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
82
|
/* Copyright (c) 2022, NVIDIA CORPORATION. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* * Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* * Neither the name of NVIDIA CORPORATION nor the names of its
* contributors may be used to endorse or promote products derived
* from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY
* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
* OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
/* Computation of Gerschgorin interval for symmetric, tridiagonal matrix */
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <cfloat>
#include "util.h"
#include "gerschgorin.h"
////////////////////////////////////////////////////////////////////////////////
//! Compute Gerschgorin interval for symmetric, tridiagonal matrix
//! @param d diagonal elements
//! @param s superdiagonal elements
//! @param n size of matrix
//! @param lg lower limit of Gerschgorin interval
//! @param ug upper limit of Gerschgorin interval
////////////////////////////////////////////////////////////////////////////////
void computeGerschgorin(float *d, float *s, unsigned int n, float &lg,
float &ug) {
lg = FLT_MAX;
ug = -FLT_MAX;
// compute bounds
for (unsigned int i = 1; i < (n - 1); ++i) {
// sum over the absolute values of all elements of row i
float sum_abs_ni = fabsf(s[i - 1]) + fabsf(s[i]);
lg = min(lg, d[i] - sum_abs_ni);
ug = max(ug, d[i] + sum_abs_ni);
}
// first and last row, only one superdiagonal element
// first row
lg = min(lg, d[0] - fabsf(s[0]));
ug = max(ug, d[0] + fabsf(s[0]));
// last row
lg = min(lg, d[n - 1] - fabsf(s[n - 2]));
ug = max(ug, d[n - 1] + fabsf(s[n - 2]));
// increase interval to avoid side effects of fp arithmetic
float bnorm = max(fabsf(ug), fabsf(lg));
// these values depend on the implementation of floating count that is
// employed in the following
float psi_0 = 11 * FLT_EPSILON * bnorm;
float psi_n = 11 * FLT_EPSILON * bnorm;
lg = lg - bnorm * 2 * n * FLT_EPSILON - psi_0;
ug = ug + bnorm * 2 * n * FLT_EPSILON + psi_n;
ug = max(lg, ug);
}
|
