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/*
Copyright (C) 2018 Fredrik Johansson
This file is part of Arb.
Arb is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include "acb_mat.h"
int main()
{
slong iter;
flint_rand_t state;
flint_printf("approx_eig_qr....");
fflush(stdout);
flint_randinit(state);
/* Test random & DFT matrices */
for (iter = 0; iter < 200 * arb_test_multiplier(); iter++)
{
acb_mat_t A, L, R;
acb_ptr E;
acb_t t;
mag_t b;
slong i, j, n, prec, goal, c0, c1, c2, c3;
int wantL, wantR, result, dft;
dft = n_randint(state, 2);
if (dft)
n = n_randint(state, 30);
else
n = n_randint(state, 15);
goal = 2 + n_randint(state, 100);
wantL = n_randint(state, 2);
wantR = n_randint(state, 2);
acb_mat_init(A, n, n);
acb_mat_init(L, n, n);
acb_mat_init(R, n, n);
acb_init(t);
mag_init(b);
E = _acb_vec_init(n);
for (prec = 32; ; prec *= 2)
{
if (dft)
{
acb_mat_dft(A, 0, prec);
}
else
{
acb_mat_randtest(A, state, 2 + n_randint(state, 200), 5);
acb_mat_get_mid(A, A);
}
acb_mat_approx_eig_qr(E, wantL ? L : NULL, wantR ? R : NULL, A, NULL, 0, prec);
if (dft)
{
/* Verify the known eigenvalues + multiplicities */
c0 = c1 = c2 = c3 = 0;
for (i = 0; i < n; i++)
{
acb_set_d_d(t, 1.0, 0.0);
acb_sub(t, t, E + i, prec);
acb_get_mag(b, t);
c0 += (mag_cmp_2exp_si(b, -goal) < 0);
acb_set_d_d(t, -1.0, 0.0);
acb_sub(t, t, E + i, prec);
acb_get_mag(b, t);
c1 += (mag_cmp_2exp_si(b, -goal) < 0);
acb_set_d_d(t, 0.0, 1.0);
acb_sub(t, t, E + i, prec);
acb_get_mag(b, t);
c2 += (mag_cmp_2exp_si(b, -goal) < 0);
acb_set_d_d(t, 0.0, -1.0);
acb_sub(t, t, E + i, prec);
acb_get_mag(b, t);
c3 += (mag_cmp_2exp_si(b, -goal) < 0);
}
result = (n == 0 || (c0 == (n+4)/4 && c1 == (n+2)/4 && c2 == (n-1)/4 && c3 == (n+1)/4));
}
else
{
result = 1;
}
if (result && wantL)
{
acb_mat_t LA, D;
acb_mat_init(LA, n, n);
acb_mat_init(D, n, n);
/* Check LA - lambda L = 0 */
acb_mat_approx_mul(LA, L, A, prec);
for (i = 0; i < n; i++)
acb_set(acb_mat_entry(D, i, i), E + i);
acb_mat_approx_mul(D, D, L, prec);
acb_mat_sub(LA, LA, D, prec);
for (i = 0; i < n; i++)
{
for (j = 0; j < n; j++)
{
acb_get_mag(b, acb_mat_entry(LA, i, j));
result = result && (mag_cmp_2exp_si(b, -goal) < 0);
}
}
acb_mat_clear(LA);
acb_mat_clear(D);
}
if (result && wantR)
{
acb_mat_t AR, D;
acb_mat_init(AR, n, n);
acb_mat_init(D, n, n);
/* Check AR - R lambda = 0 */
acb_mat_approx_mul(AR, A, R, prec);
for (i = 0; i < n; i++)
acb_set(acb_mat_entry(D, i, i), E + i);
acb_mat_approx_mul(D, R, D, prec);
acb_mat_sub(AR, AR, D, prec);
for (i = 0; i < n; i++)
{
for (j = 0; j < n; j++)
{
acb_get_mag(b, acb_mat_entry(AR, i, j));
result = result && (mag_cmp_2exp_si(b, -goal) < 0);
}
}
acb_mat_clear(AR);
acb_mat_clear(D);
}
if (result)
break;
if (prec > 2000)
{
flint_printf("FAIL (convergence, dft = %d)\n\n", dft);
flint_printf("n = %wd\n\n", n);
acb_mat_printd(A, 10);
flint_printf("\n\n");
for (i = 0; i < n; i++)
{
acb_printn(E + i, 50, 0);
flint_printf("\n");
}
flint_printf("\n");
if (wantL)
{
flint_printf("L = \n");
acb_mat_printd(L, 10);
flint_printf("\n\n");
}
if (wantR)
{
flint_printf("R = \n");
acb_mat_printd(R, 10);
flint_printf("\n\n");
}
flint_abort();
}
}
acb_mat_clear(A);
acb_mat_clear(L);
acb_mat_clear(R);
_acb_vec_clear(E, n);
acb_clear(t);
mag_clear(b);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
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