int main()
{
slong iter;
flint_rand_t state;
flint_printf("solve_tril....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 2000 * arb_test_multiplier(); iter++)
{
arb_mat_t A, X, B, Y;
slong rows, cols, prec, i, j;
int unit;
prec = 2 + n_randint(state, 200);
if (n_randint(state, 10) == 0)
{
rows = n_randint(state, 60);
cols = n_randint(state, 60);
}
else
{
rows = n_randint(state, 10);
cols = n_randint(state, 10);
}
unit = n_randint(state, 2);
arb_mat_init(A, rows, rows);
arb_mat_init(B, rows, cols);
arb_mat_init(X, rows, cols);
arb_mat_init(Y, rows, cols);
arb_mat_randtest(A, state, prec, 10);
arb_mat_randtest(X, state, prec, 10);
arb_mat_randtest(Y, state, prec, 10);
for (i = 0; i < rows; i++)
{
if (unit)
arb_one(arb_mat_entry(A, i, i));
else
arb_set_ui(arb_mat_entry(A, i, i), 1 + n_randint(state, 100));
for (j = i + 1; j < rows; j++)
arb_zero(arb_mat_entry(A, i, j));
}
arb_mat_mul(B, A, X, prec);
if (unit) /* check that diagonal entries are ignored */
{
for (i = 0; i < rows; i++)
arb_set_ui(arb_mat_entry(A, i, i), 1 + n_randint(state, 100));
}
/* Check Y = A^(-1) * (A * X) = X */
arb_mat_solve_tril(Y, A, B, unit, prec);
if (!arb_mat_overlaps(Y, X))
{
flint_printf("FAIL\n");
flint_printf("A = \n"); arb_mat_printd(A, 10); flint_printf("\n\n");
flint_printf("B = \n"); arb_mat_printd(B, 10); flint_printf("\n\n");
flint_printf("X = \n"); arb_mat_printd(X, 10); flint_printf("\n\n");
flint_printf("Y = \n"); arb_mat_printd(Y, 10); flint_printf("\n\n");
flint_abort();
}
/* Check aliasing */
arb_mat_solve_tril(B, A, B, unit, prec);
if (!arb_mat_equal(B, Y))
{
flint_printf("FAIL (aliasing)\n");
flint_printf("A = \n"); arb_mat_printd(A, 10); flint_printf("\n\n");
flint_printf("B = \n"); arb_mat_printd(B, 10); flint_printf("\n\n");
flint_printf("X = \n"); arb_mat_printd(X, 10); flint_printf("\n\n");
flint_printf("Y = \n"); arb_mat_printd(Y, 10); flint_printf("\n\n");
flint_abort();
}
arb_mat_clear(A);
arb_mat_clear(B);
arb_mat_clear(X);
arb_mat_clear(Y);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("frobenius_norm....");
fflush(stdout);
flint_randinit(state);
/* compare to the exact rational norm */
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
fmpq_mat_t Q;
fmpq_t q;
arb_mat_t A;
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(q);
arb_mat_init(A, n, n);
fmpq_mat_randtest(Q, state, qbits);
_fmpq_mat_sum_of_squares(q, Q);
arb_mat_set_fmpq_mat(A, Q, prec);
/* check that the arb interval contains the exact value */
{
arb_t a;
arb_init(a);
arb_mat_frobenius_norm(a, A, prec);
arb_mul(a, a, a, prec);
if (!arb_contains_fmpq(a, 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("frobenius_norm(Q)^2 = \n");
fmpq_print(q);
flint_printf("\n\n");
flint_printf("A = \n");
arb_mat_printd(A, 15);
flint_printf("\n\n");
flint_printf("frobenius_norm(A)^2 = \n");
arb_printd(a, 15);
flint_printf("\n\n");
flint_printf("frobenius_norm(A)^2 = \n");
arb_print(a);
flint_printf("\n\n");
abort();
}
arb_clear(a);
}
/* check that the upper bound is not less than the exact value */
{
mag_t b;
fmpq_t y;
mag_init(b);
fmpq_init(y);
arb_mat_bound_frobenius_norm(b, A);
mag_mul(b, b, b);
mag_get_fmpq(y, b);
if (fmpq_cmp(q, y) > 0)
{
flint_printf("FAIL (bound, 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("frobenius_norm(Q)^2 = \n");
fmpq_print(q);
flint_printf("\n\n");
flint_printf("A = \n");
arb_mat_printd(A, 15);
flint_printf("\n\n");
flint_printf("bound_frobenius_norm(A)^2 = \n");
mag_printd(b, 15);
flint_printf("\n\n");
flint_printf("bound_frobenius_norm(A)^2 = \n");
mag_print(b);
flint_printf("\n\n");
abort();
}
mag_clear(b);
fmpq_clear(y);
}
fmpq_mat_clear(Q);
fmpq_clear(q);
arb_mat_clear(A);
}
/* check trace(A^T A) = frobenius_norm(A)^2 */
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
slong m, n, prec;
arb_mat_t A, AT, ATA;
arb_t t;
prec = 2 + n_randint(state, 200);
m = n_randint(state, 10);
n = n_randint(state, 10);
arb_mat_init(A, m, n);
arb_mat_init(AT, n, m);
arb_mat_init(ATA, n, n);
arb_init(t);
arb_mat_randtest(A, state, 2 + n_randint(state, 100), 10);
arb_mat_transpose(AT, A);
arb_mat_mul(ATA, AT, A, prec);
arb_mat_trace(t, ATA, prec);
arb_sqrt(t, t, prec);
/* check the norm bound */
{
mag_t low, frobenius;
mag_init(low);
arb_get_mag_lower(low, t);
mag_init(frobenius);
arb_mat_bound_frobenius_norm(frobenius, A);
if (mag_cmp(low, frobenius) > 0)
{
flint_printf("FAIL (bound)\n", iter);
flint_printf("m = %wd, n = %wd, prec = %wd\n", m, n, prec);
flint_printf("\n");
flint_printf("A = \n");
arb_mat_printd(A, 15);
flint_printf("\n\n");
flint_printf("lower(sqrt(trace(A^T A))) = \n");
mag_printd(low, 15);
flint_printf("\n\n");
flint_printf("bound_frobenius_norm(A) = \n");
mag_printd(frobenius, 15);
flint_printf("\n\n");
abort();
}
mag_clear(low);
mag_clear(frobenius);
}
/* check the norm interval */
{
arb_t frobenius;
arb_init(frobenius);
arb_mat_frobenius_norm(frobenius, A, prec);
if (!arb_overlaps(t, frobenius))
{
flint_printf("FAIL (overlap)\n", iter);
flint_printf("m = %wd, n = %wd, prec = %wd\n", m, n, prec);
flint_printf("\n");
flint_printf("A = \n");
arb_mat_printd(A, 15);
flint_printf("\n\n");
flint_printf("sqrt(trace(A^T A)) = \n");
arb_printd(t, 15);
flint_printf("\n\n");
flint_printf("frobenius_norm(A) = \n");
arb_printd(frobenius, 15);
flint_printf("\n\n");
abort();
}
arb_clear(frobenius);
}
arb_mat_clear(A);
arb_mat_clear(AT);
arb_mat_clear(ATA);
arb_clear(t);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
