int fmpq_mat_inv(fmpq_mat_t B, const fmpq_mat_t A)
{
long n = A->r;
if (n == 0)
{
return 1;
}
else if (n == 1)
{
if (fmpq_is_zero(fmpq_mat_entry(A, 0, 0)))
return 0;
fmpq_inv(fmpq_mat_entry(B, 0, 0), fmpq_mat_entry(A, 0, 0));
return 1;
}
else if (n == 2)
{
fmpq_t d;
int success;
fmpq_init(d);
fmpq_mul(d, fmpq_mat_entry(A, 0, 0), fmpq_mat_entry(A, 1, 1));
fmpq_submul(d, fmpq_mat_entry(A, 0, 1), fmpq_mat_entry(A, 1, 0));
success = !fmpq_is_zero(d);
if (success)
{
fmpq_t t00, t01, t10, t11;
fmpq_inv(d, d);
fmpq_init(t00);
fmpq_init(t01);
fmpq_init(t10);
fmpq_init(t11);
fmpq_mul(t00, fmpq_mat_entry(A, 1, 1), d);
fmpq_mul(t01, fmpq_mat_entry(A, 0, 1), d);
fmpq_mul(t10, fmpq_mat_entry(A, 1, 0), d);
fmpq_mul(t11, fmpq_mat_entry(A, 0, 0), d);
fmpq_set(fmpq_mat_entry(B, 0, 0), t00);
fmpq_neg(fmpq_mat_entry(B, 0, 1), t01);
fmpq_neg(fmpq_mat_entry(B, 1, 0), t10);
fmpq_set(fmpq_mat_entry(B, 1, 1), t11);
fmpq_clear(t00);
fmpq_clear(t01);
fmpq_clear(t10);
fmpq_clear(t11);
}
fmpq_clear(d);
return success;
}
else
{
fmpz_mat_t Aclear, Bclear, I;
fmpz * den;
long i;
int success;
fmpz_mat_init(Aclear, n, n);
fmpz_mat_init(Bclear, n, n);
fmpz_mat_init(I, n, n);
den = _fmpz_vec_init(n);
fmpq_mat_get_fmpz_mat_rowwise(Aclear, den, A);
for (i = 0; i < n; i++)
fmpz_set(fmpz_mat_entry(I, i, i), den + i);
success = fmpz_mat_solve(Bclear, den, Aclear, I);
if (success)
fmpq_mat_set_fmpz_mat_div_fmpz(B, Bclear, den);
fmpz_mat_clear(Aclear);
fmpz_mat_clear(Bclear);
fmpz_mat_clear(I);
_fmpz_vec_clear(den, A->r);
return 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;
}
