1*> \brief \b ZUNGBR
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
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17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE ZUNGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
22*
23*       .. Scalar Arguments ..
24*       CHARACTER          VECT
25*       INTEGER            INFO, K, LDA, LWORK, M, N
26*       ..
27*       .. Array Arguments ..
28*       COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
29*       ..
30*
31*
32*> \par Purpose:
33*  =============
34*>
35*> \verbatim
36*>
37*> ZUNGBR generates one of the complex unitary matrices Q or P**H
38*> determined by ZGEBRD when reducing a complex matrix A to bidiagonal
39*> form: A = Q * B * P**H.  Q and P**H are defined as products of
40*> elementary reflectors H(i) or G(i) respectively.
41*>
42*> If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q
43*> is of order M:
44*> if m >= k, Q = H(1) H(2) . . . H(k) and ZUNGBR returns the first n
45*> columns of Q, where m >= n >= k;
46*> if m < k, Q = H(1) H(2) . . . H(m-1) and ZUNGBR returns Q as an
47*> M-by-M matrix.
48*>
49*> If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**H
50*> is of order N:
51*> if k < n, P**H = G(k) . . . G(2) G(1) and ZUNGBR returns the first m
52*> rows of P**H, where n >= m >= k;
53*> if k >= n, P**H = G(n-1) . . . G(2) G(1) and ZUNGBR returns P**H as
54*> an N-by-N matrix.
55*> \endverbatim
56*
57*  Arguments:
58*  ==========
59*
60*> \param[in] VECT
61*> \verbatim
62*>          VECT is CHARACTER*1
63*>          Specifies whether the matrix Q or the matrix P**H is
64*>          required, as defined in the transformation applied by ZGEBRD:
65*>          = 'Q':  generate Q;
66*>          = 'P':  generate P**H.
67*> \endverbatim
68*>
69*> \param[in] M
70*> \verbatim
71*>          M is INTEGER
72*>          The number of rows of the matrix Q or P**H to be returned.
73*>          M >= 0.
74*> \endverbatim
75*>
76*> \param[in] N
77*> \verbatim
78*>          N is INTEGER
79*>          The number of columns of the matrix Q or P**H to be returned.
80*>          N >= 0.
81*>          If VECT = 'Q', M >= N >= min(M,K);
82*>          if VECT = 'P', N >= M >= min(N,K).
83*> \endverbatim
84*>
85*> \param[in] K
86*> \verbatim
87*>          K is INTEGER
88*>          If VECT = 'Q', the number of columns in the original M-by-K
89*>          matrix reduced by ZGEBRD.
90*>          If VECT = 'P', the number of rows in the original K-by-N
91*>          matrix reduced by ZGEBRD.
92*>          K >= 0.
93*> \endverbatim
94*>
95*> \param[in,out] A
96*> \verbatim
97*>          A is COMPLEX*16 array, dimension (LDA,N)
98*>          On entry, the vectors which define the elementary reflectors,
99*>          as returned by ZGEBRD.
100*>          On exit, the M-by-N matrix Q or P**H.
101*> \endverbatim
102*>
103*> \param[in] LDA
104*> \verbatim
105*>          LDA is INTEGER
106*>          The leading dimension of the array A. LDA >= M.
107*> \endverbatim
108*>
109*> \param[in] TAU
110*> \verbatim
111*>          TAU is COMPLEX*16 array, dimension
112*>                                (min(M,K)) if VECT = 'Q'
113*>                                (min(N,K)) if VECT = 'P'
114*>          TAU(i) must contain the scalar factor of the elementary
115*>          reflector H(i) or G(i), which determines Q or P**H, as
116*>          returned by ZGEBRD in its array argument TAUQ or TAUP.
117*> \endverbatim
118*>
119*> \param[out] WORK
120*> \verbatim
121*>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
122*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
123*> \endverbatim
124*>
125*> \param[in] LWORK
126*> \verbatim
127*>          LWORK is INTEGER
128*>          The dimension of the array WORK. LWORK >= max(1,min(M,N)).
129*>          For optimum performance LWORK >= min(M,N)*NB, where NB
130*>          is the optimal blocksize.
131*>
132*>          If LWORK = -1, then a workspace query is assumed; the routine
133*>          only calculates the optimal size of the WORK array, returns
134*>          this value as the first entry of the WORK array, and no error
135*>          message related to LWORK is issued by XERBLA.
136*> \endverbatim
137*>
138*> \param[out] INFO
139*> \verbatim
140*>          INFO is INTEGER
141*>          = 0:  successful exit
142*>          < 0:  if INFO = -i, the i-th argument had an illegal value
143*> \endverbatim
144*
145*  Authors:
146*  ========
147*
148*> \author Univ. of Tennessee
149*> \author Univ. of California Berkeley
150*> \author Univ. of Colorado Denver
151*> \author NAG Ltd.
152*
153*> \ingroup complex16GBcomputational
154*
155*  =====================================================================
156      SUBROUTINE ZUNGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
157*
158*  -- LAPACK computational routine --
159*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
160*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
161*
162*     .. Scalar Arguments ..
163      CHARACTER          VECT
164      INTEGER            INFO, K, LDA, LWORK, M, N
165*     ..
166*     .. Array Arguments ..
167      COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
168*     ..
169*
170*  =====================================================================
171*
172*     .. Parameters ..
173      COMPLEX*16         ZERO, ONE
174      PARAMETER          ( ZERO = ( 0.0D+0, 0.0D+0 ),
175     $                   ONE = ( 1.0D+0, 0.0D+0 ) )
176*     ..
177*     .. Local Scalars ..
178      LOGICAL            LQUERY, WANTQ
179      INTEGER            I, IINFO, J, LWKOPT, MN
180*     ..
181*     .. External Functions ..
182      LOGICAL            LSAME
183      EXTERNAL           LSAME
184*     ..
185*     .. External Subroutines ..
186      EXTERNAL           XERBLA, ZUNGLQ, ZUNGQR
187*     ..
188*     .. Intrinsic Functions ..
189      INTRINSIC          MAX, MIN
190*     ..
191*     .. Executable Statements ..
192*
193*     Test the input arguments
194*
195      INFO = 0
196      WANTQ = LSAME( VECT, 'Q' )
197      MN = MIN( M, N )
198      LQUERY = ( LWORK.EQ.-1 )
199      IF( .NOT.WANTQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN
200         INFO = -1
201      ELSE IF( M.LT.0 ) THEN
202         INFO = -2
203      ELSE IF( N.LT.0 .OR. ( WANTQ .AND. ( N.GT.M .OR. N.LT.MIN( M,
204     $         K ) ) ) .OR. ( .NOT.WANTQ .AND. ( M.GT.N .OR. M.LT.
205     $         MIN( N, K ) ) ) ) THEN
206         INFO = -3
207      ELSE IF( K.LT.0 ) THEN
208         INFO = -4
209      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
210         INFO = -6
211      ELSE IF( LWORK.LT.MAX( 1, MN ) .AND. .NOT.LQUERY ) THEN
212         INFO = -9
213      END IF
214*
215      IF( INFO.EQ.0 ) THEN
216         WORK( 1 ) = 1
217         IF( WANTQ ) THEN
218            IF( M.GE.K ) THEN
219               CALL ZUNGQR( M, N, K, A, LDA, TAU, WORK, -1, IINFO )
220            ELSE
221               IF( M.GT.1 ) THEN
222                  CALL ZUNGQR( M-1, M-1, M-1, A, LDA, TAU, WORK, -1,
223     $                         IINFO )
224               END IF
225            END IF
226         ELSE
227            IF( K.LT.N ) THEN
228               CALL ZUNGLQ( M, N, K, A, LDA, TAU, WORK, -1, IINFO )
229            ELSE
230               IF( N.GT.1 ) THEN
231                  CALL ZUNGLQ( N-1, N-1, N-1, A, LDA, TAU, WORK, -1,
232     $                         IINFO )
233               END IF
234            END IF
235         END IF
236         LWKOPT = DBLE( WORK( 1 ) )
237         LWKOPT = MAX (LWKOPT, MN)
238      END IF
239*
240      IF( INFO.NE.0 ) THEN
241         CALL XERBLA( 'ZUNGBR', -INFO )
242         RETURN
243      ELSE IF( LQUERY ) THEN
244         WORK( 1 ) = LWKOPT
245         RETURN
246      END IF
247*
248*     Quick return if possible
249*
250      IF( M.EQ.0 .OR. N.EQ.0 ) THEN
251         WORK( 1 ) = 1
252         RETURN
253      END IF
254*
255      IF( WANTQ ) THEN
256*
257*        Form Q, determined by a call to ZGEBRD to reduce an m-by-k
258*        matrix
259*
260         IF( M.GE.K ) THEN
261*
262*           If m >= k, assume m >= n >= k
263*
264            CALL ZUNGQR( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO )
265*
266         ELSE
267*
268*           If m < k, assume m = n
269*
270*           Shift the vectors which define the elementary reflectors one
271*           column to the right, and set the first row and column of Q
272*           to those of the unit matrix
273*
274            DO 20 J = M, 2, -1
275               A( 1, J ) = ZERO
276               DO 10 I = J + 1, M
277                  A( I, J ) = A( I, J-1 )
278   10          CONTINUE
279   20       CONTINUE
280            A( 1, 1 ) = ONE
281            DO 30 I = 2, M
282               A( I, 1 ) = ZERO
283   30       CONTINUE
284            IF( M.GT.1 ) THEN
285*
286*              Form Q(2:m,2:m)
287*
288               CALL ZUNGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK,
289     $                      LWORK, IINFO )
290            END IF
291         END IF
292      ELSE
293*
294*        Form P**H, determined by a call to ZGEBRD to reduce a k-by-n
295*        matrix
296*
297         IF( K.LT.N ) THEN
298*
299*           If k < n, assume k <= m <= n
300*
301            CALL ZUNGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO )
302*
303         ELSE
304*
305*           If k >= n, assume m = n
306*
307*           Shift the vectors which define the elementary reflectors one
308*           row downward, and set the first row and column of P**H to
309*           those of the unit matrix
310*
311            A( 1, 1 ) = ONE
312            DO 40 I = 2, N
313               A( I, 1 ) = ZERO
314   40       CONTINUE
315            DO 60 J = 2, N
316               DO 50 I = J - 1, 2, -1
317                  A( I, J ) = A( I-1, J )
318   50          CONTINUE
319               A( 1, J ) = ZERO
320   60       CONTINUE
321            IF( N.GT.1 ) THEN
322*
323*              Form P**H(2:n,2:n)
324*
325               CALL ZUNGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
326     $                      LWORK, IINFO )
327            END IF
328         END IF
329      END IF
330      WORK( 1 ) = LWKOPT
331      RETURN
332*
333*     End of ZUNGBR
334*
335      END
336