LAPACK  3.10.1
LAPACK: Linear Algebra PACKage

◆ clamtsqr()

subroutine clamtsqr ( 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 
)

CLAMTSQR

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


                 SIDE = 'L'     SIDE = 'R'
 TRANS = 'N':      Q * C          C * Q
 TRANS = 'C':      Q**H * C       C * Q**H
      where Q is a complex unitary matrix defined as the product
      of blocked elementary reflectors computed by tall skinny
      QR factorization (CLATSQR)
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 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. M >= K >= 0;
[in]MB
          MB is INTEGER
          The block size to be used in the blocked QR.
          MB > N. (must be the same as CLATSQR)
[in]NB
          NB is INTEGER
          The column block size to be used in the blocked QR.
          N >= NB >= 1.
[in]A
          A is COMPLEX array, dimension (LDA,K)
          The i-th column must contain the vector which defines the
          blockedelementary reflector H(i), for i = 1,2,...,k, as
          returned by CLATSQR in the first k columns 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 COMPLEX array, dimension
          ( N * Number of blocks(CEIL(M-K/MB-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 >= NB.
[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,N)*NB;
          if SIDE = 'R', LWORK >= max(1,MB)*NB.
          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:
 Tall-Skinny QR (TSQR) performs QR 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 subdiagonal entries of a block of MB rows of A:
   Q(1) zeros out the subdiagonal entries of rows 1:MB of A
   Q(2) zeros out the bottom MB-N rows of rows [1:N,MB+1:2*MB-N] of A
   Q(3) zeros out the bottom MB-N rows of rows [1:N,2*MB-N+1:3*MB-2*N] of A
   . . .

 Q(1) is computed by GEQRT, 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 GEQRT.

 Q(i) for i>1 is computed by TPQRT, which represents Q(i) by Householder vectors
 stored in rows [(i-1)*(MB-N)+N+1:i*(MB-N)+N] of A, and by upper triangular
 block reflectors, stored in array T(1:LDT,(i-1)*N+1:i*N).
 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 clamtsqr.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  COMPLEX 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, Q
217 * ..
218 * .. External Functions ..
219  LOGICAL LSAME
220  EXTERNAL lsame
221 * .. External Subroutines ..
222  EXTERNAL cgemqrt, ctpmqrt, 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, 'C' )
231  left = lsame( side, 'L' )
232  right = lsame( side, 'R' )
233  IF (left) THEN
234  lw = n * nb
235  q = m
236  ELSE
237  lw = m * nb
238  q = n
239  END IF
240 *
241  info = 0
242  IF( .NOT.left .AND. .NOT.right ) THEN
243  info = -1
244  ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
245  info = -2
246  ELSE IF( m.LT.k ) THEN
247  info = -3
248  ELSE IF( n.LT.0 ) THEN
249  info = -4
250  ELSE IF( k.LT.0 ) THEN
251  info = -5
252  ELSE IF( k.LT.nb .OR. nb.LT.1 ) THEN
253  info = -7
254  ELSE IF( lda.LT.max( 1, q ) ) THEN
255  info = -9
256  ELSE IF( ldt.LT.max( 1, nb) ) THEN
257  info = -11
258  ELSE IF( ldc.LT.max( 1, m ) ) THEN
259  info = -13
260  ELSE IF(( lwork.LT.max(1,lw)).AND.(.NOT.lquery)) THEN
261  info = -15
262  END IF
263 *
264 * Determine the block size if it is tall skinny or short and wide
265 *
266  IF( info.EQ.0) THEN
267  work(1) = lw
268  END IF
269 *
270  IF( info.NE.0 ) THEN
271  CALL xerbla( 'CLAMTSQR', -info )
272  RETURN
273  ELSE IF (lquery) THEN
274  RETURN
275  END IF
276 *
277 * Quick return if possible
278 *
279  IF( min(m,n,k).EQ.0 ) THEN
280  RETURN
281  END IF
282 *
283  IF((mb.LE.k).OR.(mb.GE.max(m,n,k))) THEN
284  CALL cgemqrt( side, trans, m, n, k, nb, a, lda,
285  $ t, ldt, c, ldc, work, info)
286  RETURN
287  END IF
288 *
289  IF(left.AND.notran) THEN
290 *
291 * Multiply Q to the last block of C
292 *
293  kk = mod((m-k),(mb-k))
294  ctr = (m-k)/(mb-k)
295  IF (kk.GT.0) THEN
296  ii=m-kk+1
297  CALL ctpmqrt('L','N',kk , n, k, 0, nb, a(ii,1), lda,
298  $ t(1, ctr*k+1),ldt , c(1,1), ldc,
299  $ c(ii,1), ldc, work, info )
300  ELSE
301  ii=m+1
302  END IF
303 *
304  DO i=ii-(mb-k),mb+1,-(mb-k)
305 *
306 * Multiply Q to the current block of C (I:I+MB,1:N)
307 *
308  ctr = ctr - 1
309  CALL ctpmqrt('L','N',mb-k , n, k, 0,nb, a(i,1), lda,
310  $ t(1,ctr*k+1),ldt, c(1,1), ldc,
311  $ c(i,1), ldc, work, info )
312 
313  END DO
314 *
315 * Multiply Q to the first block of C (1:MB,1:N)
316 *
317  CALL cgemqrt('L','N',mb , n, k, nb, a(1,1), lda, t
318  $ ,ldt ,c(1,1), ldc, work, info )
319 *
320  ELSE IF (left.AND.tran) THEN
321 *
322 * Multiply Q to the first block of C
323 *
324  kk = mod((m-k),(mb-k))
325  ii=m-kk+1
326  ctr = 1
327  CALL cgemqrt('L','C',mb , n, k, nb, a(1,1), lda, t
328  $ ,ldt ,c(1,1), ldc, work, info )
329 *
330  DO i=mb+1,ii-mb+k,(mb-k)
331 *
332 * Multiply Q to the current block of C (I:I+MB,1:N)
333 *
334  CALL ctpmqrt('L','C',mb-k , n, k, 0,nb, a(i,1), lda,
335  $ t(1, ctr*k+1),ldt, c(1,1), ldc,
336  $ c(i,1), ldc, work, info )
337  ctr = ctr + 1
338 *
339  END DO
340  IF(ii.LE.m) THEN
341 *
342 * Multiply Q to the last block of C
343 *
344  CALL ctpmqrt('L','C',kk , n, k, 0,nb, a(ii,1), lda,
345  $ t(1,ctr*k+1), ldt, c(1,1), ldc,
346  $ c(ii,1), ldc, work, info )
347 *
348  END IF
349 *
350  ELSE IF(right.AND.tran) THEN
351 *
352 * Multiply Q to the last block of C
353 *
354  kk = mod((n-k),(mb-k))
355  ctr = (n-k)/(mb-k)
356  IF (kk.GT.0) THEN
357  ii=n-kk+1
358  CALL ctpmqrt('R','C',m , kk, k, 0, nb, a(ii,1), lda,
359  $ t(1, ctr*k+1), ldt, c(1,1), ldc,
360  $ c(1,ii), ldc, work, info )
361  ELSE
362  ii=n+1
363  END IF
364 *
365  DO i=ii-(mb-k),mb+1,-(mb-k)
366 *
367 * Multiply Q to the current block of C (1:M,I:I+MB)
368 *
369  ctr = ctr - 1
370  CALL ctpmqrt('R','C',m , mb-k, k, 0,nb, a(i,1), lda,
371  $ t(1,ctr*k+1), ldt, c(1,1), ldc,
372  $ c(1,i), ldc, work, info )
373  END DO
374 *
375 * Multiply Q to the first block of C (1:M,1:MB)
376 *
377  CALL cgemqrt('R','C',m , mb, k, nb, a(1,1), lda, t
378  $ ,ldt ,c(1,1), ldc, work, info )
379 *
380  ELSE IF (right.AND.notran) THEN
381 *
382 * Multiply Q to the first block of C
383 *
384  kk = mod((n-k),(mb-k))
385  ii=n-kk+1
386  ctr = 1
387  CALL cgemqrt('R','N', m, mb , k, nb, a(1,1), lda, t
388  $ ,ldt ,c(1,1), ldc, work, info )
389 *
390  DO i=mb+1,ii-mb+k,(mb-k)
391 *
392 * Multiply Q to the current block of C (1:M,I:I+MB)
393 *
394  CALL ctpmqrt('R','N', m, mb-k, k, 0,nb, a(i,1), lda,
395  $ t(1,ctr*k+1),ldt, c(1,1), ldc,
396  $ c(1,i), ldc, work, info )
397  ctr = ctr + 1
398 *
399  END DO
400  IF(ii.LE.n) THEN
401 *
402 * Multiply Q to the last block of C
403 *
404  CALL ctpmqrt('R','N', m, kk , k, 0,nb, a(ii,1), lda,
405  $ t(1,ctr*k+1),ldt, c(1,1), ldc,
406  $ c(1,ii), ldc, work, info )
407 *
408  END IF
409 *
410  END IF
411 *
412  work(1) = lw
413  RETURN
414 *
415 * End of CLAMTSQR
416 *
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
lsame
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
cgemqrt
subroutine cgemqrt(SIDE, TRANS, M, N, K, NB, V, LDV, T, LDT, C, LDC, WORK, INFO)
CGEMQRT
Definition: cgemqrt.f:168
ctpmqrt
subroutine ctpmqrt(SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT, A, LDA, B, LDB, WORK, INFO)
CTPMQRT
Definition: ctpmqrt.f:216
Here is the call graph for this function:
Here is the caller graph for this function: