ctpqrt.f(3)

NAME
ctpqrt.f -

SYNOPSIS

  Functions/Subroutines

subroutine ctpqrt (M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK, INFO)
CTPQRT

Function/Subroutine Documentation

  subroutine ctpqrt (integerM, integerN, integerL, integerNB, complex, dimension( lda, * )A, integerLDA, complex, dimension( ldb, * )B, integerLDB, complex, dimension( ldt, * )T, integerLDT, complex, dimension( * )WORK, integerINFO)

CTPQRT

Purpose:

     CTPQRT computes a blocked QR factorization of a complex
     "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.
              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 upper trapezoidal part of B.
              MIN(M,N) >= L >= 0.  See Further Details.

    NB

              NB is INTEGER
              The block size to be used in the blocked QR.  N >= NB >= 1.

    A

              A is COMPLEX 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.

    LDA

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

    B

              B is COMPLEX 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.

    LDB

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

    T

              T is COMPLEX array, dimension (LDT,N)
              The upper 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 >= NB.

    WORK

              WORK is COMPLEX array, dimension (NB*N)

    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:
    November 2013

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 number of blocks is B = ceiling(N/NB), where each
      block is of order NB except for the last block, which is of order
      IB = N - (B-1)*NB.  For each of the B blocks, a upper triangular block
      reflector factor is computed: T1, T2, ..., TB.  The NB-by-NB (and IB-by-IB
      for the last block) T's are stored in the NB-by-N matrix T as

                   T = [T1 T2 ... TB].

Definition at line 189 of file ctpqrt.f.

Author

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