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
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
|
---
:name: slasd4
:md5sum: 5d9cc23b9dcc49410cef1ca83143a336
:category: :subroutine
:arguments:
- n:
:type: integer
:intent: input
- i:
:type: integer
:intent: input
- d:
:type: real
:intent: input
:dims:
- n
- z:
:type: real
:intent: input
:dims:
- n
- delta:
:type: real
:intent: output
:dims:
- n
- rho:
:type: real
:intent: input
- sigma:
:type: real
:intent: output
- work:
:type: real
:intent: workspace
:dims:
- n
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE SLASD4( N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* This subroutine computes the square root of the I-th updated\n\
* eigenvalue of a positive symmetric rank-one modification to\n\
* a positive diagonal matrix whose entries are given as the squares\n\
* of the corresponding entries in the array d, and that\n\
*\n\
* 0 <= D(i) < D(j) for i < j\n\
*\n\
* and that RHO > 0. This is arranged by the calling routine, and is\n\
* no loss in generality. The rank-one modified system is thus\n\
*\n\
* diag( D ) * diag( D ) + RHO * Z * Z_transpose.\n\
*\n\
* where we assume the Euclidean norm of Z is 1.\n\
*\n\
* The method consists of approximating the rational functions in the\n\
* secular equation by simpler interpolating rational functions.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* N (input) INTEGER\n\
* The length of all arrays.\n\
*\n\
* I (input) INTEGER\n\
* The index of the eigenvalue to be computed. 1 <= I <= N.\n\
*\n\
* D (input) REAL array, dimension ( N )\n\
* The original eigenvalues. It is assumed that they are in\n\
* order, 0 <= D(I) < D(J) for I < J.\n\
*\n\
* Z (input) REAL array, dimension (N)\n\
* The components of the updating vector.\n\
*\n\
* DELTA (output) REAL array, dimension (N)\n\
* If N .ne. 1, DELTA contains (D(j) - sigma_I) in its j-th\n\
* component. If N = 1, then DELTA(1) = 1. The vector DELTA\n\
* contains the information necessary to construct the\n\
* (singular) eigenvectors.\n\
*\n\
* RHO (input) REAL\n\
* The scalar in the symmetric updating formula.\n\
*\n\
* SIGMA (output) REAL\n\
* The computed sigma_I, the I-th updated eigenvalue.\n\
*\n\
* WORK (workspace) REAL array, dimension (N)\n\
* If N .ne. 1, WORK contains (D(j) + sigma_I) in its j-th\n\
* component. If N = 1, then WORK( 1 ) = 1.\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* > 0: if INFO = 1, the updating process failed.\n\
*\n\
* Internal Parameters\n\
* ===================\n\
*\n\
* Logical variable ORGATI (origin-at-i?) is used for distinguishing\n\
* whether D(i) or D(i+1) is treated as the origin.\n\
*\n\
* ORGATI = .true. origin at i\n\
* ORGATI = .false. origin at i+1\n\
*\n\
* Logical variable SWTCH3 (switch-for-3-poles?) is for noting\n\
* if we are working with THREE poles!\n\
*\n\
* MAXIT is the maximum number of iterations allowed for each\n\
* eigenvalue.\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* Based on contributions by\n\
* Ren-Cang Li, Computer Science Division, University of California\n\
* at Berkeley, USA\n\
*\n\
* =====================================================================\n\
*\n"
|
