int
_spd_solve(arb_mat_t X, const arb_mat_t A, const arb_mat_t B, slong prec)
{
slong n, m;
int result;
arb_mat_t L;
n = arb_mat_nrows(A);
m = arb_mat_ncols(X);
if (n == 0 || m == 0)
return 1;
n = arb_mat_nrows(A);
arb_mat_init(L, n, n);
result = arb_mat_cho(L, A, prec);
if (result)
{
arb_mat_solve_cho_precomp(X, L, B, prec);
}
arb_mat_clear(L);
return result;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("cho....");
fflush(stdout);
flint_randinit(state);
/* check special matrices */
{
slong n;
for (n = 1; n < 10; n++)
{
slong lprec;
arb_mat_t L, A;
arb_mat_init(L, n, n);
arb_mat_init(A, n, n);
for (lprec = 2; lprec < 10; lprec++)
{
int result;
slong prec;
prec = 1 << lprec;
/* zero */
arb_mat_zero(A);
result = arb_mat_cho(L, A, prec);
if (result)
{
flint_printf("FAIL (zero):\n");
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("L = \n"); arb_mat_printd(L, 15);
flint_printf("\n\n");
}
/* negative identity */
arb_mat_one(A);
arb_mat_neg(A, A);
result = arb_mat_cho(L, A, prec);
if (result)
{
flint_printf("FAIL (negative identity):\n");
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("L = \n"); arb_mat_printd(L, 15);
flint_printf("\n\n");
}
/* identity */
arb_mat_one(A);
result = arb_mat_cho(L, A, prec);
if (!result || !arb_mat_equal(L, A))
{
flint_printf("FAIL (identity):\n");
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("L = \n"); arb_mat_printd(L, 15);
flint_printf("\n\n");
}
}
arb_mat_clear(L);
arb_mat_clear(A);
}
}
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
fmpq_mat_t Q;
arb_mat_t A, L, U, T;
slong n, qbits, prec;
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);
arb_mat_init(A, n, n);
arb_mat_init(L, n, n);
arb_mat_init(U, n, n);
arb_mat_init(T, n, n);
_fmpq_mat_randtest_positive_semidefinite(Q, state, qbits);
q_invertible = fmpq_mat_is_invertible(Q);
if (!q_invertible)
{
arb_mat_set_fmpq_mat(A, Q, prec);
r_invertible = arb_mat_cho(L, 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"); arb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("L = \n"); arb_mat_printd(L, 15); flint_printf("\n\n");
}
}
else
{
/* now this must converge */
while (1)
{
arb_mat_set_fmpq_mat(A, Q, prec);
r_invertible = arb_mat_cho(L, A, prec);
if (r_invertible)
{
break;
}
else
{
if (prec > 10000)
{
flint_printf("FAIL: failed to converge at 10000 bits\n");
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n");
abort();
}
prec *= 2;
}
}
arb_mat_transpose(U, L);
arb_mat_mul(T, L, U, prec);
if (!arb_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"); arb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("L = \n"); arb_mat_printd(L, 15); flint_printf("\n\n");
flint_printf("U = \n"); arb_mat_printd(U, 15); flint_printf("\n\n");
flint_printf("L*U = \n"); arb_mat_printd(T, 15); flint_printf("\n\n");
abort();
}
}
fmpq_mat_clear(Q);
arb_mat_clear(A);
arb_mat_clear(L);
arb_mat_clear(U);
arb_mat_clear(T);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
