LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ dgemlq()

 subroutine dgemlq ( character side, character trans, integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) t, integer tsize, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer lwork, integer info )

DGEMLQ

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

SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      Q * C          C * Q
TRANS = 'T':      Q**T * C       C * Q**T
where Q is a real orthogonal matrix defined as the product
of blocked elementary reflectors computed by short wide LQ
factorization (DGELQ)```
Parameters
 [in] SIDE ``` SIDE is CHARACTER*1 = 'L': apply Q or Q**T from the Left; = 'R': apply Q or Q**T from the Right.``` [in] TRANS ``` TRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'T': Transpose, apply Q**T.``` [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 DOUBLE PRECISION array, dimension (LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R' Part of the data structure to represent Q as returned by DGELQ.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,K).``` [in] T ``` T is DOUBLE PRECISION array, dimension (MAX(5,TSIZE)). Part of the data structure to represent Q as returned by DGELQ.``` [in] TSIZE ``` TSIZE is INTEGER The dimension of the array T. TSIZE >= 5.``` [in,out] C ``` C is DOUBLE PRECISION array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.``` [in] LDC ``` LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M).``` [out] WORK ` (workspace) DOUBLE PRECISION 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
DLASWLQ or DGELQT

Depending on the matrix dimensions M and N, and row and column
block sizes MB and NB returned by ILAENV, DGELQ will use either
DLASWLQ (if the matrix is wide-and-short) or DGELQT to compute
the LQ factorization.
This version of DGEMLQ will use either DLAMSWLQ or DGEMLQT to
multiply matrix Q by another matrix.
Further Details in DLAMSWLQ or DGEMLQT.```

Definition at line 171 of file dgemlq.f.

173*
174* -- LAPACK computational routine --
175* -- LAPACK is a software package provided by Univ. of Tennessee, --
176* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
177*
178* .. Scalar Arguments ..
179 CHARACTER SIDE, TRANS
180 INTEGER INFO, LDA, M, N, K, TSIZE, LWORK, LDC
181* ..
182* .. Array Arguments ..
183 DOUBLE PRECISION A( LDA, * ), T( * ), C( LDC, * ), WORK( * )
184* ..
185*
186* =====================================================================
187*
188* ..
189* .. Local Scalars ..
190 LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY
191 INTEGER MB, NB, LW, NBLCKS, MN
192* ..
193* .. External Functions ..
194 LOGICAL LSAME
195 EXTERNAL lsame
196* ..
197* .. External Subroutines ..
198 EXTERNAL dlamswlq, dgemlqt, xerbla
199* ..
200* .. Intrinsic Functions ..
201 INTRINSIC int, max, min, mod
202* ..
203* .. Executable Statements ..
204*
205* Test the input arguments
206*
207 lquery = lwork.EQ.-1
208 notran = lsame( trans, 'N' )
209 tran = lsame( trans, 'T' )
210 left = lsame( side, 'L' )
211 right = lsame( side, 'R' )
212*
213 mb = int( t( 2 ) )
214 nb = int( t( 3 ) )
215 IF( left ) THEN
216 lw = n * mb
217 mn = m
218 ELSE
219 lw = m * mb
220 mn = n
221 END IF
222*
223 IF( ( nb.GT.k ) .AND. ( mn.GT.k ) ) THEN
224 IF( mod( mn - k, nb - k ) .EQ. 0 ) THEN
225 nblcks = ( mn - k ) / ( nb - k )
226 ELSE
227 nblcks = ( mn - k ) / ( nb - k ) + 1
228 END IF
229 ELSE
230 nblcks = 1
231 END IF
232*
233 info = 0
234 IF( .NOT.left .AND. .NOT.right ) THEN
235 info = -1
236 ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
237 info = -2
238 ELSE IF( m.LT.0 ) THEN
239 info = -3
240 ELSE IF( n.LT.0 ) THEN
241 info = -4
242 ELSE IF( k.LT.0 .OR. k.GT.mn ) THEN
243 info = -5
244 ELSE IF( lda.LT.max( 1, k ) ) THEN
245 info = -7
246 ELSE IF( tsize.LT.5 ) THEN
247 info = -9
248 ELSE IF( ldc.LT.max( 1, m ) ) THEN
249 info = -11
250 ELSE IF( ( lwork.LT.max( 1, lw ) ) .AND. ( .NOT.lquery ) ) THEN
251 info = -13
252 END IF
253*
254 IF( info.EQ.0 ) THEN
255 work( 1 ) = lw
256 END IF
257*
258 IF( info.NE.0 ) THEN
259 CALL xerbla( 'DGEMLQ', -info )
260 RETURN
261 ELSE IF( lquery ) THEN
262 RETURN
263 END IF
264*
265* Quick return if possible
266*
267 IF( min( m, n, k ).EQ.0 ) THEN
268 RETURN
269 END IF
270*
271 IF( ( left .AND. m.LE.k ) .OR. ( right .AND. n.LE.k )
272 \$ .OR. ( nb.LE.k ) .OR. ( nb.GE.max( m, n, k ) ) ) THEN
273 CALL dgemlqt( side, trans, m, n, k, mb, a, lda,
274 \$ t( 6 ), mb, c, ldc, work, info )
275 ELSE
276 CALL dlamswlq( side, trans, m, n, k, mb, nb, a, lda, t( 6 ),
277 \$ mb, c, ldc, work, lwork, info )
278 END IF
279*
280 work( 1 ) = lw
281*
282 RETURN
283*
284* End of DGEMLQ
285*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine dgemlqt(side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info)
DGEMLQT
Definition dgemlqt.f:168
subroutine dlamswlq(side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)
DLAMSWLQ
Definition dlamswlq.f:197
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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