LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ slamswlq()

subroutine slamswlq ( character  SIDE,
character  TRANS,
integer  M,
integer  N,
integer  K,
integer  MB,
integer  NB,
real, dimension( lda, * )  A,
integer  LDA,
real, dimension( ldt, * )  T,
integer  LDT,
real, dimension(ldc, * )  C,
integer  LDC,
real, dimension( * )  WORK,
integer  LWORK,
integer  INFO 
)

SLAMSWLQ

Purpose:
    SLAMSWLQ 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 (SLASWLQ)
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 C.  M >=0.
[in]N
          N is INTEGER
          The number of columns of the matrix C. N >= M.
[in]K
          K is INTEGER
          The number of elementary reflectors whose product defines
          the matrix Q.
          M >= K >= 0;
[in]MB
          MB is INTEGER
          The row block size to be used in the blocked QR.
          M >= MB >= 1
[in]NB
          NB is INTEGER
          The column block size to be used in the blocked QR.
          NB > M.
[in]A
          A is REAL array, dimension
                               (LDA,M) if SIDE = 'L',
                               (LDA,N) if SIDE = 'R'
          The i-th row must contain the vector which defines the blocked
          elementary reflector H(i), for i = 1,2,...,k, as returned by
          SLASWLQ in the first k rows of its array argument A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.
          If SIDE = 'L', LDA >= max(1,M);
          if SIDE = 'R', LDA >= max(1,N).
[in]T
          T is REAL array, dimension
          ( M * Number of blocks(CEIL(N-K/NB-K)),
          The blocked upper triangular block reflectors stored in compact form
          as a sequence of upper triangular blocks.  See below
          for further details.
[in]LDT
          LDT is INTEGER
          The leading dimension of the array T.  LDT >= MB.
[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 SIDE = 'L', LWORK >= max(1,NB) * MB;
          if SIDE = 'R', LWORK >= max(1,M) * MB.
          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.
[out]INFO
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
 Short-Wide LQ (SWLQ) performs LQ by a sequence of orthogonal transformations,
 representing Q as a product of other orthogonal matrices
   Q = Q(1) * Q(2) * . . . * Q(k)
 where each Q(i) zeros out upper diagonal entries of a block of NB rows of A:
   Q(1) zeros out the upper diagonal entries of rows 1:NB of A
   Q(2) zeros out the bottom MB-N rows of rows [1:M,NB+1:2*NB-M] of A
   Q(3) zeros out the bottom MB-N rows of rows [1:M,2*NB-M+1:3*NB-2*M] of A
   . . .

 Q(1) is computed by GELQT, which represents Q(1) by Householder vectors
 stored under the diagonal of rows 1:MB of A, and by upper triangular
 block reflectors, stored in array T(1:LDT,1:N).
 For more information see Further Details in GELQT.

 Q(i) for i>1 is computed by TPLQT, which represents Q(i) by Householder vectors
 stored in columns [(i-1)*(NB-M)+M+1:i*(NB-M)+M] of A, and by upper triangular
 block reflectors, stored in array T(1:LDT,(i-1)*M+1:i*M).
 The last Q(k) may use fewer rows.
 For more information see Further Details in TPQRT.

 For more details of the overall algorithm, see the description of
 Sequential TSQR in Section 2.2 of [1].

 [1] “Communication-Optimal Parallel and Sequential QR and LU Factorizations,”
     J. Demmel, L. Grigori, M. Hoemmen, J. Langou,
     SIAM J. Sci. Comput, vol. 34, no. 1, 2012

Definition at line 195 of file slamswlq.f.

197 *
198 * -- LAPACK computational routine --
199 * -- LAPACK is a software package provided by Univ. of Tennessee, --
200 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
201 *
202 * .. Scalar Arguments ..
203  CHARACTER SIDE, TRANS
204  INTEGER INFO, LDA, M, N, K, MB, NB, LDT, LWORK, LDC
205 * ..
206 * .. Array Arguments ..
207  REAL A( LDA, * ), WORK( * ), C(LDC, * ),
208  $ T( LDT, * )
209 * ..
210 *
211 * =====================================================================
212 *
213 * ..
214 * .. Local Scalars ..
215  LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY
216  INTEGER I, II, KK, LW, CTR
217 * ..
218 * .. External Functions ..
219  LOGICAL LSAME
220  EXTERNAL lsame
221 * .. External Subroutines ..
222  EXTERNAL stpmlqt, sgemlqt, xerbla
223 * ..
224 * .. Executable Statements ..
225 *
226 * Test the input arguments
227 *
228  lquery = lwork.LT.0
229  notran = lsame( trans, 'N' )
230  tran = lsame( trans, 'T' )
231  left = lsame( side, 'L' )
232  right = lsame( side, 'R' )
233  IF (left) THEN
234  lw = n * mb
235  ELSE
236  lw = m * mb
237  END IF
238 *
239  info = 0
240  IF( .NOT.left .AND. .NOT.right ) THEN
241  info = -1
242  ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
243  info = -2
244  ELSE IF( m.LT.0 ) THEN
245  info = -3
246  ELSE IF( n.LT.0 ) THEN
247  info = -4
248  ELSE IF( k.LT.0 ) THEN
249  info = -5
250  ELSE IF( lda.LT.max( 1, k ) ) THEN
251  info = -9
252  ELSE IF( ldt.LT.max( 1, mb) ) THEN
253  info = -11
254  ELSE IF( ldc.LT.max( 1, m ) ) THEN
255  info = -13
256  ELSE IF(( lwork.LT.max(1,lw)).AND.(.NOT.lquery)) THEN
257  info = -15
258  END IF
259 *
260  IF( info.NE.0 ) THEN
261  CALL xerbla( 'SLAMSWLQ', -info )
262  work(1) = lw
263  RETURN
264  ELSE IF (lquery) THEN
265  work(1) = lw
266  RETURN
267  END IF
268 *
269 * Quick return if possible
270 *
271  IF( min(m,n,k).EQ.0 ) THEN
272  RETURN
273  END IF
274 *
275  IF((nb.LE.k).OR.(nb.GE.max(m,n,k))) THEN
276  CALL sgemlqt( side, trans, m, n, k, mb, a, lda,
277  $ t, ldt, c, ldc, work, info)
278  RETURN
279  END IF
280 *
281  IF(left.AND.tran) THEN
282 *
283 * Multiply Q to the last block of C
284 *
285  kk = mod((m-k),(nb-k))
286  ctr = (m-k)/(nb-k)
287 *
288  IF (kk.GT.0) THEN
289  ii=m-kk+1
290  CALL stpmlqt('L','T',kk , n, k, 0, mb, a(1,ii), lda,
291  $ t(1,ctr*k+1), ldt, c(1,1), ldc,
292  $ c(ii,1), ldc, work, info )
293  ELSE
294  ii=m+1
295  END IF
296 *
297  DO i=ii-(nb-k),nb+1,-(nb-k)
298 *
299 * Multiply Q to the current block of C (1:M,I:I+NB)
300 *
301  ctr = ctr - 1
302  CALL stpmlqt('L','T',nb-k , n, k, 0,mb, a(1,i), lda,
303  $ t(1,ctr*k+1),ldt, c(1,1), ldc,
304  $ c(i,1), ldc, work, info )
305  END DO
306 *
307 * Multiply Q to the first block of C (1:M,1:NB)
308 *
309  CALL sgemlqt('L','T',nb , n, k, mb, a(1,1), lda, t
310  $ ,ldt ,c(1,1), ldc, work, info )
311 *
312  ELSE IF (left.AND.notran) THEN
313 *
314 * Multiply Q to the first block of C
315 *
316  kk = mod((m-k),(nb-k))
317  ii=m-kk+1
318  ctr = 1
319  CALL sgemlqt('L','N',nb , n, k, mb, a(1,1), lda, t
320  $ ,ldt ,c(1,1), ldc, work, info )
321 *
322  DO i=nb+1,ii-nb+k,(nb-k)
323 *
324 * Multiply Q to the current block of C (I:I+NB,1:N)
325 *
326  CALL stpmlqt('L','N',nb-k , n, k, 0,mb, a(1,i), lda,
327  $ t(1,ctr * k+1), ldt, c(1,1), ldc,
328  $ c(i,1), ldc, work, info )
329  ctr = ctr + 1
330 *
331  END DO
332  IF(ii.LE.m) THEN
333 *
334 * Multiply Q to the last block of C
335 *
336  CALL stpmlqt('L','N',kk , n, k, 0, mb, a(1,ii), lda,
337  $ t(1,ctr*k+1), ldt, c(1,1), ldc,
338  $ c(ii,1), ldc, work, info )
339 *
340  END IF
341 *
342  ELSE IF(right.AND.notran) THEN
343 *
344 * Multiply Q to the last block of C
345 *
346  kk = mod((n-k),(nb-k))
347  ctr = (n-k)/(nb-k)
348  IF (kk.GT.0) THEN
349  ii=n-kk+1
350  CALL stpmlqt('R','N',m , kk, k, 0, mb, a(1, ii), lda,
351  $ t(1,ctr*k+1), ldt, c(1,1), ldc,
352  $ c(1,ii), ldc, work, info )
353  ELSE
354  ii=n+1
355  END IF
356 *
357  DO i=ii-(nb-k),nb+1,-(nb-k)
358 *
359 * Multiply Q to the current block of C (1:M,I:I+MB)
360 *
361  ctr = ctr - 1
362  CALL stpmlqt('R','N', m, nb-k, k, 0, mb, a(1, i), lda,
363  $ t(1,ctr*k+1), ldt, c(1,1), ldc,
364  $ c(1,i), ldc, work, info )
365 
366  END DO
367 *
368 * Multiply Q to the first block of C (1:M,1:MB)
369 *
370  CALL sgemlqt('R','N',m , nb, k, mb, a(1,1), lda, t
371  $ ,ldt ,c(1,1), ldc, work, info )
372 *
373  ELSE IF (right.AND.tran) THEN
374 *
375 * Multiply Q to the first block of C
376 *
377  kk = mod((n-k),(nb-k))
378  ii=n-kk+1
379  ctr = 1
380  CALL sgemlqt('R','T',m , nb, k, mb, a(1,1), lda, t
381  $ ,ldt ,c(1,1), ldc, work, info )
382 *
383  DO i=nb+1,ii-nb+k,(nb-k)
384 *
385 * Multiply Q to the current block of C (1:M,I:I+MB)
386 *
387  CALL stpmlqt('R','T',m , nb-k, k, 0,mb, a(1,i), lda,
388  $ t(1, ctr*k+1), ldt, c(1,1), ldc,
389  $ c(1,i), ldc, work, info )
390  ctr = ctr + 1
391 *
392  END DO
393  IF(ii.LE.n) THEN
394 *
395 * Multiply Q to the last block of C
396 *
397  CALL stpmlqt('R','T',m , kk, k, 0,mb, a(1,ii), lda,
398  $ t(1,ctr*k+1),ldt, c(1,1), ldc,
399  $ c(1,ii), ldc, work, info )
400 *
401  END IF
402 *
403  END IF
404 *
405  work(1) = lw
406  RETURN
407 *
408 * End of SLAMSWLQ
409 *
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
lsame
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
sgemlqt
subroutine sgemlqt(SIDE, TRANS, M, N, K, MB, V, LDV, T, LDT, C, LDC, WORK, INFO)
SGEMLQT
Definition: sgemlqt.f:153
stpmlqt
subroutine stpmlqt(SIDE, TRANS, M, N, K, L, MB, V, LDV, T, LDT, A, LDA, B, LDB, WORK, INFO)
STPMLQT
Definition: stpmlqt.f:216
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