1*> \brief \b ZUNM2R multiplies a general matrix by the unitary matrix from a QR factorization determined by cgeqrf (unblocked algorithm).
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 ZUNM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
22*                          WORK, INFO )
23*
24*       .. Scalar Arguments ..
25*       CHARACTER          SIDE, TRANS
26*       INTEGER            INFO, K, 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*> ZUNM2R 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 ZGEQRF. 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] A
96*> \verbatim
97*>          A is COMPLEX*16 array, dimension (LDA,K)
98*>          The i-th column must contain the vector which defines the
99*>          elementary reflector H(i), for i = 1,2,...,k, as returned by
100*>          ZGEQRF in the first k columns of its array argument A.
101*>          A is modified by the routine but restored on exit.
102*> \endverbatim
103*>
104*> \param[in] LDA
105*> \verbatim
106*>          LDA is INTEGER
107*>          The leading dimension of the array A.
108*>          If SIDE = 'L', LDA >= max(1,M);
109*>          if SIDE = 'R', LDA >= max(1,N).
110*> \endverbatim
111*>
112*> \param[in] TAU
113*> \verbatim
114*>          TAU is COMPLEX*16 array, dimension (K)
115*>          TAU(i) must contain the scalar factor of the elementary
116*>          reflector H(i), as returned by ZGEQRF.
117*> \endverbatim
118*>
119*> \param[in,out] C
120*> \verbatim
121*>          C is COMPLEX*16 array, dimension (LDC,N)
122*>          On entry, the m-by-n matrix C.
123*>          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
124*> \endverbatim
125*>
126*> \param[in] LDC
127*> \verbatim
128*>          LDC is INTEGER
129*>          The leading dimension of the array C. LDC >= max(1,M).
130*> \endverbatim
131*>
132*> \param[out] WORK
133*> \verbatim
134*>          WORK is COMPLEX*16 array, dimension
135*>                                   (N) if SIDE = 'L',
136*>                                   (M) if SIDE = 'R'
137*> \endverbatim
138*>
139*> \param[out] INFO
140*> \verbatim
141*>          INFO is INTEGER
142*>          = 0: successful exit
143*>          < 0: if INFO = -i, the i-th argument had an illegal value
144*> \endverbatim
145*
146*  Authors:
147*  ========
148*
149*> \author Univ. of Tennessee
150*> \author Univ. of California Berkeley
151*> \author Univ. of Colorado Denver
152*> \author NAG Ltd.
153*
154*> \ingroup complex16OTHERcomputational
155*
156*  =====================================================================
157      SUBROUTINE ZUNM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
158     $                   WORK, INFO )
159*
160*  -- LAPACK computational routine --
161*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
162*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
163*
164*     .. Scalar Arguments ..
165      CHARACTER          SIDE, TRANS
166      INTEGER            INFO, K, LDA, LDC, M, N
167*     ..
168*     .. Array Arguments ..
169      COMPLEX*16         A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
170*     ..
171*
172*  =====================================================================
173*
174*     .. Parameters ..
175      COMPLEX*16         ONE
176      PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ) )
177*     ..
178*     .. Local Scalars ..
179      LOGICAL            LEFT, NOTRAN
180      INTEGER            I, I1, I2, I3, IC, JC, MI, NI, NQ
181      COMPLEX*16         AII, TAUI
182*     ..
183*     .. External Functions ..
184      LOGICAL            LSAME
185      EXTERNAL           LSAME
186*     ..
187*     .. External Subroutines ..
188      EXTERNAL           XERBLA, ZLARF
189*     ..
190*     .. Intrinsic Functions ..
191      INTRINSIC          DCONJG, MAX
192*     ..
193*     .. Executable Statements ..
194*
195*     Test the input arguments
196*
197      INFO = 0
198      LEFT = LSAME( SIDE, 'L' )
199      NOTRAN = LSAME( TRANS, 'N' )
200*
201*     NQ is the order of Q
202*
203      IF( LEFT ) THEN
204         NQ = M
205      ELSE
206         NQ = N
207      END IF
208      IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
209         INFO = -1
210      ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
211         INFO = -2
212      ELSE IF( M.LT.0 ) THEN
213         INFO = -3
214      ELSE IF( N.LT.0 ) THEN
215         INFO = -4
216      ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
217         INFO = -5
218      ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN
219         INFO = -7
220      ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
221         INFO = -10
222      END IF
223      IF( INFO.NE.0 ) THEN
224         CALL XERBLA( 'ZUNM2R', -INFO )
225         RETURN
226      END IF
227*
228*     Quick return if possible
229*
230      IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 )
231     $   RETURN
232*
233      IF( ( LEFT .AND. .NOT.NOTRAN .OR. .NOT.LEFT .AND. NOTRAN ) ) THEN
234         I1 = 1
235         I2 = K
236         I3 = 1
237      ELSE
238         I1 = K
239         I2 = 1
240         I3 = -1
241      END IF
242*
243      IF( LEFT ) THEN
244         NI = N
245         JC = 1
246      ELSE
247         MI = M
248         IC = 1
249      END IF
250*
251      DO 10 I = I1, I2, I3
252         IF( LEFT ) THEN
253*
254*           H(i) or H(i)**H is applied to C(i:m,1:n)
255*
256            MI = M - I + 1
257            IC = I
258         ELSE
259*
260*           H(i) or H(i)**H is applied to C(1:m,i:n)
261*
262            NI = N - I + 1
263            JC = I
264         END IF
265*
266*        Apply H(i) or H(i)**H
267*
268         IF( NOTRAN ) THEN
269            TAUI = TAU( I )
270         ELSE
271            TAUI = DCONJG( TAU( I ) )
272         END IF
273         AII = A( I, I )
274         A( I, I ) = ONE
275         CALL ZLARF( SIDE, MI, NI, A( I, I ), 1, TAUI, C( IC, JC ), LDC,
276     $               WORK )
277         A( I, I ) = AII
278   10 CONTINUE
279      RETURN
280*
281*     End of ZUNM2R
282*
283      END
284