pqc/external/flint-2.4.3/fq_mat_templates/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
Copyright (C) 2013 Mike Hansen
******************************************************************************/
#ifdef T
#include "templates.h"
#include <stdlib.h>
#include <gmp.h>
#include "flint.h"
#include "perm.h"
slong
TEMPLATE(T, mat_rref) (TEMPLATE(T, mat_t) A, const TEMPLATE(T, ctx_t) ctx)
{
slong i, j, k, n, rank;
slong *pivots;
slong *nonpivots;
slong *P;
TEMPLATE(T, struct) * e;
TEMPLATE(T, mat_t) U, V;
n = A->c;
P = _perm_init(TEMPLATE(T, mat_nrows) (A, ctx));
rank = TEMPLATE(T, mat_lu) (P, A, 0, ctx);
_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++)
TEMPLATE(T, zero) (TEMPLATE(T, mat_entry) (A, i, j), ctx);
/* 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. */
TEMPLATE(T, mat_init) (U, rank, rank, ctx);
TEMPLATE(T, mat_init) (V, rank, n - rank, ctx);
pivots = flint_malloc(sizeof(slong) * rank);
nonpivots = flint_malloc(sizeof(slong) * (n - rank));
for (i = j = k = 0; i < rank; i++)
{
while (TEMPLATE(T, is_zero) (TEMPLATE(T, mat_entry) (A, i, j), ctx))
{
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++)
{
e = TEMPLATE(T, mat_entry) (A, j, pivots[i]);
TEMPLATE(T, mat_entry_set) (U, j, i, e, ctx);
}
}
for (i = 0; i < n - rank; i++)
{
for (j = 0; j < rank; j++)
{
e = TEMPLATE(T, mat_entry) (A, j, nonpivots[i]);
TEMPLATE(T, mat_entry_set) (V, j, i, e, ctx);
}
}
TEMPLATE(T, mat_solve_triu) (V, U, V, 0, ctx);
/* Clear pivot columns */
for (i = 0; i < rank; i++)
{
for (j = 0; j <= i; j++)
{
if (i == j)
{
TEMPLATE(T, one) (TEMPLATE(T, mat_entry) (A, j, pivots[i]),
ctx);
}
else
{
TEMPLATE(T, zero) (TEMPLATE(T, mat_entry) (A, j, pivots[i]),
ctx);
}
}
}
/* Write back the actual content */
for (i = 0; i < n - rank; i++)
{
for (j = 0; j < rank; j++)
TEMPLATE(T, mat_entry_set) (A, j, nonpivots[i],
TEMPLATE(T, mat_entry) (V, j, i), ctx);
}
TEMPLATE(T, mat_clear) (U, ctx);
TEMPLATE(T, mat_clear) (V, ctx);
flint_free(pivots);
flint_free(nonpivots);
return rank;
}
#endif