 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ 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 169 of file dgemlq.f.

171 *
172 * -- LAPACK computational routine --
173 * -- LAPACK is a software package provided by Univ. of Tennessee, --
174 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
175 *
176 * .. Scalar Arguments ..
177  CHARACTER SIDE, TRANS
178  INTEGER INFO, LDA, M, N, K, TSIZE, LWORK, LDC
179 * ..
180 * .. Array Arguments ..
181  DOUBLE PRECISION A( LDA, * ), T( * ), C( LDC, * ), WORK( * )
182 * ..
183 *
184 * =====================================================================
185 *
186 * ..
187 * .. Local Scalars ..
188  LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY
189  INTEGER MB, NB, LW, NBLCKS, MN
190 * ..
191 * .. External Functions ..
192  LOGICAL LSAME
193  EXTERNAL lsame
194 * ..
195 * .. External Subroutines ..
196  EXTERNAL dlamswlq, dgemlqt, xerbla
197 * ..
198 * .. Intrinsic Functions ..
199  INTRINSIC int, max, min, mod
200 * ..
201 * .. Executable Statements ..
202 *
203 * Test the input arguments
204 *
205  lquery = lwork.EQ.-1
206  notran = lsame( trans, 'N' )
207  tran = lsame( trans, 'T' )
208  left = lsame( side, 'L' )
209  right = lsame( side, 'R' )
210 *
211  mb = int( t( 2 ) )
212  nb = int( t( 3 ) )
213  IF( left ) THEN
214  lw = n * mb
215  mn = m
216  ELSE
217  lw = m * mb
218  mn = n
219  END IF
220 *
221  IF( ( nb.GT.k ) .AND. ( mn.GT.k ) ) THEN
222  IF( mod( mn - k, nb - k ) .EQ. 0 ) THEN
223  nblcks = ( mn - k ) / ( nb - k )
224  ELSE
225  nblcks = ( mn - k ) / ( nb - k ) + 1
226  END IF
227  ELSE
228  nblcks = 1
229  END IF
230 *
231  info = 0
232  IF( .NOT.left .AND. .NOT.right ) THEN
233  info = -1
234  ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
235  info = -2
236  ELSE IF( m.LT.0 ) THEN
237  info = -3
238  ELSE IF( n.LT.0 ) THEN
239  info = -4
240  ELSE IF( k.LT.0 .OR. k.GT.mn ) THEN
241  info = -5
242  ELSE IF( lda.LT.max( 1, k ) ) THEN
243  info = -7
244  ELSE IF( tsize.LT.5 ) THEN
245  info = -9
246  ELSE IF( ldc.LT.max( 1, m ) ) THEN
247  info = -11
248  ELSE IF( ( lwork.LT.max( 1, lw ) ) .AND. ( .NOT.lquery ) ) THEN
249  info = -13
250  END IF
251 *
252  IF( info.EQ.0 ) THEN
253  work( 1 ) = lw
254  END IF
255 *
256  IF( info.NE.0 ) THEN
257  CALL xerbla( 'DGEMLQ', -info )
258  RETURN
259  ELSE IF( lquery ) THEN
260  RETURN
261  END IF
262 *
263 * Quick return if possible
264 *
265  IF( min( m, n, k ).EQ.0 ) THEN
266  RETURN
267  END IF
268 *
269  IF( ( left .AND. m.LE.k ) .OR. ( right .AND. n.LE.k )
270  \$ .OR. ( nb.LE.k ) .OR. ( nb.GE.max( m, n, k ) ) ) THEN
271  CALL dgemlqt( side, trans, m, n, k, mb, a, lda,
272  \$ t( 6 ), mb, c, ldc, work, info )
273  ELSE
274  CALL dlamswlq( side, trans, m, n, k, mb, nb, a, lda, t( 6 ),
275  \$ mb, c, ldc, work, lwork, info )
276  END IF
277 *
278  work( 1 ) = lw
279 *
280  RETURN
281 *
282 * End of DGEMLQ
283 *
subroutine dlamswlq(SIDE, TRANS, M, N, K, MB, NB, A, LDA, T, LDT, C, LDC, WORK, LWORK, INFO)
DLAMSWLQ
Definition: dlamswlq.f:195
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dgemlqt(SIDE, TRANS, M, N, K, MB, V, LDV, T, LDT, C, LDC, WORK, INFO)
DGEMLQT
Definition: dgemlqt.f:168
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