dtplqt.f(3)

NAME
dtplqt.f

SYNOPSIS

  Functions/Subroutines
subroutine dtplqt (M, N, L, MB, A, LDA, B, LDB, T, LDT, WORK, INFO)
DTPLQT

Function/Subroutine Documentation

  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)

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
    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 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.

    LDA

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

    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.

    LDB

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

    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.

    LDT

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

    WORK

              WORK is DOUBLE PRECISION 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 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.

Author

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