LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
Searching...
No Matches
zgemqrt.f
Go to the documentation of this file.
1*> \brief \b ZGEMQRT
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgemqrt.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgemqrt.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgemqrt.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE ZGEMQRT( 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*16 V( LDV, * ), C( LDC, * ), T( LDT, * ), WORK( * )
30* ..
31*
32*
33*> \par Purpose:
34* =============
35*>
36*> \verbatim
37*>
38*> ZGEMQRT 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 ZGEQRT.
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 ZGEQRT.
98*> \endverbatim
99*>
100*> \param[in] V
101*> \verbatim
102*> V is COMPLEX*16 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*> ZGEQRT 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*16 array, dimension (LDT,K)
119*> The upper triangular factors of the block reflectors
120*> as returned by ZGEQRT, 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*16 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*16 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 complex16GEcomputational
164*
165* =====================================================================
166 SUBROUTINE zgemqrt( 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*16 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, zlarfb
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( 'ZGEMQRT', -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 zlarfb( '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 zlarfb( '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 zlarfb( '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 zlarfb( '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 ZGEMQRT
287*
288 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zgemqrt(SIDE, TRANS, M, N, K, NB, V, LDV, T, LDT, C, LDC, WORK, INFO)
ZGEMQRT
Definition: zgemqrt.f:168
subroutine zlarfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
ZLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix.
Definition: zlarfb.f:197