LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ stplqt()

subroutine stplqt ( integer  M,
integer  N,
integer  L,
integer  MB,
real, dimension( lda, * )  A,
integer  LDA,
real, dimension( ldb, * )  B,
integer  LDB,
real, dimension( ldt, * )  T,
integer  LDT,
real, dimension( * )  WORK,
integer  INFO 
)

STPLQT

Download DTPQRT + 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 REAL 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 REAL 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 REAL 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 REAL 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.
Date
June 2017
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].
Purpose:

STPLQT 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 REAL array, dimension (LDA,N)
          On entry, the lower triangular N-by-N 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,N).
[in,out]B
          B is REAL 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 REAL 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 REAL 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.
Date
December 2016
Further Details:

The input matrix C is a M-by-(M+N) matrix

C = [ A ] [ B ]

where A is an lower triangular N-by-N 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 upper trapezoidal.

The lower trapezoidal matrix B2 consists of the first L columns of a N-by-N 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 N-by-N [ B ] <- M-by-N pentagonal

so that W can be represented as [ W ] = [ I ] [ V ] [ I ] <- identity, N-by-N [ 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 191 of file stplqt.f.

191 *
192 * -- LAPACK computational routine (version 3.7.1) --
193 * -- LAPACK is a software package provided by Univ. of Tennessee, --
194 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
195 * June 2017
196 *
197 * .. Scalar Arguments ..
198  INTEGER info, lda, ldb, ldt, n, m, l, mb
199 * ..
200 * .. Array Arguments ..
201  REAL a( lda, * ), b( ldb, * ), t( ldt, * ), work( * )
202 * ..
203 *
204 * =====================================================================
205 *
206 * ..
207 * .. Local Scalars ..
208  INTEGER i, ib, lb, nb, iinfo
209 * ..
210 * .. External Subroutines ..
211  EXTERNAL stplqt2, stprfb, xerbla
212 * ..
213 * .. Executable Statements ..
214 *
215 * Test the input arguments
216 *
217  info = 0
218  IF( m.LT.0 ) THEN
219  info = -1
220  ELSE IF( n.LT.0 ) THEN
221  info = -2
222  ELSE IF( l.LT.0 .OR. (l.GT.min(m,n) .AND. min(m,n).GE.0)) THEN
223  info = -3
224  ELSE IF( mb.LT.1 .OR. (mb.GT.m .AND. m.GT.0)) THEN
225  info = -4
226  ELSE IF( lda.LT.max( 1, m ) ) THEN
227  info = -6
228  ELSE IF( ldb.LT.max( 1, m ) ) THEN
229  info = -8
230  ELSE IF( ldt.LT.mb ) THEN
231  info = -10
232  END IF
233  IF( info.NE.0 ) THEN
234  CALL xerbla( 'STPLQT', -info )
235  RETURN
236  END IF
237 *
238 * Quick return if possible
239 *
240  IF( m.EQ.0 .OR. n.EQ.0 ) RETURN
241 *
242  DO i = 1, m, mb
243 *
244 * Compute the QR factorization of the current block
245 *
246  ib = min( m-i+1, mb )
247  nb = min( n-l+i+ib-1, n )
248  IF( i.GE.l ) THEN
249  lb = 0
250  ELSE
251  lb = nb-n+l-i+1
252  END IF
253 *
254  CALL stplqt2( ib, nb, lb, a(i,i), lda, b( i, 1 ), ldb,
255  $ t(1, i ), ldt, iinfo )
256 *
257 * Update by applying H**T to B(I+IB:M,:) from the right
258 *
259  IF( i+ib.LE.m ) THEN
260  CALL stprfb( 'R', 'N', 'F', 'R', m-i-ib+1, nb, ib, lb,
261  $ b( i, 1 ), ldb, t( 1, i ), ldt,
262  $ a( i+ib, i ), lda, b( i+ib, 1 ), ldb,
263  $ work, m-i-ib+1)
264  END IF
265  END DO
266  RETURN
267 *
268 * End of STPLQT
269 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine stplqt2(M, N, L, A, LDA, B, LDB, T, LDT, INFO)
STPLQT2 computes a LQ factorization of a real or complex "triangular-pentagonal" matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q.
Definition: stplqt2.f:179
subroutine stprfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK)
STPRFB applies a real or complex "triangular-pentagonal" blocked reflector to a real or complex matri...
Definition: stprfb.f:253
Here is the call graph for this function:
Here is the caller graph for this function: