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dlatsqr.f File Reference

Go to the source code of this file.

Functions/Subroutines

subroutine dlatsqr (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
 DLATSQR

Function/Subroutine Documentation

◆ dlatsqr()

subroutine dlatsqr ( integer m,
integer n,
integer mb,
integer nb,
double precision, dimension( lda, * ) a,
integer lda,
double precision, dimension(ldt, *) t,
integer ldt,
double precision, dimension( * ) work,
integer lwork,
integer info )

DLATSQR

Purpose:
!>
!> DLATSQR computes a blocked Tall-Skinny QR factorization of
!> a real 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 > 0.
!>
[in]NB
!>          NB is INTEGER
!>          The column block size to be used in the blocked QR.
!>          N >= NB >= 1.
!>
[in,out]A
!>          A is DOUBLE PRECISION 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 DOUBLE PRECISION 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) DOUBLE PRECISION 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 dlatsqr.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 DOUBLE PRECISION 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 dgeqrt, dtpqrt, 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.LT.1 ) 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 = -6
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( 'DLATSQR', -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 dgeqrt( m, n, nb, a, lda, t, ldt, work, info)
236 RETURN
237 END IF
238*
239 kk = mod((m-n),(mb-n))
240 ii=m-kk+1
241*
242* Compute the QR factorization of the first block A(1:MB,1:N)
243*
244 CALL dgeqrt( mb, n, nb, a(1,1), lda, t, ldt, work, info )
245*
246 ctr = 1
247 DO i = mb+1, ii-mb+n , (mb-n)
248*
249* Compute the QR factorization of the current block A(I:I+MB-N,1:N)
250*
251 CALL dtpqrt( mb-n, n, 0, nb, a(1,1), lda, a( i, 1 ), lda,
252 $ t(1, ctr * n + 1),
253 $ ldt, work, info )
254 ctr = ctr + 1
255 END DO
256*
257* Compute the QR factorization of the last block A(II:M,1:N)
258*
259 IF (ii.LE.m) THEN
260 CALL dtpqrt( kk, n, 0, nb, a(1,1), lda, a( ii, 1 ), lda,
261 $ t(1, ctr * n + 1), ldt,
262 $ work, info )
263 END IF
264*
265 work( 1 ) = n*nb
266 RETURN
267*
268* End of DLATSQR
269*
xerbla
subroutine xerbla(srname, info)
XERBLA
Definition xerbla.f:60
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:53
dgeqrt
subroutine dgeqrt(m, n, nb, a, lda, t, ldt, work, info)
DGEQRT
Definition dgeqrt.f:141
dtpqrt
subroutine dtpqrt(m, n, l, nb, a, lda, b, ldb, t, ldt, work, info)
DTPQRT
Definition dtpqrt.f:189
min
#define min(a, b)
Definition macros.h:20
max
#define max(a, b)
Definition macros.h:21