123 lines
3.2 KiB
C
123 lines
3.2 KiB
C
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/*=============================================================================
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This file is part of FLINT.
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FLINT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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FLINT 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
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with FLINT; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2011 Fredrik Johansson
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******************************************************************************/
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#include <stdlib.h>
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#include <gmp.h>
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#include "flint.h"
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#include "nmod_mat.h"
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#include "perm.h"
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slong
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nmod_mat_rref(nmod_mat_t A)
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{
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slong i, j, k, n, rank;
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slong * pivots;
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slong * nonpivots;
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slong * P;
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nmod_mat_t U, V;
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n = A->c;
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P = _perm_init(nmod_mat_nrows(A));
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rank = nmod_mat_lu(P, A, 0);
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_perm_clear(P);
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if (rank == 0)
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return rank;
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/* Clear L */
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for (i = 0; i < A->r; i++)
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for (j = 0; j < FLINT_MIN(i, rank); j++)
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nmod_mat_entry(A, i, j) = UWORD(0);
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/* We now reorder U to proper upper triangular form U | V
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with U full-rank triangular, set V = U^(-1) V, and then
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put the column back in the original order.
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An improvement for some matrices would be to compress V by
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discarding columns containing nothing but zeros. */
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nmod_mat_init(U, rank, rank, A->mod.n);
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nmod_mat_init(V, rank, n - rank, A->mod.n);
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pivots = flint_malloc(sizeof(slong) * rank);
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nonpivots = flint_malloc(sizeof(slong) * (n - rank));
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for (i = j = k = 0; i < rank; i++)
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{
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while (nmod_mat_entry(A, i, j) == UWORD(0))
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{
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nonpivots[k] = j;
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k++;
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j++;
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}
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pivots[i] = j;
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j++;
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}
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while (k < n - rank)
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{
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nonpivots[k] = j;
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k++;
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j++;
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}
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for (i = 0; i < rank; i++)
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{
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for (j = 0; j <= i; j++)
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nmod_mat_entry(U, j, i) = nmod_mat_entry(A, j, pivots[i]);
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}
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for (i = 0; i < n - rank; i++)
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{
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for (j = 0; j < rank; j++)
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nmod_mat_entry(V, j, i) = nmod_mat_entry(A, j, nonpivots[i]);
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}
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nmod_mat_solve_triu(V, U, V, 0);
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/* Clear pivot columns */
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for (i = 0; i < rank; i++)
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{
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for (j = 0; j <= i; j++)
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nmod_mat_entry(A, j, pivots[i]) = (i == j);
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}
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/* Write back the actual content */
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for (i = 0; i < n - rank; i++)
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{
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for (j = 0; j < rank; j++)
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nmod_mat_entry(A, j, nonpivots[i]) = nmod_mat_entry(V, j, i);
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}
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nmod_mat_clear(U);
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nmod_mat_clear(V);
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flint_free(pivots);
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flint_free(nonpivots);
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return rank;
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}
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