1*> \brief \b CUNMBR
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download CUNMBR + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cunmbr.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cunmbr.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cunmbr.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE CUNMBR( 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            A( LDA, * ), C( LDC, * ), TAU( * ),
30*      $                   WORK( * )
31*       ..
32*
33*
34*> \par Purpose:
35*  =============
36*>
37*> \verbatim
38*>
39*> If VECT = 'Q', CUNMBR overwrites the general complex M-by-N matrix C
40*> with
41*>                 SIDE = 'L'     SIDE = 'R'
42*> TRANS = 'N':      Q * C          C * Q
43*> TRANS = 'C':      Q**H * C       C * Q**H
44*>
45*> If VECT = 'P', CUNMBR overwrites the general complex M-by-N matrix C
46*> with
47*>                 SIDE = 'L'     SIDE = 'R'
48*> TRANS = 'N':      P * C          C * P
49*> TRANS = 'C':      P**H * C       C * P**H
50*>
51*> Here Q and P**H are the unitary matrices determined by CGEBRD when
52*> reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q
53*> and P**H are defined as products of elementary reflectors H(i) and
54*> G(i) respectively.
55*>
56*> Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
57*> order of the unitary matrix Q or P**H that is applied.
58*>
59*> If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
60*> if nq >= k, Q = H(1) H(2) . . . H(k);
61*> if nq < k, Q = H(1) H(2) . . . H(nq-1).
62*>
63*> If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
64*> if k < nq, P = G(1) G(2) . . . G(k);
65*> if k >= nq, P = G(1) G(2) . . . G(nq-1).
66*> \endverbatim
67*
68*  Arguments:
69*  ==========
70*
71*> \param[in] VECT
72*> \verbatim
73*>          VECT is CHARACTER*1
74*>          = 'Q': apply Q or Q**H;
75*>          = 'P': apply P or P**H.
76*> \endverbatim
77*>
78*> \param[in] SIDE
79*> \verbatim
80*>          SIDE is CHARACTER*1
81*>          = 'L': apply Q, Q**H, P or P**H from the Left;
82*>          = 'R': apply Q, Q**H, P or P**H from the Right.
83*> \endverbatim
84*>
85*> \param[in] TRANS
86*> \verbatim
87*>          TRANS is CHARACTER*1
88*>          = 'N':  No transpose, apply Q or P;
89*>          = 'C':  Conjugate transpose, apply Q**H or P**H.
90*> \endverbatim
91*>
92*> \param[in] M
93*> \verbatim
94*>          M is INTEGER
95*>          The number of rows of the matrix C. M >= 0.
96*> \endverbatim
97*>
98*> \param[in] N
99*> \verbatim
100*>          N is INTEGER
101*>          The number of columns of the matrix C. N >= 0.
102*> \endverbatim
103*>
104*> \param[in] K
105*> \verbatim
106*>          K is INTEGER
107*>          If VECT = 'Q', the number of columns in the original
108*>          matrix reduced by CGEBRD.
109*>          If VECT = 'P', the number of rows in the original
110*>          matrix reduced by CGEBRD.
111*>          K >= 0.
112*> \endverbatim
113*>
114*> \param[in] A
115*> \verbatim
116*>          A is COMPLEX array, dimension
117*>                                (LDA,min(nq,K)) if VECT = 'Q'
118*>                                (LDA,nq)        if VECT = 'P'
119*>          The vectors which define the elementary reflectors H(i) and
120*>          G(i), whose products determine the matrices Q and P, as
121*>          returned by CGEBRD.
122*> \endverbatim
123*>
124*> \param[in] LDA
125*> \verbatim
126*>          LDA is INTEGER
127*>          The leading dimension of the array A.
128*>          If VECT = 'Q', LDA >= max(1,nq);
129*>          if VECT = 'P', LDA >= max(1,min(nq,K)).
130*> \endverbatim
131*>
132*> \param[in] TAU
133*> \verbatim
134*>          TAU is COMPLEX array, dimension (min(nq,K))
135*>          TAU(i) must contain the scalar factor of the elementary
136*>          reflector H(i) or G(i) which determines Q or P, as returned
137*>          by CGEBRD in the array argument TAUQ or TAUP.
138*> \endverbatim
139*>
140*> \param[in,out] C
141*> \verbatim
142*>          C is COMPLEX array, dimension (LDC,N)
143*>          On entry, the M-by-N matrix C.
144*>          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q
145*>          or P*C or P**H*C or C*P or C*P**H.
146*> \endverbatim
147*>
148*> \param[in] LDC
149*> \verbatim
150*>          LDC is INTEGER
151*>          The leading dimension of the array C. LDC >= max(1,M).
152*> \endverbatim
153*>
154*> \param[out] WORK
155*> \verbatim
156*>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
157*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
158*> \endverbatim
159*>
160*> \param[in] LWORK
161*> \verbatim
162*>          LWORK is INTEGER
163*>          The dimension of the array WORK.
164*>          If SIDE = 'L', LWORK >= max(1,N);
165*>          if SIDE = 'R', LWORK >= max(1,M);
166*>          if N = 0 or M = 0, LWORK >= 1.
167*>          For optimum performance LWORK >= max(1,N*NB) if SIDE = 'L',
168*>          and LWORK >= max(1,M*NB) if SIDE = 'R', where NB is the
169*>          optimal blocksize. (NB = 0 if M = 0 or N = 0.)
170*>
171*>          If LWORK = -1, then a workspace query is assumed; the routine
172*>          only calculates the optimal size of the WORK array, returns
173*>          this value as the first entry of the WORK array, and no error
174*>          message related to LWORK is issued by XERBLA.
175*> \endverbatim
176*>
177*> \param[out] INFO
178*> \verbatim
179*>          INFO is INTEGER
180*>          = 0:  successful exit
181*>          < 0:  if INFO = -i, the i-th argument had an illegal value
182*> \endverbatim
183*
184*  Authors:
185*  ========
186*
187*> \author Univ. of Tennessee
188*> \author Univ. of California Berkeley
189*> \author Univ. of Colorado Denver
190*> \author NAG Ltd.
191*
192*> \ingroup complexOTHERcomputational
193*
194*  =====================================================================
195      SUBROUTINE CUNMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
196     $                   LDC, WORK, LWORK, INFO )
197*
198*  -- LAPACK computational routine --
199*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
200*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
201*
202*     .. Scalar Arguments ..
203      CHARACTER          SIDE, TRANS, VECT
204      INTEGER            INFO, K, LDA, LDC, LWORK, M, N
205*     ..
206*     .. Array Arguments ..
207      COMPLEX            A( LDA, * ), C( LDC, * ), TAU( * ),
208     $                   WORK( * )
209*     ..
210*
211*  =====================================================================
212*
213*     .. Local Scalars ..
214      LOGICAL            APPLYQ, LEFT, LQUERY, NOTRAN
215      CHARACTER          TRANST
216      INTEGER            I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW
217*     ..
218*     .. External Functions ..
219      LOGICAL            LSAME
220      INTEGER            ILAENV
221      EXTERNAL           ILAENV, LSAME
222*     ..
223*     .. External Subroutines ..
224      EXTERNAL           CUNMLQ, CUNMQR, XERBLA
225*     ..
226*     .. Intrinsic Functions ..
227      INTRINSIC          MAX, MIN
228*     ..
229*     .. Executable Statements ..
230*
231*     Test the input arguments
232*
233      INFO = 0
234      APPLYQ = LSAME( VECT, 'Q' )
235      LEFT = LSAME( SIDE, 'L' )
236      NOTRAN = LSAME( TRANS, 'N' )
237      LQUERY = ( LWORK.EQ.-1 )
238*
239*     NQ is the order of Q or P and NW is the minimum dimension of WORK
240*
241      IF( LEFT ) THEN
242         NQ = M
243         NW = MAX( 1, N )
244      ELSE
245         NQ = N
246         NW = MAX( 1, M )
247      END IF
248      IF( .NOT.APPLYQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN
249         INFO = -1
250      ELSE IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
251         INFO = -2
252      ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
253         INFO = -3
254      ELSE IF( M.LT.0 ) THEN
255         INFO = -4
256      ELSE IF( N.LT.0 ) THEN
257         INFO = -5
258      ELSE IF( K.LT.0 ) THEN
259         INFO = -6
260      ELSE IF( ( APPLYQ .AND. LDA.LT.MAX( 1, NQ ) ) .OR.
261     $         ( .NOT.APPLYQ .AND. LDA.LT.MAX( 1, MIN( NQ, K ) ) ) )
262     $          THEN
263         INFO = -8
264      ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
265         INFO = -11
266      ELSE IF( LWORK.LT.NW .AND. .NOT.LQUERY ) THEN
267         INFO = -13
268      END IF
269*
270      IF( INFO.EQ.0 ) THEN
271         IF( M.GT.0 .AND. N.GT.0 ) THEN
272            IF( APPLYQ ) THEN
273               IF( LEFT ) THEN
274                  NB = ILAENV( 1, 'CUNMQR', SIDE // TRANS, M-1, N, M-1,
275     $                         -1 )
276               ELSE
277                  NB = ILAENV( 1, 'CUNMQR', SIDE // TRANS, M, N-1, N-1,
278     $                         -1 )
279               END IF
280            ELSE
281               IF( LEFT ) THEN
282                  NB = ILAENV( 1, 'CUNMLQ', SIDE // TRANS, M-1, N, M-1,
283     $                         -1 )
284               ELSE
285                  NB = ILAENV( 1, 'CUNMLQ', SIDE // TRANS, M, N-1, N-1,
286     $                         -1 )
287               END IF
288            END IF
289            LWKOPT = NW*NB
290         ELSE
291            LWKOPT = 1
292         END IF
293         WORK( 1 ) = LWKOPT
294      END IF
295*
296      IF( INFO.NE.0 ) THEN
297         CALL XERBLA( 'CUNMBR', -INFO )
298         RETURN
299      ELSE IF( LQUERY ) THEN
300         RETURN
301      END IF
302*
303*     Quick return if possible
304*
305      IF( M.EQ.0 .OR. N.EQ.0 )
306     $   RETURN
307*
308      IF( APPLYQ ) THEN
309*
310*        Apply Q
311*
312         IF( NQ.GE.K ) THEN
313*
314*           Q was determined by a call to CGEBRD with nq >= k
315*
316            CALL CUNMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
317     $                   WORK, LWORK, IINFO )
318         ELSE IF( NQ.GT.1 ) THEN
319*
320*           Q was determined by a call to CGEBRD with nq < k
321*
322            IF( LEFT ) THEN
323               MI = M - 1
324               NI = N
325               I1 = 2
326               I2 = 1
327            ELSE
328               MI = M
329               NI = N - 1
330               I1 = 1
331               I2 = 2
332            END IF
333            CALL CUNMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU,
334     $                   C( I1, I2 ), LDC, WORK, LWORK, IINFO )
335         END IF
336      ELSE
337*
338*        Apply P
339*
340         IF( NOTRAN ) THEN
341            TRANST = 'C'
342         ELSE
343            TRANST = 'N'
344         END IF
345         IF( NQ.GT.K ) THEN
346*
347*           P was determined by a call to CGEBRD with nq > k
348*
349            CALL CUNMLQ( SIDE, TRANST, M, N, K, A, LDA, TAU, C, LDC,
350     $                   WORK, LWORK, IINFO )
351         ELSE IF( NQ.GT.1 ) THEN
352*
353*           P was determined by a call to CGEBRD with nq <= k
354*
355            IF( LEFT ) THEN
356               MI = M - 1
357               NI = N
358               I1 = 2
359               I2 = 1
360            ELSE
361               MI = M
362               NI = N - 1
363               I1 = 1
364               I2 = 2
365            END IF
366            CALL CUNMLQ( SIDE, TRANST, MI, NI, NQ-1, A( 1, 2 ), LDA,
367     $                   TAU, C( I1, I2 ), LDC, WORK, LWORK, IINFO )
368         END IF
369      END IF
370      WORK( 1 ) = LWKOPT
371      RETURN
372*
373*     End of CUNMBR
374*
375      END
376