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/*
Copyright (C) 2014 Abhinav Baid
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 "fmpz.h"
#include "fmpz_mat.h"
TEST_FUNCTION_START(fmpz_mat_is_spd, state)
{
slong iter;
/* Test:
- fails for non-square matrices
- fails for non-symmetric matrices
- Gram matrices are positive definite iff full rank */
for (iter = 0; iter < 100 * flint_test_multiplier(); iter++)
{
slong n = n_randint(state, 10);
slong rk;
fmpz_mat_t A, B, C;
slong j, k;
int res;
fmpz_mat_init(A, n, n + 1 + n_randint(state, 10));
fmpz_mat_init(B, n, n);
fmpz_mat_init(C, n, n);
fmpz_mat_one(A);
if (fmpz_mat_is_spd(A))
{
flint_printf("FAIL (square)\n");
flint_abort();
}
fmpz_mat_randtest(B, state, 1 + n_randint(state, 200));
fmpz_mat_gram(B, B);
if (n > 1)
{
fmpz_mat_set(C, B);
j = n_randint(state, n - 1);
k = j + 1 + n_randint(state, n - j - 1);
fmpz_add_si(fmpz_mat_entry(C, j, k), fmpz_mat_entry(C, j, k), 1);
if (fmpz_mat_is_spd(C))
{
flint_printf("FAIL (symmetric)\n");
flint_abort();
}
}
rk = fmpz_mat_rank(B);
res = fmpz_mat_is_spd(B);
if ((rk < n && res) || (rk == n && !res))
{
flint_printf("FAIL\n");
flint_printf("n = %wd, rk = %wd, res = %wd\n", n, rk, res);
fmpz_mat_print_pretty(B);
flint_printf("\n");
flint_abort();
}
fmpz_mat_clear(A);
fmpz_mat_clear(B);
fmpz_mat_clear(C);
}
TEST_FUNCTION_END(state);
}