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## ctplqt2()

subroutine ctplqt2 | ( | integer | m,
|  | integer | n,
|  | integer | l,
|  | complex, dimension( lda, * ) | a,
|  | integer | lda,
|  | complex, dimension( ldb, * ) | b,
|  | integer | ldb,
|  | complex, dimension( ldt, * ) | t,
|  | integer | ldt,
|  | integer | info )

CTPLQT2

Purpose:

      !>
      !> CTPLQT2 computes a LQ a factorization of a complex
      !> 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 total number of rows of the matrix B.
      !>          M >= 0.
      !>

  [in]

  N

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

  A

      !>          A is COMPLEX 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 COMPLEX 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 COMPLEX array, dimension (LDT,M)
      !>          The N-by-N upper triangular factor T of the block reflector.
      !>          See Further Details.
      !>

  [in]

  LDT

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