistency (faster without but output not defined if
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* system is not consistent). \return 0 if a solution was
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* found, -1 otherwise
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* \return 0 if a solution was found, -1 otherwise
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*/
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int _mzd_pluq_solve_left(mzd_t const *A, rci_t rank,
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mzp_t const *P, mzp_t const *Q,
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mzd_t *B, int const cutoff, int const inconsistency_check);
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/**
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* \brief Solves A X = B with A and B matrices.
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*
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* The solution X is stored inplace on B.
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*
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* This version assumes that the matrices are at an even position on
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* the m4ri_radix grid and that their dimension is a multiple of m4ri_radix.
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*
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* \param A Input matrix (overwritten).
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* \param B Input matrix, being overwritten by the solution matrix X.
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* \param cutoff Minimal dimension for Strassen recursion (default: 0).
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* \param inconsistency_check decide whether or not to perform a check
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* for incosistency (faster without but output not defined if
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* system is not consistent). \return 0 if a solution was
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* found, -1 otherwise
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* \return 0 if a solution was found, -1 otherwise
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*/
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int _mzd_solve_left(mzd_t *A, mzd_t *B, int const cutoff, int const inconsistency_check);
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/**
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* \brief Solve X for A X = 0.
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*
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* If r is the rank of the nr x nc matrix A, return the nc x (nc-r)
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* matrix X such that A*X == 0 and that the columns of X are linearly
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* independent.
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*
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* \param A Input matrix (overwritten).
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* \param cutoff Minimal dimension for Strassen recursion (default: 0).
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*
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* \sa mzd_pluq()
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*
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* \return X, NULL if kernel is empty
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*/
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mzd_t *mzd_kernel_left_pluq(mzd_t *A, int const cutoff);
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#endif // M4RI_SOLVE_H
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