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## ctzrzf()

subroutine ctzrzf | ( | integer | m,
|  | integer | n,
|  | complex, dimension( lda, * ) | a,
|  | integer | lda,
|  | complex, dimension( * ) | tau,
|  | complex, dimension( * ) | work,
|  | integer | lwork,
|  | integer | info )

CTZRZF

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

Purpose:

      !>
      !> CTZRZF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A
      !> to upper triangular form by means of unitary transformations.
      !>
      !> The upper trapezoidal matrix A is factored as
      !>
      !>    A = ( R  0 ) * Z,
      !>
      !> where Z is an N-by-N unitary matrix and R is an M-by-M upper
      !> triangular matrix.
      !>

Parameters

  [in]

  M

      !>          M is INTEGER
      !>          The number of rows of the matrix A.  M >= 0.
      !>

  [in]

  N

      !>          N is INTEGER
      !>          The number of columns of the matrix A.  N >= M.
      !>

  [in,out]

  A

      !>          A is COMPLEX array, dimension (LDA,N)
      !>          On entry, the leading M-by-N upper trapezoidal part of the
      !>          array A must contain the matrix to be factorized.
      !>          On exit, the leading M-by-M upper triangular part of A
      !>          contains the upper triangular matrix R, and elements M+1 to
      !>          N of the first M rows of A, with the array TAU, represent the
      !>          unitary matrix Z as a product of M elementary reflectors.
      !>

  [in]

  LDA

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

  [out]

  TAU

      !>          TAU is COMPLEX array, dimension (M)
      !>          The scalar factors of the elementary reflectors.
      !>

  [out]

  WORK

      !>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
      !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
      !>

  [in]

  LWORK

      !>          LWORK is INTEGER
      !>          The dimension of the array WORK.  LWORK >= max(1,M).
      !>          For optimum performance LWORK >= M*NB, where NB is
      !>          the optimal blocksize.
      !>
      !>          If LWORK = -1, then a workspace query is assumed; the routine
      !>          only calculates the optimal size of the WORK array, returns
      !>          this value as the first entry of the WORK array, and no error
      !>          message related to LWORK is issued by XERBLA.
      !>

  [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.

Contributors:
  A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details:

      !>
      !>  The N-by-N matrix Z can be computed by
      !>
      !>     Z =  Z(1)*Z(2)* ... *Z(M)
      !>
      !>  where each N-by-N Z(k) is given by
      !>
      !>     Z(k) = I - tau(k)*v(k)*v(k)**H
      !>
      !>  with v(k) is the kth row vector of the M-by-N matrix
      !>
      !>     V = ( I   A(:,M+1:N) )
      !>
      !>  I is the M-by-M identity matrix, A(:,M+1:N)
      !>  is the output stored in A on exit from CTZRZF,
      !>  and tau(k) is the kth element of the array TAU.
      !>
      !>