1*> \brief \b CUNMQL
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 CUNMQL( 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            A( LDA, * ), C( LDC, * ), TAU( * ),
30*      $                   WORK( * )
31*       ..
32*
33*
34*> \par Purpose:
35*  =============
36*>
37*> \verbatim
38*>
39*> CUNMQL overwrites the general complex M-by-N matrix C with
40*>
41*>                 SIDE = 'L'     SIDE = 'R'
42*> TRANS = 'N':      Q * C          C * Q
43*> TRANS = 'C':      Q**H * C       C * Q**H
44*>
45*> where Q is a complex unitary matrix defined as the product of k
46*> elementary reflectors
47*>
48*>       Q = H(k) . . . H(2) H(1)
49*>
50*> as returned by CGEQLF. Q is of order M if SIDE = 'L' and of order N
51*> if SIDE = 'R'.
52*> \endverbatim
53*
54*  Arguments:
55*  ==========
56*
57*> \param[in] SIDE
58*> \verbatim
59*>          SIDE is CHARACTER*1
60*>          = 'L': apply Q or Q**H from the Left;
61*>          = 'R': apply Q or Q**H from the Right.
62*> \endverbatim
63*>
64*> \param[in] TRANS
65*> \verbatim
66*>          TRANS is CHARACTER*1
67*>          = 'N':  No transpose, apply Q;
68*>          = 'C':  Conjugate transpose, apply Q**H.
69*> \endverbatim
70*>
71*> \param[in] M
72*> \verbatim
73*>          M is INTEGER
74*>          The number of rows of the matrix C. M >= 0.
75*> \endverbatim
76*>
77*> \param[in] N
78*> \verbatim
79*>          N is INTEGER
80*>          The number of columns of the matrix C. N >= 0.
81*> \endverbatim
82*>
83*> \param[in] K
84*> \verbatim
85*>          K is INTEGER
86*>          The number of elementary reflectors whose product defines
87*>          the matrix Q.
88*>          If SIDE = 'L', M >= K >= 0;
89*>          if SIDE = 'R', N >= K >= 0.
90*> \endverbatim
91*>
92*> \param[in] A
93*> \verbatim
94*>          A is COMPLEX array, dimension (LDA,K)
95*>          The i-th column must contain the vector which defines the
96*>          elementary reflector H(i), for i = 1,2,...,k, as returned by
97*>          CGEQLF in the last k columns of its array argument A.
98*> \endverbatim
99*>
100*> \param[in] LDA
101*> \verbatim
102*>          LDA is INTEGER
103*>          The leading dimension of the array A.
104*>          If SIDE = 'L', LDA >= max(1,M);
105*>          if SIDE = 'R', LDA >= max(1,N).
106*> \endverbatim
107*>
108*> \param[in] TAU
109*> \verbatim
110*>          TAU is COMPLEX array, dimension (K)
111*>          TAU(i) must contain the scalar factor of the elementary
112*>          reflector H(i), as returned by CGEQLF.
113*> \endverbatim
114*>
115*> \param[in,out] C
116*> \verbatim
117*>          C is COMPLEX array, dimension (LDC,N)
118*>          On entry, the M-by-N matrix C.
119*>          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
120*> \endverbatim
121*>
122*> \param[in] LDC
123*> \verbatim
124*>          LDC is INTEGER
125*>          The leading dimension of the array C. LDC >= max(1,M).
126*> \endverbatim
127*>
128*> \param[out] WORK
129*> \verbatim
130*>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
131*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
132*> \endverbatim
133*>
134*> \param[in] LWORK
135*> \verbatim
136*>          LWORK is INTEGER
137*>          The dimension of the array WORK.
138*>          If SIDE = 'L', LWORK >= max(1,N);
139*>          if SIDE = 'R', LWORK >= max(1,M).
140*>          For good performance, LWORK should generally be larger.
141*>
142*>          If LWORK = -1, then a workspace query is assumed; the routine
143*>          only calculates the optimal size of the WORK array, returns
144*>          this value as the first entry of the WORK array, and no error
145*>          message related to LWORK is issued by XERBLA.
146*> \endverbatim
147*>
148*> \param[out] INFO
149*> \verbatim
150*>          INFO is INTEGER
151*>          = 0:  successful exit
152*>          < 0:  if INFO = -i, the i-th argument had an illegal value
153*> \endverbatim
154*
155*  Authors:
156*  ========
157*
158*> \author Univ. of Tennessee
159*> \author Univ. of California Berkeley
160*> \author Univ. of Colorado Denver
161*> \author NAG Ltd.
162*
163*> \ingroup complexOTHERcomputational
164*
165*  =====================================================================
166      SUBROUTINE CUNMQL( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
167     $                   WORK, LWORK, INFO )
168*
169*  -- LAPACK computational routine --
170*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
171*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
172*
173*     .. Scalar Arguments ..
174      CHARACTER          SIDE, TRANS
175      INTEGER            INFO, K, LDA, LDC, LWORK, M, N
176*     ..
177*     .. Array Arguments ..
178      COMPLEX            A( LDA, * ), C( LDC, * ), TAU( * ),
179     $                   WORK( * )
180*     ..
181*
182*  =====================================================================
183*
184*     .. Parameters ..
185      INTEGER            NBMAX, LDT, TSIZE
186      PARAMETER          ( NBMAX = 64, LDT = NBMAX+1,
187     $                     TSIZE = LDT*NBMAX )
188*     ..
189*     .. Local Scalars ..
190      LOGICAL            LEFT, LQUERY, NOTRAN
191      INTEGER            I, I1, I2, I3, IB, IINFO, IWT, LDWORK, LWKOPT,
192     $                   MI, NB, NBMIN, NI, NQ, NW
193*     ..
194*     .. External Functions ..
195      LOGICAL            LSAME
196      INTEGER            ILAENV
197      EXTERNAL           LSAME, ILAENV
198*     ..
199*     .. External Subroutines ..
200      EXTERNAL           CLARFB, CLARFT, CUNM2L, XERBLA
201*     ..
202*     .. Intrinsic Functions ..
203      INTRINSIC          MAX, MIN
204*     ..
205*     .. Executable Statements ..
206*
207*     Test the input arguments
208*
209      INFO = 0
210      LEFT = LSAME( SIDE, 'L' )
211      NOTRAN = LSAME( TRANS, 'N' )
212      LQUERY = ( LWORK.EQ.-1 )
213*
214*     NQ is the order of Q and NW is the minimum dimension of WORK
215*
216      IF( LEFT ) THEN
217         NQ = M
218         NW = MAX( 1, N )
219      ELSE
220         NQ = N
221         NW = MAX( 1, M )
222      END IF
223      IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
224         INFO = -1
225      ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
226         INFO = -2
227      ELSE IF( M.LT.0 ) THEN
228         INFO = -3
229      ELSE IF( N.LT.0 ) THEN
230         INFO = -4
231      ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
232         INFO = -5
233      ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN
234         INFO = -7
235      ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
236         INFO = -10
237      ELSE IF( LWORK.LT.NW .AND. .NOT.LQUERY ) THEN
238         INFO = -12
239      END IF
240*
241      IF( INFO.EQ.0 ) THEN
242*
243*        Compute the workspace requirements
244*
245         IF( M.EQ.0 .OR. N.EQ.0 ) THEN
246            LWKOPT = 1
247         ELSE
248            NB = MIN( NBMAX, ILAENV( 1, 'CUNMQL', SIDE // TRANS, M, N,
249     $                               K, -1 ) )
250            LWKOPT = NW*NB + TSIZE
251         END IF
252         WORK( 1 ) = LWKOPT
253      END IF
254*
255      IF( INFO.NE.0 ) THEN
256         CALL XERBLA( 'CUNMQL', -INFO )
257         RETURN
258      ELSE IF( LQUERY ) THEN
259         RETURN
260      END IF
261*
262*     Quick return if possible
263*
264      IF( M.EQ.0 .OR. N.EQ.0 ) THEN
265         RETURN
266      END IF
267*
268*     Determine the block size
269*
270      NBMIN = 2
271      LDWORK = NW
272      IF( NB.GT.1 .AND. NB.LT.K ) THEN
273         IF( LWORK.LT.LWKOPT ) THEN
274            NB = (LWORK-TSIZE) / LDWORK
275            NBMIN = MAX( 2, ILAENV( 2, 'CUNMQL', SIDE // TRANS, M, N, K,
276     $              -1 ) )
277         END IF
278      END IF
279*
280      IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN
281*
282*        Use unblocked code
283*
284         CALL CUNM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK,
285     $                IINFO )
286      ELSE
287*
288*        Use blocked code
289*
290         IWT = 1 + NW*NB
291         IF( ( LEFT .AND. NOTRAN ) .OR.
292     $       ( .NOT.LEFT .AND. .NOT.NOTRAN ) ) THEN
293            I1 = 1
294            I2 = K
295            I3 = NB
296         ELSE
297            I1 = ( ( K-1 ) / NB )*NB + 1
298            I2 = 1
299            I3 = -NB
300         END IF
301*
302         IF( LEFT ) THEN
303            NI = N
304         ELSE
305            MI = M
306         END IF
307*
308         DO 10 I = I1, I2, I3
309            IB = MIN( NB, K-I+1 )
310*
311*           Form the triangular factor of the block reflector
312*           H = H(i+ib-1) . . . H(i+1) H(i)
313*
314            CALL CLARFT( 'Backward', 'Columnwise', NQ-K+I+IB-1, IB,
315     $                   A( 1, I ), LDA, TAU( I ), WORK( IWT ), LDT )
316            IF( LEFT ) THEN
317*
318*              H or H**H is applied to C(1:m-k+i+ib-1,1:n)
319*
320               MI = M - K + I + IB - 1
321            ELSE
322*
323*              H or H**H is applied to C(1:m,1:n-k+i+ib-1)
324*
325               NI = N - K + I + IB - 1
326            END IF
327*
328*           Apply H or H**H
329*
330            CALL CLARFB( SIDE, TRANS, 'Backward', 'Columnwise', MI, NI,
331     $                   IB, A( 1, I ), LDA, WORK( IWT ), LDT, C, LDC,
332     $                   WORK, LDWORK )
333   10    CONTINUE
334      END IF
335      WORK( 1 ) = LWKOPT
336      RETURN
337*
338*     End of CUNMQL
339*
340      END
341