LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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◆ zgemlq()

 subroutine zgemlq ( character SIDE, character TRANS, integer M, integer N, integer K, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( * ) T, integer TSIZE, complex*16, dimension( ldc, * ) C, integer LDC, complex*16, dimension( * ) WORK, integer LWORK, integer INFO )

ZGEMLQ

Purpose:
```     ZGEMLQ overwrites the general real M-by-N matrix C with

SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      Q * C          C * Q
TRANS = 'C':      Q**H * C       C * Q**H
where Q is a complex unitary matrix defined as the product
of blocked elementary reflectors computed by short wide
LQ factorization (ZGELQ)```
Parameters
 [in] SIDE ``` SIDE is CHARACTER*1 = 'L': apply Q or Q**H from the Left; = 'R': apply Q or Q**H from the Right.``` [in] TRANS ``` TRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'C': Conjugate transpose, apply Q**H.``` [in] M ``` M is INTEGER The number of rows of the matrix A. M >=0.``` [in] N ``` N is INTEGER The number of columns of the matrix C. N >= 0.``` [in] K ``` K is INTEGER The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0.``` [in] A ``` A is COMPLEX*16 array, dimension (LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R' Part of the data structure to represent Q as returned by ZGELQ.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,K).``` [in] T ``` T is COMPLEX*16 array, dimension (MAX(5,TSIZE)). Part of the data structure to represent Q as returned by ZGELQ.``` [in] TSIZE ``` TSIZE is INTEGER The dimension of the array T. TSIZE >= 5.``` [in,out] C ``` C is COMPLEX*16 array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.``` [in] LDC ``` LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M).``` [out] WORK ` (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))` [in] LWORK ``` LWORK is INTEGER The dimension of the array WORK. If LWORK = -1, then a workspace query is assumed. The routine only calculates the size of the WORK array, returns this value as WORK(1), and no error message related to WORK is issued by XERBLA.``` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```
Further Details
``` These details are particular for this LAPACK implementation. Users should not
take them for granted. These details may change in the future, and are not likely
true for another LAPACK implementation. These details are relevant if one wants
to try to understand the code. They are not part of the interface.

In this version,

T(2): row block size (MB)
T(3): column block size (NB)
T(6:TSIZE): data structure needed for Q, computed by
ZLASWLQ or ZGELQT

Depending on the matrix dimensions M and N, and row and column
block sizes MB and NB returned by ILAENV, ZGELQ will use either
ZLASWLQ (if the matrix is wide-and-short) or ZGELQT to compute
the LQ factorization.
This version of ZGEMLQ will use either ZLAMSWLQ or ZGEMLQT to
multiply matrix Q by another matrix.
Further Details in ZLAMSWLQ or ZGEMLQT.```

Definition at line 167 of file zgemlq.f.

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*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zgemlqt(SIDE, TRANS, M, N, K, MB, V, LDV, T, LDT, C, LDC, WORK, INFO)
ZGEMLQT
Definition: zgemlqt.f:168
subroutine zlamswlq(SIDE, TRANS, M, N, K, MB, NB, A, LDA, T, LDT, C, LDC, WORK, LWORK, INFO)
ZLAMSWLQ
Definition: zlamswlq.f:195
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