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/*
Copyright (C) 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 "test_helpers.h"
#include "perm.h"
#include "nmod.h"
#include "nmod_mat.h"
int check_rref_form(slong * perm, nmod_mat_t A, slong rank)
{
slong i, j, k, prev_pivot;
/* bottom should be zero */
for (i = rank; i < A->r; i++)
for (j = 0; j < A->c; j++)
if (nmod_mat_entry(A, i, j) != 0)
return 0;
prev_pivot = -1;
for (i = 0; i < rank; i++)
{
for (j = 0; j < A->c; j++)
{
if (nmod_mat_entry(A, i, j) != 0)
{
/* pivot should have a higher column index than previous */
if (j <= prev_pivot)
return 0;
/* column should be 0 ... 0 1 0 ... 0 */
for (k = 0; k < rank; k++)
if (nmod_mat_entry(A, k, j) != (i == k))
return 0;
prev_pivot = j;
break;
}
}
}
return 1;
}
TEST_FUNCTION_START(nmod_mat_rref, state)
{
slong i;
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
nmod_mat_t A, B, C, D;
ulong mod;
slong j, k, m, n, rank1, rank2;
slong *perm;
int equal;
ulong c;
mod = n_randtest_prime(state, 0);
m = n_randint(state, 20);
n = n_randint(state, 20);
perm = _perm_init(2*m);
nmod_mat_init(A, m, n, mod);
nmod_mat_init(D, 2*m, n, mod);
nmod_mat_randtest(A, state);
nmod_mat_init_set(B, A);
nmod_mat_init_set(C, A);
rank1 = nmod_mat_rref(B);
if (!check_rref_form(perm, B, rank1))
TEST_FUNCTION_FAIL(
"Malformed rref\n"
"A = %{nmod_mat}\n"
"B = %{nmod_mat}\n",
A, B);
/* Concatenate the original matrix with the rref, scramble the rows,
and check that the rref is the same */
_perm_randtest(perm, 2 * m, state);
for (j = 0; j < m; j++)
{
do { c = n_randint(state, mod); } while (c == 0);
for (k = 0; k < n; k++)
nmod_mat_entry(D, perm[j], k) =
nmod_mul(nmod_mat_entry(A, j, k), c, A->mod);
}
for (j = 0; j < m; j++)
{
do { c = n_randint(state, mod); } while (c == 0);
for (k = 0; k < n; k++)
nmod_mat_entry(D, perm[m + j], k) =
nmod_mul(nmod_mat_entry(B, j, k), c, A->mod);
}
rank2 = nmod_mat_rref(D);
equal = (rank1 == rank2);
if (equal)
{
for (j = 0; j < rank2; j++)
for (k = 0; k < n; k++)
equal = equal && (nmod_mat_entry(B, j, k) ==
nmod_mat_entry(D, j, k));
for (j = rank2; j < 2 * rank2; j++)
for (k = 0; k < n; k++)
equal = equal && (nmod_mat_entry(D, j, k) == 0);
}
if (!equal)
TEST_FUNCTION_FAIL(
"rank1 = %wd, rank2 = %wd\n"
"A = %{nmod_mat}\n"
"B = %{nmod_mat}\n"
"D = %{nmod_mat}\n",
rank1, rank2, A, B, D);
_perm_clear(perm);
nmod_mat_clear(A);
nmod_mat_clear(B);
nmod_mat_clear(C);
nmod_mat_clear(D);
}
TEST_FUNCTION_END(state);
}