int
main(void)
{
int i;
FLINT_TEST_INIT(state);
flint_printf("multi_CRT_ui....");
fflush(stdout);
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
slong bits, prime_bits, rows, cols, num_primes, j;
fmpz_t mod;
fmpz_mat_t A, B, C;
nmod_mat_t Amod[1000];
mp_limb_t primes[1000];
bits = n_randint(state, 500) + 1;
rows = n_randint(state, 10);
cols = n_randint(state, 10);
prime_bits = 1 + n_randint(state, FLINT_BITS - 1);
fmpz_mat_init(A, rows, cols);
fmpz_mat_init(B, rows, cols);
fmpz_mat_init(C, rows, cols);
fmpz_mat_randtest(A, state, bits);
fmpz_init(mod);
num_primes = 0;
primes[0] = n_nextprime(UWORD(1) << prime_bits, 0);
fmpz_set_ui(mod, primes[0]);
/* + 1 for sign */
while (fmpz_bits(mod) <= bits + 1)
{
primes[num_primes + 1] = n_nextprime(primes[num_primes], 0);
fmpz_mul_ui(mod, mod, primes[num_primes + 1]);
num_primes++;
}
num_primes++;
for (j = 0; j < num_primes; j++)
nmod_mat_init(Amod[j], rows, cols, primes[j]);
fmpz_mat_multi_mod_ui(Amod, num_primes, A);
fmpz_mat_multi_CRT_ui(B, Amod, num_primes, 1);
if (!fmpz_mat_equal(B, A))
{
flint_printf("FAIL!\n");
flint_printf("primes: ");
for (j = 0; j < num_primes; j++)
flint_printf("%wu ", primes[j]);
flint_printf("\nA: \n");
fmpz_mat_print_pretty(A);
flint_printf("\nB: \n");
fmpz_mat_print_pretty(B);
flint_printf("\n");
abort();
}
for (j = 0; j < num_primes; j++)
nmod_mat_clear(Amod[j]);
fmpz_mat_clear(A);
fmpz_mat_clear(B);
fmpz_mat_clear(C);
fmpz_clear(mod);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int
main(void)
{
fmpz_mat_t A;
flint_rand_t state;
long i, m;
fmpz_t det1, det2;
printf("det_multi_mod....");
fflush(stdout);
flint_randinit(state);
for (i = 0; i < 10000; i++)
{
int proved = n_randlimb(state) % 2;
m = n_randint(state, 10);
fmpz_mat_init(A, m, m);
fmpz_init(det1);
fmpz_init(det2);
fmpz_mat_randtest(A, state, 1+n_randint(state,200));
fmpz_mat_det_bareiss(det1, A);
fmpz_mat_det_multi_mod(det2, A, proved);
if (!fmpz_equal(det1, det2))
{
printf("FAIL:\n");
printf("different determinants!\n");
fmpz_mat_print_pretty(A), printf("\n");
printf("det1: "), fmpz_print(det1), printf("\n");
printf("det2: "), fmpz_print(det2), printf("\n");
abort();
}
fmpz_clear(det1);
fmpz_clear(det2);
fmpz_mat_clear(A);
}
for (i = 0; i < 10000; i++)
{
m = 2 + n_randint(state, 10);
fmpz_mat_init(A, m, m);
fmpz_init(det2);
fmpz_mat_randrank(A, state, 1+n_randint(state, m - 1), 1+n_randint(state, 10));
fmpz_mat_randops(A, state, n_randint(state, 2*m*m + 1));
fmpz_mat_det_multi_mod(det2, A, 0);
if (*det2)
{
printf("FAIL:\n");
printf("expected zero determinant!\n");
fmpz_mat_print_pretty(A), printf("\n");
abort();
}
fmpz_mat_clear(A);
fmpz_clear(det2);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
int
main(void)
{
fmpz_mat_t A, X, B, AX;
fmpz_t den;
slong i, m, n, r;
int success;
FLINT_TEST_INIT(state);
flint_printf("solve_cramer....");
fflush(stdout);
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
m = n_randint(state, 4);
n = n_randint(state, 10);
fmpz_mat_init(A, m, m);
fmpz_mat_init(B, m, n);
fmpz_mat_init(X, m, n);
fmpz_mat_init(AX, m, n);
fmpz_init(den);
fmpz_mat_randrank(A, state, m, 1+n_randint(state, 2)*n_randint(state, 100));
fmpz_mat_randtest(B, state, 1+n_randint(state, 2)*n_randint(state, 100));
/* Dense */
if (n_randint(state, 2))
fmpz_mat_randops(A, state, 1+n_randint(state, 1 + m*m));
success = fmpz_mat_solve_cramer(X, den, A, B);
fmpz_mat_mul(AX, A, X);
fmpz_mat_scalar_divexact_fmpz(AX, AX, den);
if (!fmpz_mat_equal(AX, B) || !success)
{
flint_printf("FAIL:\n");
flint_printf("AX != B!\n");
flint_printf("A:\n"), fmpz_mat_print_pretty(A), flint_printf("\n");
flint_printf("B:\n"), fmpz_mat_print_pretty(B), flint_printf("\n");
flint_printf("X:\n"), fmpz_mat_print_pretty(X), flint_printf("\n");
flint_printf("den(X) = "), fmpz_print(den), flint_printf("\n");
flint_printf("AX:\n"), fmpz_mat_print_pretty(AX), flint_printf("\n");
abort();
}
fmpz_mat_clear(A);
fmpz_mat_clear(B);
fmpz_mat_clear(X);
fmpz_mat_clear(AX);
fmpz_clear(den);
}
/* Test singular systems */
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
m = 1 + n_randint(state, 3);
n = 1 + n_randint(state, 10);
r = n_randint(state, m);
fmpz_mat_init(A, m, m);
fmpz_mat_init(B, m, n);
fmpz_mat_init(X, m, n);
fmpz_mat_init(AX, m, n);
fmpz_init(den);
fmpz_mat_randrank(A, state, r, 1+n_randint(state, 2)*n_randint(state, 100));
fmpz_mat_randtest(B, state, 1+n_randint(state, 2)*n_randint(state, 100));
/* Dense */
if (n_randint(state, 2))
fmpz_mat_randops(A, state, 1+n_randint(state, 1 + m*m));
success = fmpz_mat_solve_cramer(X, den, A, B);
if (!fmpz_is_zero(den) || success)
{
flint_printf("FAIL:\n");
flint_printf("singular system gave nonzero determinant\n");
abort();
}
fmpz_mat_clear(A);
fmpz_mat_clear(B);
fmpz_mat_clear(X);
fmpz_mat_clear(AX);
fmpz_clear(den);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int
main(void)
{
fmpz_mat_t A, X, B, AX, AXm, Bm;
fmpz_t mod;
slong i, m, n, r;
int success;
FLINT_TEST_INIT(state);
flint_printf("solve_dixon....");
fflush(stdout);
for (i = 0; i < 100 * flint_test_multiplier(); i++)
{
m = n_randint(state, 20);
n = n_randint(state, 20);
fmpz_mat_init(A, m, m);
fmpz_mat_init(B, m, n);
fmpz_mat_init(Bm, m, n);
fmpz_mat_init(X, m, n);
fmpz_mat_init(AX, m, n);
fmpz_mat_init(AXm, m, n);
fmpz_init(mod);
fmpz_mat_randrank(A, state, m, 1+n_randint(state, 2)*n_randint(state, 100));
fmpz_mat_randtest(B, state, 1+n_randint(state, 2)*n_randint(state, 100));
/* Dense */
if (n_randint(state, 2))
fmpz_mat_randops(A, state, 1+n_randint(state, 1 + m*m));
success = fmpz_mat_solve_dixon(X, mod, A, B);
fmpz_mat_set(AXm, X);
fmpz_mat_mul(AX, A, AXm);
fmpz_mat_scalar_mod_fmpz(AXm, AX, mod);
fmpz_mat_scalar_mod_fmpz(Bm, B, mod);
if (!fmpz_mat_equal(AXm, Bm) || !success)
{
flint_printf("FAIL:\n");
flint_printf("AX != B!\n");
flint_printf("A:\n"), fmpz_mat_print_pretty(A), flint_printf("\n");
flint_printf("B:\n"), fmpz_mat_print_pretty(B), flint_printf("\n");
flint_printf("X:\n"), fmpz_mat_print_pretty(X), flint_printf("\n");
flint_printf("mod = "), fmpz_print(mod), flint_printf("\n");
flint_printf("AX:\n"), fmpz_mat_print_pretty(AX), flint_printf("\n");
abort();
}
fmpz_mat_clear(A);
fmpz_mat_clear(B);
fmpz_mat_clear(Bm);
fmpz_mat_clear(X);
fmpz_mat_clear(AX);
fmpz_mat_clear(AXm);
fmpz_clear(mod);
}
/* Test singular systems */
for (i = 0; i < 100 * flint_test_multiplier(); i++)
{
m = 1 + n_randint(state, 10);
n = 1 + n_randint(state, 10);
r = n_randint(state, m);
fmpz_mat_init(A, m, m);
fmpz_mat_init(B, m, n);
fmpz_mat_init(X, m, n);
fmpz_init(mod);
fmpz_mat_randrank(A, state, r, 1+n_randint(state, 2)*n_randint(state, 100));
fmpz_mat_randtest(B, state, 1+n_randint(state, 2)*n_randint(state, 100));
/* Dense */
if (n_randint(state, 2))
fmpz_mat_randops(A, state, 1+n_randint(state, 1 + m*m));
if (fmpz_mat_solve_dixon(X, mod, A, B) != 0)
{
flint_printf("FAIL:\n");
flint_printf("singular system, returned nonzero\n");
abort();
}
fmpz_mat_clear(A);
fmpz_mat_clear(B);
fmpz_mat_clear(X);
fmpz_clear(mod);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
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()
{
long iter;
flint_rand_t state;
printf("forward_nmod_mat....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000; iter++)
{
fmpz_holonomic_t op;
fmpz_mat_t M1;
fmpz_t Q1;
nmod_mat_t M2, L, R;
mp_limb_t Q2;
long start, n, r;
mp_limb_t p;
fmpz_holonomic_init(op);
fmpz_holonomic_randtest(op, state, 4, 4, 10);
r = fmpz_holonomic_order(op);
start = n_randint(state, 10);
n = n_randint(state, 100);
p = n_randtest_prime(state, 0);
fmpz_mat_init(M1, r, r);
fmpz_init(Q1);
nmod_mat_init(M2, r, r, p);
nmod_mat_init(L, r, r, p);
nmod_mat_init(R, r, r, p);
fmpz_holonomic_forward_fmpz_mat(M1, Q1, op, start, n);
fmpz_holonomic_forward_nmod_mat(M2, &Q2, op, start, n);
fmpz_mat_get_nmod_mat(L, M1);
nmod_mat_scalar_mul(L, L, Q2);
nmod_mat_scalar_mul(R, M2, fmpz_fdiv_ui(Q1, p));
/* check Q2 * M1 = Q1 * M2 */
if (!nmod_mat_equal(L, R))
{
printf("FAIL\n");
fmpz_holonomic_print(op, "n", "Sn"); printf("\n\n");
printf("start = %lu, n = %lu\n", start, n);
fmpz_mat_print_pretty(M1); printf("\n\n");
fmpz_print(Q1); printf("\n\n");
nmod_mat_print_pretty(M2); printf("\n\n");
printf("%lu\n\n", Q2);
abort();
}
fmpz_mat_clear(M1);
fmpz_clear(Q1);
nmod_mat_clear(M2);
nmod_mat_clear(L);
nmod_mat_clear(R);
fmpz_holonomic_clear(op);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
