1*> \brief \b ZUPMTR
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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14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zupmtr.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE ZUPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK,
22*                          INFO )
23*
24*       .. Scalar Arguments ..
25*       CHARACTER          SIDE, TRANS, UPLO
26*       INTEGER            INFO, LDC, M, N
27*       ..
28*       .. Array Arguments ..
29*       COMPLEX*16         AP( * ), C( LDC, * ), TAU( * ), WORK( * )
30*       ..
31*
32*
33*> \par Purpose:
34*  =============
35*>
36*> \verbatim
37*>
38*> ZUPMTR 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 of order nq, with nq = m if
45*> SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
46*> nq-1 elementary reflectors, as returned by ZHPTRD using packed
47*> storage:
48*>
49*> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
50*>
51*> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
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] UPLO
65*> \verbatim
66*>          UPLO is CHARACTER*1
67*>          = 'U': Upper triangular packed storage used in previous
68*>                 call to ZHPTRD;
69*>          = 'L': Lower triangular packed storage used in previous
70*>                 call to ZHPTRD.
71*> \endverbatim
72*>
73*> \param[in] TRANS
74*> \verbatim
75*>          TRANS is CHARACTER*1
76*>          = 'N':  No transpose, apply Q;
77*>          = 'C':  Conjugate transpose, apply Q**H.
78*> \endverbatim
79*>
80*> \param[in] M
81*> \verbatim
82*>          M is INTEGER
83*>          The number of rows of the matrix C. M >= 0.
84*> \endverbatim
85*>
86*> \param[in] N
87*> \verbatim
88*>          N is INTEGER
89*>          The number of columns of the matrix C. N >= 0.
90*> \endverbatim
91*>
92*> \param[in] AP
93*> \verbatim
94*>          AP is COMPLEX*16 array, dimension
95*>                               (M*(M+1)/2) if SIDE = 'L'
96*>                               (N*(N+1)/2) if SIDE = 'R'
97*>          The vectors which define the elementary reflectors, as
98*>          returned by ZHPTRD.  AP is modified by the routine but
99*>          restored on exit.
100*> \endverbatim
101*>
102*> \param[in] TAU
103*> \verbatim
104*>          TAU is COMPLEX*16 array, dimension (M-1) if SIDE = 'L'
105*>                                     or (N-1) if SIDE = 'R'
106*>          TAU(i) must contain the scalar factor of the elementary
107*>          reflector H(i), as returned by ZHPTRD.
108*> \endverbatim
109*>
110*> \param[in,out] C
111*> \verbatim
112*>          C is COMPLEX*16 array, dimension (LDC,N)
113*>          On entry, the M-by-N matrix C.
114*>          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
115*> \endverbatim
116*>
117*> \param[in] LDC
118*> \verbatim
119*>          LDC is INTEGER
120*>          The leading dimension of the array C. LDC >= max(1,M).
121*> \endverbatim
122*>
123*> \param[out] WORK
124*> \verbatim
125*>          WORK is COMPLEX*16 array, dimension
126*>                                   (N) if SIDE = 'L'
127*>                                   (M) if SIDE = 'R'
128*> \endverbatim
129*>
130*> \param[out] INFO
131*> \verbatim
132*>          INFO is INTEGER
133*>          = 0:  successful exit
134*>          < 0:  if INFO = -i, the i-th argument had an illegal value
135*> \endverbatim
136*
137*  Authors:
138*  ========
139*
140*> \author Univ. of Tennessee
141*> \author Univ. of California Berkeley
142*> \author Univ. of Colorado Denver
143*> \author NAG Ltd.
144*
145*> \ingroup complex16OTHERcomputational
146*
147*  =====================================================================
148      SUBROUTINE ZUPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK,
149     $                   INFO )
150*
151*  -- LAPACK computational routine --
152*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
153*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
154*
155*     .. Scalar Arguments ..
156      CHARACTER          SIDE, TRANS, UPLO
157      INTEGER            INFO, LDC, M, N
158*     ..
159*     .. Array Arguments ..
160      COMPLEX*16         AP( * ), C( LDC, * ), TAU( * ), WORK( * )
161*     ..
162*
163*  =====================================================================
164*
165*     .. Parameters ..
166      COMPLEX*16         ONE
167      PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ) )
168*     ..
169*     .. Local Scalars ..
170      LOGICAL            FORWRD, LEFT, NOTRAN, UPPER
171      INTEGER            I, I1, I2, I3, IC, II, JC, MI, NI, NQ
172      COMPLEX*16         AII, TAUI
173*     ..
174*     .. External Functions ..
175      LOGICAL            LSAME
176      EXTERNAL           LSAME
177*     ..
178*     .. External Subroutines ..
179      EXTERNAL           XERBLA, ZLARF
180*     ..
181*     .. Intrinsic Functions ..
182      INTRINSIC          DCONJG, MAX
183*     ..
184*     .. Executable Statements ..
185*
186*     Test the input arguments
187*
188      INFO = 0
189      LEFT = LSAME( SIDE, 'L' )
190      NOTRAN = LSAME( TRANS, 'N' )
191      UPPER = LSAME( UPLO, 'U' )
192*
193*     NQ is the order of Q
194*
195      IF( LEFT ) THEN
196         NQ = M
197      ELSE
198         NQ = N
199      END IF
200      IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
201         INFO = -1
202      ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
203         INFO = -2
204      ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
205         INFO = -3
206      ELSE IF( M.LT.0 ) THEN
207         INFO = -4
208      ELSE IF( N.LT.0 ) THEN
209         INFO = -5
210      ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
211         INFO = -9
212      END IF
213      IF( INFO.NE.0 ) THEN
214         CALL XERBLA( 'ZUPMTR', -INFO )
215         RETURN
216      END IF
217*
218*     Quick return if possible
219*
220      IF( M.EQ.0 .OR. N.EQ.0 )
221     $   RETURN
222*
223      IF( UPPER ) THEN
224*
225*        Q was determined by a call to ZHPTRD with UPLO = 'U'
226*
227         FORWRD = ( LEFT .AND. NOTRAN ) .OR.
228     $            ( .NOT.LEFT .AND. .NOT.NOTRAN )
229*
230         IF( FORWRD ) THEN
231            I1 = 1
232            I2 = NQ - 1
233            I3 = 1
234            II = 2
235         ELSE
236            I1 = NQ - 1
237            I2 = 1
238            I3 = -1
239            II = NQ*( NQ+1 ) / 2 - 1
240         END IF
241*
242         IF( LEFT ) THEN
243            NI = N
244         ELSE
245            MI = M
246         END IF
247*
248         DO 10 I = I1, I2, I3
249            IF( LEFT ) THEN
250*
251*              H(i) or H(i)**H is applied to C(1:i,1:n)
252*
253               MI = I
254            ELSE
255*
256*              H(i) or H(i)**H is applied to C(1:m,1:i)
257*
258               NI = I
259            END IF
260*
261*           Apply H(i) or H(i)**H
262*
263            IF( NOTRAN ) THEN
264               TAUI = TAU( I )
265            ELSE
266               TAUI = DCONJG( TAU( I ) )
267            END IF
268            AII = AP( II )
269            AP( II ) = ONE
270            CALL ZLARF( SIDE, MI, NI, AP( II-I+1 ), 1, TAUI, C, LDC,
271     $                  WORK )
272            AP( II ) = AII
273*
274            IF( FORWRD ) THEN
275               II = II + I + 2
276            ELSE
277               II = II - I - 1
278            END IF
279   10    CONTINUE
280      ELSE
281*
282*        Q was determined by a call to ZHPTRD with UPLO = 'L'.
283*
284         FORWRD = ( LEFT .AND. .NOT.NOTRAN ) .OR.
285     $            ( .NOT.LEFT .AND. NOTRAN )
286*
287         IF( FORWRD ) THEN
288            I1 = 1
289            I2 = NQ - 1
290            I3 = 1
291            II = 2
292         ELSE
293            I1 = NQ - 1
294            I2 = 1
295            I3 = -1
296            II = NQ*( NQ+1 ) / 2 - 1
297         END IF
298*
299         IF( LEFT ) THEN
300            NI = N
301            JC = 1
302         ELSE
303            MI = M
304            IC = 1
305         END IF
306*
307         DO 20 I = I1, I2, I3
308            AII = AP( II )
309            AP( II ) = ONE
310            IF( LEFT ) THEN
311*
312*              H(i) or H(i)**H is applied to C(i+1:m,1:n)
313*
314               MI = M - I
315               IC = I + 1
316            ELSE
317*
318*              H(i) or H(i)**H is applied to C(1:m,i+1:n)
319*
320               NI = N - I
321               JC = I + 1
322            END IF
323*
324*           Apply H(i) or H(i)**H
325*
326            IF( NOTRAN ) THEN
327               TAUI = TAU( I )
328            ELSE
329               TAUI = DCONJG( TAU( I ) )
330            END IF
331            CALL ZLARF( SIDE, MI, NI, AP( II ), 1, TAUI, C( IC, JC ),
332     $                  LDC, WORK )
333            AP( II ) = AII
334*
335            IF( FORWRD ) THEN
336               II = II + NQ - I + 1
337            ELSE
338               II = II - NQ + I - 2
339            END IF
340   20    CONTINUE
341      END IF
342      RETURN
343*
344*     End of ZUPMTR
345*
346      END
347