pqc/external/flint-2.4.3/nmod_mat/nullspace.c
2014-05-24 23:16:06 +02:00

96 lines
2.5 KiB
C

/*=============================================================================
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"
slong
nmod_mat_nullspace(nmod_mat_t X, const nmod_mat_t A)
{
slong i, j, k, m, n, rank, nullity;
slong * p;
slong * pivots;
slong * nonpivots;
nmod_mat_t tmp;
m = A->r;
n = A->c;
p = flint_malloc(sizeof(slong) * FLINT_MAX(m, n));
nmod_mat_init_set(tmp, A);
rank = nmod_mat_rref(tmp);
nullity = n - rank;
nmod_mat_zero(X);
if (rank == 0)
{
for (i = 0; i < nullity; i++)
nmod_mat_entry(X, i, i) = UWORD(1);
}
else if (nullity)
{
pivots = p; /* length = rank */
nonpivots = p + rank; /* length = nullity */
for (i = j = k = 0; i < rank; i++)
{
while (nmod_mat_entry(tmp, i, j) == UWORD(0))
{
nonpivots[k] = j;
k++;
j++;
}
pivots[i] = j;
j++;
}
while (k < nullity)
{
nonpivots[k] = j;
k++;
j++;
}
for (i = 0; i < nullity; i++)
{
for (j = 0; j < rank; j++)
{
mp_limb_t c = nmod_mat_entry(tmp, j, nonpivots[i]);
nmod_mat_entry(X, pivots[j], i) = nmod_neg(c, A->mod);
}
nmod_mat_entry(X, nonpivots[i], i) = UWORD(1);
}
}
flint_free(p);
nmod_mat_clear(tmp);
return nullity;
}