1*> \brief \b ZUNMLQ
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
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16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE ZUNMLQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
22*                          WORK, LWORK, INFO )
23*
24*       .. Scalar Arguments ..
25*       CHARACTER          SIDE, TRANS
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*> ZUNMLQ overwrites the general complex M-by-N matrix C with
39*>
40*>                 SIDE = 'L'     SIDE = 'R'
41*> TRANS = 'N':      Q * C          C * Q
42*> TRANS = 'C':      Q**H * C       C * Q**H
43*>
44*> where Q is a complex unitary matrix defined as the product of k
45*> elementary reflectors
46*>
47*>       Q = H(k)**H . . . H(2)**H H(1)**H
48*>
49*> as returned by ZGELQF. Q is of order M if SIDE = 'L' and of order N
50*> if SIDE = 'R'.
51*> \endverbatim
52*
53*  Arguments:
54*  ==========
55*
56*> \param[in] SIDE
57*> \verbatim
58*>          SIDE is CHARACTER*1
59*>          = 'L': apply Q or Q**H from the Left;
60*>          = 'R': apply Q or Q**H from the Right.
61*> \endverbatim
62*>
63*> \param[in] TRANS
64*> \verbatim
65*>          TRANS is CHARACTER*1
66*>          = 'N':  No transpose, apply Q;
67*>          = 'C':  Conjugate transpose, apply Q**H.
68*> \endverbatim
69*>
70*> \param[in] M
71*> \verbatim
72*>          M is INTEGER
73*>          The number of rows of the matrix C. M >= 0.
74*> \endverbatim
75*>
76*> \param[in] N
77*> \verbatim
78*>          N is INTEGER
79*>          The number of columns of the matrix C. N >= 0.
80*> \endverbatim
81*>
82*> \param[in] K
83*> \verbatim
84*>          K is INTEGER
85*>          The number of elementary reflectors whose product defines
86*>          the matrix Q.
87*>          If SIDE = 'L', M >= K >= 0;
88*>          if SIDE = 'R', N >= K >= 0.
89*> \endverbatim
90*>
91*> \param[in] A
92*> \verbatim
93*>          A is COMPLEX*16 array, dimension
94*>                               (LDA,M) if SIDE = 'L',
95*>                               (LDA,N) if SIDE = 'R'
96*>          The i-th row must contain the vector which defines the
97*>          elementary reflector H(i), for i = 1,2,...,k, as returned by
98*>          ZGELQF in the first k rows of its array argument A.
99*> \endverbatim
100*>
101*> \param[in] LDA
102*> \verbatim
103*>          LDA is INTEGER
104*>          The leading dimension of the array A. LDA >= max(1,K).
105*> \endverbatim
106*>
107*> \param[in] TAU
108*> \verbatim
109*>          TAU is COMPLEX*16 array, dimension (K)
110*>          TAU(i) must contain the scalar factor of the elementary
111*>          reflector H(i), as returned by ZGELQF.
112*> \endverbatim
113*>
114*> \param[in,out] C
115*> \verbatim
116*>          C is COMPLEX*16 array, dimension (LDC,N)
117*>          On entry, the M-by-N matrix C.
118*>          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
119*> \endverbatim
120*>
121*> \param[in] LDC
122*> \verbatim
123*>          LDC is INTEGER
124*>          The leading dimension of the array C. LDC >= max(1,M).
125*> \endverbatim
126*>
127*> \param[out] WORK
128*> \verbatim
129*>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
130*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
131*> \endverbatim
132*>
133*> \param[in] LWORK
134*> \verbatim
135*>          LWORK is INTEGER
136*>          The dimension of the array WORK.
137*>          If SIDE = 'L', LWORK >= max(1,N);
138*>          if SIDE = 'R', LWORK >= max(1,M).
139*>          For optimum performance LWORK >= N*NB if SIDE 'L', and
140*>          LWORK >= M*NB if SIDE = 'R', where NB is the optimal
141*>          blocksize.
142*>
143*>          If LWORK = -1, then a workspace query is assumed; the routine
144*>          only calculates the optimal size of the WORK array, returns
145*>          this value as the first entry of the WORK array, and no error
146*>          message related to LWORK is issued by XERBLA.
147*> \endverbatim
148*>
149*> \param[out] INFO
150*> \verbatim
151*>          INFO is INTEGER
152*>          = 0:  successful exit
153*>          < 0:  if INFO = -i, the i-th argument had an illegal value
154*> \endverbatim
155*
156*  Authors:
157*  ========
158*
159*> \author Univ. of Tennessee
160*> \author Univ. of California Berkeley
161*> \author Univ. of Colorado Denver
162*> \author NAG Ltd.
163*
164*> \date November 2011
165*
166*> \ingroup complex16OTHERcomputational
167*
168*  =====================================================================
169      SUBROUTINE ZUNMLQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
170     $                   WORK, LWORK, INFO )
171*
172*  -- LAPACK computational routine (version 3.4.0) --
173*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
174*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
175*     November 2011
176*
177*     .. Scalar Arguments ..
178      CHARACTER          SIDE, TRANS
179      INTEGER            INFO, K, LDA, LDC, LWORK, M, N
180*     ..
181*     .. Array Arguments ..
182      COMPLEX*16         A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
183*     ..
184*
185*  =====================================================================
186*
187*     .. Parameters ..
188      INTEGER            NBMAX, LDT
189      PARAMETER          ( NBMAX = 64, LDT = NBMAX+1 )
190*     ..
191*     .. Local Scalars ..
192      LOGICAL            LEFT, LQUERY, NOTRAN
193      CHARACTER          TRANST
194      INTEGER            I, I1, I2, I3, IB, IC, IINFO, IWS, JC, LDWORK,
195     $                   LWKOPT, MI, NB, NBMIN, NI, NQ, NW
196*     ..
197*     .. Local Arrays ..
198      COMPLEX*16         T( LDT, NBMAX )
199*     ..
200*     .. External Functions ..
201      LOGICAL            LSAME
202      INTEGER            ILAENV
203      EXTERNAL           LSAME, ILAENV
204*     ..
205*     .. External Subroutines ..
206      EXTERNAL           XERBLA, ZLARFB, ZLARFT, ZUNML2
207*     ..
208*     .. Intrinsic Functions ..
209      INTRINSIC          MAX, MIN
210*     ..
211*     .. Executable Statements ..
212*
213*     Test the input arguments
214*
215      INFO = 0
216      LEFT = LSAME( SIDE, 'L' )
217      NOTRAN = LSAME( TRANS, 'N' )
218      LQUERY = ( LWORK.EQ.-1 )
219*
220*     NQ is the order of Q and NW is the minimum dimension of WORK
221*
222      IF( LEFT ) THEN
223         NQ = M
224         NW = N
225      ELSE
226         NQ = N
227         NW = M
228      END IF
229      IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
230         INFO = -1
231      ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
232         INFO = -2
233      ELSE IF( M.LT.0 ) THEN
234         INFO = -3
235      ELSE IF( N.LT.0 ) THEN
236         INFO = -4
237      ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
238         INFO = -5
239      ELSE IF( LDA.LT.MAX( 1, K ) ) THEN
240         INFO = -7
241      ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
242         INFO = -10
243      ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
244         INFO = -12
245      END IF
246*
247      IF( INFO.EQ.0 ) THEN
248*
249*        Determine the block size.  NB may be at most NBMAX, where NBMAX
250*        is used to define the local array T.
251*
252         NB = MIN( NBMAX, ILAENV( 1, 'ZUNMLQ', SIDE // TRANS, M, N, K,
253     $        -1 ) )
254         LWKOPT = MAX( 1, NW )*NB
255         WORK( 1 ) = LWKOPT
256      END IF
257*
258      IF( INFO.NE.0 ) THEN
259         CALL XERBLA( 'ZUNMLQ', -INFO )
260         RETURN
261      ELSE IF( LQUERY ) THEN
262         RETURN
263      END IF
264*
265*     Quick return if possible
266*
267      IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN
268         WORK( 1 ) = 1
269         RETURN
270      END IF
271*
272      NBMIN = 2
273      LDWORK = NW
274      IF( NB.GT.1 .AND. NB.LT.K ) THEN
275         IWS = NW*NB
276         IF( LWORK.LT.IWS ) THEN
277            NB = LWORK / LDWORK
278            NBMIN = MAX( 2, ILAENV( 2, 'ZUNMLQ', SIDE // TRANS, M, N, K,
279     $              -1 ) )
280         END IF
281      ELSE
282         IWS = NW
283      END IF
284*
285      IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN
286*
287*        Use unblocked code
288*
289         CALL ZUNML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK,
290     $                IINFO )
291      ELSE
292*
293*        Use blocked code
294*
295         IF( ( LEFT .AND. NOTRAN ) .OR.
296     $       ( .NOT.LEFT .AND. .NOT.NOTRAN ) ) THEN
297            I1 = 1
298            I2 = K
299            I3 = NB
300         ELSE
301            I1 = ( ( K-1 ) / NB )*NB + 1
302            I2 = 1
303            I3 = -NB
304         END IF
305*
306         IF( LEFT ) THEN
307            NI = N
308            JC = 1
309         ELSE
310            MI = M
311            IC = 1
312         END IF
313*
314         IF( NOTRAN ) THEN
315            TRANST = 'C'
316         ELSE
317            TRANST = 'N'
318         END IF
319*
320         DO 10 I = I1, I2, I3
321            IB = MIN( NB, K-I+1 )
322*
323*           Form the triangular factor of the block reflector
324*           H = H(i) H(i+1) . . . H(i+ib-1)
325*
326            CALL ZLARFT( 'Forward', 'Rowwise', NQ-I+1, IB, A( I, I ),
327     $                   LDA, TAU( I ), T, LDT )
328            IF( LEFT ) THEN
329*
330*              H or H**H is applied to C(i:m,1:n)
331*
332               MI = M - I + 1
333               IC = I
334            ELSE
335*
336*              H or H**H is applied to C(1:m,i:n)
337*
338               NI = N - I + 1
339               JC = I
340            END IF
341*
342*           Apply H or H**H
343*
344            CALL ZLARFB( SIDE, TRANST, 'Forward', 'Rowwise', MI, NI, IB,
345     $                   A( I, I ), LDA, T, LDT, C( IC, JC ), LDC, WORK,
346     $                   LDWORK )
347   10    CONTINUE
348      END IF
349      WORK( 1 ) = LWKOPT
350      RETURN
351*
352*     End of ZUNMLQ
353*
354      END
355c $Id$
356