int main()
{
slong iter;
flint_rand_t state;
flint_printf("all_pairs_longest_walk....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
{
slong m, degree;
bool_mat_t A;
fmpz_mat_t B, C, D;
m = n_randint(state, 50);
bool_mat_init(A, m, m);
fmpz_mat_init(B, m, m);
fmpz_mat_init(C, m, m);
fmpz_mat_init(D, m, m);
bool_mat_randtest(A, state);
degree = bool_mat_all_pairs_longest_walk(B, A);
/* entrywise reasonability */
if (!_is_superficially_ok_entrywise(B))
{
flint_printf("FAIL (entrywise)\n");
bool_mat_print(A); flint_printf("\n");
fmpz_mat_print_pretty(B); flint_printf("\n");
abort();
}
/* nilpotency degree */
{
slong nildegree = bool_mat_nilpotency_degree(A);
if (nildegree != degree + 1)
{
flint_printf("FAIL (nilpotency degree)\n");
bool_mat_print(A); flint_printf("\n");
fmpz_mat_print_pretty(B); flint_printf("\n");
flint_printf("nildegree=%wd degree=%wd\n", nildegree, degree);
abort();
}
}
/* transitive closure */
{
slong i, j;
bool_mat_t U, V;
bool_mat_init(U, m, m);
bool_mat_transitive_closure(U, A);
bool_mat_init(V, m, m);
for (i = 0; i < m; i++)
{
for (j = 0; j < m; j++)
{
slong x = fmpz_get_si(fmpz_mat_entry(B, i, j));
bool_mat_set_entry(V, i, j, (x != -1 && x != 0));
}
}
if (!bool_mat_equal(U, V))
{
flint_printf("FAIL (transitive closure)\n");
bool_mat_print(A); flint_printf("\n");
fmpz_mat_print_pretty(B); flint_printf("\n");
bool_mat_print(U); flint_printf("\n");
bool_mat_print(V); flint_printf("\n");
abort();
}
bool_mat_clear(U);
bool_mat_clear(V);
}
/* test commutativity of all-pairs-longest-walk with permutation */
{
bool_mat_t Ap;
slong *perm;
bool_mat_init(Ap, m, m);
perm = flint_malloc(m * sizeof(slong));
_perm_randtest(perm, m, state);
/* C is the all-pairs-longest-walk of the permutation of A */
_bool_mat_permute(Ap, A, perm);
bool_mat_all_pairs_longest_walk(C, Ap);
/* D is the permutation of the all-pairs-longest-walk of A */
_fmpz_mat_permute(D, B, perm);
if (!fmpz_mat_equal(C, D))
{
flint_printf("FAIL (permutation)\n");
bool_mat_print(A); flint_printf("\n");
fmpz_mat_print_pretty(B); flint_printf("\n");
fmpz_mat_print_pretty(C); flint_printf("\n");
fmpz_mat_print_pretty(D); flint_printf("\n");
abort();
}
flint_free(perm);
bool_mat_clear(Ap);
}
bool_mat_clear(A);
fmpz_mat_clear(B);
fmpz_mat_clear(C);
fmpz_mat_clear(D);
}
/* use powering to check small random examples */
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
{
slong m;
bool_mat_t A;
fmpz_mat_t B, C;
m = n_randint(state, 10);
bool_mat_init(A, m, m);
fmpz_mat_init(B, m, m);
fmpz_mat_init(C, m, m);
bool_mat_randtest(A, state);
bool_mat_all_pairs_longest_walk(B, A);
_brute_force_all_pairs_longest_walk(C, A);
if (!fmpz_mat_equal(B, C))
{
flint_printf("FAIL (powering)\n");
bool_mat_print(A); flint_printf("\n");
fmpz_mat_print_pretty(B); flint_printf("\n");
fmpz_mat_print_pretty(C); flint_printf("\n");
abort();
}
bool_mat_clear(A);
fmpz_mat_clear(B);
fmpz_mat_clear(C);
}
/* special matrices */
{
slong m;
for (m = 1; m < 100; m++)
{
slong i, j, length;
bool_mat_t A;
fmpz_mat_t B;
bool_mat_init(A, m, m);
fmpz_mat_init(B, m, m);
/* directed path */
{
bool_mat_directed_path(A);
length = bool_mat_all_pairs_longest_walk(B, A);
if (length != m-1)
{
flint_printf("FAIL (directed path)\n");
bool_mat_print(A); flint_printf("\n");
fmpz_mat_print_pretty(B); flint_printf("\n");
flint_printf("m=%wd length=%wd\n", m, length);
abort();
}
for (i = 0; i < m; i++)
{
for (j = 0; j < m; j++)
{
if (fmpz_get_si(fmpz_mat_entry(B, i, j)) !=
FLINT_MAX(-1, j - i))
{
flint_printf("FAIL (directed path)\n");
bool_mat_print(A); flint_printf("\n");
fmpz_mat_print_pretty(B); flint_printf("\n");
abort();
}
}
}
}
/* directed cycle */
{
bool_mat_directed_cycle(A);
length = bool_mat_all_pairs_longest_walk(B, A);
if (length != -2)
{
flint_printf("FAIL (directed cycle)\n");
bool_mat_print(A); flint_printf("\n");
fmpz_mat_print_pretty(B); flint_printf("\n");
flint_printf("m=%wd length=%wd\n", m, length);
abort();
}
for (i = 0; i < m; i++)
{
for (j = 0; j < m; j++)
{
if (fmpz_get_si(fmpz_mat_entry(B, i, j)) != -2)
{
flint_printf("FAIL (directed cycle)\n");
bool_mat_print(A); flint_printf("\n");
fmpz_mat_print_pretty(B); flint_printf("\n");
abort();
}
}
}
}
bool_mat_clear(A);
fmpz_mat_clear(B);
}
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("trace....");
fflush(stdout);
flint_randinit(state);
/* trace(empty) == 0 */
{
bool_mat_t A;
bool_mat_init(A, 0, 0);
bool_mat_one(A);
if (bool_mat_trace(A) != 0)
{
flint_printf("FAIL (empty)\n");
flint_printf("A = \n"); bool_mat_print(A); flint_printf("\n\n");
abort();
}
bool_mat_clear(A);
}
/* trace(zero) == 0 */
{
slong n;
bool_mat_t A;
for (n = 1; n < 10; n++)
{
bool_mat_init(A, n, n);
bool_mat_zero(A);
if (bool_mat_trace(A) != 0)
{
flint_printf("FAIL (zero)\n");
flint_printf("A = \n"); bool_mat_print(A); flint_printf("\n\n");
abort();
}
bool_mat_clear(A);
}
}
/* trace(one) == 1 */
{
slong n;
bool_mat_t A;
for (n = 1; n < 10; n++)
{
bool_mat_init(A, n, n);
bool_mat_one(A);
if (bool_mat_trace(A) != 1)
{
flint_printf("FAIL (one)\n");
flint_printf("A = \n"); bool_mat_print(A); flint_printf("\n\n");
abort();
}
bool_mat_clear(A);
}
}
/* traces of random matrices with modified diagonal */
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
slong n, i;
bool_mat_t A;
n = n_randint(state, 10) + 1;
bool_mat_init(A, n, n);
bool_mat_randtest(A, state);
i = (slong) n_randint(state, n);
bool_mat_set_entry(A, i, i, 1);
if (bool_mat_trace(A) != 1)
{
flint_printf("FAIL (diagonal has a non-zero entry)\n");
flint_printf("A = \n"); bool_mat_print(A); flint_printf("\n\n");
abort();
}
for (i = 0; i < n; i++)
{
bool_mat_set_entry(A, i, i, 0);
}
if (bool_mat_trace(A) != 0)
{
flint_printf("FAIL (diagonal is zero)\n");
flint_printf("A = \n"); bool_mat_print(A); flint_printf("\n\n");
abort();
}
bool_mat_clear(A);
}
/* trace(A + B) == trace(A) + trace(B) */
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
slong n;
bool_mat_t A, B, C;
n = n_randint(state, 10);
bool_mat_init(A, n, n);
bool_mat_init(B, n, n);
bool_mat_init(C, n, n);
bool_mat_randtest(A, state);
bool_mat_randtest(B, state);
bool_mat_add(C, A, B);
if (bool_mat_trace(C) != (bool_mat_trace(A) | bool_mat_trace(B)))
{
flint_printf("FAIL (trace(A+B) == trace(A) | trace(B))\n");
flint_printf("A = \n"); bool_mat_print(A); flint_printf("\n\n");
flint_printf("B = \n"); bool_mat_print(B); flint_printf("\n\n");
flint_printf("A+B = \n"); bool_mat_print(C); flint_printf("\n\n");
abort();
}
bool_mat_clear(A);
bool_mat_clear(B);
bool_mat_clear(C);
}
/* trace(A*B) == trace(B*A) */
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
slong n, m;
bool_mat_t A, B, AB, BA;
n = n_randint(state, 10);
m = n_randint(state, 10);
bool_mat_init(A, n, m);
bool_mat_init(B, m, n);
bool_mat_init(AB, n, n);
bool_mat_init(BA, m, m);
bool_mat_randtest(A, state);
bool_mat_randtest(B, state);
bool_mat_mul(AB, A, B);
bool_mat_mul(BA, B, A);
if (bool_mat_trace(AB) != bool_mat_trace(BA))
{
flint_printf("FAIL (trace(AB) == trace(BA))\n");
flint_printf("A = \n"); bool_mat_print(A); flint_printf("\n\n");
flint_printf("B = \n"); bool_mat_print(B); flint_printf("\n\n");
flint_printf("AB = \n"); bool_mat_print(AB); flint_printf("\n\n");
flint_printf("BA = \n"); bool_mat_print(BA); flint_printf("\n\n");
abort();
}
bool_mat_clear(A);
bool_mat_clear(B);
bool_mat_clear(AB);
bool_mat_clear(BA);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("is_transitive....");
fflush(stdout);
flint_randinit(state);
/* special matrices */
{
slong n;
for (n = 0; n < 10; n++)
{
bool_mat_t A;
bool_mat_init(A, n, n);
/* identity matrices are transitive */
bool_mat_one(A);
if (!bool_mat_is_transitive(A))
{
flint_printf("FAIL (identity matrix)\n");
flint_abort();
}
/* square zero matrices are transitive */
bool_mat_zero(A);
if (!bool_mat_is_transitive(A))
{
flint_printf("FAIL (zero matrix)\n");
flint_abort();
}
bool_mat_clear(A);
}
}
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
slong n;
bool_mat_t A;
n = n_randint(state, 10);
bool_mat_init(A, n, n);
/* all square diagonal matrices are transitive */
bool_mat_randtest_diagonal(A, state);
if (!bool_mat_is_transitive(A))
{
flint_printf("FAIL (diagonal)\n");
flint_printf("A:\n"); bool_mat_print(A); flint_printf("\n");
flint_abort();
}
bool_mat_clear(A);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}