LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ clamswlq()

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

CLAMSWLQ

Purpose:
    CLAMSWLQ overwrites the general complex M-by-N matrix C with


                    SIDE = 'L'     SIDE = 'R'
    TRANS = 'N':      Q * C          C * Q
    TRANS = 'T':      Q**H * C       C * Q**H
    where Q is a complex unitary matrix defined as the product of blocked
    elementary reflectors computed by short wide LQ
    factorization (CLASWLQ)
Parameters
[in]SIDE
          SIDE is CHARACTER*1
          = 'L': apply Q or Q**H from the Left;
          = 'R': apply Q or Q**H from the Right.
[in]TRANS
          TRANS is CHARACTER*1
          = 'N':  No transpose, apply Q;
          = 'C':  Conjugate transpose, apply Q**H.
[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 >= 0.
[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 LQ.
          M >= MB >= 1
[in]NB
          NB is INTEGER
          The column block size to be used in the blocked LQ.
          NB > M.
[in]A
          A is COMPLEX 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
          CLASWLQ in the first k rows of its array argument A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A. LDA => max(1,K).
[in]T
          T is COMPLEX 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 COMPLEX array, dimension (LDC,N)
          On entry, the M-by-N matrix C.
          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
[in]LDC
          LDC is INTEGER
          The leading dimension of the array C. LDC >= max(1,M).
[out]WORK
         (workspace) COMPLEX 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 unitary transformations,
 representing Q as a product of other unitary 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 TPLQT.

 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 193 of file clamswlq.f.

195*
196* -- LAPACK computational routine --
197* -- LAPACK is a software package provided by Univ. of Tennessee, --
198* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
199*
200* .. Scalar Arguments ..
201 CHARACTER SIDE, TRANS
202 INTEGER INFO, LDA, M, N, K, MB, NB, LDT, LWORK, LDC
203* ..
204* .. Array Arguments ..
205 COMPLEX A( LDA, * ), WORK( * ), C(LDC, * ),
206 $ T( LDT, * )
207* ..
208*
209* =====================================================================
210*
211* ..
212* .. Local Scalars ..
213 LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY
214 INTEGER I, II, KK, LW, CTR
215* ..
216* .. External Functions ..
217 LOGICAL LSAME
218 EXTERNAL lsame
219* .. External Subroutines ..
220 EXTERNAL ctpmlqt, cgemlqt, xerbla
221* ..
222* .. Executable Statements ..
223*
224* Test the input arguments
225*
226 lquery = lwork.LT.0
227 notran = lsame( trans, 'N' )
228 tran = lsame( trans, 'C' )
229 left = lsame( side, 'L' )
230 right = lsame( side, 'R' )
231 IF (left) THEN
232 lw = n * mb
233 ELSE
234 lw = m * mb
235 END IF
236*
237 info = 0
238 IF( .NOT.left .AND. .NOT.right ) THEN
239 info = -1
240 ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
241 info = -2
242 ELSE IF( k.LT.0 ) THEN
243 info = -5
244 ELSE IF( m.LT.k ) THEN
245 info = -3
246 ELSE IF( n.LT.0 ) THEN
247 info = -4
248 ELSE IF( k.LT.mb .OR. mb.LT.1) THEN
249 info = -6
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( 'CLAMSWLQ', -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 cgemlqt( 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 IF (kk.GT.0) THEN
288 ii=m-kk+1
289 CALL ctpmlqt('L','C',kk , n, k, 0, mb, a(1,ii), lda,
290 $ t(1,ctr*k+1), ldt, c(1,1), ldc,
291 $ c(ii,1), ldc, work, info )
292 ELSE
293 ii=m+1
294 END IF
295*
296 DO i=ii-(nb-k),nb+1,-(nb-k)
297*
298* Multiply Q to the current block of C (1:M,I:I+NB)
299*
300 ctr = ctr - 1
301 CALL ctpmlqt('L','C',nb-k , n, k, 0,mb, a(1,i), lda,
302 $ t(1,ctr*k+1),ldt, c(1,1), ldc,
303 $ c(i,1), ldc, work, info )
304
305 END DO
306*
307* Multiply Q to the first block of C (1:M,1:NB)
308*
309 CALL cgemlqt('L','C',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 cgemlqt('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 ctpmlqt('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 ctpmlqt('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 ctpmlqt('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 ctpmlqt('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 END DO
366*
367* Multiply Q to the first block of C (1:M,1:MB)
368*
369 CALL cgemlqt('R','N',m , nb, k, mb, a(1,1), lda, t
370 $ ,ldt ,c(1,1), ldc, work, info )
371*
372 ELSE IF (right.AND.tran) THEN
373*
374* Multiply Q to the first block of C
375*
376 kk = mod((n-k),(nb-k))
377 ii=n-kk+1
378 ctr = 1
379 CALL cgemlqt('R','C',m , nb, k, mb, a(1,1), lda, t
380 $ ,ldt ,c(1,1), ldc, work, info )
381*
382 DO i=nb+1,ii-nb+k,(nb-k)
383*
384* Multiply Q to the current block of C (1:M,I:I+MB)
385*
386 CALL ctpmlqt('R','C',m , nb-k, k, 0,mb, a(1,i), lda,
387 $ t(1,ctr*k+1), ldt, c(1,1), ldc,
388 $ c(1,i), ldc, work, info )
389 ctr = ctr + 1
390*
391 END DO
392 IF(ii.LE.n) THEN
393*
394* Multiply Q to the last block of C
395*
396 CALL ctpmlqt('R','C',m , kk, k, 0,mb, a(1,ii), lda,
397 $ t(1,ctr*k+1),ldt, c(1,1), ldc,
398 $ c(1,ii), ldc, work, info )
399*
400 END IF
401*
402 END IF
403*
404 work(1) = lw
405 RETURN
406*
407* End of CLAMSWLQ
408*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine cgemlqt(SIDE, TRANS, M, N, K, MB, V, LDV, T, LDT, C, LDC, WORK, INFO)
CGEMLQT
Definition: cgemlqt.f:153
subroutine ctpmlqt(SIDE, TRANS, M, N, K, L, MB, V, LDV, T, LDT, A, LDA, B, LDB, WORK, INFO)
CTPMLQT
Definition: ctpmlqt.f:199
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