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
|
---
:name: ctgex2
:md5sum: 291e324cd2dab391083a4d6d15ee8c8d
:category: :subroutine
:arguments:
- wantq:
:type: logical
:intent: input
- wantz:
:type: logical
:intent: input
- n:
:type: integer
:intent: input
- a:
:type: complex
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- b:
:type: complex
:intent: input/output
:dims:
- ldb
- n
- ldb:
:type: integer
:intent: input
- q:
:type: complex
:intent: input/output
:dims:
- "wantq ? ldq : 0"
- "wantq ? n : 0"
- ldq:
:type: integer
:intent: input
- z:
:type: complex
:intent: input/output
:dims:
- "wantq ? ldz : 0"
- "wantq ? n : 0"
- ldz:
:type: integer
:intent: input
- j1:
:type: integer
:intent: input
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE CTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, J1, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* CTGEX2 swaps adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22)\n\
* in an upper triangular matrix pair (A, B) by an unitary equivalence\n\
* transformation.\n\
*\n\
* (A, B) must be in generalized Schur canonical form, that is, A and\n\
* B are both upper triangular.\n\
*\n\
* Optionally, the matrices Q and Z of generalized Schur vectors are\n\
* updated.\n\
*\n\
* Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)'\n\
* Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'\n\
*\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* WANTQ (input) LOGICAL\n\
* .TRUE. : update the left transformation matrix Q;\n\
* .FALSE.: do not update Q.\n\
*\n\
* WANTZ (input) LOGICAL\n\
* .TRUE. : update the right transformation matrix Z;\n\
* .FALSE.: do not update Z.\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrices A and B. N >= 0.\n\
*\n\
* A (input/output) COMPLEX arrays, dimensions (LDA,N)\n\
* On entry, the matrix A in the pair (A, B).\n\
* On exit, the updated matrix A.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,N).\n\
*\n\
* B (input/output) COMPLEX arrays, dimensions (LDB,N)\n\
* On entry, the matrix B in the pair (A, B).\n\
* On exit, the updated matrix B.\n\
*\n\
* LDB (input) INTEGER\n\
* The leading dimension of the array B. LDB >= max(1,N).\n\
*\n\
* Q (input/output) COMPLEX array, dimension (LDZ,N)\n\
* If WANTQ = .TRUE, on entry, the unitary matrix Q. On exit,\n\
* the updated matrix Q.\n\
* Not referenced if WANTQ = .FALSE..\n\
*\n\
* LDQ (input) INTEGER\n\
* The leading dimension of the array Q. LDQ >= 1;\n\
* If WANTQ = .TRUE., LDQ >= N.\n\
*\n\
* Z (input/output) COMPLEX array, dimension (LDZ,N)\n\
* If WANTZ = .TRUE, on entry, the unitary matrix Z. On exit,\n\
* the updated matrix Z.\n\
* Not referenced if WANTZ = .FALSE..\n\
*\n\
* LDZ (input) INTEGER\n\
* The leading dimension of the array Z. LDZ >= 1;\n\
* If WANTZ = .TRUE., LDZ >= N.\n\
*\n\
* J1 (input) INTEGER\n\
* The index to the first block (A11, B11).\n\
*\n\
* INFO (output) INTEGER\n\
* =0: Successful exit.\n\
* =1: The transformed matrix pair (A, B) would be too far\n\
* from generalized Schur form; the problem is ill-\n\
* conditioned.\n\
*\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* Based on contributions by\n\
* Bo Kagstrom and Peter Poromaa, Department of Computing Science,\n\
* Umea University, S-901 87 Umea, Sweden.\n\
*\n\
* In the current code both weak and strong stability tests are\n\
* performed. The user can omit the strong stability test by changing\n\
* the internal logical parameter WANDS to .FALSE.. See ref. [2] for\n\
* details.\n\
*\n\
* [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the\n\
* Generalized Real Schur Form of a Regular Matrix Pair (A, B), in\n\
* M.S. Moonen et al (eds), Linear Algebra for Large Scale and\n\
* Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.\n\
*\n\
* [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified\n\
* Eigenvalues of a Regular Matrix Pair (A, B) and Condition\n\
* Estimation: Theory, Algorithms and Software, Report UMINF-94.04,\n\
* Department of Computing Science, Umea University, S-901 87 Umea,\n\
* Sweden, 1994. Also as LAPACK Working Note 87. To appear in\n\
* Numerical Algorithms, 1996.\n\
*\n\
* =====================================================================\n\
*\n"
|
