1*> \brief \b ZUNMRZ
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 ZUNMRZ( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
22*                          WORK, LWORK, INFO )
23*
24*       .. Scalar Arguments ..
25*       CHARACTER          SIDE, TRANS
26*       INTEGER            INFO, K, L, 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*> ZUNMRZ 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(1) H(2) . . . H(k)
48*>
49*> as returned by ZTZRZF. 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] L
92*> \verbatim
93*>          L is INTEGER
94*>          The number of columns of the matrix A containing
95*>          the meaningful part of the Householder reflectors.
96*>          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
97*> \endverbatim
98*>
99*> \param[in] A
100*> \verbatim
101*>          A is COMPLEX*16 array, dimension
102*>                               (LDA,M) if SIDE = 'L',
103*>                               (LDA,N) if SIDE = 'R'
104*>          The i-th row must contain the vector which defines the
105*>          elementary reflector H(i), for i = 1,2,...,k, as returned by
106*>          ZTZRZF in the last k rows of its array argument A.
107*>          A is modified by the routine but restored on exit.
108*> \endverbatim
109*>
110*> \param[in] LDA
111*> \verbatim
112*>          LDA is INTEGER
113*>          The leading dimension of the array A. LDA >= max(1,K).
114*> \endverbatim
115*>
116*> \param[in] TAU
117*> \verbatim
118*>          TAU is COMPLEX*16 array, dimension (K)
119*>          TAU(i) must contain the scalar factor of the elementary
120*>          reflector H(i), as returned by ZTZRZF.
121*> \endverbatim
122*>
123*> \param[in,out] C
124*> \verbatim
125*>          C is COMPLEX*16 array, dimension (LDC,N)
126*>          On entry, the M-by-N matrix C.
127*>          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
128*> \endverbatim
129*>
130*> \param[in] LDC
131*> \verbatim
132*>          LDC is INTEGER
133*>          The leading dimension of the array C. LDC >= max(1,M).
134*> \endverbatim
135*>
136*> \param[out] WORK
137*> \verbatim
138*>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
139*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
140*> \endverbatim
141*>
142*> \param[in] LWORK
143*> \verbatim
144*>          LWORK is INTEGER
145*>          The dimension of the array WORK.
146*>          If SIDE = 'L', LWORK >= max(1,N);
147*>          if SIDE = 'R', LWORK >= max(1,M).
148*>          For good performance, LWORK should generally be larger.
149*>
150*>          If LWORK = -1, then a workspace query is assumed; the routine
151*>          only calculates the optimal size of the WORK array, returns
152*>          this value as the first entry of the WORK array, and no error
153*>          message related to LWORK is issued by XERBLA.
154*> \endverbatim
155*>
156*> \param[out] INFO
157*> \verbatim
158*>          INFO is INTEGER
159*>          = 0:  successful exit
160*>          < 0:  if INFO = -i, the i-th argument had an illegal value
161*> \endverbatim
162*
163*  Authors:
164*  ========
165*
166*> \author Univ. of Tennessee
167*> \author Univ. of California Berkeley
168*> \author Univ. of Colorado Denver
169*> \author NAG Ltd.
170*
171*> \date November 2015
172*
173*> \ingroup complex16OTHERcomputational
174*
175*> \par Contributors:
176*  ==================
177*>
178*>    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
179*
180*> \par Further Details:
181*  =====================
182*>
183*> \verbatim
184*> \endverbatim
185*>
186*  =====================================================================
187      SUBROUTINE ZUNMRZ( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
188     $                   WORK, LWORK, INFO )
189*
190*  -- LAPACK computational routine (version 3.6.0) --
191*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
192*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
193*     November 2015
194*
195*     .. Scalar Arguments ..
196      CHARACTER          SIDE, TRANS
197      INTEGER            INFO, K, L, LDA, LDC, LWORK, M, N
198*     ..
199*     .. Array Arguments ..
200      COMPLEX*16         A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
201*     ..
202*
203*  =====================================================================
204*
205*     .. Parameters ..
206      INTEGER            NBMAX, LDT, TSIZE
207      PARAMETER          ( NBMAX = 64, LDT = NBMAX+1,
208     $                     TSIZE = LDT*NBMAX )
209*     ..
210*     .. Local Scalars ..
211      LOGICAL            LEFT, LQUERY, NOTRAN
212      CHARACTER          TRANST
213      INTEGER            I, I1, I2, I3, IB, IC, IINFO, IWT, JA, JC,
214     $                   LDWORK, LWKOPT, MI, NB, NBMIN, NI, NQ, NW
215*     ..
216*     .. External Functions ..
217      LOGICAL            LSAME
218      INTEGER            ILAENV
219      EXTERNAL           LSAME, ILAENV
220*     ..
221*     .. External Subroutines ..
222      EXTERNAL           XERBLA, ZLARZB, ZLARZT, ZUNMR3
223*     ..
224*     .. Intrinsic Functions ..
225      INTRINSIC          MAX, MIN
226*     ..
227*     .. Executable Statements ..
228*
229*     Test the input arguments
230*
231      INFO = 0
232      LEFT = LSAME( SIDE, 'L' )
233      NOTRAN = LSAME( TRANS, 'N' )
234      LQUERY = ( LWORK.EQ.-1 )
235*
236*     NQ is the order of Q and NW is the minimum dimension of WORK
237*
238      IF( LEFT ) THEN
239         NQ = M
240         NW = MAX( 1, N )
241      ELSE
242         NQ = N
243         NW = MAX( 1, M )
244      END IF
245      IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
246         INFO = -1
247      ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
248         INFO = -2
249      ELSE IF( M.LT.0 ) THEN
250         INFO = -3
251      ELSE IF( N.LT.0 ) THEN
252         INFO = -4
253      ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
254         INFO = -5
255      ELSE IF( L.LT.0 .OR. ( LEFT .AND. ( L.GT.M ) ) .OR.
256     $         ( .NOT.LEFT .AND. ( L.GT.N ) ) ) THEN
257         INFO = -6
258      ELSE IF( LDA.LT.MAX( 1, K ) ) THEN
259         INFO = -8
260      ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
261         INFO = -11
262      ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
263         INFO = -13
264      END IF
265*
266      IF( INFO.EQ.0 ) THEN
267*
268*        Compute the workspace requirements
269*
270         IF( M.EQ.0 .OR. N.EQ.0 ) THEN
271            LWKOPT = 1
272         ELSE
273            NB = MIN( NBMAX, ILAENV( 1, 'ZUNMRQ', SIDE // TRANS, M, N,
274     $                               K, -1 ) )
275            LWKOPT = NW*NB + TSIZE
276         END IF
277         WORK( 1 ) = LWKOPT
278      END IF
279*
280      IF( INFO.NE.0 ) THEN
281         CALL XERBLA( 'ZUNMRZ', -INFO )
282         RETURN
283      ELSE IF( LQUERY ) THEN
284         RETURN
285      END IF
286*
287*     Quick return if possible
288*
289      IF( M.EQ.0 .OR. N.EQ.0 ) THEN
290         RETURN
291      END IF
292*
293*     Determine the block size.  NB may be at most NBMAX, where NBMAX
294*     is used to define the local array T.
295*
296      NB = MIN( NBMAX, ILAENV( 1, 'ZUNMRQ', SIDE // TRANS, M, N, K,
297     $     -1 ) )
298      NBMIN = 2
299      LDWORK = NW
300      IF( NB.GT.1 .AND. NB.LT.K ) THEN
301         IF( LWORK.LT.NW*NB+TSIZE ) THEN
302            NB = (LWORK-TSIZE) / LDWORK
303            NBMIN = MAX( 2, ILAENV( 2, 'ZUNMRQ', SIDE // TRANS, M, N, K,
304     $              -1 ) )
305         END IF
306      END IF
307*
308      IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN
309*
310*        Use unblocked code
311*
312         CALL ZUNMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
313     $                WORK, IINFO )
314      ELSE
315*
316*        Use blocked code
317*
318         IWT = 1 + NW*NB
319         IF( ( LEFT .AND. .NOT.NOTRAN ) .OR.
320     $       ( .NOT.LEFT .AND. NOTRAN ) ) THEN
321            I1 = 1
322            I2 = K
323            I3 = NB
324         ELSE
325            I1 = ( ( K-1 ) / NB )*NB + 1
326            I2 = 1
327            I3 = -NB
328         END IF
329*
330         IF( LEFT ) THEN
331            NI = N
332            JC = 1
333            JA = M - L + 1
334         ELSE
335            MI = M
336            IC = 1
337            JA = N - L + 1
338         END IF
339*
340         IF( NOTRAN ) THEN
341            TRANST = 'C'
342         ELSE
343            TRANST = 'N'
344         END IF
345*
346         DO 10 I = I1, I2, I3
347            IB = MIN( NB, K-I+1 )
348*
349*           Form the triangular factor of the block reflector
350*           H = H(i+ib-1) . . . H(i+1) H(i)
351*
352            CALL ZLARZT( 'Backward', 'Rowwise', L, IB, A( I, JA ), LDA,
353     $                   TAU( I ), WORK( IWT ), LDT )
354*
355            IF( LEFT ) THEN
356*
357*              H or H**H is applied to C(i:m,1:n)
358*
359               MI = M - I + 1
360               IC = I
361            ELSE
362*
363*              H or H**H is applied to C(1:m,i:n)
364*
365               NI = N - I + 1
366               JC = I
367            END IF
368*
369*           Apply H or H**H
370*
371            CALL ZLARZB( SIDE, TRANST, 'Backward', 'Rowwise', MI, NI,
372     $                   IB, L, A( I, JA ), LDA, WORK( IWT ), LDT,
373     $                   C( IC, JC ), LDC, WORK, LDWORK )
374   10    CONTINUE
375*
376      END IF
377*
378      WORK( 1 ) = LWKOPT
379*
380      RETURN
381*
382*     End of ZUNMRZ
383*
384      END
385