ztzrzf.f(3)

NAME
ztzrzf.f -

SYNOPSIS

  Functions/Subroutines
subroutine ZTZRZF (M, N, A, LDA, TAU, WORK, LWORK, INFO)
ZTZRZF

Function/Subroutine Documentation

  subroutine ZTZRZF (INTEGERM, INTEGERN, COMPLEX*16, dimension( lda, * )A, INTEGERLDA, COMPLEX*16, dimension( * )TAU, COMPLEX*16, dimension( * )WORK, INTEGERLWORK, INTEGERINFO)

ZTZRZF

Purpose:

     ZTZRZF 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:
    M

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

    N

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

    A

              A is COMPLEX*16 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.

    LDA

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

    TAU

              TAU is COMPLEX*16 array, dimension (M)
              The scalar factors of the elementary reflectors.

    WORK

              WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    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.

    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 2011

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

Further Details:

      The factorization is obtained by Householder's method.  The kth
      transformation matrix, Z( k ), which is used to introduce zeros into
      the ( m - k + 1 )th row of A, is given in the form
         Z( k ) = ( I     0   ),
                  ( 0  T( k ) )
      where
         T( k ) = I - tau*u( k )*u( k )**H,   u( k ) = (   1    ),
                                                     (   0    )
                                                     ( z( k ) )
      tau is a scalar and z( k ) is an ( n - m ) element vector.
      tau and z( k ) are chosen to annihilate the elements of the kth row
      of X.
      The scalar tau is returned in the kth element of TAU and the vector
      u( k ) in the kth row of A, such that the elements of z( k ) are
      in  a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in
      the upper triangular part of A.
      Z is given by
         Z =  Z( 1 ) * Z( 2 ) * ... * Z( m ).

Definition at line 161 of file ztzrzf.f'.

Author

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