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; }