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/*
Copyright (C) 2011-2012 Fredrik Johansson
This file is part of FLINT.
FLINT is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include "fmpz.h"
#include "fmpz_mat.h"
slong
fmpz_mat_rref_fflu(fmpz_mat_t R, fmpz_t den, const fmpz_mat_t A)
{
slong i, j, k, m, n, rank;
slong *pivots, *nonpivots;
rank = fmpz_mat_fflu(R, den, NULL, A, 0);
m = fmpz_mat_nrows(R);
n = fmpz_mat_ncols(R);
/* clear bottom */
for (i = rank; i < m; i++)
for (j = 0; j < n; j++)
fmpz_zero(fmpz_mat_entry(R, i, j));
/* Convert row echelon form to reduced row echelon form */
if (rank > 1)
{
fmpz_t tmp;
fmpz_init(tmp);
pivots = flint_malloc(sizeof(slong) * n);
nonpivots = pivots + rank;
for (i = j = k = 0; i < rank; i++)
{
while (fmpz_is_zero(fmpz_mat_entry(R, i, j)))
{
nonpivots[k] = j;
k++;
j++;
}
pivots[i] = j;
j++;
}
while (k < n - rank)
{
nonpivots[k] = j;
k++;
j++;
}
for (k = 0; k < n - rank; k++)
{
for (i = rank - 2; i >= 0; i--)
{
fmpz_mul(tmp, den, fmpz_mat_entry(R, i, nonpivots[k]));
for (j = i + 1; j < rank; j++)
{
fmpz_submul(tmp, fmpz_mat_entry(R, i, pivots[j]),
fmpz_mat_entry(R, j, nonpivots[k]));
}
fmpz_divexact(fmpz_mat_entry(R, i, nonpivots[k]),
tmp, fmpz_mat_entry(R, i, pivots[i]));
}
}
/* clear pivot columns */
for (i = 0; i < rank; i++)
{
for (j = 0; j < rank; j++)
{
if (i == j)
fmpz_set(fmpz_mat_entry(R, j, pivots[i]), den);
else
fmpz_zero(fmpz_mat_entry(R, j, pivots[i]));
}
}
flint_free(pivots);
fmpz_clear(tmp);
}
return rank;
}