LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ 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 )
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 unlikely not 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 169 of file sgemlq.f.

169 *
170 * -- LAPACK computational routine (version 3.7.0) --
171 * -- LAPACK is a software package provided by Univ. of Tennessee, --
172 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
173 * December 2016
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 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine slamswlq(SIDE, TRANS, M, N, K, MB, NB, A, LDA, T, LDT, C, LDC, WORK, LWORK, INFO)
Definition: slamswlq.f:204
subroutine sgemlqt(SIDE, TRANS, M, N, K, MB, V, LDV, T, LDT, C, LDC, WORK, INFO)
Definition: sgemlqt.f:153
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
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