int
main(void)
{
long i;
flint_rand_t state;
flint_randinit(state);
printf("solve_triu_recursive....");
fflush(stdout);
for (i = 0; i < 1000; i++)
{
nmod_mat_t A, X, B, Y;
mp_limb_t m;
long rows, cols;
int unit;
m = n_randtest_prime(state, 0);
rows = n_randint(state, 100);
cols = n_randint(state, 100);
unit = n_randint(state, 2);
nmod_mat_init(A, rows, rows, m);
nmod_mat_init(B, rows, cols, m);
nmod_mat_init(X, rows, cols, m);
nmod_mat_init(Y, rows, cols, m);
nmod_mat_randtriu(A, state, unit);
nmod_mat_randtest(X, state);
nmod_mat_mul(B, A, X);
/* Check Y = A^(-1) * (A * X) = X */
nmod_mat_solve_triu_recursive(Y, A, B, unit);
if (!nmod_mat_equal(Y, X))
{
printf("FAIL!\n");
printf("A:\n");
nmod_mat_print_pretty(A);
printf("X:\n");
nmod_mat_print_pretty(X);
printf("B:\n");
nmod_mat_print_pretty(B);
printf("Y:\n");
nmod_mat_print_pretty(Y);
abort();
}
/* Check aliasing */
nmod_mat_solve_triu_recursive(B, A, B, unit);
if (!nmod_mat_equal(B, X))
{
printf("FAIL!\n");
printf("aliasing test failed");
printf("A:\n");
nmod_mat_print_pretty(A);
printf("B:\n");
nmod_mat_print_pretty(B);
abort();
}
nmod_mat_clear(A);
nmod_mat_clear(B);
nmod_mat_clear(X);
nmod_mat_clear(Y);
}
flint_randclear(state);
printf("PASS\n");
return 0;
}
int
main(void)
{
flint_rand_t state;
long i;
printf("nullspace....");
fflush(stdout);
flint_randinit(state);
for (i = 0; i < 10000; i++)
{
nmod_mat_t A, B, ker;
mp_limb_t mod;
long m, n, d, r, nullity, nulrank;
m = n_randint(state, 30);
n = n_randint(state, 30);
for (r = 0; r <= FLINT_MIN(m,n); r++)
{
mod = n_randtest_prime(state, 0);
d = n_randint(state, 2*m*n + 1);
nmod_mat_init(A, m, n, mod);
nmod_mat_init(ker, n, n, mod);
nmod_mat_init(B, m, n, mod);
nmod_mat_randrank(A, state, r);
/* Densify */
if (n_randlimb(state) % 2)
nmod_mat_randops(A, d, state);
nullity = nmod_mat_nullspace(ker, A);
nulrank = nmod_mat_rank(ker);
if (nullity != nulrank)
{
printf("FAIL:\n");
printf("rank(ker) != nullity!\n");
nmod_mat_print_pretty(A);
printf("\n");
abort();
}
if (nullity + r != n)
{
printf("FAIL:\n");
printf("nullity + rank != n\n");
nmod_mat_print_pretty(A);
printf("\n");
abort();
}
nmod_mat_mul(B, A, ker);
if (nmod_mat_rank(B) != 0)
{
printf("FAIL:\n");
printf("A * ker != 0\n");
nmod_mat_print_pretty(A);
printf("\n");
abort();
}
nmod_mat_clear(A);
nmod_mat_clear(ker);
nmod_mat_clear(B);
}
}
flint_randclear(state);
printf("PASS\n");
return 0;
}
int
main(void)
{
long i;
flint_rand_t state;
flint_randinit(state);
printf("mul....");
fflush(stdout);
for (i = 0; i < 10000; i++)
{
nmod_mat_t A, B, C, D;
mp_limb_t mod;
long m, k, n;
m = n_randint(state, 50);
k = n_randint(state, 50);
n = n_randint(state, 50);
/* We want to generate matrices with many entries close to half
or full limbs with high probability, to stress overflow handling */
switch (n_randint(state, 3))
{
case 0:
mod = n_randtest_not_zero(state);
break;
case 1:
mod = ULONG_MAX/2 + 1 - n_randbits(state, 4);
break;
case 2:
default:
mod = ULONG_MAX - n_randbits(state, 4);
break;
}
nmod_mat_init(A, m, n, mod);
nmod_mat_init(B, n, k, mod);
nmod_mat_init(C, m, k, mod);
nmod_mat_init(D, m, k, mod);
if (n_randint(state, 2))
nmod_mat_randtest(A, state);
else
nmod_mat_randfull(A, state);
if (n_randint(state, 2))
nmod_mat_randtest(B, state);
else
nmod_mat_randfull(B, state);
nmod_mat_randtest(C, state); /* make sure noise in the output is ok */
nmod_mat_mul(C, A, B);
nmod_mat_mul_check(D, A, B);
if (!nmod_mat_equal(C, D))
{
printf("FAIL: results not equal\n");
nmod_mat_print_pretty(A);
nmod_mat_print_pretty(B);
nmod_mat_print_pretty(C);
nmod_mat_print_pretty(D);
abort();
}
nmod_mat_clear(A);
nmod_mat_clear(B);
nmod_mat_clear(C);
nmod_mat_clear(D);
}
flint_randclear(state);
printf("PASS\n");
return 0;
}
int
main(void)
{
slong i;
FLINT_TEST_INIT(state);
flint_printf("rref....");
fflush(stdout);
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
nmod_mat_t A, B, C, D;
mp_limb_t mod;
slong j, k, m, n, rank1, rank2;
slong *perm;
int equal;
mp_limb_t c;
mod = n_randtest_prime(state, 0);
m = n_randint(state, 20);
n = n_randint(state, 20);
perm = _perm_init(2*m);
nmod_mat_init(A, m, n, mod);
nmod_mat_init(D, 2*m, n, mod);
nmod_mat_randtest(A, state);
nmod_mat_init_set(B, A);
nmod_mat_init_set(C, A);
rank1 = nmod_mat_rref(B);
if (!check_rref_form(perm, B, rank1))
{
flint_printf("FAIL (malformed rref)\n");
nmod_mat_print_pretty(A); flint_printf("\n\n");
nmod_mat_print_pretty(B); flint_printf("\n\n");
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++)
{
do { c = n_randint(state, mod); } while (c == 0);
for (k = 0; k < n; k++)
nmod_mat_entry(D, perm[j], k) =
nmod_mul(nmod_mat_entry(A, j, k), c, A->mod);
}
for (j = 0; j < m; j++)
{
do { c = n_randint(state, mod); } while (c == 0);
for (k = 0; k < n; k++)
nmod_mat_entry(D, perm[m + j], k) =
nmod_mul(nmod_mat_entry(B, j, k), c, A->mod);
}
rank2 = nmod_mat_rref(D);
equal = (rank1 == rank2);
if (equal)
{
for (j = 0; j < rank2; j++)
for (k = 0; k < n; k++)
equal = equal && (nmod_mat_entry(B, j, k) ==
nmod_mat_entry(D, j, k));
for (j = rank2; j < 2 * rank2; j++)
for (k = 0; k < n; k++)
equal = equal && (nmod_mat_entry(D, j, k) == 0);
}
if (!equal)
{
flint_printf("FAIL (rank1 = %wd, rank2 = %wd)!\n", rank1, rank2);
nmod_mat_print_pretty(A); flint_printf("\n\n");
nmod_mat_print_pretty(B); flint_printf("\n\n");
nmod_mat_print_pretty(D); flint_printf("\n\n");
abort();
}
_perm_clear(perm);
nmod_mat_clear(A);
nmod_mat_clear(B);
nmod_mat_clear(C);
nmod_mat_clear(D);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
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;
}
int
main(void)
{
slong i;
FLINT_TEST_INIT(state);
flint_printf("solve_triu....");
fflush(stdout);
for (i = 0; i < 10 * flint_test_multiplier(); i++)
{
nmod_mat_t A, X, B, Y;
mp_limb_t m;
slong rows, cols;
int unit;
m = n_randtest_prime(state, 0);
rows = n_randint(state, 200);
cols = n_randint(state, 200);
unit = n_randint(state, 2);
nmod_mat_init(A, rows, rows, m);
nmod_mat_init(B, rows, cols, m);
nmod_mat_init(X, rows, cols, m);
nmod_mat_init(Y, rows, cols, m);
nmod_mat_randtriu(A, state, unit);
nmod_mat_randtest(X, state);
nmod_mat_mul(B, A, X);
/* Check Y = A^(-1) * (A * X) = X */
nmod_mat_solve_triu(Y, A, B, unit);
if (!nmod_mat_equal(Y, X))
{
flint_printf("FAIL!\n");
flint_printf("A:\n");
nmod_mat_print_pretty(A);
flint_printf("X:\n");
nmod_mat_print_pretty(X);
flint_printf("B:\n");
nmod_mat_print_pretty(B);
flint_printf("Y:\n");
nmod_mat_print_pretty(Y);
abort();
}
/* Check aliasing */
nmod_mat_solve_triu(B, A, B, unit);
if (!nmod_mat_equal(B, X))
{
flint_printf("FAIL!\n");
flint_printf("aliasing test failed");
flint_printf("A:\n");
nmod_mat_print_pretty(A);
flint_printf("B:\n");
nmod_mat_print_pretty(B);
abort();
}
nmod_mat_clear(A);
nmod_mat_clear(B);
nmod_mat_clear(X);
nmod_mat_clear(Y);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
