LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ clatsqr()

subroutine clatsqr ( integer  M,
integer  N,
integer  MB,
integer  NB,
complex, dimension( lda, * )  A,
integer  LDA,
complex, dimension(ldt, *)  T,
integer  LDT,
complex, dimension( * )  WORK,
integer  LWORK,
integer  INFO 
)

CLATSQR

Purpose:
 CLATSQR computes a blocked Tall-Skinny QR factorization of
 a complex M-by-N matrix A for M >= N:

    A = Q * ( R ),
            ( 0 )

 where:

    Q is a M-by-M orthogonal matrix, stored on exit in an implicit
    form in the elements below the diagonal of the array A and in
    the elements of the array T;

    R is an upper-triangular N-by-N matrix, stored on exit in
    the elements on and above the diagonal of the array A.

    0 is a (M-N)-by-N zero matrix, and is not stored.
Parameters
[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 A. M >= N >= 0.
[in]MB
          MB is INTEGER
          The row block size to be used in the blocked QR.
          MB > N.
[in]NB
          NB is INTEGER
          The column block size to be used in the blocked QR.
          N >= NB >= 1.
[in,out]A
          A is COMPLEX array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit, the elements on and above the diagonal
          of the array contain the N-by-N upper triangular matrix R;
          the elements below the diagonal represent Q by the columns
          of blocked V (see Further Details).
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).
[out]T
          T is COMPLEX array,
          dimension (LDT, N * Number_of_row_blocks)
          where Number_of_row_blocks = CEIL((M-N)/(MB-N))
          The blocked upper triangular block reflectors stored in compact form
          as a sequence of upper triangular blocks.
          See Further Details below.
[in]LDT
          LDT is INTEGER
          The leading dimension of the array T.  LDT >= NB.
[out]WORK
         (workspace) COMPLEX array, dimension (MAX(1,LWORK))
[in]LWORK
          The dimension of the array WORK.  LWORK >= NB*N.
          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 orthogonal transformations,
 representing Q as a product of other orthogonal 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 164 of file clatsqr.f.

166 *
167 * -- LAPACK computational routine --
168 * -- LAPACK is a software package provided by Univ. of Tennessee, --
169 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd. --
170 *
171 * .. Scalar Arguments ..
172  INTEGER INFO, LDA, M, N, MB, NB, LDT, LWORK
173 * ..
174 * .. Array Arguments ..
175  COMPLEX A( LDA, * ), WORK( * ), T(LDT, *)
176 * ..
177 *
178 * =====================================================================
179 *
180 * ..
181 * .. Local Scalars ..
182  LOGICAL LQUERY
183  INTEGER I, II, KK, CTR
184 * ..
185 * .. EXTERNAL FUNCTIONS ..
186  LOGICAL LSAME
187  EXTERNAL lsame
188 * .. EXTERNAL SUBROUTINES ..
189  EXTERNAL cgeqrt, ctpqrt, xerbla
190 * .. INTRINSIC FUNCTIONS ..
191  INTRINSIC max, min, mod
192 * ..
193 * .. EXECUTABLE STATEMENTS ..
194 *
195 * TEST THE INPUT ARGUMENTS
196 *
197  info = 0
198 *
199  lquery = ( lwork.EQ.-1 )
200 *
201  IF( m.LT.0 ) THEN
202  info = -1
203  ELSE IF( n.LT.0 .OR. m.LT.n ) THEN
204  info = -2
205  ELSE IF( mb.LE.n ) THEN
206  info = -3
207  ELSE IF( nb.LT.1 .OR. ( nb.GT.n .AND. n.GT.0 )) THEN
208  info = -4
209  ELSE IF( lda.LT.max( 1, m ) ) THEN
210  info = -5
211  ELSE IF( ldt.LT.nb ) THEN
212  info = -8
213  ELSE IF( lwork.LT.(n*nb) .AND. (.NOT.lquery) ) THEN
214  info = -10
215  END IF
216  IF( info.EQ.0) THEN
217  work(1) = nb*n
218  END IF
219  IF( info.NE.0 ) THEN
220  CALL xerbla( 'CLATSQR', -info )
221  RETURN
222  ELSE IF (lquery) THEN
223  RETURN
224  END IF
225 *
226 * Quick return if possible
227 *
228  IF( min(m,n).EQ.0 ) THEN
229  RETURN
230  END IF
231 *
232 * The QR Decomposition
233 *
234  IF ((mb.LE.n).OR.(mb.GE.m)) THEN
235  CALL cgeqrt( m, n, nb, a, lda, t, ldt, work, info)
236  RETURN
237  END IF
238  kk = mod((m-n),(mb-n))
239  ii=m-kk+1
240 *
241 * Compute the QR factorization of the first block A(1:MB,1:N)
242 *
243  CALL cgeqrt( mb, n, nb, a(1,1), lda, t, ldt, work, info )
244  ctr = 1
245 *
246  DO i = mb+1, ii-mb+n , (mb-n)
247 *
248 * Compute the QR factorization of the current block A(I:I+MB-N,1:N)
249 *
250  CALL ctpqrt( mb-n, n, 0, nb, a(1,1), lda, a( i, 1 ), lda,
251  $ t(1,ctr * n + 1),
252  $ ldt, work, info )
253  ctr = ctr + 1
254  END DO
255 *
256 * Compute the QR factorization of the last block A(II:M,1:N)
257 *
258  IF (ii.LE.m) THEN
259  CALL ctpqrt( kk, n, 0, nb, a(1,1), lda, a( ii, 1 ), lda,
260  $ t(1, ctr * n + 1), ldt,
261  $ work, info )
262  END IF
263 *
264  work( 1 ) = n*nb
265  RETURN
266 *
267 * End of CLATSQR
268 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine cgeqrt(M, N, NB, A, LDA, T, LDT, WORK, INFO)
CGEQRT
Definition: cgeqrt.f:141
subroutine ctpqrt(M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK, INFO)
CTPQRT
Definition: ctpqrt.f:189
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