int main() { slong iter; flint_rand_t state; flint_printf("lu...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { fmpq_mat_t Q; acb_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); acb_mat_init(A, n, n); acb_mat_init(LU, n, n); acb_mat_init(P, n, n); acb_mat_init(L, n, n); acb_mat_init(U, n, n); acb_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) { acb_mat_set_fmpq_mat(A, Q, prec); r_invertible = acb_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"); acb_mat_printd(A, 15); flint_printf("\n\n"); flint_printf("LU = \n"); acb_mat_printd(LU, 15); flint_printf("\n\n"); } } else { /* now this must converge */ while (1) { acb_mat_set_fmpq_mat(A, Q, prec); r_invertible = acb_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; } } acb_mat_one(L); for (i = 0; i < n; i++) for (j = 0; j < i; j++) acb_set(acb_mat_entry(L, i, j), acb_mat_entry(LU, i, j)); for (i = 0; i < n; i++) for (j = i; j < n; j++) acb_set(acb_mat_entry(U, i, j), acb_mat_entry(LU, i, j)); for (i = 0; i < n; i++) acb_one(acb_mat_entry(P, perm[i], i)); acb_mat_mul(T, P, L, prec); acb_mat_mul(T, T, U, prec); if (!acb_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"); acb_mat_printd(A, 15); flint_printf("\n\n"); flint_printf("LU = \n"); acb_mat_printd(LU, 15); flint_printf("\n\n"); flint_printf("L = \n"); acb_mat_printd(L, 15); flint_printf("\n\n"); flint_printf("U = \n"); acb_mat_printd(U, 15); flint_printf("\n\n"); flint_printf("P*L*U = \n"); acb_mat_printd(T, 15); flint_printf("\n\n"); abort(); } } fmpq_mat_clear(Q); acb_mat_clear(A); acb_mat_clear(LU); acb_mat_clear(P); acb_mat_clear(L); acb_mat_clear(U); acb_mat_clear(T); _perm_clear(perm); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
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 main() { slong iter; flint_rand_t state; flint_printf("mul_threaded...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 5000 * arb_test_multiplier(); iter++) { slong m, n, k, qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_mat_t A, B, C; acb_mat_t a, b, c, d; flint_set_num_threads(1 + n_randint(state, 5)); 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); k = n_randint(state, 10); fmpq_mat_init(A, m, n); fmpq_mat_init(B, n, k); fmpq_mat_init(C, m, k); acb_mat_init(a, m, n); acb_mat_init(b, n, k); acb_mat_init(c, m, k); acb_mat_init(d, m, k); fmpq_mat_randtest(A, state, qbits1); fmpq_mat_randtest(B, state, qbits2); fmpq_mat_mul(C, A, B); acb_mat_set_fmpq_mat(a, A, rbits1); acb_mat_set_fmpq_mat(b, B, rbits2); acb_mat_mul_threaded(c, a, b, rbits3); if (!acb_mat_contains_fmpq_mat(c, C)) { flint_printf("FAIL\n\n"); flint_printf("threads = %d, m = %wd, n = %wd, k = %wd, bits3 = %wd\n", flint_get_num_threads(), m, n, k, 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 = "); acb_mat_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_mat_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_mat_printd(c, 15); flint_printf("\n\n"); flint_abort(); } /* test aliasing with a */ if (acb_mat_nrows(a) == acb_mat_nrows(c) && acb_mat_ncols(a) == acb_mat_ncols(c)) { acb_mat_set(d, a); acb_mat_mul_threaded(d, d, b, rbits3); if (!acb_mat_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); flint_abort(); } } /* test aliasing with b */ if (acb_mat_nrows(b) == acb_mat_nrows(c) && acb_mat_ncols(b) == acb_mat_ncols(c)) { acb_mat_set(d, b); acb_mat_mul_threaded(d, a, d, rbits3); if (!acb_mat_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); flint_abort(); } } fmpq_mat_clear(A); fmpq_mat_clear(B); fmpq_mat_clear(C); acb_mat_clear(a); acb_mat_clear(b); acb_mat_clear(c); acb_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("mul...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++) { slong m, n, k, qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_mat_t A, B, C; acb_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); k = n_randint(state, 10); fmpq_mat_init(A, m, n); fmpq_mat_init(B, n, k); fmpq_mat_init(C, m, k); acb_mat_init(a, m, n); acb_mat_init(b, n, k); acb_mat_init(c, m, k); acb_mat_init(d, m, k); fmpq_mat_randtest(A, state, qbits1); fmpq_mat_randtest(B, state, qbits2); fmpq_mat_mul(C, A, B); acb_mat_set_fmpq_mat(a, A, rbits1); acb_mat_set_fmpq_mat(b, B, rbits2); acb_mat_mul(c, a, b, rbits3); if (!acb_mat_contains_fmpq_mat(c, C)) { flint_printf("FAIL\n\n"); flint_printf("m = %wd, n = %wd, k = %wd, bits3 = %wd\n", m, n, k, 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 = "); acb_mat_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_mat_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_mat_printd(c, 15); flint_printf("\n\n"); abort(); } /* test aliasing with a */ if (acb_mat_nrows(a) == acb_mat_nrows(c) && acb_mat_ncols(a) == acb_mat_ncols(c)) { acb_mat_set(d, a); acb_mat_mul(d, d, b, rbits3); if (!acb_mat_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } } /* test aliasing with b */ if (acb_mat_nrows(b) == acb_mat_nrows(c) && acb_mat_ncols(b) == acb_mat_ncols(c)) { acb_mat_set(d, b); acb_mat_mul(d, a, d, rbits3); if (!acb_mat_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } } fmpq_mat_clear(A); fmpq_mat_clear(B); fmpq_mat_clear(C); acb_mat_clear(a); acb_mat_clear(b); acb_mat_clear(c); acb_mat_clear(d); } /* check algebraic properties like associativity and distributivity */ for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++) { slong m, n, k, l; slong rbits; acb_mat_t a, b, c, d, ab, ac, bd, cd, s; rbits = 2 + n_randint(state, 200); m = n_randint(state, 10); n = n_randint(state, 10); k = n_randint(state, 10); l = n_randint(state, 10); _acb_mat_init_randtest(a, m, n, state); _acb_mat_init_randtest(b, n, k, state); _acb_mat_init_randtest(c, n, k, state); _acb_mat_init_randtest(d, k, l, state); acb_mat_init(ab, m, k); acb_mat_init(ac, m, k); acb_mat_init(bd, n, l); acb_mat_init(cd, n, l); acb_mat_init(s, n, k); acb_mat_mul(ab, a, b, rbits); acb_mat_mul(ac, a, c, rbits); acb_mat_mul(bd, b, d, rbits); acb_mat_mul(cd, c, d, rbits); acb_mat_add(s, b, c, rbits); /* check associativity of multiplication */ /* (A*B)*D = A*(B*D) */ { acb_mat_t lhs, rhs; acb_mat_init(lhs, m, l); acb_mat_init(rhs, m, l); acb_mat_mul(lhs, ab, d, rbits); acb_mat_mul(rhs, a, bd, rbits); if (!acb_mat_overlaps(lhs, rhs)) { flint_printf("FAIL\n\n"); flint_printf("m, n, k, l = %wd, %wd, %wd, %wd\n", m, n, k, l); flint_printf("rbits = %wd\n", rbits); _acb_mat_nprintd("a", a); _acb_mat_nprintd("b", b); _acb_mat_nprintd("d", d); _acb_mat_nprintd("(a*b)*d", lhs); _acb_mat_nprintd("a*(b*d)", rhs); abort(); } acb_mat_clear(lhs); acb_mat_clear(rhs); } /* check left distributivity of multiplication over addition */ /* A*(B + C) = A*B + A*C */ { acb_mat_t lhs, rhs; acb_mat_init(lhs, m, k); acb_mat_init(rhs, m, k); acb_mat_mul(lhs, a, s, rbits); acb_mat_add(rhs, ab, ac, rbits); if (!acb_mat_overlaps(lhs, rhs)) { flint_printf("FAIL\n\n"); flint_printf("m, n, k, l = %wd, %wd, %wd, %wd\n", m, n, k, l); flint_printf("rbits = %wd\n", rbits); _acb_mat_nprintd("a", a); _acb_mat_nprintd("b", b); _acb_mat_nprintd("c", c); _acb_mat_nprintd("a*(b + c)", lhs); _acb_mat_nprintd("a*b + b*c", rhs); abort(); } acb_mat_clear(lhs); acb_mat_clear(rhs); } /* check right distributivity of multiplication over addition */ /* (B + C)*D = B*D + C*D */ { acb_mat_t lhs, rhs; acb_mat_init(lhs, n, l); acb_mat_init(rhs, n, l); acb_mat_mul(lhs, s, d, rbits); acb_mat_add(rhs, bd, cd, rbits); if (!acb_mat_overlaps(lhs, rhs)) { flint_printf("FAIL\n\n"); flint_printf("m, n, k, l = %wd, %wd, %wd, %wd\n", m, n, k, l); flint_printf("rbits = %wd\n", rbits); _acb_mat_nprintd("b", b); _acb_mat_nprintd("c", c); _acb_mat_nprintd("d", d); _acb_mat_nprintd("(b + c)*d", lhs); _acb_mat_nprintd("b*d + c*d", rhs); abort(); } acb_mat_clear(lhs); acb_mat_clear(rhs); } /* check left multiplicative identity I*D = D */ { acb_mat_t one, lhs; acb_mat_init(one, k, k); acb_mat_init(lhs, k, l); acb_mat_one(one); acb_mat_mul(lhs, one, d, rbits); if (!acb_mat_contains(lhs, d)) { flint_printf("FAIL\n\n"); flint_printf("k = %wd, l = %wd\n", k, l); flint_printf("rbits = %wd\n", rbits); _acb_mat_nprintd("identity * d", lhs); _acb_mat_nprintd("d", d); abort(); } acb_mat_clear(one); acb_mat_clear(lhs); } /* check right multiplicative identity A*I = A */ { acb_mat_t one, lhs; acb_mat_init(one, n, n); acb_mat_init(lhs, m, n); acb_mat_one(one); acb_mat_mul(lhs, a, one, rbits); if (!acb_mat_contains(lhs, a)) { flint_printf("FAIL\n\n"); flint_printf("m = %wd, n = %wd\n", m, n); flint_printf("rbits = %wd\n", rbits); _acb_mat_nprintd("a * identity", lhs); _acb_mat_nprintd("a", a); abort(); } acb_mat_clear(one); acb_mat_clear(lhs); } acb_mat_clear(a); acb_mat_clear(b); acb_mat_clear(c); acb_mat_clear(d); acb_mat_clear(ab); acb_mat_clear(ac); acb_mat_clear(bd); acb_mat_clear(cd); acb_mat_clear(s); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
int main() { slong iter; flint_rand_t state; flint_printf("sqr...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++) { slong n, qbits1, rbits1, rbits2; fmpq_mat_t A, B; acb_mat_t a, b, c; qbits1 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); n = n_randint(state, 10); fmpq_mat_init(A, n, n); fmpq_mat_init(B, n, n); acb_mat_init(a, n, n); acb_mat_init(b, n, n); acb_mat_init(c, n, n); fmpq_mat_randtest(A, state, qbits1); fmpq_mat_mul(B, A, A); acb_mat_set_fmpq_mat(a, A, rbits1); acb_mat_sqr(b, a, rbits2); if (!acb_mat_contains_fmpq_mat(b, B)) { flint_printf("FAIL\n\n"); flint_printf("n = %wd, bits2 = %wd\n", n, rbits2); flint_printf("A = "); fmpq_mat_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_mat_print(B); flint_printf("\n\n"); flint_printf("a = "); acb_mat_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_mat_printd(b, 15); flint_printf("\n\n"); abort(); } /* test aliasing */ acb_mat_set(c, a); acb_mat_sqr(c, c, rbits2); if (!acb_mat_equal(c, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpq_mat_clear(A); fmpq_mat_clear(B); acb_mat_clear(a); acb_mat_clear(b); acb_mat_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }