int main(void) { flint_rand_t state; long i; printf("inv...."); fflush(stdout); flint_randinit(state); /* Test aliasing */ for (i = 0; i < 400; i++) { fmpz_poly_mat_t A, Ainv; fmpz_poly_t den1, den2; long n, bits, deg; float density; int ns1, ns2; int result; n = n_randint(state, 8); deg = 1 + n_randint(state, 5); bits = 1 + n_randint(state, 100); density = n_randint(state, 100) * 0.01; fmpz_poly_mat_init(A, n, n); fmpz_poly_mat_init(Ainv, n, n); fmpz_poly_init(den1); fmpz_poly_init(den2); fmpz_poly_mat_randtest_sparse(A, state, deg, bits, density); ns1 = fmpz_poly_mat_inv(Ainv, den1, A); ns2 = fmpz_poly_mat_inv(A, den2, A); result = ns1 == ns2; if (result && ns1 != 0) { result = fmpz_poly_equal(den1, den2) && fmpz_poly_mat_equal(A, Ainv); } if (!result) { printf("FAIL (aliasing)!\n"); fmpz_poly_mat_print(A, "x"); printf("\n"); fmpz_poly_mat_print(Ainv, "x"); printf("\n"); abort(); } fmpz_poly_mat_clear(A); fmpz_poly_mat_clear(Ainv); fmpz_poly_clear(den1); fmpz_poly_clear(den2); } /* Check A^(-1) = A = 1 */ for (i = 0; i < 1000; i++) { fmpz_poly_mat_t A, Ainv, B, Iden; fmpz_poly_t den, det; long n, bits, deg; float density; int nonsingular; n = n_randint(state, 10); deg = 1 + n_randint(state, 5); bits = 1 + n_randint(state, 100); density = n_randint(state, 100) * 0.01; fmpz_poly_mat_init(A, n, n); fmpz_poly_mat_init(Ainv, n, n); fmpz_poly_mat_init(B, n, n); fmpz_poly_mat_init(Iden, n, n); fmpz_poly_init(den); fmpz_poly_init(det); fmpz_poly_mat_randtest_sparse(A, state, deg, bits, density); nonsingular = fmpz_poly_mat_inv(Ainv, den, A); fmpz_poly_mat_det_interpolate(det, A); if (n == 0) { if (nonsingular == 0 || !fmpz_poly_is_one(den)) { printf("FAIL: expected empty matrix to pass\n"); abort(); } } else { if (!fmpz_poly_equal(den, det)) { fmpz_poly_neg(det, det); printf("FAIL: den != det(A)\n"); abort(); } fmpz_poly_mat_mul(B, Ainv, A); fmpz_poly_mat_one(Iden); fmpz_poly_mat_scalar_mul_fmpz_poly(Iden, Iden, den); if (!fmpz_poly_mat_equal(B, Iden)) { printf("FAIL:\n"); printf("A:\n"); fmpz_poly_mat_print(A, "x"); printf("Ainv:\n"); fmpz_poly_mat_print(Ainv, "x"); printf("B:\n"); fmpz_poly_mat_print(B, "x"); printf("den:\n"); fmpz_poly_print_pretty(den, "x"); abort(); } } fmpz_poly_clear(den); fmpz_poly_clear(det); fmpz_poly_mat_clear(A); fmpz_poly_mat_clear(Ainv); fmpz_poly_mat_clear(B); fmpz_poly_mat_clear(Iden); } flint_randclear(state); _fmpz_cleanup(); printf("PASS\n"); return 0; }
int main(void) { slong i; FLINT_TEST_INIT(state); flint_printf("nullspace...."); fflush(stdout); for (i = 0; i < 200 * flint_test_multiplier(); i++) { fmpz_poly_mat_t A, N, AN; slong n, m, bits, deg, rank, nullity; float density; m = n_randint(state, 13); n = n_randint(state, 13); deg = 1 + n_randint(state, 5); bits = 1 + n_randint(state, 100); density = n_randint(state, 100) * 0.01; fmpz_poly_mat_init(A, m, n); fmpz_poly_mat_init(N, n, n); fmpz_poly_mat_init(AN, m, n); fmpz_poly_mat_randtest_sparse(A, state, deg, bits, density); rank = fmpz_poly_mat_rank(A); nullity = fmpz_poly_mat_nullspace(N, A); if (nullity + rank != n) { flint_printf("FAIL: wrong nullity!\n"); flint_printf("rank = %wd\n", rank); flint_printf("nullity = %wd\n", nullity); fmpz_poly_mat_print(A, "x"); flint_printf("\n"); fmpz_poly_mat_print(N, "x"); flint_printf("\n"); abort(); } if (fmpz_poly_mat_rank(N) != nullity) { flint_printf("FAIL: wrong rank(N) != nullity!\n"); abort(); } fmpz_poly_mat_mul(AN, A, N); if (!fmpz_poly_mat_is_zero(AN)) { flint_printf("FAIL: A * N != 0\n"); abort(); } fmpz_poly_mat_clear(A); fmpz_poly_mat_clear(N); fmpz_poly_mat_clear(AN); } FLINT_TEST_CLEANUP(state); flint_printf("PASS\n"); return 0; }