1*> \brief \b CGEMQRT
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download CGEMQRT + dependencies
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14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgemqrt.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE CGEMQRT( SIDE, TRANS, M, N, K, NB, V, LDV, T, LDT,
22*                          C, LDC, WORK, INFO )
23*
24*       .. Scalar Arguments ..
25*       CHARACTER SIDE, TRANS
26*       INTEGER   INFO, K, LDV, LDC, M, N, NB, LDT
27*       ..
28*       .. Array Arguments ..
29*       COMPLEX   V( LDV, * ), C( LDC, * ), T( LDT, * ), WORK( * )
30*       ..
31*
32*
33*> \par Purpose:
34*  =============
35*>
36*> \verbatim
37*>
38*> CGEMQRT 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 orthogonal matrix defined as the product of K
45*> elementary reflectors:
46*>
47*>       Q = H(1) H(2) . . . H(K) = I - V T V**H
48*>
49*> generated using the compact WY representation as returned by CGEQRT.
50*>
51*> Q is of order M if SIDE = 'L' and of order N  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] NB
93*> \verbatim
94*>          NB is INTEGER
95*>          The block size used for the storage of T.  K >= NB >= 1.
96*>          This must be the same value of NB used to generate T
97*>          in CGEQRT.
98*> \endverbatim
99*>
100*> \param[in] V
101*> \verbatim
102*>          V is COMPLEX array, dimension (LDV,K)
103*>          The i-th column must contain the vector which defines the
104*>          elementary reflector H(i), for i = 1,2,...,k, as returned by
105*>          CGEQRT in the first K columns of its array argument A.
106*> \endverbatim
107*>
108*> \param[in] LDV
109*> \verbatim
110*>          LDV is INTEGER
111*>          The leading dimension of the array V.
112*>          If SIDE = 'L', LDA >= max(1,M);
113*>          if SIDE = 'R', LDA >= max(1,N).
114*> \endverbatim
115*>
116*> \param[in] T
117*> \verbatim
118*>          T is COMPLEX array, dimension (LDT,K)
119*>          The upper triangular factors of the block reflectors
120*>          as returned by CGEQRT, stored as a NB-by-N matrix.
121*> \endverbatim
122*>
123*> \param[in] LDT
124*> \verbatim
125*>          LDT is INTEGER
126*>          The leading dimension of the array T.  LDT >= NB.
127*> \endverbatim
128*>
129*> \param[in,out] C
130*> \verbatim
131*>          C is COMPLEX array, dimension (LDC,N)
132*>          On entry, the M-by-N matrix C.
133*>          On exit, C is overwritten by Q C, Q**H C, C Q**H or C Q.
134*> \endverbatim
135*>
136*> \param[in] LDC
137*> \verbatim
138*>          LDC is INTEGER
139*>          The leading dimension of the array C. LDC >= max(1,M).
140*> \endverbatim
141*>
142*> \param[out] WORK
143*> \verbatim
144*>          WORK is COMPLEX array. The dimension of WORK is
145*>           N*NB if SIDE = 'L', or  M*NB if SIDE = 'R'.
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 complexGEcomputational
164*
165*  =====================================================================
166      SUBROUTINE CGEMQRT( SIDE, TRANS, M, N, K, NB, V, LDV, T, LDT,
167     $                   C, LDC, WORK, 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, LDV, LDC, M, N, NB, LDT
176*     ..
177*     .. Array Arguments ..
178      COMPLEX   V( LDV, * ), C( LDC, * ), T( LDT, * ), WORK( * )
179*     ..
180*
181*  =====================================================================
182*
183*     ..
184*     .. Local Scalars ..
185      LOGICAL            LEFT, RIGHT, TRAN, NOTRAN
186      INTEGER            I, IB, LDWORK, KF, Q
187*     ..
188*     .. External Functions ..
189      LOGICAL            LSAME
190      EXTERNAL           LSAME
191*     ..
192*     .. External Subroutines ..
193      EXTERNAL           XERBLA, CLARFB
194*     ..
195*     .. Intrinsic Functions ..
196      INTRINSIC          MAX, MIN
197*     ..
198*     .. Executable Statements ..
199*
200*     .. Test the input arguments ..
201*
202      INFO   = 0
203      LEFT   = LSAME( SIDE,  'L' )
204      RIGHT  = LSAME( SIDE,  'R' )
205      TRAN   = LSAME( TRANS, 'C' )
206      NOTRAN = LSAME( TRANS, 'N' )
207*
208      IF( LEFT ) THEN
209         LDWORK = MAX( 1, N )
210         Q = M
211      ELSE IF ( RIGHT ) THEN
212         LDWORK = MAX( 1, M )
213         Q = N
214      END IF
215      IF( .NOT.LEFT .AND. .NOT.RIGHT ) THEN
216         INFO = -1
217      ELSE IF( .NOT.TRAN .AND. .NOT.NOTRAN ) THEN
218         INFO = -2
219      ELSE IF( M.LT.0 ) THEN
220         INFO = -3
221      ELSE IF( N.LT.0 ) THEN
222         INFO = -4
223      ELSE IF( K.LT.0 .OR. K.GT.Q ) THEN
224         INFO = -5
225      ELSE IF( NB.LT.1 .OR. (NB.GT.K .AND. K.GT.0)) THEN
226         INFO = -6
227      ELSE IF( LDV.LT.MAX( 1, Q ) ) THEN
228         INFO = -8
229      ELSE IF( LDT.LT.NB ) THEN
230         INFO = -10
231      ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
232         INFO = -12
233      END IF
234*
235      IF( INFO.NE.0 ) THEN
236         CALL XERBLA( 'CGEMQRT', -INFO )
237         RETURN
238      END IF
239*
240*     .. Quick return if possible ..
241*
242      IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) RETURN
243*
244      IF( LEFT .AND. TRAN ) THEN
245*
246         DO I = 1, K, NB
247            IB = MIN( NB, K-I+1 )
248            CALL CLARFB( 'L', 'C', 'F', 'C', M-I+1, N, IB,
249     $                   V( I, I ), LDV, T( 1, I ), LDT,
250     $                   C( I, 1 ), LDC, WORK, LDWORK )
251         END DO
252*
253      ELSE IF( RIGHT .AND. NOTRAN ) THEN
254*
255         DO I = 1, K, NB
256            IB = MIN( NB, K-I+1 )
257            CALL CLARFB( 'R', 'N', 'F', 'C', M, N-I+1, IB,
258     $                   V( I, I ), LDV, T( 1, I ), LDT,
259     $                   C( 1, I ), LDC, WORK, LDWORK )
260         END DO
261*
262      ELSE IF( LEFT .AND. NOTRAN ) THEN
263*
264         KF = ((K-1)/NB)*NB+1
265         DO I = KF, 1, -NB
266            IB = MIN( NB, K-I+1 )
267            CALL CLARFB( 'L', 'N', 'F', 'C', M-I+1, N, IB,
268     $                   V( I, I ), LDV, T( 1, I ), LDT,
269     $                   C( I, 1 ), LDC, WORK, LDWORK )
270         END DO
271*
272      ELSE IF( RIGHT .AND. TRAN ) THEN
273*
274         KF = ((K-1)/NB)*NB+1
275         DO I = KF, 1, -NB
276            IB = MIN( NB, K-I+1 )
277            CALL CLARFB( 'R', 'C', 'F', 'C', M, N-I+1, IB,
278     $                   V( I, I ), LDV, T( 1, I ), LDT,
279     $                   C( 1, I ), LDC, WORK, LDWORK )
280         END DO
281*
282      END IF
283*
284      RETURN
285*
286*     End of CGEMQRT
287*
288      END
289