LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
zunmbr.f
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1 *> \brief \b ZUNMBR
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
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16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZUNMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
22 * LDC, WORK, LWORK, INFO )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER SIDE, TRANS, VECT
26 * INTEGER INFO, K, LDA, LDC, LWORK, M, N
27 * ..
28 * .. Array Arguments ..
29 * COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> If VECT = 'Q', ZUNMBR overwrites the general complex M-by-N matrix C
39 *> with
40 *> SIDE = 'L' SIDE = 'R'
41 *> TRANS = 'N': Q * C C * Q
42 *> TRANS = 'C': Q**H * C C * Q**H
43 *>
44 *> If VECT = 'P', ZUNMBR overwrites the general complex M-by-N matrix C
45 *> with
46 *> SIDE = 'L' SIDE = 'R'
47 *> TRANS = 'N': P * C C * P
48 *> TRANS = 'C': P**H * C C * P**H
49 *>
50 *> Here Q and P**H are the unitary matrices determined by ZGEBRD when
51 *> reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q
52 *> and P**H are defined as products of elementary reflectors H(i) and
53 *> G(i) respectively.
54 *>
55 *> Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
56 *> order of the unitary matrix Q or P**H that is applied.
57 *>
58 *> If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
59 *> if nq >= k, Q = H(1) H(2) . . . H(k);
60 *> if nq < k, Q = H(1) H(2) . . . H(nq-1).
61 *>
62 *> If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
63 *> if k < nq, P = G(1) G(2) . . . G(k);
64 *> if k >= nq, P = G(1) G(2) . . . G(nq-1).
65 *> \endverbatim
66 *
67 * Arguments:
68 * ==========
69 *
70 *> \param[in] VECT
71 *> \verbatim
72 *> VECT is CHARACTER*1
73 *> = 'Q': apply Q or Q**H;
74 *> = 'P': apply P or P**H.
75 *> \endverbatim
76 *>
77 *> \param[in] SIDE
78 *> \verbatim
79 *> SIDE is CHARACTER*1
80 *> = 'L': apply Q, Q**H, P or P**H from the Left;
81 *> = 'R': apply Q, Q**H, P or P**H from the Right.
82 *> \endverbatim
83 *>
84 *> \param[in] TRANS
85 *> \verbatim
86 *> TRANS is CHARACTER*1
87 *> = 'N': No transpose, apply Q or P;
88 *> = 'C': Conjugate transpose, apply Q**H or P**H.
89 *> \endverbatim
90 *>
91 *> \param[in] M
92 *> \verbatim
93 *> M is INTEGER
94 *> The number of rows of the matrix C. M >= 0.
95 *> \endverbatim
96 *>
97 *> \param[in] N
98 *> \verbatim
99 *> N is INTEGER
100 *> The number of columns of the matrix C. N >= 0.
101 *> \endverbatim
102 *>
103 *> \param[in] K
104 *> \verbatim
105 *> K is INTEGER
106 *> If VECT = 'Q', the number of columns in the original
107 *> matrix reduced by ZGEBRD.
108 *> If VECT = 'P', the number of rows in the original
109 *> matrix reduced by ZGEBRD.
110 *> K >= 0.
111 *> \endverbatim
112 *>
113 *> \param[in] A
114 *> \verbatim
115 *> A is COMPLEX*16 array, dimension
116 *> (LDA,min(nq,K)) if VECT = 'Q'
117 *> (LDA,nq) if VECT = 'P'
118 *> The vectors which define the elementary reflectors H(i) and
119 *> G(i), whose products determine the matrices Q and P, as
120 *> returned by ZGEBRD.
121 *> \endverbatim
122 *>
123 *> \param[in] LDA
124 *> \verbatim
125 *> LDA is INTEGER
126 *> The leading dimension of the array A.
127 *> If VECT = 'Q', LDA >= max(1,nq);
128 *> if VECT = 'P', LDA >= max(1,min(nq,K)).
129 *> \endverbatim
130 *>
131 *> \param[in] TAU
132 *> \verbatim
133 *> TAU is COMPLEX*16 array, dimension (min(nq,K))
134 *> TAU(i) must contain the scalar factor of the elementary
135 *> reflector H(i) or G(i) which determines Q or P, as returned
136 *> by ZGEBRD in the array argument TAUQ or TAUP.
137 *> \endverbatim
138 *>
139 *> \param[in,out] C
140 *> \verbatim
141 *> C is COMPLEX*16 array, dimension (LDC,N)
142 *> On entry, the M-by-N matrix C.
143 *> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q
144 *> or P*C or P**H*C or C*P or C*P**H.
145 *> \endverbatim
146 *>
147 *> \param[in] LDC
148 *> \verbatim
149 *> LDC is INTEGER
150 *> The leading dimension of the array C. LDC >= max(1,M).
151 *> \endverbatim
152 *>
153 *> \param[out] WORK
154 *> \verbatim
155 *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
156 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
157 *> \endverbatim
158 *>
159 *> \param[in] LWORK
160 *> \verbatim
161 *> LWORK is INTEGER
162 *> The dimension of the array WORK.
163 *> If SIDE = 'L', LWORK >= max(1,N);
164 *> if SIDE = 'R', LWORK >= max(1,M);
165 *> if N = 0 or M = 0, LWORK >= 1.
166 *> For optimum performance LWORK >= max(1,N*NB) if SIDE = 'L',
167 *> and LWORK >= max(1,M*NB) if SIDE = 'R', where NB is the
168 *> optimal blocksize. (NB = 0 if M = 0 or N = 0.)
169 *>
170 *> If LWORK = -1, then a workspace query is assumed; the routine
171 *> only calculates the optimal size of the WORK array, returns
172 *> this value as the first entry of the WORK array, and no error
173 *> message related to LWORK is issued by XERBLA.
174 *> \endverbatim
175 *>
176 *> \param[out] INFO
177 *> \verbatim
178 *> INFO is INTEGER
179 *> = 0: successful exit
180 *> < 0: if INFO = -i, the i-th argument had an illegal value
181 *> \endverbatim
182 *
183 * Authors:
184 * ========
185 *
186 *> \author Univ. of Tennessee
187 *> \author Univ. of California Berkeley
188 *> \author Univ. of Colorado Denver
189 *> \author NAG Ltd.
190 *
191 *> \date November 2011
192 *
193 *> \ingroup complex16OTHERcomputational
194 *
195 * =====================================================================
196  SUBROUTINE zunmbr( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
197  \$ ldc, work, lwork, info )
198 *
199 * -- LAPACK computational routine (version 3.4.0) --
200 * -- LAPACK is a software package provided by Univ. of Tennessee, --
201 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
202 * November 2011
203 *
204 * .. Scalar Arguments ..
205  CHARACTER SIDE, TRANS, VECT
206  INTEGER INFO, K, LDA, LDC, LWORK, M, N
207 * ..
208 * .. Array Arguments ..
209  COMPLEX*16 A( lda, * ), C( ldc, * ), TAU( * ), WORK( * )
210 * ..
211 *
212 * =====================================================================
213 *
214 * .. Local Scalars ..
215  LOGICAL APPLYQ, LEFT, LQUERY, NOTRAN
216  CHARACTER TRANST
217  INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW
218 * ..
219 * .. External Functions ..
220  LOGICAL LSAME
221  INTEGER ILAENV
222  EXTERNAL lsame, ilaenv
223 * ..
224 * .. External Subroutines ..
225  EXTERNAL xerbla, zunmlq, zunmqr
226 * ..
227 * .. Intrinsic Functions ..
228  INTRINSIC max, min
229 * ..
230 * .. Executable Statements ..
231 *
232 * Test the input arguments
233 *
234  info = 0
235  applyq = lsame( vect, 'Q' )
236  left = lsame( side, 'L' )
237  notran = lsame( trans, 'N' )
238  lquery = ( lwork.EQ.-1 )
239 *
240 * NQ is the order of Q or P and NW is the minimum dimension of WORK
241 *
242  IF( left ) THEN
243  nq = m
244  nw = n
245  ELSE
246  nq = n
247  nw = m
248  END IF
249  IF( m.EQ.0 .OR. n.EQ.0 ) THEN
250  nw = 0
251  END IF
252  IF( .NOT.applyq .AND. .NOT.lsame( vect, 'P' ) ) THEN
253  info = -1
254  ELSE IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
255  info = -2
256  ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'C' ) ) THEN
257  info = -3
258  ELSE IF( m.LT.0 ) THEN
259  info = -4
260  ELSE IF( n.LT.0 ) THEN
261  info = -5
262  ELSE IF( k.LT.0 ) THEN
263  info = -6
264  ELSE IF( ( applyq .AND. lda.LT.max( 1, nq ) ) .OR.
265  \$ ( .NOT.applyq .AND. lda.LT.max( 1, min( nq, k ) ) ) )
266  \$ THEN
267  info = -8
268  ELSE IF( ldc.LT.max( 1, m ) ) THEN
269  info = -11
270  ELSE IF( lwork.LT.max( 1, nw ) .AND. .NOT.lquery ) THEN
271  info = -13
272  END IF
273 *
274  IF( info.EQ.0 ) THEN
275  IF( nw.GT.0 ) THEN
276  IF( applyq ) THEN
277  IF( left ) THEN
278  nb = ilaenv( 1, 'ZUNMQR', side // trans, m-1, n, m-1,
279  \$ -1 )
280  ELSE
281  nb = ilaenv( 1, 'ZUNMQR', side // trans, m, n-1, n-1,
282  \$ -1 )
283  END IF
284  ELSE
285  IF( left ) THEN
286  nb = ilaenv( 1, 'ZUNMLQ', side // trans, m-1, n, m-1,
287  \$ -1 )
288  ELSE
289  nb = ilaenv( 1, 'ZUNMLQ', side // trans, m, n-1, n-1,
290  \$ -1 )
291  END IF
292  END IF
293  lwkopt = max( 1, nw*nb )
294  ELSE
295  lwkopt = 1
296  END IF
297  work( 1 ) = lwkopt
298  END IF
299 *
300  IF( info.NE.0 ) THEN
301  CALL xerbla( 'ZUNMBR', -info )
302  RETURN
303  ELSE IF( lquery ) THEN
304  RETURN
305  END IF
306 *
307 * Quick return if possible
308 *
309  IF( m.EQ.0 .OR. n.EQ.0 )
310  \$ RETURN
311 *
312  IF( applyq ) THEN
313 *
314 * Apply Q
315 *
316  IF( nq.GE.k ) THEN
317 *
318 * Q was determined by a call to ZGEBRD with nq >= k
319 *
320  CALL zunmqr( side, trans, m, n, k, a, lda, tau, c, ldc,
321  \$ work, lwork, iinfo )
322  ELSE IF( nq.GT.1 ) THEN
323 *
324 * Q was determined by a call to ZGEBRD with nq < k
325 *
326  IF( left ) THEN
327  mi = m - 1
328  ni = n
329  i1 = 2
330  i2 = 1
331  ELSE
332  mi = m
333  ni = n - 1
334  i1 = 1
335  i2 = 2
336  END IF
337  CALL zunmqr( side, trans, mi, ni, nq-1, a( 2, 1 ), lda, tau,
338  \$ c( i1, i2 ), ldc, work, lwork, iinfo )
339  END IF
340  ELSE
341 *
342 * Apply P
343 *
344  IF( notran ) THEN
345  transt = 'C'
346  ELSE
347  transt = 'N'
348  END IF
349  IF( nq.GT.k ) THEN
350 *
351 * P was determined by a call to ZGEBRD with nq > k
352 *
353  CALL zunmlq( side, transt, m, n, k, a, lda, tau, c, ldc,
354  \$ work, lwork, iinfo )
355  ELSE IF( nq.GT.1 ) THEN
356 *
357 * P was determined by a call to ZGEBRD with nq <= k
358 *
359  IF( left ) THEN
360  mi = m - 1
361  ni = n
362  i1 = 2
363  i2 = 1
364  ELSE
365  mi = m
366  ni = n - 1
367  i1 = 1
368  i2 = 2
369  END IF
370  CALL zunmlq( side, transt, mi, ni, nq-1, a( 1, 2 ), lda,
371  \$ tau, c( i1, i2 ), ldc, work, lwork, iinfo )
372  END IF
373  END IF
374  work( 1 ) = lwkopt
375  RETURN
376 *
377 * End of ZUNMBR
378 *
379  END
subroutine zunmbr(VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
ZUNMBR
Definition: zunmbr.f:198
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine zunmqr(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
ZUNMQR
Definition: zunmqr.f:169
subroutine zunmlq(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
ZUNMLQ
Definition: zunmlq.f:169