File: cunbdb

package info (click to toggle)
ruby-lapack 1.8.2-1
  • links: PTS, VCS
  • area: main
  • in suites: bookworm, forky, sid, trixie
  • size: 28,572 kB
  • sloc: ansic: 191,612; ruby: 3,937; makefile: 6
file content (270 lines) | stat: -rw-r--r-- 8,966 bytes parent folder | download | duplicates (5)
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
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
--- 
:name: cunbdb
:md5sum: f3d37f59c9a21d3cf112e287fa50b474
:category: :subroutine
:arguments: 
- trans: 
    :type: char
    :intent: input
- signs: 
    :type: char
    :intent: input
- m: 
    :type: integer
    :intent: input
- p: 
    :type: integer
    :intent: input
- q: 
    :type: integer
    :intent: input
- x11: 
    :type: complex
    :intent: input/output
    :dims: 
    - ldx11
    - q
- ldx11: 
    :type: integer
    :intent: input
- x12: 
    :type: complex
    :intent: input/output
    :dims: 
    - ldx12
    - m-q
- ldx12: 
    :type: integer
    :intent: input
- x21: 
    :type: complex
    :intent: input/output
    :dims: 
    - ldx21
    - q
- ldx21: 
    :type: integer
    :intent: input
- x22: 
    :type: complex
    :intent: input/output
    :dims: 
    - ldx22
    - m-q
- ldx22: 
    :type: integer
    :intent: input
- theta: 
    :type: real
    :intent: output
    :dims: 
    - q
- phi: 
    :type: real
    :intent: output
    :dims: 
    - q-1
- taup1: 
    :type: complex
    :intent: output
    :dims: 
    - p
- taup2: 
    :type: complex
    :intent: output
    :dims: 
    - m-p
- tauq1: 
    :type: complex
    :intent: output
    :dims: 
    - q
- tauq2: 
    :type: complex
    :intent: output
    :dims: 
    - m-q
- work: 
    :type: complex
    :intent: workspace
    :dims: 
    - MAX(1,lwork)
- lwork: 
    :type: integer
    :intent: input
    :option: true
    :default: m-q
- info: 
    :type: integer
    :intent: output
:substitutions: 
  p: ldx11
  ldx12: p
  ldx21: p
  ldx22: p
:fortran_help: "      SUBROUTINE CUNBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, X21, LDX21, X22, LDX22, THETA, PHI, TAUP1, TAUP2, TAUQ1, TAUQ2, WORK, LWORK, INFO )\n\n\
  *  Purpose\n\
  *  =======\n\
  *\n\
  *  CUNBDB simultaneously bidiagonalizes the blocks of an M-by-M\n\
  *  partitioned unitary matrix X:\n\
  *\n\
  *                                  [ B11 | B12 0  0 ]\n\
  *      [ X11 | X12 ]   [ P1 |    ] [  0  |  0 -I  0 ] [ Q1 |    ]**H\n\
  *  X = [-----------] = [---------] [----------------] [---------]   .\n\
  *      [ X21 | X22 ]   [    | P2 ] [ B21 | B22 0  0 ] [    | Q2 ]\n\
  *                                  [  0  |  0  0  I ]\n\
  *\n\
  *  X11 is P-by-Q. Q must be no larger than P, M-P, or M-Q. (If this is\n\
  *  not the case, then X must be transposed and/or permuted. This can be\n\
  *  done in constant time using the TRANS and SIGNS options. See CUNCSD\n\
  *  for details.)\n\
  *\n\
  *  The unitary matrices P1, P2, Q1, and Q2 are P-by-P, (M-P)-by-\n\
  *  (M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. They are\n\
  *  represented implicitly by Householder vectors.\n\
  *\n\
  *  B11, B12, B21, and B22 are Q-by-Q bidiagonal matrices represented\n\
  *  implicitly by angles THETA, PHI.\n\
  *\n\n\
  *  Arguments\n\
  *  =========\n\
  *\n\
  *  TRANS   (input) CHARACTER\n\
  *          = 'T':      X, U1, U2, V1T, and V2T are stored in row-major\n\
  *                      order;\n\
  *          otherwise:  X, U1, U2, V1T, and V2T are stored in column-\n\
  *                      major order.\n\
  *\n\
  *  SIGNS   (input) CHARACTER\n\
  *          = 'O':      The lower-left block is made nonpositive (the\n\
  *                      \"other\" convention);\n\
  *          otherwise:  The upper-right block is made nonpositive (the\n\
  *                      \"default\" convention).\n\
  *\n\
  *  M       (input) INTEGER\n\
  *          The number of rows and columns in X.\n\
  *\n\
  *  P       (input) INTEGER\n\
  *          The number of rows in X11 and X12. 0 <= P <= M.\n\
  *\n\
  *  Q       (input) INTEGER\n\
  *          The number of columns in X11 and X21. 0 <= Q <=\n\
  *          MIN(P,M-P,M-Q).\n\
  *\n\
  *  X11     (input/output) COMPLEX array, dimension (LDX11,Q)\n\
  *          On entry, the top-left block of the unitary matrix to be\n\
  *          reduced. On exit, the form depends on TRANS:\n\
  *          If TRANS = 'N', then\n\
  *             the columns of tril(X11) specify reflectors for P1,\n\
  *             the rows of triu(X11,1) specify reflectors for Q1;\n\
  *          else TRANS = 'T', and\n\
  *             the rows of triu(X11) specify reflectors for P1,\n\
  *             the columns of tril(X11,-1) specify reflectors for Q1.\n\
  *\n\
  *  LDX11   (input) INTEGER\n\
  *          The leading dimension of X11. If TRANS = 'N', then LDX11 >=\n\
  *          P; else LDX11 >= Q.\n\
  *\n\
  *  X12     (input/output) CMPLX array, dimension (LDX12,M-Q)\n\
  *          On entry, the top-right block of the unitary matrix to\n\
  *          be reduced. On exit, the form depends on TRANS:\n\
  *          If TRANS = 'N', then\n\
  *             the rows of triu(X12) specify the first P reflectors for\n\
  *             Q2;\n\
  *          else TRANS = 'T', and\n\
  *             the columns of tril(X12) specify the first P reflectors\n\
  *             for Q2.\n\
  *\n\
  *  LDX12   (input) INTEGER\n\
  *          The leading dimension of X12. If TRANS = 'N', then LDX12 >=\n\
  *          P; else LDX11 >= M-Q.\n\
  *\n\
  *  X21     (input/output) COMPLEX array, dimension (LDX21,Q)\n\
  *          On entry, the bottom-left block of the unitary matrix to\n\
  *          be reduced. On exit, the form depends on TRANS:\n\
  *          If TRANS = 'N', then\n\
  *             the columns of tril(X21) specify reflectors for P2;\n\
  *          else TRANS = 'T', and\n\
  *             the rows of triu(X21) specify reflectors for P2.\n\
  *\n\
  *  LDX21   (input) INTEGER\n\
  *          The leading dimension of X21. If TRANS = 'N', then LDX21 >=\n\
  *          M-P; else LDX21 >= Q.\n\
  *\n\
  *  X22     (input/output) COMPLEX array, dimension (LDX22,M-Q)\n\
  *          On entry, the bottom-right block of the unitary matrix to\n\
  *          be reduced. On exit, the form depends on TRANS:\n\
  *          If TRANS = 'N', then\n\
  *             the rows of triu(X22(Q+1:M-P,P+1:M-Q)) specify the last\n\
  *             M-P-Q reflectors for Q2,\n\
  *          else TRANS = 'T', and\n\
  *             the columns of tril(X22(P+1:M-Q,Q+1:M-P)) specify the last\n\
  *             M-P-Q reflectors for P2.\n\
  *\n\
  *  LDX22   (input) INTEGER\n\
  *          The leading dimension of X22. If TRANS = 'N', then LDX22 >=\n\
  *          M-P; else LDX22 >= M-Q.\n\
  *\n\
  *  THETA   (output) REAL array, dimension (Q)\n\
  *          The entries of the bidiagonal blocks B11, B12, B21, B22 can\n\
  *          be computed from the angles THETA and PHI. See Further\n\
  *          Details.\n\
  *\n\
  *  PHI     (output) REAL array, dimension (Q-1)\n\
  *          The entries of the bidiagonal blocks B11, B12, B21, B22 can\n\
  *          be computed from the angles THETA and PHI. See Further\n\
  *          Details.\n\
  *\n\
  *  TAUP1   (output) COMPLEX array, dimension (P)\n\
  *          The scalar factors of the elementary reflectors that define\n\
  *          P1.\n\
  *\n\
  *  TAUP2   (output) COMPLEX array, dimension (M-P)\n\
  *          The scalar factors of the elementary reflectors that define\n\
  *          P2.\n\
  *\n\
  *  TAUQ1   (output) COMPLEX array, dimension (Q)\n\
  *          The scalar factors of the elementary reflectors that define\n\
  *          Q1.\n\
  *\n\
  *  TAUQ2   (output) COMPLEX array, dimension (M-Q)\n\
  *          The scalar factors of the elementary reflectors that define\n\
  *          Q2.\n\
  *\n\
  *  WORK    (workspace) COMPLEX array, dimension (LWORK)\n\
  *\n\
  *  LWORK   (input) INTEGER\n\
  *          The dimension of the array WORK. LWORK >= M-Q.\n\
  *\n\
  *          If LWORK = -1, then a workspace query is assumed; the routine\n\
  *          only calculates the optimal size of the WORK array, returns\n\
  *          this value as the first entry of the WORK array, and no error\n\
  *          message related to LWORK is issued by XERBLA.\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 bidiagonal blocks B11, B12, B21, and B22 are represented\n\
  *  implicitly by angles THETA(1), ..., THETA(Q) and PHI(1), ...,\n\
  *  PHI(Q-1). B11 and B21 are upper bidiagonal, while B21 and B22 are\n\
  *  lower bidiagonal. Every entry in each bidiagonal band is a product\n\
  *  of a sine or cosine of a THETA with a sine or cosine of a PHI. See\n\
  *  [1] or CUNCSD for details.\n\
  *\n\
  *  P1, P2, Q1, and Q2 are represented as products of elementary\n\
  *  reflectors. See CUNCSD for details on generating P1, P2, Q1, and Q2\n\
  *  using CUNGQR and CUNGLQ.\n\
  *\n\
  *  Reference\n\
  *  =========\n\
  *\n\
  *  [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.\n\
  *      Algorithms, 50(1):33-65, 2009.\n\
  *\n\
  *  ====================================================================\n\
  *\n"