int main(void) { int i, result; FLINT_TEST_INIT(state); flint_printf("one...."); fflush(stdout); /* 1 * A == A * 1 == A */ for (i = 0; i < 100 * flint_test_multiplier(); i++) { fmpq_mat_t A, B, C, I; slong n, bits; n = n_randint(state, 10); bits = 1 + n_randint(state, 100); fmpq_mat_init(A, n, n); fmpq_mat_init(B, n, n); fmpq_mat_init(C, n, n); fmpq_mat_init(I, n, n); fmpq_mat_randtest(A, state, bits); fmpq_mat_one(I); fmpq_mat_mul(B, I, A); fmpq_mat_mul(C, A, I); result = fmpq_mat_equal(A, B) && fmpq_mat_equal(A, C); if (!result) { flint_printf("FAIL:\n"); flint_printf("A:\n"); fmpq_mat_print(A); flint_printf("B:\n"); fmpq_mat_print(B); flint_printf("C:\n"); fmpq_mat_print(C); flint_printf("I:\n"); fmpq_mat_print(I); abort(); } fmpq_mat_clear(A); fmpq_mat_clear(B); fmpq_mat_clear(C); fmpq_mat_clear(I); } FLINT_TEST_CLEANUP(state); flint_printf("PASS\n"); return EXIT_SUCCESS; }
inline void subtractMultipleTo(DMatQQFlint& C, const DMatQQFlint& A, const DMatQQFlint& B) { DMatQQFlint D(C.ring(), A.numRows(), B.numColumns()); fmpq_mat_mul(D.fmpq_mat(), A.fmpq_mat(), B.fmpq_mat()); fmpq_mat_sub(C.fmpq_mat(), C.fmpq_mat(), D.fmpq_mat()); }
inline void mult(const DMatQQFlint& A, const DMatQQFlint& B, DMatQQFlint& result_product) { // The A and B on the next line are switched because the memory layout expected // is the transpose of what we have for DMat. fmpq_mat_mul(result_product.fmpq_mat(), A.fmpq_mat(), B.fmpq_mat()); }
inline void mult(const DMatQQ& A, const DMatQQ& B, DMatQQ& result_product) { FlintQQMat A1(A); FlintQQMat B1(B); FlintQQMat result1(A.numRows(), B.numColumns()); fmpq_mat_mul(result1.value(), A1.value(), B1.value()); result1.toDMat(result_product); }
void _fmpq_mat_randtest_positive_semidefinite(fmpq_mat_t mat, flint_rand_t state, mp_bitcnt_t bits) { slong n; fmpq_mat_t R, RT; if (!fmpq_mat_is_square(mat)) abort(); /* assert */ n = fmpq_mat_nrows(mat); fmpq_mat_init(R, n, n); fmpq_mat_init(RT, n, n); fmpq_mat_randtest(R, state, bits); fmpq_mat_transpose(RT, R); fmpq_mat_mul(mat, R, RT); fmpq_mat_clear(R); fmpq_mat_clear(RT); }
inline void subtractMultipleTo(DMatQQ& C, const DMatQQ& A, const DMatQQ& B) { FlintQQMat A1(A); FlintQQMat B1(B); FlintQQMat C1(C); FlintQQMat result1(A.numRows(), B.numColumns()); FlintQQMat D1(A.numRows(), B.numColumns()); fmpq_mat_mul(D1.value(), A1.value(), B1.value()); fmpq_mat_sub(C1.value(), C1.value(), D1.value()); C1.toDMat(C); }
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("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("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; }
int main(void) { int i; FLINT_TEST_INIT(state); flint_printf("solve_dixon...."); fflush(stdout); /* Solve nonsingular systems */ for (i = 0; i < 100 * flint_test_multiplier(); i++) { fmpq_mat_t A, B, X, AX; fmpq_t d; int success; slong n, m, bits; n = n_randint(state, 10); m = n_randint(state, 10); bits = 1 + n_randint(state, 100); fmpq_mat_init(A, n, n); fmpq_mat_init(B, n, m); fmpq_mat_init(X, n, m); fmpq_mat_init(AX, n, m); fmpq_init(d); /* XXX: replace with a randtest function */ do { fmpq_mat_randtest(A, state, bits); fmpq_mat_det(d, A); } while (fmpq_is_zero(d)); fmpq_clear(d); fmpq_mat_randtest(B, state, bits); success = fmpq_mat_solve_dixon(X, A, B); fmpq_mat_mul(AX, A, X); if (!fmpq_mat_equal(AX, B) || !success) { flint_printf("FAIL!\n"); flint_printf("success: %d\n", success); flint_printf("A:\n"); fmpq_mat_print(A); flint_printf("B:\n"); fmpq_mat_print(B); flint_printf("X:\n"); fmpq_mat_print(X); flint_printf("AX:\n"); fmpq_mat_print(AX); abort(); } fmpq_mat_clear(A); fmpq_mat_clear(B); fmpq_mat_clear(X); fmpq_mat_clear(AX); } /* Check singular systems */ for (i = 0; i < 100 * flint_test_multiplier(); i++) { fmpq_mat_t A, B, X; fmpz_mat_t M; fmpz_t den; slong n, m, bits; int success; n = 1 + n_randint(state, 10); m = 1 + n_randint(state, 10); bits = 1 + n_randint(state, 100); fmpz_init(den); fmpz_mat_init(M, n, n); fmpz_mat_randrank(M, state, n_randint(state, n), bits); if (i % 2) fmpz_mat_randops(M, state, n_randint(state, 2*m*n + 1)); fmpz_randtest_not_zero(den, state, bits); fmpq_mat_init(A, n, n); fmpq_mat_set_fmpz_mat_div_fmpz(A, M, den); fmpq_mat_init(B, n, m); fmpq_mat_randtest(B, state, bits); fmpq_mat_init(X, n, m); success = fmpq_mat_solve_dixon(X, A, B); if (success != 0) { flint_printf("FAIL!\n"); flint_printf("Expected success = 0\n"); fmpq_mat_print(A); flint_printf("\n"); abort(); } fmpq_mat_clear(A); fmpq_mat_clear(B); fmpq_mat_clear(X); fmpz_mat_clear(M); fmpz_clear(den); } FLINT_TEST_CLEANUP(state); flint_printf("PASS\n"); return 0; }
int main(void) { long i; flint_rand_t state; printf("trace...."); fflush(stdout); flint_randinit(state); /* Test trace(AB) = trace(BA) */ for (i = 0; i < 1000; i++) { fmpq_mat_t A, B, AB, BA; fmpq_t trab, trba; long m, n; m = n_randint(state, 10); n = n_randint(state, 10); fmpq_mat_init(A, m, n); fmpq_mat_init(B, n, m); fmpq_mat_init(AB, m, m); fmpq_mat_init(BA, n, n); fmpq_init(trab); fmpq_init(trba); fmpq_mat_randtest(A, state, 1 + n_randint(state, 100)); fmpq_mat_randtest(B, state, 1 + n_randint(state, 100)); fmpq_mat_mul(AB, A, B); fmpq_mat_mul(BA, B, A); fmpq_mat_trace(trab, AB); fmpq_mat_trace(trba, BA); if (!fmpq_equal(trab, trba)) { printf("FAIL:\n"); fmpq_mat_print(A), printf("\n"); fmpq_mat_print(B), printf("\n"); fmpq_mat_print(AB), printf("\n"); fmpq_mat_print(BA), printf("\n"); printf("tr(AB): "), fmpq_print(trab), printf("\n"); printf("tr(BA): "), fmpq_print(trba), printf("\n"); abort(); } fmpq_mat_clear(A); fmpq_mat_clear(B); fmpq_mat_clear(AB); fmpq_mat_clear(BA); fmpq_clear(trab); fmpq_clear(trba); } flint_randclear(state); _fmpz_cleanup(); printf("PASS\n"); return 0; }