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/*
Copyright (C) 2020 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 "ca_mat.h"
int
ca_mat_rref_fflu(slong * res_rank, ca_mat_t R, const ca_mat_t A, ca_ctx_t ctx)
{
slong i, j, k, m, n, rank;
slong *pivots, *nonpivots;
ca_t den;
int success;
ca_init(den, ctx);
success = ca_mat_fflu(&rank, NULL, R, den, A, 0, ctx);
if (!success)
{
ca_clear(den, ctx);
return 0;
}
m = ca_mat_nrows(R);
n = ca_mat_ncols(R);
/* clear bottom */
for (i = rank; i < m; i++)
for (j = 0; j < n; j++)
ca_zero(ca_mat_entry(R, i, j), ctx);
/* Convert row echelon form to reduced row echelon form */
if (rank > 1)
{
ca_t t, u;
ca_init(t, ctx);
ca_init(u, ctx);
pivots = flint_malloc(sizeof(slong) * n);
nonpivots = pivots + rank;
for (i = j = k = 0; i < rank; i++)
{
while (1)
{
/* Todo: this should not be T_UNKNOWN. Should we save
the pivot data in the lu algorithm? */
truth_t is_zero = ca_check_is_zero(ca_mat_entry(R, i, j), ctx);
if (is_zero == T_FALSE)
{
break;
}
else if (is_zero == T_TRUE)
{
nonpivots[k] = j;
k++;
j++;
}
else
{
success = 0;
goto cleanup1;
}
}
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--)
{
ca_mul(t, den, ca_mat_entry(R, i, nonpivots[k]), ctx);
for (j = i + 1; j < rank; j++)
{
ca_mul(u, ca_mat_entry(R, i, pivots[j]), ca_mat_entry(R, j, nonpivots[k]), ctx);
ca_sub(t, t, u, ctx);
}
ca_div(ca_mat_entry(R, i, nonpivots[k]), t, ca_mat_entry(R, i, pivots[i]), ctx);
}
}
/* clear pivot columns */
for (i = 0; i < rank; i++)
{
for (j = 0; j < rank; j++)
{
if (i == j)
ca_one(ca_mat_entry(R, j, pivots[i]), ctx);
else
ca_zero(ca_mat_entry(R, j, pivots[i]), ctx);
}
}
/* divide out denominator */
if (ca_check_is_one(den, ctx) != T_TRUE)
for (i = 0; i < rank; i++)
for (j = 0; j < n - rank; j++)
ca_div(ca_mat_entry(R, i, nonpivots[j]), ca_mat_entry(R, i, nonpivots[j]), den, ctx);
cleanup1:
flint_free(pivots);
ca_clear(t, ctx);
ca_clear(u, ctx);
}
else if (rank == 1 && ca_check_is_one(den, ctx) != T_TRUE)
{
for (i = 0; i < n; i++)
ca_div(ca_mat_entry(R, 0, i), ca_mat_entry(R, 0, i), den, ctx);
}
ca_clear(den, ctx);
*res_rank = rank;
return success;
}