forked from Reference-LAPACK/lapack
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathcupmtr.f
349 lines (349 loc) · 8.84 KB
/
cupmtr.f
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
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
*> \brief \b CUPMTR
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CUPMTR + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cupmtr.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cupmtr.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cupmtr.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CUPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK,
* INFO )
*
* .. Scalar Arguments ..
* CHARACTER SIDE, TRANS, UPLO
* INTEGER INFO, LDC, M, N
* ..
* .. Array Arguments ..
* COMPLEX AP( * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CUPMTR overwrites the general complex M-by-N matrix C with
*>
*> SIDE = 'L' SIDE = 'R'
*> TRANS = 'N': Q * C C * Q
*> TRANS = 'C': Q**H * C C * Q**H
*>
*> where Q is a complex unitary matrix of order nq, with nq = m if
*> SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
*> nq-1 elementary reflectors, as returned by CHPTRD using packed
*> storage:
*>
*> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
*>
*> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] SIDE
*> \verbatim
*> SIDE is CHARACTER*1
*> = 'L': apply Q or Q**H from the Left;
*> = 'R': apply Q or Q**H from the Right.
*> \endverbatim
*>
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> = 'U': Upper triangular packed storage used in previous
*> call to CHPTRD;
*> = 'L': Lower triangular packed storage used in previous
*> call to CHPTRD.
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*> TRANS is CHARACTER*1
*> = 'N': No transpose, apply Q;
*> = 'C': Conjugate transpose, apply Q**H.
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix C. M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrix C. N >= 0.
*> \endverbatim
*>
*> \param[in] AP
*> \verbatim
*> AP is COMPLEX array, dimension
*> (M*(M+1)/2) if SIDE = 'L'
*> (N*(N+1)/2) if SIDE = 'R'
*> The vectors which define the elementary reflectors, as
*> returned by CHPTRD. AP is modified by the routine but
*> restored on exit.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*> TAU is COMPLEX array, dimension (M-1) if SIDE = 'L'
*> or (N-1) if SIDE = 'R'
*> TAU(i) must contain the scalar factor of the elementary
*> reflector H(i), as returned by CHPTRD.
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*> C is COMPLEX array, dimension (LDC,N)
*> On entry, the M-by-N matrix C.
*> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
*> \endverbatim
*>
*> \param[in] LDC
*> \verbatim
*> LDC is INTEGER
*> The leading dimension of the array C. LDC >= max(1,M).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX array, dimension
*> (N) if SIDE = 'L'
*> (M) if SIDE = 'R'
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup complexOTHERcomputational
*
* =====================================================================
SUBROUTINE CUPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK,
$ INFO )
*
* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
CHARACTER SIDE, TRANS, UPLO
INTEGER INFO, LDC, M, N
* ..
* .. Array Arguments ..
COMPLEX AP( * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX ONE
PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
LOGICAL FORWRD, LEFT, NOTRAN, UPPER
INTEGER I, I1, I2, I3, IC, II, JC, MI, NI, NQ
COMPLEX AII, TAUI
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL CLARF, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC CONJG, MAX
* ..
* .. Executable Statements ..
*
* Test the input arguments
*
INFO = 0
LEFT = LSAME( SIDE, 'L' )
NOTRAN = LSAME( TRANS, 'N' )
UPPER = LSAME( UPLO, 'U' )
*
* NQ is the order of Q
*
IF( LEFT ) THEN
NQ = M
ELSE
NQ = N
END IF
IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
INFO = -1
ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -2
ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
INFO = -3
ELSE IF( M.LT.0 ) THEN
INFO = -4
ELSE IF( N.LT.0 ) THEN
INFO = -5
ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
INFO = -9
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CUPMTR', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( M.EQ.0 .OR. N.EQ.0 )
$ RETURN
*
IF( UPPER ) THEN
*
* Q was determined by a call to CHPTRD with UPLO = 'U'
*
FORWRD = ( LEFT .AND. NOTRAN ) .OR.
$ ( .NOT.LEFT .AND. .NOT.NOTRAN )
*
IF( FORWRD ) THEN
I1 = 1
I2 = NQ - 1
I3 = 1
II = 2
ELSE
I1 = NQ - 1
I2 = 1
I3 = -1
II = NQ*( NQ+1 ) / 2 - 1
END IF
*
IF( LEFT ) THEN
NI = N
ELSE
MI = M
END IF
*
DO 10 I = I1, I2, I3
IF( LEFT ) THEN
*
* H(i) or H(i)**H is applied to C(1:i,1:n)
*
MI = I
ELSE
*
* H(i) or H(i)**H is applied to C(1:m,1:i)
*
NI = I
END IF
*
* Apply H(i) or H(i)**H
*
IF( NOTRAN ) THEN
TAUI = TAU( I )
ELSE
TAUI = CONJG( TAU( I ) )
END IF
AII = AP( II )
AP( II ) = ONE
CALL CLARF( SIDE, MI, NI, AP( II-I+1 ), 1, TAUI, C, LDC,
$ WORK )
AP( II ) = AII
*
IF( FORWRD ) THEN
II = II + I + 2
ELSE
II = II - I - 1
END IF
10 CONTINUE
ELSE
*
* Q was determined by a call to CHPTRD with UPLO = 'L'.
*
FORWRD = ( LEFT .AND. .NOT.NOTRAN ) .OR.
$ ( .NOT.LEFT .AND. NOTRAN )
*
IF( FORWRD ) THEN
I1 = 1
I2 = NQ - 1
I3 = 1
II = 2
ELSE
I1 = NQ - 1
I2 = 1
I3 = -1
II = NQ*( NQ+1 ) / 2 - 1
END IF
*
IF( LEFT ) THEN
NI = N
JC = 1
ELSE
MI = M
IC = 1
END IF
*
DO 20 I = I1, I2, I3
AII = AP( II )
AP( II ) = ONE
IF( LEFT ) THEN
*
* H(i) or H(i)**H is applied to C(i+1:m,1:n)
*
MI = M - I
IC = I + 1
ELSE
*
* H(i) or H(i)**H is applied to C(1:m,i+1:n)
*
NI = N - I
JC = I + 1
END IF
*
* Apply H(i) or H(i)**H
*
IF( NOTRAN ) THEN
TAUI = TAU( I )
ELSE
TAUI = CONJG( TAU( I ) )
END IF
CALL CLARF( SIDE, MI, NI, AP( II ), 1, TAUI, C( IC, JC ),
$ LDC, WORK )
AP( II ) = AII
*
IF( FORWRD ) THEN
II = II + NQ - I + 1
ELSE
II = II - NQ + I - 2
END IF
20 CONTINUE
END IF
RETURN
*
* End of CUPMTR
*
END