int
bool_mat_is_transitive(const bool_mat_t mat)
{
slong n, i, j, k;
if (!bool_mat_is_square(mat))
{
flint_printf("bool_mat_is_transitive: a square matrix is required!\n");
abort();
}
if (bool_mat_is_empty(mat))
return 1;
n = bool_mat_nrows(mat);
for (i = 0; i < n; i++)
for (j = 0; j < n; j++)
for (k = 0; k < n; k++)
if (bool_mat_get_entry(mat, i, j) &&
bool_mat_get_entry(mat, j, k) &&
!bool_mat_get_entry(mat, i, k))
{
return 0;
}
return 1;
}
void
_bool_mat_permute(bool_mat_t B, const bool_mat_t A, const slong *perm)
{
slong n, i, j;
if (!bool_mat_is_square(A)) abort(); /* assert */
if (A == B) abort(); /* assert */
n = bool_mat_nrows(A);
for (i = 0; i < n; i++)
{
for (j = 0; j < n; j++)
{
bool_mat_set_entry(
B, perm[i], perm[j], bool_mat_get_entry(A, i, j));
}
}
}
/* following Tarjan */
slong
bool_mat_get_strongly_connected_components(slong *partition, const bool_mat_t A)
{
slong i, n, result;
_tarjan_t t;
if (!bool_mat_is_square(A))
{
flint_printf("bool_mat_get_strongly_connected_components: "
"a square matrix is required!\n");
flint_abort();
}
if (bool_mat_is_empty(A))
return 0;
n = bool_mat_nrows(A);
if (n == 1)
{
partition[0] = 0;
return 1;
}
_tarjan_init(t, n);
for (i = 0; i < n; i++)
{
partition[i] = _tarjan_UNDEFINED;
}
for (i = 0; i < n; i++)
{
if (*_tarjan_index(t, i) == _tarjan_UNDEFINED)
{
_tarjan_strongconnect(partition, t, A, i);
}
}
result = t->nsccs;
_tarjan_clear(t);
return result;
}
slong
bool_mat_nilpotency_degree(const bool_mat_t A)
{
slong n;
if (!bool_mat_is_square(A))
{
flint_printf("bool_mat_nilpotency_degree: a square matrix is required!\n");
abort();
}
if (bool_mat_is_empty(A))
return 0;
n = bool_mat_nrows(A);
if (n == 1)
{
return bool_mat_get_entry(A, 0, 0) ? -1 : 1;
}
else
{
_toposort_s s;
slong i;
int has_cycle;
int result;
_toposort_init(&s, n);
for (has_cycle = 0, i = 0; !has_cycle && i < n; i++)
if (!s.v[i])
has_cycle = _toposort_visit(&s, A, i);
if (has_cycle)
{
result = -1;
}
else
{
/* Find the length of the longest path within the DAG */
/* http://stackoverflow.com/a/10737524/4072759 */
slong x, y, z;
slong max_overall;
fmpz_mat_t E;
fmpz_mat_init(E, n, n);
fmpz_mat_zero(E);
max_overall = 0;
for (i = n - 1; i >= 0; i--)
{
slong max_in = 0;
y = s.post[i];
for (x = 0; x < n; x++)
{
max_in = FLINT_MAX(max_in,
fmpz_get_si(fmpz_mat_entry(E, x, y)));
}
for (z = 0; z < n; z++)
{
if (bool_mat_get_entry(A, y, z))
{
fmpz_set_si(fmpz_mat_entry(E, y, z), max_in + 1);
max_overall = FLINT_MAX(max_overall, max_in + 1);
}
}
}
fmpz_mat_clear(E);
result = max_overall + 1;
}
_toposort_clear(&s);
return result;
}
}