LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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zgemlq.f
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1*> \brief \b ZGEMLQ
2*
3* Definition:
4* ===========
5*
6* SUBROUTINE ZGEMLQ( SIDE, TRANS, M, N, K, A, LDA, T,
7* \$ TSIZE, C, LDC, WORK, LWORK, INFO )
8*
9*
10* .. Scalar Arguments ..
11* CHARACTER SIDE, TRANS
12* INTEGER INFO, LDA, M, N, K, LDT, TSIZE, LWORK, LDC
13* ..
14* .. Array Arguments ..
15* COMPLEX*16 A( LDA, * ), T( * ), C(LDC, * ), WORK( * )
16*> \par Purpose:
17* =============
18*>
19*> \verbatim
20*>
21*> ZGEMLQ overwrites the general real M-by-N matrix C with
22*>
23*> SIDE = 'L' SIDE = 'R'
24*> TRANS = 'N': Q * C C * Q
25*> TRANS = 'C': Q**H * C C * Q**H
26*> where Q is a complex unitary matrix defined as the product
27*> of blocked elementary reflectors computed by short wide
28*> LQ factorization (ZGELQ)
29*>
30*> \endverbatim
31*
32* Arguments:
33* ==========
34*
35*> \param[in] SIDE
36*> \verbatim
37*> SIDE is CHARACTER*1
38*> = 'L': apply Q or Q**H from the Left;
39*> = 'R': apply Q or Q**H from the Right.
40*> \endverbatim
41*>
42*> \param[in] TRANS
43*> \verbatim
44*> TRANS is CHARACTER*1
45*> = 'N': No transpose, apply Q;
46*> = 'C': Conjugate transpose, apply Q**H.
47*> \endverbatim
48*>
49*> \param[in] M
50*> \verbatim
51*> M is INTEGER
52*> The number of rows of the matrix A. M >=0.
53*> \endverbatim
54*>
55*> \param[in] N
56*> \verbatim
57*> N is INTEGER
58*> The number of columns of the matrix C. N >= 0.
59*> \endverbatim
60*>
61*> \param[in] K
62*> \verbatim
63*> K is INTEGER
64*> The number of elementary reflectors whose product defines
65*> the matrix Q.
66*> If SIDE = 'L', M >= K >= 0;
67*> if SIDE = 'R', N >= K >= 0.
68*>
69*> \endverbatim
70*>
71*> \param[in] A
72*> \verbatim
73*> A is COMPLEX*16 array, dimension
74*> (LDA,M) if SIDE = 'L',
75*> (LDA,N) if SIDE = 'R'
76*> Part of the data structure to represent Q as returned by ZGELQ.
77*> \endverbatim
78*>
79*> \param[in] LDA
80*> \verbatim
81*> LDA is INTEGER
82*> The leading dimension of the array A. LDA >= max(1,K).
83*> \endverbatim
84*>
85*> \param[in] T
86*> \verbatim
87*> T is COMPLEX*16 array, dimension (MAX(5,TSIZE)).
88*> Part of the data structure to represent Q as returned by ZGELQ.
89*> \endverbatim
90*>
91*> \param[in] TSIZE
92*> \verbatim
93*> TSIZE is INTEGER
94*> The dimension of the array T. TSIZE >= 5.
95*> \endverbatim
96*>
97*> \param[in,out] C
98*> \verbatim
99*> C is COMPLEX*16 array, dimension (LDC,N)
100*> On entry, the M-by-N matrix C.
101*> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
102*> \endverbatim
103*>
104*> \param[in] LDC
105*> \verbatim
106*> LDC is INTEGER
107*> The leading dimension of the array C. LDC >= max(1,M).
108*> \endverbatim
109*>
110*> \param[out] WORK
111*> \verbatim
112*> (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))
113*> \endverbatim
114*>
115*> \param[in] LWORK
116*> \verbatim
117*> LWORK is INTEGER
118*> The dimension of the array WORK.
119*> If LWORK = -1, then a workspace query is assumed. The routine
120*> only calculates the size of the WORK array, returns this
121*> value as WORK(1), and no error message related to WORK
122*> is issued by XERBLA.
123*> \endverbatim
124*>
125*> \param[out] INFO
126*> \verbatim
127*> INFO is INTEGER
128*> = 0: successful exit
129*> < 0: if INFO = -i, the i-th argument had an illegal value
130*> \endverbatim
131*
132* Authors:
133* ========
134*
135*> \author Univ. of Tennessee
136*> \author Univ. of California Berkeley
137*> \author Univ. of Colorado Denver
138*> \author NAG Ltd.
139*
140*> \par Further Details
141* ====================
142*>
143*> \verbatim
144*>
145*> These details are particular for this LAPACK implementation. Users should not
146*> take them for granted. These details may change in the future, and are not likely
147*> true for another LAPACK implementation. These details are relevant if one wants
148*> to try to understand the code. They are not part of the interface.
149*>
150*> In this version,
151*>
152*> T(2): row block size (MB)
153*> T(3): column block size (NB)
154*> T(6:TSIZE): data structure needed for Q, computed by
155*> ZLASWLQ or ZGELQT
156*>
157*> Depending on the matrix dimensions M and N, and row and column
158*> block sizes MB and NB returned by ILAENV, ZGELQ will use either
159*> ZLASWLQ (if the matrix is wide-and-short) or ZGELQT to compute
160*> the LQ factorization.
161*> This version of ZGEMLQ will use either ZLAMSWLQ or ZGEMLQT to
162*> multiply matrix Q by another matrix.
163*> Further Details in ZLAMSWLQ or ZGEMLQT.
164*> \endverbatim
165*>
166* =====================================================================
167 SUBROUTINE zgemlq( SIDE, TRANS, M, N, K, A, LDA, T, TSIZE,
168 \$ C, LDC, WORK, LWORK, INFO )
169*
170* -- LAPACK computational routine --
171* -- LAPACK is a software package provided by Univ. of Tennessee, --
172* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
173*
174* .. Scalar Arguments ..
175 CHARACTER SIDE, TRANS
176 INTEGER INFO, LDA, M, N, K, TSIZE, LWORK, LDC
177* ..
178* .. Array Arguments ..
179 COMPLEX*16 A( LDA, * ), T( * ), C( LDC, * ), WORK( * )
180* ..
181*
182* =====================================================================
183*
184* ..
185* .. Local Scalars ..
186 LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY
187 INTEGER MB, NB, LW, NBLCKS, MN
188* ..
189* .. External Functions ..
190 LOGICAL LSAME
191 EXTERNAL lsame
192* ..
193* .. External Subroutines ..
194 EXTERNAL zlamswlq, zgemlqt, xerbla
195* ..
196* .. Intrinsic Functions ..
197 INTRINSIC int, max, min, mod
198* ..
199* .. Executable Statements ..
200*
201* Test the input arguments
202*
203 lquery = lwork.EQ.-1
204 notran = lsame( trans, 'N' )
205 tran = lsame( trans, 'C' )
206 left = lsame( side, 'L' )
207 right = lsame( side, 'R' )
208*
209 mb = int( t( 2 ) )
210 nb = int( t( 3 ) )
211 IF( left ) THEN
212 lw = n * mb
213 mn = m
214 ELSE
215 lw = m * mb
216 mn = n
217 END IF
218*
219 IF( ( nb.GT.k ) .AND. ( mn.GT.k ) ) THEN
220 IF( mod( mn - k, nb - k ) .EQ. 0 ) THEN
221 nblcks = ( mn - k ) / ( nb - k )
222 ELSE
223 nblcks = ( mn - k ) / ( nb - k ) + 1
224 END IF
225 ELSE
226 nblcks = 1
227 END IF
228*
229 info = 0
230 IF( .NOT.left .AND. .NOT.right ) THEN
231 info = -1
232 ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
233 info = -2
234 ELSE IF( m.LT.0 ) THEN
235 info = -3
236 ELSE IF( n.LT.0 ) THEN
237 info = -4
238 ELSE IF( k.LT.0 .OR. k.GT.mn ) THEN
239 info = -5
240 ELSE IF( lda.LT.max( 1, k ) ) THEN
241 info = -7
242 ELSE IF( tsize.LT.5 ) THEN
243 info = -9
244 ELSE IF( ldc.LT.max( 1, m ) ) THEN
245 info = -11
246 ELSE IF( ( lwork.LT.max( 1, lw ) ) .AND. ( .NOT.lquery ) ) THEN
247 info = -13
248 END IF
249*
250 IF( info.EQ.0 ) THEN
251 work( 1 ) = lw
252 END IF
253*
254 IF( info.NE.0 ) THEN
255 CALL xerbla( 'ZGEMLQ', -info )
256 RETURN
257 ELSE IF( lquery ) THEN
258 RETURN
259 END IF
260*
261* Quick return if possible
262*
263 IF( min( m, n, k ).EQ.0 ) THEN
264 RETURN
265 END IF
266*
267 IF( ( left .AND. m.LE.k ) .OR. ( right .AND. n.LE.k )
268 \$ .OR. ( nb.LE.k ) .OR. ( nb.GE.max( m, n, k ) ) ) THEN
269 CALL zgemlqt( side, trans, m, n, k, mb, a, lda,
270 \$ t( 6 ), mb, c, ldc, work, info )
271 ELSE
272 CALL zlamswlq( side, trans, m, n, k, mb, nb, a, lda, t( 6 ),
273 \$ mb, c, ldc, work, lwork, info )
274 END IF
275*
276 work( 1 ) = lw
277*
278 RETURN
279*
280* End of ZGEMLQ
281*
282 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zgemlqt(SIDE, TRANS, M, N, K, MB, V, LDV, T, LDT, C, LDC, WORK, INFO)
ZGEMLQT
Definition: zgemlqt.f:168
subroutine zgemlq(SIDE, TRANS, M, N, K, A, LDA, T, TSIZE, C, LDC, WORK, LWORK, INFO)
ZGEMLQ
Definition: zgemlq.f:169
subroutine zlamswlq(SIDE, TRANS, M, N, K, MB, NB, A, LDA, T, LDT, C, LDC, WORK, LWORK, INFO)
ZLAMSWLQ
Definition: zlamswlq.f:195