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

92 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 "fmpz_mat.h"
slong
fmpz_mat_nullspace(fmpz_mat_t res, const fmpz_mat_t mat)
{
slong i, j, k, n, rank, nullity;
slong * pivots;
slong * nonpivots;
fmpz_mat_t tmp;
fmpz_t den;
n = mat->c;
fmpz_mat_init_set(tmp, mat);
fmpz_init(den);
rank = fmpz_mat_rref(tmp, den, mat);
nullity = n - rank;
fmpz_mat_zero(res);
if (rank == 0)
{
for (i = 0; i < nullity; i++)
fmpz_one(res->rows[i] + i);
}
else if (nullity)
{
pivots = flint_malloc(rank * sizeof(slong));
nonpivots = flint_malloc(nullity * sizeof(slong));
for (i = j = k = 0; i < rank; i++)
{
while (fmpz_is_zero(tmp->rows[i] + j))
{
nonpivots[k] = j;
k++;
j++;
}
pivots[i] = j;
j++;
}
while (k < nullity)
{
nonpivots[k] = j;
k++;
j++;
}
fmpz_set(den, tmp->rows[0] + pivots[0]);
for (i = 0; i < nullity; i++)
{
for (j = 0; j < rank; j++)
fmpz_set(res->rows[pivots[j]] + i, tmp->rows[j] + nonpivots[i]);
fmpz_neg(res->rows[nonpivots[i]] + i, den);
}
flint_free(pivots);
flint_free(nonpivots);
}
fmpz_clear(den);
fmpz_mat_clear(tmp);
return nullity;
}