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/*
Copyright (C) 2012 Fredrik Johansson
Copyright (C) 2013 Mike Hansen
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/>.
*/
#ifdef T
#include "test_helpers.h"
#include "templates.h"
#include "perm.h"
int
check_rref_form(slong * perm, TEMPLATE(T, mat_t) A, slong rank,
const TEMPLATE(T, ctx_t) ctx)
{
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 (!TEMPLATE(T, is_zero) (TEMPLATE(T, mat_entry) (A, i, j), ctx))
return 0;
prev_pivot = -1;
for (i = 0; i < rank; i++)
{
for (j = 0; j < A->c; j++)
{
if (!TEMPLATE(T, is_zero) (TEMPLATE(T, mat_entry) (A, i, j), ctx))
{
/* 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 (i == k)
{
if (!TEMPLATE(T, is_one)
(TEMPLATE(T, mat_entry) (A, k, j), ctx))
return 0;
}
else
{
if (!TEMPLATE(T, is_zero)
(TEMPLATE(T, mat_entry) (A, k, j), ctx))
return 0;
}
}
prev_pivot = j;
break;
}
}
}
return 1;
}
TEST_TEMPLATE_FUNCTION_START(T, mat_rref, state)
{
slong i;
for (i = 0; i < 10 * flint_test_multiplier(); i++)
{
TEMPLATE(T, ctx_t) ctx;
TEMPLATE(T, mat_t) A, B, C, D;
TEMPLATE(T, t) c;
slong j, k, m, n, rank1, rank2;
slong *perm;
int equal;
TEMPLATE(T, ctx_init_randtest)(ctx, state, 3);
TEMPLATE(T, init) (c, ctx);
m = n_randint(state, 20);
n = n_randint(state, 20);
perm = _perm_init(2 * m);
TEMPLATE(T, mat_init) (A, m, n, ctx);
TEMPLATE(T, mat_init) (D, 2 * m, n, ctx);
TEMPLATE(T, mat_randtest) (A, state, ctx);
TEMPLATE(T, mat_init_set) (B, A, ctx);
TEMPLATE(T, mat_init_set) (C, A, ctx);
rank1 = TEMPLATE(T, mat_rref) (B, B, ctx);
if (!check_rref_form(perm, B, rank1, ctx))
{
printf("FAIL (malformed rref)\n");
TEMPLATE(T, mat_print_pretty) (A, ctx);
printf("\n\n");
TEMPLATE(T, mat_print_pretty) (B, ctx);
printf("\n\n");
fflush(stdout);
flint_abort();
}
/* 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++)
{
TEMPLATE(T, randtest_not_zero) (c, state, ctx);
for (k = 0; k < n; k++)
{
TEMPLATE(T, mul) (TEMPLATE(T, mat_entry) (D, perm[j], k),
TEMPLATE(T, mat_entry) (A, j, k), c, ctx);
}
}
for (j = 0; j < m; j++)
{
TEMPLATE(T, randtest_not_zero) (c, state, ctx);
for (k = 0; k < n; k++)
{
TEMPLATE(T, mul) (TEMPLATE(T, mat_entry) (D, perm[m + j], k),
TEMPLATE(T, mat_entry) (B, j, k), c, ctx);
}
}
rank2 = TEMPLATE(T, mat_rref) (D, D, ctx);
equal = (rank1 == rank2);
if (equal)
{
for (j = 0; j < rank2; j++)
for (k = 0; k < n; k++)
{
equal = equal
&& TEMPLATE(T,
equal) (TEMPLATE(T, mat_entry) (B, j, k),
TEMPLATE(T, mat_entry) (D, j, k),
ctx);
}
for (j = rank2; j < 2 * rank2; j++)
for (k = 0; k < n; k++)
{
equal = equal
&& TEMPLATE(T,
is_zero) (TEMPLATE(T, mat_entry) (D, j, k),
ctx);
}
}
if (!equal)
{
flint_printf("FAIL (rank1 = %wd, rank2 = %wd)!\n", rank1, rank2);
TEMPLATE(T, mat_print_pretty) (A, ctx);
printf("\n\n");
TEMPLATE(T, mat_print_pretty) (B, ctx);
printf("\n\n");
TEMPLATE(T, mat_print_pretty) (D, ctx);
printf("\n\n");
fflush(stdout);
flint_abort();
}
_perm_clear(perm);
TEMPLATE(T, mat_clear) (A, ctx);
TEMPLATE(T, mat_clear) (B, ctx);
TEMPLATE(T, mat_clear) (C, ctx);
TEMPLATE(T, mat_clear) (D, ctx);
TEMPLATE(T, clear) (c, ctx);
TEMPLATE(T, ctx_clear) (ctx);
}
TEST_FUNCTION_END(state);
}
#endif