int main()
{
slong iter;
flint_rand_t state;
flint_printf("dft....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100 * arb_test_multiplier(); iter++)
{
acb_mat_t A, Ainv, AT;
slong n, prec;
n = n_randint(state, 10);
prec = 53 + n_randint(state, 30);
acb_mat_init(A, n, n);
acb_mat_init(Ainv, n, n);
acb_mat_init(AT, n, n);
acb_mat_randtest(A, state, 100, 10);
acb_mat_dft(A, 0, prec);
if (!acb_mat_inv(Ainv, A, prec))
{
flint_printf("FAIL: small DFT matrix (n = %wd) not invertible\n", n);
flint_abort();
}
acb_mat_conjugate_transpose(AT, A);
if (!acb_mat_overlaps(AT, Ainv))
{
flint_printf("FAIL: overlap (n = %wd)\n", n);
flint_printf("A = \n"); acb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("Ainv = \n"); acb_mat_printd(Ainv, 15); flint_printf("\n\n");
flint_printf("AT = \n"); acb_mat_printd(AT, 15); flint_printf("\n\n");
flint_abort();
}
acb_mat_clear(A);
acb_mat_clear(Ainv);
acb_mat_clear(AT);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int
acb_mat_inv(acb_mat_t X, const acb_mat_t A, long prec)
{
if (X == A)
{
int r;
acb_mat_t T;
acb_mat_init(T, acb_mat_nrows(A), acb_mat_ncols(A));
r = acb_mat_inv(T, A, prec);
acb_mat_swap(T, X);
acb_mat_clear(T);
return r;
}
acb_mat_one(X);
return acb_mat_solve(X, A, X, prec);
}
void tau_matrix(acb_mat_t tau, const acb_mat_t omega0, const acb_mat_t omega1, slong prec)
{
acb_mat_inv(tau, omega1, prec);
acb_mat_mul(tau, tau, omega0, prec);
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("inv....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000; iter++)
{
fmpq_mat_t Q, Qinv;
acb_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);
acb_mat_init(A, n, n);
acb_mat_init(Ainv, n, n);
fmpq_mat_randtest(Q, state, qbits);
q_invertible = fmpq_mat_inv(Qinv, Q);
if (!q_invertible)
{
acb_mat_set_fmpq_mat(A, Q, prec);
r_invertible = acb_mat_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"); acb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("Ainv = \n"); acb_mat_printd(Ainv, 15); flint_printf("\n\n");
abort();
}
}
else
{
/* now this must converge */
while (1)
{
acb_mat_set_fmpq_mat(A, Q, prec);
r_invertible = acb_mat_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"); acb_mat_printd(A, 15); flint_printf("\n\n");
abort();
}
prec *= 2;
}
}
if (!acb_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"); acb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("Ainv = \n"); acb_mat_printd(Ainv, 15); flint_printf("\n\n");
abort();
}
/* test aliasing */
r_invertible2 = acb_mat_inv(A, A, prec);
if (!acb_mat_equal(A, Ainv) || r_invertible != r_invertible2)
{
flint_printf("FAIL (aliasing)\n");
flint_printf("A = \n"); acb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("Ainv = \n"); acb_mat_printd(Ainv, 15); flint_printf("\n\n");
abort();
}
}
fmpq_mat_clear(Q);
fmpq_mat_clear(Qinv);
acb_mat_clear(A);
acb_mat_clear(Ainv);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int
acb_mat_eig_simple_rump(acb_ptr E, acb_mat_t L, acb_mat_t R,
const acb_mat_t A, acb_srcptr E_approx, const acb_mat_t R_approx, slong prec)
{
slong i, j, n;
acb_mat_t X, R2;
int result;
n = acb_mat_nrows(A);
if (n == 0)
return 1;
if (n == 1)
{
acb_set_round(E, acb_mat_entry(A, 0, 0), prec);
if (L != NULL)
acb_one(acb_mat_entry(L, 0, 0));
if (R != NULL)
acb_one(acb_mat_entry(R, 0, 0));
return 1;
}
acb_mat_init(X, n, 1);
acb_mat_init(R2, n, n);
result = 1;
for (i = 0; i < n && result; i++)
{
for (j = 0; j < n; j++)
acb_set(acb_mat_entry(X, j, 0), acb_mat_entry(R_approx, j, i));
acb_mat_eig_enclosure_rump(E + i, NULL, X, A, E_approx + i, X, prec);
if (!acb_is_finite(E + i))
result = 0;
for (j = 0; j < i; j++)
if (acb_overlaps(E + i, E + j))
result = 0;
for (j = 0; j < n; j++)
acb_set(acb_mat_entry(R2, j, i), acb_mat_entry(X, j, 0));
}
if (R != NULL)
{
if (result)
acb_mat_set(R, R2);
else
acb_mat_indeterminate(R);
}
if (L != NULL)
{
if (!result || !acb_mat_inv(L, R, prec))
acb_mat_indeterminate(L);
}
if (!result)
_acb_vec_indeterminate(E, n);
acb_mat_clear(X);
acb_mat_clear(R2);
return result;
}
