-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathEIGENCCO.SIF
190 lines (127 loc) · 3.55 KB
/
EIGENCCO.SIF
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
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
***************************
* SET UP THE INITIAL DATA *
***************************
NAME EIGENCCO
* Problem :
* --------
* Solving symmetric eigenvalue problems as systems of
* nonlinear equations.
* The problem is, given a symmetric matrix A, to find an orthogonal
* matrix Q and diagonal matrix D such that A = Q(T) D Q.
* Example C: a tridiagonal matrix suggested by J. H. Wilkinson.
* Source: An idea by Nick Gould
* Constrained optimization version
* SIF input: Nick Gould, Nov 1992.
* classification SQR2-AN-V-V
* The dimension of the matrix is 2 M + 1.
*IE M 2 $-PARAMETER
*IE M 10 $-PARAMETER original value
IE M 25 $-PARAMETER
* other parameter definitions
RI RM M
IA M+1 M 1
I+ N M+1 M
IE 1 1
IE 2 2
IA N-1 N -1
* Define the upper triangular part of the matrix.
A= A(1,1) RM
DO J 2 N
IA J-1 J -1
IA J-2 J -2
I- M+1-J M J-1
RI RM+1-J M+1-J
DO I 1 J-2
AE A(I,J) 0.0
OD I
AE A(J-1,J) 1.0
A= A(J,J) RM+1-J
OD J
VARIABLES
DO J 1 N
* Define the eigenvalues
X D(J)
DO I 1 N
* Define the eigenvectors
X Q(I,J)
ND
GROUPS
DO J 1 N
DO I 1 J
* Introduce the eigen-equations Q(T) D Q - A = 0.
XN E(I,J)
* Introduce the orthogonality-equations Q(T) Q - I = 0.
XE O(I,J)
ND
CONSTANTS
DO J 1 N
X EIGENCCO O(J,J) 1.0
DO I 1 J
Z EIGENCCO E(I,J) A(I,J)
ND
BOUNDS
FR EIGENCCO 'DEFAULT'
START POINT
XV EIGENCCO 'DEFAULT' 0.0
DO J 1 N
XV EIGENCCO D(J) 1.0
XV EIGENCCO Q(J,J) 1.0
ND
ELEMENT TYPE
EV 2PROD Q1 Q2
EV 3PROD Q1 Q2
EV 3PROD D
ELEMENT USES
DO J 1 N
DO I 1 J
DO K 1 N
XT E(I,J,K) 3PROD
ZV E(I,J,K) Q1 Q(K,I)
ZV E(I,J,K) Q2 Q(K,J)
ZV E(I,J,K) D D(K)
XT O(I,J,K) 2PROD
ZV O(I,J,K) Q1 Q(K,I)
ZV O(I,J,K) Q2 Q(K,J)
ND
GROUP TYPE
GV L2 GVAR
GROUP USES
DO J 1 N
DO I 1 J
DO K 1 N
XT E(I,J) L2
XE E(I,J) E(I,J,K)
XE O(I,J) O(I,J,K)
ND
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS EIGENCCO
INDIVIDUALS
T 2PROD
F Q1 * Q2
G Q1 Q2
G Q2 Q1
H Q1 Q2 1.0D+0
T 3PROD
F Q1 * Q2 * D
G Q1 Q2 * D
G Q2 Q1 * D
G D Q1 * Q2
H Q1 Q2 D
H Q1 D Q2
H Q2 D Q1
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS EIGENCCO
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0D+0
ENDATA