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## dtpqrt2()

subroutine dtpqrt2 | ( | 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 )

DTPQRT2 computes a QR 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.

Download DTPQRT2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> DTPQRT2 computes a QR 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

  [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 upper trapezoidal part of B.
      !>          MIN(M,N) >= L >= 0.  See Further Details.
      !>

  [in,out]

  A

      !>          A is DOUBLE PRECISION array, dimension (LDA,N)
      !>          On entry, the upper triangular N-by-N matrix A.
      !>          On exit, the elements on and above the diagonal of the array
      !>          contain the upper triangular matrix R.
      !>

  [in]

  LDA

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

  [in,out]

  B

      !>          B is DOUBLE PRECISION array, dimension (LDB,N)
      !>          On entry, the pentagonal M-by-N matrix B.  The first M-L rows
      !>          are rectangular, and the last L rows are upper 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 DOUBLE PRECISION array, dimension (LDT,N)
      !>          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,N)
      !>

  [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 (N+M)-by-N matrix
      !>
      !>               C = [ A ]
      !>                   [ B ]
      !>
      !>  where A is an upper triangular N-by-N matrix, and B is M-by-N pentagonal
      !>  matrix consisting of a (M-L)-by-N rectangular matrix B1 on top of a L-by-N
      !>  upper trapezoidal matrix B2:
      !>
      !>               B = [ B1 ]  <- (M-L)-by-N rectangular
      !>                   [ B2 ]  <-     L-by-N upper trapezoidal.
      !>
      !>  The upper trapezoidal matrix B2 consists of the first L rows of a
      !>  N-by-N upper triangular matrix, where 0 <= L <= MIN(M,N).  If L=0,
      !>  B is rectangular M-by-N; if M=L=N, B is upper triangular.
      !>
      !>  The matrix W stores the elementary reflectors H(i) in the i-th column
      !>  below the diagonal (of A) in the (N+M)-by-N input matrix C
      !>
      !>               C = [ A ]  <- upper triangular N-by-N
      !>                   [ B ]  <- M-by-N pentagonal
      !>
      !>  so that W can be represented as
      !>
      !>               W = [ 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 ] <- (M-L)-by-N rectangular
      !>                   [ V2 ] <-     L-by-N upper trapezoidal.
      !>
      !>  The columns 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 * W**T
      !>
      !>  where W^H is the conjugate transpose of W and T is the upper triangular
      !>  factor of the block reflector.
      !>