int fmpq_mat_is_invertible(const fmpq_mat_t A)
{
int r;
fmpq_t t;
fmpq_init(t);
fmpq_mat_det(t, A);
r = !fmpq_is_zero(t);
fmpq_clear(t);
return r;
}
inline void determinant(const DMatQQFlint& A,
M2::ARingQQFlint::ElementType& result_det)
{
fmpq_mat_det(&result_det, A.fmpq_mat());
}
int main()
{
long iter;
flint_rand_t state;
printf("det....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000; iter++)
{
fmpq_mat_t Q;
fmpq_t Qdet;
acb_mat_t A;
acb_t Adet, imagunit;
long n, qbits, prec;
int imaginary;
n = n_randint(state, 8);
qbits = 1 + n_randint(state, 100);
prec = 2 + n_randint(state, 200);
imaginary = n_randint(state, 2);
fmpq_mat_init(Q, n, n);
fmpq_init(Qdet);
acb_mat_init(A, n, n);
acb_init(Adet);
acb_init(imagunit);
fmpq_mat_randtest(Q, state, qbits);
fmpq_mat_det(Qdet, Q);
acb_mat_set_fmpq_mat(A, Q, prec);
if (imaginary)
{
acb_onei(imagunit);
acb_mat_scalar_mul_acb(A, A, imagunit, prec);
}
acb_mat_det(Adet, A, prec);
if (imaginary)
{
acb_onei(imagunit);
acb_inv(imagunit, imagunit, prec);
acb_pow_ui(imagunit, imagunit, n, prec);
acb_mul(Adet, Adet, imagunit, prec);
}
if (!acb_contains_fmpq(Adet, Qdet))
{
printf("FAIL (containment, iter = %ld)\n", iter);
printf("n = %ld, prec = %ld\n", n, prec);
printf("\n");
printf("Q = \n"); fmpq_mat_print(Q); printf("\n\n");
printf("Qdet = \n"); fmpq_print(Qdet); printf("\n\n");
printf("A = \n"); acb_mat_printd(A, 15); printf("\n\n");
printf("Adet = \n"); acb_printd(Adet, 15); printf("\n\n");
printf("Adet = \n"); acb_print(Adet); printf("\n\n");
abort();
}
fmpq_mat_clear(Q);
fmpq_clear(Qdet);
acb_mat_clear(A);
acb_clear(Adet);
acb_clear(imagunit);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("det....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100000; iter++)
{
fmpq_mat_t Q;
fmpq_t Qdet;
arb_mat_t A;
arb_t Adet;
slong n, qbits, prec;
n = n_randint(state, 8);
qbits = 1 + n_randint(state, 100);
prec = 2 + n_randint(state, 200);
fmpq_mat_init(Q, n, n);
fmpq_init(Qdet);
arb_mat_init(A, n, n);
arb_init(Adet);
fmpq_mat_randtest(Q, state, qbits);
fmpq_mat_det(Qdet, Q);
arb_mat_set_fmpq_mat(A, Q, prec);
arb_mat_det(Adet, A, prec);
if (!arb_contains_fmpq(Adet, Qdet))
{
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("Qdet = \n"); fmpq_print(Qdet); flint_printf("\n\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("Adet = \n"); arb_printd(Adet, 15); flint_printf("\n\n");
flint_printf("Adet = \n"); arb_print(Adet); flint_printf("\n\n");
abort();
}
fmpq_mat_clear(Q);
fmpq_clear(Qdet);
arb_mat_clear(A);
arb_clear(Adet);
}
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;
}
