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
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
|
/*
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
acb_mat_eig_simple_rump(acb_ptr E, acb_mat_t L, acb_mat_t R,
const acb_mat_t A, acb_srcptr E_approx, const acb_mat_t R_approx, slong prec)
{
slong i, j, n;
acb_mat_t X, R2;
int result;
n = acb_mat_nrows(A);
if (n == 0)
return 1;
if (n == 1)
{
acb_set_round(E, acb_mat_entry(A, 0, 0), prec);
if (L != NULL)
acb_one(acb_mat_entry(L, 0, 0));
if (R != NULL)
acb_one(acb_mat_entry(R, 0, 0));
return 1;
}
acb_mat_init(X, n, 1);
acb_mat_init(R2, n, n);
result = 1;
for (i = 0; i < n && result; i++)
{
for (j = 0; j < n; j++)
acb_set(acb_mat_entry(X, j, 0), acb_mat_entry(R_approx, j, i));
acb_mat_eig_enclosure_rump(E + i, NULL, X, A, E_approx + i, X, prec);
if (!acb_is_finite(E + i))
result = 0;
for (j = 0; j < i; j++)
if (acb_overlaps(E + i, E + j))
result = 0;
for (j = 0; j < n; j++)
acb_set(acb_mat_entry(R2, j, i), acb_mat_entry(X, j, 0));
}
if (R != NULL)
{
if (result)
acb_mat_set(R, R2);
else
acb_mat_indeterminate(R);
}
if (L != NULL)
{
if (!result || !acb_mat_inv(L, R2, prec))
acb_mat_indeterminate(L);
}
if (!result)
_acb_vec_indeterminate(E, n);
acb_mat_clear(X);
acb_mat_clear(R2);
return result;
}
|
