int arb_mat_inv(arb_mat_t X, const arb_mat_t A, slong prec) { if (X == A) { int r; arb_mat_t T; arb_mat_init(T, arb_mat_nrows(A), arb_mat_ncols(A)); r = arb_mat_inv(T, A, prec); arb_mat_swap(T, X); arb_mat_clear(T); return r; } arb_mat_one(X); return arb_mat_solve(X, A, X, prec); }
int main() { slong iter; flint_rand_t state; flint_printf("solve...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000 * 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(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_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"); flint_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_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"); flint_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"); flint_abort(); } /* test aliasing */ r_invertible2 = arb_mat_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"); flint_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; }