1*> \brief \b ZUNMR3 multiplies a general matrix by the unitary matrix from a RZ factorization determined by ctzrzf (unblocked algorithm).
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
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15*> [TXT]</a>
16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE ZUNMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
22*                          WORK, INFO )
23*
24*       .. Scalar Arguments ..
25*       CHARACTER          SIDE, TRANS
26*       INTEGER            INFO, K, L, LDA, LDC, 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*> ZUNMR3 overwrites the general complex m by n matrix C with
39*>
40*>       Q * C  if SIDE = 'L' and TRANS = 'N', or
41*>
42*>       Q**H* C  if SIDE = 'L' and TRANS = 'C', or
43*>
44*>       C * Q  if SIDE = 'R' and TRANS = 'N', or
45*>
46*>       C * Q**H if SIDE = 'R' and TRANS = 'C',
47*>
48*> where Q is a complex unitary matrix defined as the product of k
49*> elementary reflectors
50*>
51*>       Q = H(1) H(2) . . . H(k)
52*>
53*> as returned by ZTZRZF. Q is of order m if SIDE = 'L' and of order n
54*> if SIDE = 'R'.
55*> \endverbatim
56*
57*  Arguments:
58*  ==========
59*
60*> \param[in] SIDE
61*> \verbatim
62*>          SIDE is CHARACTER*1
63*>          = 'L': apply Q or Q**H from the Left
64*>          = 'R': apply Q or Q**H from the Right
65*> \endverbatim
66*>
67*> \param[in] TRANS
68*> \verbatim
69*>          TRANS is CHARACTER*1
70*>          = 'N': apply Q  (No transpose)
71*>          = 'C': apply Q**H (Conjugate transpose)
72*> \endverbatim
73*>
74*> \param[in] M
75*> \verbatim
76*>          M is INTEGER
77*>          The number of rows of the matrix C. M >= 0.
78*> \endverbatim
79*>
80*> \param[in] N
81*> \verbatim
82*>          N is INTEGER
83*>          The number of columns of the matrix C. N >= 0.
84*> \endverbatim
85*>
86*> \param[in] K
87*> \verbatim
88*>          K is INTEGER
89*>          The number of elementary reflectors whose product defines
90*>          the matrix Q.
91*>          If SIDE = 'L', M >= K >= 0;
92*>          if SIDE = 'R', N >= K >= 0.
93*> \endverbatim
94*>
95*> \param[in] L
96*> \verbatim
97*>          L is INTEGER
98*>          The number of columns of the matrix A containing
99*>          the meaningful part of the Householder reflectors.
100*>          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
101*> \endverbatim
102*>
103*> \param[in] A
104*> \verbatim
105*>          A is COMPLEX*16 array, dimension
106*>                               (LDA,M) if SIDE = 'L',
107*>                               (LDA,N) if SIDE = 'R'
108*>          The i-th row must contain the vector which defines the
109*>          elementary reflector H(i), for i = 1,2,...,k, as returned by
110*>          ZTZRZF in the last k rows of its array argument A.
111*>          A is modified by the routine but restored on exit.
112*> \endverbatim
113*>
114*> \param[in] LDA
115*> \verbatim
116*>          LDA is INTEGER
117*>          The leading dimension of the array A. LDA >= max(1,K).
118*> \endverbatim
119*>
120*> \param[in] TAU
121*> \verbatim
122*>          TAU is COMPLEX*16 array, dimension (K)
123*>          TAU(i) must contain the scalar factor of the elementary
124*>          reflector H(i), as returned by ZTZRZF.
125*> \endverbatim
126*>
127*> \param[in,out] C
128*> \verbatim
129*>          C is COMPLEX*16 array, dimension (LDC,N)
130*>          On entry, the m-by-n matrix C.
131*>          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
132*> \endverbatim
133*>
134*> \param[in] LDC
135*> \verbatim
136*>          LDC is INTEGER
137*>          The leading dimension of the array C. LDC >= max(1,M).
138*> \endverbatim
139*>
140*> \param[out] WORK
141*> \verbatim
142*>          WORK is COMPLEX*16 array, dimension
143*>                                   (N) if SIDE = 'L',
144*>                                   (M) if SIDE = 'R'
145*> \endverbatim
146*>
147*> \param[out] INFO
148*> \verbatim
149*>          INFO is INTEGER
150*>          = 0: successful exit
151*>          < 0: if INFO = -i, the i-th argument had an illegal value
152*> \endverbatim
153*
154*  Authors:
155*  ========
156*
157*> \author Univ. of Tennessee
158*> \author Univ. of California Berkeley
159*> \author Univ. of Colorado Denver
160*> \author NAG Ltd.
161*
162*> \date September 2012
163*
164*> \ingroup complex16OTHERcomputational
165*
166*> \par Contributors:
167*  ==================
168*>
169*>    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
170*
171*> \par Further Details:
172*  =====================
173*>
174*> \verbatim
175*> \endverbatim
176*>
177*  =====================================================================
178      SUBROUTINE ZUNMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
179     $                   WORK, INFO )
180*
181*  -- LAPACK computational routine (version 3.4.2) --
182*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
183*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
184*     September 2012
185*
186*     .. Scalar Arguments ..
187      CHARACTER          SIDE, TRANS
188      INTEGER            INFO, K, L, LDA, LDC, M, N
189*     ..
190*     .. Array Arguments ..
191      COMPLEX*16         A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
192*     ..
193*
194*  =====================================================================
195*
196*     .. Local Scalars ..
197      LOGICAL            LEFT, NOTRAN
198      INTEGER            I, I1, I2, I3, IC, JA, JC, MI, NI, NQ
199      COMPLEX*16         TAUI
200*     ..
201*     .. External Functions ..
202      LOGICAL            LSAME
203      EXTERNAL           LSAME
204*     ..
205*     .. External Subroutines ..
206      EXTERNAL           XERBLA, ZLARZ
207*     ..
208*     .. Intrinsic Functions ..
209      INTRINSIC          DCONJG, MAX
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*
219*     NQ is the order of Q
220*
221      IF( LEFT ) THEN
222         NQ = M
223      ELSE
224         NQ = N
225      END IF
226      IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
227         INFO = -1
228      ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
229         INFO = -2
230      ELSE IF( M.LT.0 ) THEN
231         INFO = -3
232      ELSE IF( N.LT.0 ) THEN
233         INFO = -4
234      ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
235         INFO = -5
236      ELSE IF( L.LT.0 .OR. ( LEFT .AND. ( L.GT.M ) ) .OR.
237     $         ( .NOT.LEFT .AND. ( L.GT.N ) ) ) THEN
238         INFO = -6
239      ELSE IF( LDA.LT.MAX( 1, K ) ) THEN
240         INFO = -8
241      ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
242         INFO = -11
243      END IF
244      IF( INFO.NE.0 ) THEN
245         CALL XERBLA( 'ZUNMR3', -INFO )
246         RETURN
247      END IF
248*
249*     Quick return if possible
250*
251      IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 )
252     $   RETURN
253*
254      IF( ( LEFT .AND. .NOT.NOTRAN .OR. .NOT.LEFT .AND. NOTRAN ) ) THEN
255         I1 = 1
256         I2 = K
257         I3 = 1
258      ELSE
259         I1 = K
260         I2 = 1
261         I3 = -1
262      END IF
263*
264      IF( LEFT ) THEN
265         NI = N
266         JA = M - L + 1
267         JC = 1
268      ELSE
269         MI = M
270         JA = N - L + 1
271         IC = 1
272      END IF
273*
274      DO 10 I = I1, I2, I3
275         IF( LEFT ) THEN
276*
277*           H(i) or H(i)**H is applied to C(i:m,1:n)
278*
279            MI = M - I + 1
280            IC = I
281         ELSE
282*
283*           H(i) or H(i)**H is applied to C(1:m,i:n)
284*
285            NI = N - I + 1
286            JC = I
287         END IF
288*
289*        Apply H(i) or H(i)**H
290*
291         IF( NOTRAN ) THEN
292            TAUI = TAU( I )
293         ELSE
294            TAUI = DCONJG( TAU( I ) )
295         END IF
296         CALL ZLARZ( SIDE, MI, NI, L, A( I, JA ), LDA, TAUI,
297     $               C( IC, JC ), LDC, WORK )
298*
299   10 CONTINUE
300*
301      RETURN
302*
303*     End of ZUNMR3
304*
305      END
306