1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
|
/*
Copyright 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"
void
acb_mat_eig_global_enclosure(mag_t eps, const acb_mat_t A, acb_srcptr E, const acb_mat_t R, slong prec)
{
acb_mat_t Y, R1, R2;
slong i, j, n;
mag_t r1, r2;
n = acb_mat_nrows(A);
acb_mat_init(Y, n, n);
acb_mat_init(R1, n, n);
acb_mat_init(R2, n, n);
mag_init(r1);
mag_init(r2);
/* Y ~= inv(R) */
acb_mat_one(R1);
acb_mat_approx_solve(Y, R, R1, prec);
/* R2 = Y*R - I */
acb_mat_mul(R2, Y, R, prec);
for (i = 0; i < n; i++)
acb_sub_ui(acb_mat_entry(R2, i, i), acb_mat_entry(R2, i, i), 1, prec);
acb_mat_bound_inf_norm(r2, R2);
if (mag_cmp_2exp_si(r2, 0) < 0)
{
/* R1 = Y*(AR - RD) */
acb_mat_mul(R2, A, R, prec);
for (i = 0; i < n; i++)
for (j = 0; j < n; j++)
acb_submul(acb_mat_entry(R2, i, j), acb_mat_entry(R, i, j), E + j, prec);
acb_mat_mul(R1, Y, R2, prec);
acb_mat_bound_inf_norm(r1, R1);
mag_geom_series(r2, r2, 0);
mag_mul(eps, r1, r2);
}
else
{
mag_inf(eps);
}
acb_mat_clear(R1);
acb_mat_clear(R2);
acb_mat_clear(Y);
mag_clear(r1);
mag_clear(r2);
}
|
