LAPACK 3.12.0 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 170 of file sgemlq.f.

172*
173* -- LAPACK computational routine --
174* -- LAPACK is a software package provided by Univ. of Tennessee, --
175* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
176*
177* .. Scalar Arguments ..
178 CHARACTER SIDE, TRANS
179 INTEGER INFO, LDA, M, N, K, TSIZE, LWORK, LDC
180* ..
181* .. Array Arguments ..
182 REAL A( LDA, * ), T( * ), C( LDC, * ), WORK( * )
183* ..
184*
185* =====================================================================
186*
187* ..
188* .. Local Scalars ..
189 LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY
190 INTEGER MB, NB, LW, NBLCKS, MN
191* ..
192* .. External Functions ..
193 LOGICAL LSAME
194 EXTERNAL lsame
195* ..
196* .. External Functions ..
197 REAL SROUNDUP_LWORK
198 EXTERNAL sroundup_lwork
199* ..
200* .. External Subroutines ..
201 EXTERNAL slamswlq, sgemlqt, xerbla
202* ..
203* .. Intrinsic Functions ..
204 INTRINSIC int, max, min, mod
205* ..
206* .. Executable Statements ..
207*
208* Test the input arguments
209*
210 lquery = lwork.EQ.-1
211 notran = lsame( trans, 'N' )
212 tran = lsame( trans, 'T' )
213 left = lsame( side, 'L' )
214 right = lsame( side, 'R' )
215*
216 mb = int( t( 2 ) )
217 nb = int( t( 3 ) )
218 IF( left ) THEN
219 lw = n * mb
220 mn = m
221 ELSE
222 lw = m * mb
223 mn = n
224 END IF
225*
226 IF( ( nb.GT.k ) .AND. ( mn.GT.k ) ) THEN
227 IF( mod( mn - k, nb - k ) .EQ. 0 ) THEN
228 nblcks = ( mn - k ) / ( nb - k )
229 ELSE
230 nblcks = ( mn - k ) / ( nb - k ) + 1
231 END IF
232 ELSE
233 nblcks = 1
234 END IF
235*
236 info = 0
237 IF( .NOT.left .AND. .NOT.right ) THEN
238 info = -1
239 ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
240 info = -2
241 ELSE IF( m.LT.0 ) THEN
242 info = -3
243 ELSE IF( n.LT.0 ) THEN
244 info = -4
245 ELSE IF( k.LT.0 .OR. k.GT.mn ) THEN
246 info = -5
247 ELSE IF( lda.LT.max( 1, k ) ) THEN
248 info = -7
249 ELSE IF( tsize.LT.5 ) THEN
250 info = -9
251 ELSE IF( ldc.LT.max( 1, m ) ) THEN
252 info = -11
253 ELSE IF( ( lwork.LT.max( 1, lw ) ) .AND. ( .NOT.lquery ) ) THEN
254 info = -13
255 END IF
256*
257 IF( info.EQ.0 ) THEN
258 work( 1 ) = sroundup_lwork( lw )
259 END IF
260*
261 IF( info.NE.0 ) THEN
262 CALL xerbla( 'SGEMLQ', -info )
263 RETURN
264 ELSE IF( lquery ) THEN
265 RETURN
266 END IF
267*
268* Quick return if possible
269*
270 IF( min( m, n, k ).EQ.0 ) THEN
271 RETURN
272 END IF
273*
274 IF( ( left .AND. m.LE.k ) .OR. ( right .AND. n.LE.k )
275 \$ .OR. ( nb.LE.k ) .OR. ( nb.GE.max( m, n, k ) ) ) THEN
276 CALL sgemlqt( side, trans, m, n, k, mb, a, lda,
277 \$ t( 6 ), mb, c, ldc, work, info )
278 ELSE
279 CALL slamswlq( side, trans, m, n, k, mb, nb, a, lda, t( 6 ),
280 \$ mb, c, ldc, work, lwork, info )
281 END IF
282*
283 work( 1 ) = sroundup_lwork( lw )
284*
285 RETURN
286*
287* End of SGEMLQ
288*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
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:197
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
real function sroundup_lwork(lwork)
SROUNDUP_LWORK
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