int main()
{
slong iter;
flint_rand_t state;
flint_printf("inv_ldl_precomp....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
fmpq_mat_t Q, Qinv;
arb_mat_t A, Ainv;
slong n, qbits, prec;
int q_invertible, r_invertible, r_invertible2;
n = n_randint(state, 8);
qbits = 1 + n_randint(state, 30);
prec = 2 + n_randint(state, 200);
fmpq_mat_init(Q, n, n);
fmpq_mat_init(Qinv, n, n);
arb_mat_init(A, n, n);
arb_mat_init(Ainv, n, n);
_fmpq_mat_randtest_positive_semidefinite(Q, state, qbits);
q_invertible = fmpq_mat_inv(Qinv, Q);
if (!q_invertible)
{
arb_mat_set_fmpq_mat(A, Q, prec);
r_invertible = _spd_inv(Ainv, A, prec);
if (r_invertible)
{
flint_printf("FAIL: matrix is singular over Q but not over R\n");
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("\n");
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("Ainv = \n"); arb_mat_printd(Ainv, 15); flint_printf("\n\n");
abort();
}
}
else
{
/* now this must converge */
while (1)
{
arb_mat_set_fmpq_mat(A, Q, prec);
r_invertible = _spd_inv(Ainv, A, prec);
if (r_invertible)
{
break;
}
else
{
if (prec > 10000)
{
flint_printf("FAIL: failed to converge at 10000 bits\n");
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
abort();
}
prec *= 2;
}
}
if (!arb_mat_contains_fmpq_mat(Ainv, Qinv))
{
flint_printf("FAIL (containment, iter = %wd)\n", iter);
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("\n");
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("Qinv = \n"); fmpq_mat_print(Qinv); flint_printf("\n\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("Ainv = \n"); arb_mat_printd(Ainv, 15); flint_printf("\n\n");
abort();
}
/* test aliasing */
r_invertible2 = _spd_inv(A, A, prec);
if (!arb_mat_equal(A, Ainv) || r_invertible != r_invertible2)
{
flint_printf("FAIL (aliasing)\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("Ainv = \n"); arb_mat_printd(Ainv, 15); flint_printf("\n\n");
abort();
}
}
fmpq_mat_clear(Q);
fmpq_mat_clear(Qinv);
arb_mat_clear(A);
arb_mat_clear(Ainv);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("ldl....");
fflush(stdout);
flint_randinit(state);
/* check special matrices */
{
slong n;
for (n = 1; n < 10; n++)
{
slong lprec;
arb_mat_t L, A;
arb_mat_init(L, n, n);
arb_mat_init(A, n, n);
for (lprec = 2; lprec < 10; lprec++)
{
int result;
slong prec;
prec = 1 << lprec;
/* zero */
arb_mat_zero(A);
result = arb_mat_ldl(L, A, prec);
if (result)
{
flint_printf("FAIL (zero):\n");
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("L = \n"); arb_mat_printd(L, 15);
flint_printf("\n\n");
}
/* negative identity */
arb_mat_one(A);
arb_mat_neg(A, A);
result = arb_mat_ldl(L, A, prec);
if (result)
{
flint_printf("FAIL (negative identity):\n");
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("L = \n"); arb_mat_printd(L, 15);
flint_printf("\n\n");
}
/* identity */
arb_mat_one(A);
result = arb_mat_ldl(L, A, prec);
if (!result || !arb_mat_equal(L, A))
{
flint_printf("FAIL (identity):\n");
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("L = \n"); arb_mat_printd(L, 15);
flint_printf("\n\n");
}
}
arb_mat_clear(L);
arb_mat_clear(A);
}
}
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
fmpq_mat_t Q;
arb_mat_t A, L, D, U, T;
slong n, qbits, prec;
int q_invertible, r_invertible;
n = n_randint(state, 8);
qbits = 1 + n_randint(state, 100);
prec = 2 + n_randint(state, 202);
fmpq_mat_init(Q, n, n);
arb_mat_init(A, n, n);
arb_mat_init(L, n, n);
arb_mat_init(D, n, n);
arb_mat_init(U, n, n);
arb_mat_init(T, n, n);
_fmpq_mat_randtest_positive_semidefinite(Q, state, qbits);
q_invertible = fmpq_mat_is_invertible(Q);
if (!q_invertible)
{
arb_mat_set_fmpq_mat(A, Q, prec);
r_invertible = arb_mat_ldl(L, A, prec);
if (r_invertible)
{
flint_printf("FAIL: matrix is singular over Q but not over R\n");
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("\n");
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("L = \n"); arb_mat_printd(L, 15); flint_printf("\n\n");
}
}
else
{
/* now this must converge */
while (1)
{
arb_mat_set_fmpq_mat(A, Q, prec);
r_invertible = arb_mat_ldl(L, A, prec);
if (r_invertible)
{
break;
}
else
{
if (prec > 10000)
{
flint_printf("FAIL: failed to converge at 10000 bits\n");
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
abort();
}
prec *= 2;
}
}
/* multiply out the decomposition */
{
slong i;
arb_mat_zero(D);
arb_mat_transpose(U, L);
for (i = 0; i < n; i++)
{
arb_set(arb_mat_entry(D, i, i), arb_mat_entry(L, i, i));
arb_one(arb_mat_entry(L, i, i));
arb_one(arb_mat_entry(U, i, i));
}
arb_mat_mul(T, L, D, prec);
arb_mat_mul(T, T, U, prec);
}
if (!arb_mat_contains_fmpq_mat(T, Q))
{
flint_printf("FAIL (containment, iter = %wd)\n", iter);
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("\n");
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("L = \n"); arb_mat_printd(L, 15); flint_printf("\n\n");
flint_printf("U = \n"); arb_mat_printd(U, 15); flint_printf("\n\n");
flint_printf("L*U = \n"); arb_mat_printd(T, 15); flint_printf("\n\n");
abort();
}
}
fmpq_mat_clear(Q);
arb_mat_clear(A);
arb_mat_clear(L);
arb_mat_clear(D);
arb_mat_clear(U);
arb_mat_clear(T);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("mul_entrywise....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
slong m, n, qbits1, qbits2, rbits1, rbits2, rbits3;
fmpq_mat_t A, B, C;
arb_mat_t a, b, c, d;
qbits1 = 2 + n_randint(state, 200);
qbits2 = 2 + n_randint(state, 200);
rbits1 = 2 + n_randint(state, 200);
rbits2 = 2 + n_randint(state, 200);
rbits3 = 2 + n_randint(state, 200);
m = n_randint(state, 10);
n = n_randint(state, 10);
fmpq_mat_init(A, m, n);
fmpq_mat_init(B, m, n);
fmpq_mat_init(C, m, n);
arb_mat_init(a, m, n);
arb_mat_init(b, m, n);
arb_mat_init(c, m, n);
arb_mat_init(d, m, n);
fmpq_mat_randtest(A, state, qbits1);
fmpq_mat_randtest(B, state, qbits2);
_fmpq_mat_mul_entrywise(C, A, B);
arb_mat_set_fmpq_mat(a, A, rbits1);
arb_mat_set_fmpq_mat(b, B, rbits2);
arb_mat_mul_entrywise(c, a, b, rbits3);
if (!arb_mat_contains_fmpq_mat(c, C))
{
flint_printf("FAIL\n\n");
flint_printf("m = %wd, n = %wd, bits3 = %wd\n", m, n, rbits3);
flint_printf("A = "); fmpq_mat_print(A); flint_printf("\n\n");
flint_printf("B = "); fmpq_mat_print(B); flint_printf("\n\n");
flint_printf("C = "); fmpq_mat_print(C); flint_printf("\n\n");
flint_printf("a = "); arb_mat_printd(a, 15); flint_printf("\n\n");
flint_printf("b = "); arb_mat_printd(b, 15); flint_printf("\n\n");
flint_printf("c = "); arb_mat_printd(c, 15); flint_printf("\n\n");
abort();
}
/* test aliasing with a */
if (arb_mat_nrows(a) == arb_mat_nrows(c) &&
arb_mat_ncols(a) == arb_mat_ncols(c))
{
arb_mat_set(d, a);
arb_mat_mul_entrywise(d, d, b, rbits3);
if (!arb_mat_equal(d, c))
{
flint_printf("FAIL (aliasing 1)\n\n");
abort();
}
}
/* test aliasing with b */
if (arb_mat_nrows(b) == arb_mat_nrows(c) &&
arb_mat_ncols(b) == arb_mat_ncols(c))
{
arb_mat_set(d, b);
arb_mat_mul_entrywise(d, a, d, rbits3);
if (!arb_mat_equal(d, c))
{
flint_printf("FAIL (aliasing 2)\n\n");
abort();
}
}
fmpq_mat_clear(A);
fmpq_mat_clear(B);
fmpq_mat_clear(C);
arb_mat_clear(a);
arb_mat_clear(b);
arb_mat_clear(c);
arb_mat_clear(d);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("spd_solve....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
fmpq_mat_t Q, QX, QB;
arb_mat_t A, X, B;
slong n, m, qbits, prec;
int q_invertible, r_invertible, r_invertible2;
n = n_randint(state, 8);
m = n_randint(state, 8);
qbits = 1 + n_randint(state, 30);
prec = 2 + n_randint(state, 200);
fmpq_mat_init(Q, n, n);
fmpq_mat_init(QX, n, m);
fmpq_mat_init(QB, n, m);
arb_mat_init(A, n, n);
arb_mat_init(X, n, m);
arb_mat_init(B, n, m);
_fmpq_mat_randtest_positive_semidefinite(Q, state, qbits);
fmpq_mat_randtest(QB, state, qbits);
q_invertible = fmpq_mat_solve_fraction_free(QX, Q, QB);
if (!q_invertible)
{
arb_mat_set_fmpq_mat(A, Q, prec);
r_invertible = arb_mat_spd_solve(X, A, B, prec);
if (r_invertible)
{
flint_printf("FAIL: matrix is singular over Q but not over R\n");
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("\n");
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("QX = \n"); fmpq_mat_print(QX); flint_printf("\n\n");
flint_printf("QB = \n"); fmpq_mat_print(QB); flint_printf("\n\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
abort();
}
}
else
{
/* now this must converge */
while (1)
{
arb_mat_set_fmpq_mat(A, Q, prec);
arb_mat_set_fmpq_mat(B, QB, prec);
r_invertible = arb_mat_spd_solve(X, A, B, prec);
if (r_invertible)
{
break;
}
else
{
if (prec > 10000)
{
flint_printf("FAIL: failed to converge at 10000 bits\n");
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("QX = \n"); fmpq_mat_print(QX); flint_printf("\n\n");
flint_printf("QB = \n"); fmpq_mat_print(QB); flint_printf("\n\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
abort();
}
prec *= 2;
}
}
if (!arb_mat_contains_fmpq_mat(X, QX))
{
flint_printf("FAIL (containment, iter = %wd)\n", iter);
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("\n");
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("QB = \n"); fmpq_mat_print(QB); flint_printf("\n\n");
flint_printf("QX = \n"); fmpq_mat_print(QX); flint_printf("\n\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("B = \n"); arb_mat_printd(B, 15); flint_printf("\n\n");
flint_printf("X = \n"); arb_mat_printd(X, 15); flint_printf("\n\n");
abort();
}
/* test aliasing */
r_invertible2 = arb_mat_spd_solve(B, A, B, prec);
if (!arb_mat_equal(X, B) || r_invertible != r_invertible2)
{
flint_printf("FAIL (aliasing)\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("B = \n"); arb_mat_printd(B, 15); flint_printf("\n\n");
flint_printf("X = \n"); arb_mat_printd(X, 15); flint_printf("\n\n");
abort();
}
}
fmpq_mat_clear(Q);
fmpq_mat_clear(QB);
fmpq_mat_clear(QX);
arb_mat_clear(A);
arb_mat_clear(B);
arb_mat_clear(X);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("lu....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100000; iter++)
{
fmpq_mat_t Q;
arb_mat_t A, LU, P, L, U, T;
slong i, j, n, qbits, prec, *perm;
int q_invertible, r_invertible;
n = n_randint(state, 8);
qbits = 1 + n_randint(state, 100);
prec = 2 + n_randint(state, 202);
fmpq_mat_init(Q, n, n);
arb_mat_init(A, n, n);
arb_mat_init(LU, n, n);
arb_mat_init(P, n, n);
arb_mat_init(L, n, n);
arb_mat_init(U, n, n);
arb_mat_init(T, n, n);
perm = _perm_init(n);
fmpq_mat_randtest(Q, state, qbits);
q_invertible = fmpq_mat_is_invertible(Q);
if (!q_invertible)
{
arb_mat_set_fmpq_mat(A, Q, prec);
r_invertible = arb_mat_lu(perm, LU, A, prec);
if (r_invertible)
{
flint_printf("FAIL: matrix is singular over Q but not over R\n");
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("\n");
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("LU = \n"); arb_mat_printd(LU, 15); flint_printf("\n\n");
}
}
else
{
/* now this must converge */
while (1)
{
arb_mat_set_fmpq_mat(A, Q, prec);
r_invertible = arb_mat_lu(perm, LU, A, prec);
if (r_invertible)
{
break;
}
else
{
if (prec > 10000)
{
flint_printf("FAIL: failed to converge at 10000 bits\n");
abort();
}
prec *= 2;
}
}
arb_mat_one(L);
for (i = 0; i < n; i++)
for (j = 0; j < i; j++)
arb_set(arb_mat_entry(L, i, j),
arb_mat_entry(LU, i, j));
for (i = 0; i < n; i++)
for (j = i; j < n; j++)
arb_set(arb_mat_entry(U, i, j),
arb_mat_entry(LU, i, j));
for (i = 0; i < n; i++)
arb_one(arb_mat_entry(P, perm[i], i));
arb_mat_mul(T, P, L, prec);
arb_mat_mul(T, T, U, prec);
if (!arb_mat_contains_fmpq_mat(T, Q))
{
flint_printf("FAIL (containment, iter = %wd)\n", iter);
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("\n");
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("LU = \n"); arb_mat_printd(LU, 15); flint_printf("\n\n");
flint_printf("L = \n"); arb_mat_printd(L, 15); flint_printf("\n\n");
flint_printf("U = \n"); arb_mat_printd(U, 15); flint_printf("\n\n");
flint_printf("P*L*U = \n"); arb_mat_printd(T, 15); flint_printf("\n\n");
abort();
}
}
fmpq_mat_clear(Q);
arb_mat_clear(A);
arb_mat_clear(LU);
arb_mat_clear(P);
arb_mat_clear(L);
arb_mat_clear(U);
arb_mat_clear(T);
_perm_clear(perm);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}