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
|
---
:name: ctrevc
:md5sum: d514272127683844e93020ff209cd3db
:category: :subroutine
:arguments:
- side:
:type: char
:intent: input
- howmny:
:type: char
:intent: input
- select:
:type: logical
:intent: input
:dims:
- n
- n:
:type: integer
:intent: input
- t:
:type: complex
:intent: input/output
:dims:
- ldt
- n
- ldt:
:type: integer
:intent: input
- vl:
:type: complex
:intent: input/output
:dims:
- ldvl
- mm
- ldvl:
:type: integer
:intent: input
- vr:
:type: complex
:intent: input/output
:dims:
- ldvr
- mm
- ldvr:
:type: integer
:intent: input
- mm:
:type: integer
:intent: input
- m:
:type: integer
:intent: output
- work:
:type: complex
:intent: workspace
:dims:
- 2*n
- rwork:
:type: real
:intent: workspace
:dims:
- n
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE CTREVC( SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* CTREVC computes some or all of the right and/or left eigenvectors of\n\
* a complex upper triangular matrix T.\n\
* Matrices of this type are produced by the Schur factorization of\n\
* a complex general matrix: A = Q*T*Q**H, as computed by CHSEQR.\n\
* \n\
* The right eigenvector x and the left eigenvector y of T corresponding\n\
* to an eigenvalue w are defined by:\n\
* \n\
* T*x = w*x, (y**H)*T = w*(y**H)\n\
* \n\
* where y**H denotes the conjugate transpose of the vector y.\n\
* The eigenvalues are not input to this routine, but are read directly\n\
* from the diagonal of T.\n\
* \n\
* This routine returns the matrices X and/or Y of right and left\n\
* eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an\n\
* input matrix. If Q is the unitary factor that reduces a matrix A to\n\
* Schur form T, then Q*X and Q*Y are the matrices of right and left\n\
* eigenvectors of A.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* SIDE (input) CHARACTER*1\n\
* = 'R': compute right eigenvectors only;\n\
* = 'L': compute left eigenvectors only;\n\
* = 'B': compute both right and left eigenvectors.\n\
*\n\
* HOWMNY (input) CHARACTER*1\n\
* = 'A': compute all right and/or left eigenvectors;\n\
* = 'B': compute all right and/or left eigenvectors,\n\
* backtransformed using the matrices supplied in\n\
* VR and/or VL;\n\
* = 'S': compute selected right and/or left eigenvectors,\n\
* as indicated by the logical array SELECT.\n\
*\n\
* SELECT (input) LOGICAL array, dimension (N)\n\
* If HOWMNY = 'S', SELECT specifies the eigenvectors to be\n\
* computed.\n\
* The eigenvector corresponding to the j-th eigenvalue is\n\
* computed if SELECT(j) = .TRUE..\n\
* Not referenced if HOWMNY = 'A' or 'B'.\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix T. N >= 0.\n\
*\n\
* T (input/output) COMPLEX array, dimension (LDT,N)\n\
* The upper triangular matrix T. T is modified, but restored\n\
* on exit.\n\
*\n\
* LDT (input) INTEGER\n\
* The leading dimension of the array T. LDT >= max(1,N).\n\
*\n\
* VL (input/output) COMPLEX array, dimension (LDVL,MM)\n\
* On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must\n\
* contain an N-by-N matrix Q (usually the unitary matrix Q of\n\
* Schur vectors returned by CHSEQR).\n\
* On exit, if SIDE = 'L' or 'B', VL contains:\n\
* if HOWMNY = 'A', the matrix Y of left eigenvectors of T;\n\
* if HOWMNY = 'B', the matrix Q*Y;\n\
* if HOWMNY = 'S', the left eigenvectors of T specified by\n\
* SELECT, stored consecutively in the columns\n\
* of VL, in the same order as their\n\
* eigenvalues.\n\
* Not referenced if SIDE = 'R'.\n\
*\n\
* LDVL (input) INTEGER\n\
* The leading dimension of the array VL. LDVL >= 1, and if\n\
* SIDE = 'L' or 'B', LDVL >= N.\n\
*\n\
* VR (input/output) COMPLEX array, dimension (LDVR,MM)\n\
* On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must\n\
* contain an N-by-N matrix Q (usually the unitary matrix Q of\n\
* Schur vectors returned by CHSEQR).\n\
* On exit, if SIDE = 'R' or 'B', VR contains:\n\
* if HOWMNY = 'A', the matrix X of right eigenvectors of T;\n\
* if HOWMNY = 'B', the matrix Q*X;\n\
* if HOWMNY = 'S', the right eigenvectors of T specified by\n\
* SELECT, stored consecutively in the columns\n\
* of VR, in the same order as their\n\
* eigenvalues.\n\
* Not referenced if SIDE = 'L'.\n\
*\n\
* LDVR (input) INTEGER\n\
* The leading dimension of the array VR. LDVR >= 1, and if\n\
* SIDE = 'R' or 'B'; LDVR >= N.\n\
*\n\
* MM (input) INTEGER\n\
* The number of columns in the arrays VL and/or VR. MM >= M.\n\
*\n\
* M (output) INTEGER\n\
* The number of columns in the arrays VL and/or VR actually\n\
* used to store the eigenvectors. If HOWMNY = 'A' or 'B', M\n\
* is set to N. Each selected eigenvector occupies one\n\
* column.\n\
*\n\
* WORK (workspace) COMPLEX array, dimension (2*N)\n\
*\n\
* RWORK (workspace) REAL array, dimension (N)\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* < 0: if INFO = -i, the i-th argument had an illegal value\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* The algorithm used in this program is basically backward (forward)\n\
* substitution, with scaling to make the the code robust against\n\
* possible overflow.\n\
*\n\
* Each eigenvector is normalized so that the element of largest\n\
* magnitude has magnitude 1; here the magnitude of a complex number\n\
* (x,y) is taken to be |x| + |y|.\n\
*\n\
* =====================================================================\n\
*\n"
|
