 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ sgemlq()

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

SGEMLQ

Purpose:
```     SGEMLQ 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 (SGELQ)```
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 REAL 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 REAL array, dimension (MAX(5,TSIZE)). Part of the data structure to represent Q as returned by SGELQ.``` [in] TSIZE ``` TSIZE is INTEGER The dimension of the array T. TSIZE >= 5.``` [in,out] C ``` C is REAL 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) REAL 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
SLASWLQ or SGELQT

Depending on the matrix dimensions M and N, and row and column
block sizes MB and NB returned by ILAENV, SGELQ will use either
SLASWLQ (if the matrix is wide-and-short) or SGELQT to compute
the LQ factorization.
This version of SGEMLQ will use either SLAMSWLQ or SGEMLQT to
multiply matrix Q by another matrix.
Further Details in SLAMSWLQ or SGEMLQT.```

Definition at line 168 of file sgemlq.f.

170*
171* -- LAPACK computational routine --
172* -- LAPACK is a software package provided by Univ. of Tennessee, --
173* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
174*
175* .. Scalar Arguments ..
176 CHARACTER SIDE, TRANS
177 INTEGER INFO, LDA, M, N, K, TSIZE, LWORK, LDC
178* ..
179* .. Array Arguments ..
180 REAL A( LDA, * ), T( * ), C( LDC, * ), WORK( * )
181* ..
182*
183* =====================================================================
184*
185* ..
186* .. Local Scalars ..
187 LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY
188 INTEGER MB, NB, LW, NBLCKS, MN
189* ..
190* .. External Functions ..
191 LOGICAL LSAME
192 EXTERNAL lsame
193* ..
194* .. External Subroutines ..
195 EXTERNAL slamswlq, sgemlqt, xerbla
196* ..
197* .. Intrinsic Functions ..
198 INTRINSIC int, max, min, mod
199* ..
200* .. Executable Statements ..
201*
202* Test the input arguments
203*
204 lquery = lwork.EQ.-1
205 notran = lsame( trans, 'N' )
206 tran = lsame( trans, 'T' )
207 left = lsame( side, 'L' )
208 right = lsame( side, 'R' )
209*
210 mb = int( t( 2 ) )
211 nb = int( t( 3 ) )
212 IF( left ) THEN
213 lw = n * mb
214 mn = m
215 ELSE
216 lw = m * mb
217 mn = n
218 END IF
219*
220 IF( ( nb.GT.k ) .AND. ( mn.GT.k ) ) THEN
221 IF( mod( mn - k, nb - k ) .EQ. 0 ) THEN
222 nblcks = ( mn - k ) / ( nb - k )
223 ELSE
224 nblcks = ( mn - k ) / ( nb - k ) + 1
225 END IF
226 ELSE
227 nblcks = 1
228 END IF
229*
230 info = 0
231 IF( .NOT.left .AND. .NOT.right ) THEN
232 info = -1
233 ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
234 info = -2
235 ELSE IF( m.LT.0 ) THEN
236 info = -3
237 ELSE IF( n.LT.0 ) THEN
238 info = -4
239 ELSE IF( k.LT.0 .OR. k.GT.mn ) THEN
240 info = -5
241 ELSE IF( lda.LT.max( 1, k ) ) THEN
242 info = -7
243 ELSE IF( tsize.LT.5 ) THEN
244 info = -9
245 ELSE IF( ldc.LT.max( 1, m ) ) THEN
246 info = -11
247 ELSE IF( ( lwork.LT.max( 1, lw ) ) .AND. ( .NOT.lquery ) ) THEN
248 info = -13
249 END IF
250*
251 IF( info.EQ.0 ) THEN
252 work( 1 ) = real( lw )
253 END IF
254*
255 IF( info.NE.0 ) THEN
256 CALL xerbla( 'SGEMLQ', -info )
257 RETURN
258 ELSE IF( lquery ) THEN
259 RETURN
260 END IF
261*
262* Quick return if possible
263*
264 IF( min( m, n, k ).EQ.0 ) THEN
265 RETURN
266 END IF
267*
268 IF( ( left .AND. m.LE.k ) .OR. ( right .AND. n.LE.k )
269 \$ .OR. ( nb.LE.k ) .OR. ( nb.GE.max( m, n, k ) ) ) THEN
270 CALL sgemlqt( side, trans, m, n, k, mb, a, lda,
271 \$ t( 6 ), mb, c, ldc, work, info )
272 ELSE
273 CALL slamswlq( side, trans, m, n, k, mb, nb, a, lda, t( 6 ),
274 \$ mb, c, ldc, work, lwork, info )
275 END IF
276*
277 work( 1 ) = real( lw )
278*
279 RETURN
280*
281* End of SGEMLQ
282*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine sgemlqt(SIDE, TRANS, M, N, K, MB, V, LDV, T, LDT, C, LDC, WORK, INFO)
SGEMLQT
Definition: sgemlqt.f:153
subroutine slamswlq(SIDE, TRANS, M, N, K, MB, NB, A, LDA, T, LDT, C, LDC, WORK, LWORK, INFO)
SLAMSWLQ
Definition: slamswlq.f:195
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