pqc/external/flint-2.4.3/nmod_mat/rref.c

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2014-05-18 22:03:37 +00:00
/*=============================================================================
This file is part of FLINT.
FLINT is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
FLINT 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.
You should have received a copy of the GNU General Public License
along with FLINT; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2011 Fredrik Johansson
******************************************************************************/
#include <stdlib.h>
#include <gmp.h>
#include "flint.h"
#include "nmod_mat.h"
#include "perm.h"
slong
nmod_mat_rref(nmod_mat_t A)
{
slong i, j, k, n, rank;
slong * pivots;
slong * nonpivots;
slong * P;
nmod_mat_t U, V;
n = A->c;
P = _perm_init(nmod_mat_nrows(A));
rank = nmod_mat_lu(P, A, 0);
_perm_clear(P);
if (rank == 0)
return rank;
/* Clear L */
for (i = 0; i < A->r; i++)
for (j = 0; j < FLINT_MIN(i, rank); j++)
nmod_mat_entry(A, i, j) = UWORD(0);
/* We now reorder U to proper upper triangular form U | V
with U full-rank triangular, set V = U^(-1) V, and then
put the column back in the original order.
An improvement for some matrices would be to compress V by
discarding columns containing nothing but zeros. */
nmod_mat_init(U, rank, rank, A->mod.n);
nmod_mat_init(V, rank, n - rank, A->mod.n);
pivots = flint_malloc(sizeof(slong) * rank);
nonpivots = flint_malloc(sizeof(slong) * (n - rank));
for (i = j = k = 0; i < rank; i++)
{
while (nmod_mat_entry(A, i, j) == UWORD(0))
{
nonpivots[k] = j;
k++;
j++;
}
pivots[i] = j;
j++;
}
while (k < n - rank)
{
nonpivots[k] = j;
k++;
j++;
}
for (i = 0; i < rank; i++)
{
for (j = 0; j <= i; j++)
nmod_mat_entry(U, j, i) = nmod_mat_entry(A, j, pivots[i]);
}
for (i = 0; i < n - rank; i++)
{
for (j = 0; j < rank; j++)
nmod_mat_entry(V, j, i) = nmod_mat_entry(A, j, nonpivots[i]);
}
nmod_mat_solve_triu(V, U, V, 0);
/* Clear pivot columns */
for (i = 0; i < rank; i++)
{
for (j = 0; j <= i; j++)
nmod_mat_entry(A, j, pivots[i]) = (i == j);
}
/* Write back the actual content */
for (i = 0; i < n - rank; i++)
{
for (j = 0; j < rank; j++)
nmod_mat_entry(A, j, nonpivots[i]) = nmod_mat_entry(V, j, i);
}
nmod_mat_clear(U);
nmod_mat_clear(V);
flint_free(pivots);
flint_free(nonpivots);
return rank;
}