dtplqt2.f(3)

NAME
dtplqt2.f

SYNOPSIS

  Functions/Subroutines
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, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q.

Function/Subroutine Documentation

  subroutine dtplqt2 (integer M, integer N, integer L, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( ldt, * ) T, integer LDT, integer INFO)

DTPLQT2 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.

Purpose:

     DTPLQT2 computes a LQ a 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 total number of rows of the matrix B.
              M >= 0.

    N

              N is INTEGER
              The number of columns of the matrix B, and the order of
              the triangular matrix A.
              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.

    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,M)
              The N-by-N upper triangular factor T of the block reflector.
              See Further Details.

    LDT

              LDT is INTEGER
              The leading dimension of the array T.  LDT >= max(1,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.

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 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
      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 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,
                   W = [ 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 (M+N)-by-(M+N) block reflector H is then given by
                   H = I - W**T * T * W
      where W^H is the conjugate transpose of W and T is the upper triangular
      factor of the block reflector.

Definition at line 179 of file dtplqt2.f.

Author

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