LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ dtplqt()

subroutine dtplqt ( integer  m,
integer  n,
integer  l,
integer  mb,
double precision, dimension( lda, * )  a,
integer  lda,
double precision, dimension( ldb, * )  b,
integer  ldb,
double precision, dimension( ldt, * )  t,
integer  ldt,
double precision, dimension( * )  work,
integer  info 
)

DTPLQT

Download DTPLQT + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 DTPLQT computes a blocked LQ factorization of a real
 "triangular-pentagonal" matrix C, which is composed of a
 triangular block A and pentagonal block B, using the compact
 WY representation for Q.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix B, and the order of the
          triangular matrix A.
          M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix B.
          N >= 0.
[in]L
          L is INTEGER
          The number of rows of the lower trapezoidal part of B.
          MIN(M,N) >= L >= 0.  See Further Details.
[in]MB
          MB is INTEGER
          The block size to be used in the blocked QR.  M >= MB >= 1.
[in,out]A
          A is DOUBLE PRECISION array, dimension (LDA,M)
          On entry, the lower triangular M-by-M matrix A.
          On exit, the elements on and below the diagonal of the array
          contain the lower triangular matrix L.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).
[in,out]B
          B is DOUBLE PRECISION array, dimension (LDB,N)
          On entry, the pentagonal M-by-N matrix B.  The first N-L columns
          are rectangular, and the last L columns are lower trapezoidal.
          On exit, B contains the pentagonal matrix V.  See Further Details.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,M).
[out]T
          T is DOUBLE PRECISION array, dimension (LDT,N)
          The lower triangular block reflectors stored in compact form
          as a sequence of upper triangular blocks.  See Further Details.
[in]LDT
          LDT is INTEGER
          The leading dimension of the array T.  LDT >= MB.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (MB*M)
[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:
  The input matrix C is a M-by-(M+N) matrix

               C = [ A ] [ B ]


  where A is an lower triangular M-by-M matrix, and B is M-by-N pentagonal
  matrix consisting of a M-by-(N-L) rectangular matrix B1 on left of a M-by-L
  upper trapezoidal matrix B2:
          [ B ] = [ B1 ] [ B2 ]
                   [ B1 ]  <- M-by-(N-L) rectangular
                   [ B2 ]  <-     M-by-L lower trapezoidal.

  The lower trapezoidal matrix B2 consists of the first L columns of a
  M-by-M lower triangular matrix, where 0 <= L <= MIN(M,N).  If L=0,
  B is rectangular M-by-N; if M=L=N, B is lower triangular.

  The matrix W stores the elementary reflectors H(i) in the i-th row
  above the diagonal (of A) in the M-by-(M+N) input matrix C
            [ C ] = [ A ] [ B ]
                   [ A ]  <- lower triangular M-by-M
                   [ B ]  <- M-by-N pentagonal

  so that W can be represented as
            [ W ] = [ I ] [ V ]
                   [ I ]  <- identity, M-by-M
                   [ V ]  <- M-by-N, same form as B.

  Thus, all of information needed for W is contained on exit in B, which
  we call V above.  Note that V has the same form as B; that is,
            [ V ] = [ V1 ] [ V2 ]
                   [ V1 ] <- M-by-(N-L) rectangular
                   [ V2 ] <-     M-by-L lower trapezoidal.

  The rows of V represent the vectors which define the H(i)'s.

  The number of blocks is B = ceiling(M/MB), where each
  block is of order MB except for the last block, which is of order
  IB = M - (M-1)*MB.  For each of the B blocks, a upper triangular block
  reflector factor is computed: T1, T2, ..., TB.  The MB-by-MB (and IB-by-IB
  for the last block) T's are stored in the MB-by-N matrix T as

               T = [T1 T2 ... TB].

Definition at line 187 of file dtplqt.f.

189*
190* -- LAPACK computational routine --
191* -- LAPACK is a software package provided by Univ. of Tennessee, --
192* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
193*
194* .. Scalar Arguments ..
195 INTEGER INFO, LDA, LDB, LDT, N, M, L, MB
196* ..
197* .. Array Arguments ..
198 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
199* ..
200*
201* =====================================================================
202*
203* ..
204* .. Local Scalars ..
205 INTEGER I, IB, LB, NB, IINFO
206* ..
207* .. External Subroutines ..
208 EXTERNAL dtplqt2, dtprfb, xerbla
209* ..
210* .. Executable Statements ..
211*
212* Test the input arguments
213*
214 info = 0
215 IF( m.LT.0 ) THEN
216 info = -1
217 ELSE IF( n.LT.0 ) THEN
218 info = -2
219 ELSE IF( l.LT.0 .OR. (l.GT.min(m,n) .AND. min(m,n).GE.0)) THEN
220 info = -3
221 ELSE IF( mb.LT.1 .OR. (mb.GT.m .AND. m.GT.0)) THEN
222 info = -4
223 ELSE IF( lda.LT.max( 1, m ) ) THEN
224 info = -6
225 ELSE IF( ldb.LT.max( 1, m ) ) THEN
226 info = -8
227 ELSE IF( ldt.LT.mb ) THEN
228 info = -10
229 END IF
230 IF( info.NE.0 ) THEN
231 CALL xerbla( 'DTPLQT', -info )
232 RETURN
233 END IF
234*
235* Quick return if possible
236*
237 IF( m.EQ.0 .OR. n.EQ.0 ) RETURN
238*
239 DO i = 1, m, mb
240*
241* Compute the QR factorization of the current block
242*
243 ib = min( m-i+1, mb )
244 nb = min( n-l+i+ib-1, n )
245 IF( i.GE.l ) THEN
246 lb = 0
247 ELSE
248 lb = nb-n+l-i+1
249 END IF
250*
251 CALL dtplqt2( ib, nb, lb, a(i,i), lda, b( i, 1 ), ldb,
252 $ t(1, i ), ldt, iinfo )
253*
254* Update by applying H**T to B(I+IB:M,:) from the right
255*
256 IF( i+ib.LE.m ) THEN
257 CALL dtprfb( 'R', 'N', 'F', 'R', m-i-ib+1, nb, ib, lb,
258 $ b( i, 1 ), ldb, t( 1, i ), ldt,
259 $ a( i+ib, i ), lda, b( i+ib, 1 ), ldb,
260 $ work, m-i-ib+1)
261 END IF
262 END DO
263 RETURN
264*
265* End of DTPLQT
266*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine dtplqt2(m, n, l, a, lda, b, ldb, t, ldt, info)
DTPLQT2 computes a LQ factorization of a real or complex "triangular-pentagonal" matrix,...
Definition dtplqt2.f:177
subroutine dtprfb(side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, a, lda, b, ldb, work, ldwork)
DTPRFB applies a real "triangular-pentagonal" block reflector to a real matrix, which is composed of ...
Definition dtprfb.f:251
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