TESTING/LIN/stplqt.f(3)    Library Functions Manual    TESTING/LIN/stplqt.f(3)

NAME
       TESTING/LIN/stplqt.f

SYNOPSIS
   Functions/Subroutines
       subroutine stplqt (m, n, l, mb, a, lda, b, ldb, t, ldt, work, info)
           STPLQT

Function/Subroutine Documentation
   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

       Purpose:


           !>
           !> STPLQT computes a blocked LQ factorization of a real
           !>  matrix C, which is composed of a
           !> triangular block A and pentagonal block B, using the compact
           !> WY representation for Q.
           !>

       Parameters
           M

           !>          M is INTEGER
           !>          The number of rows of the matrix B, and the order of the
           !>          triangular matrix A.
           !>          M >= 0.
           !>

           N

           !>          N is INTEGER
           !>          The number of columns of the matrix B.
           !>          N >= 0.
           !>

           L

           !>          L is INTEGER
           !>          The number of rows of the lower trapezoidal part of B.
           !>          MIN(M,N) >= L >= 0.  See Further Details.
           !>

           MB

           !>          MB is INTEGER
           !>          The block size to be used in the blocked QR.  M >= MB >= 1.
           !>

           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.
           !>

           LDA

           !>          LDA is INTEGER
           !>          The leading dimension of the array A.  LDA >= max(1,N).
           !>

           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.
           !>

           LDB

           !>          LDB is INTEGER
           !>          The leading dimension of the array B.  LDB >= max(1,M).
           !>

           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.
           !>

           LDT

           !>          LDT is INTEGER
           !>          The leading dimension of the array T.  LDT >= MB.
           !>

           WORK

           !>          WORK is REAL array, dimension (MB*M)
           !>

           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 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 187 of file stplqt.f.

Author
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LAPACK                          Version 3.12.0         TESTING/LIN/stplqt.f(3)