SRC/zlatrz.f(3)

NAME
SRC/zlatrz.f

SYNOPSIS

  Functions/Subroutines
subroutine zlatrz (m, n, l, a, lda, tau, work)
ZLATRZ factors an upper trapezoidal matrix by means of unitary transformations.

Function/Subroutine Documentation

  subroutine zlatrz (integer m, integer n, integer l, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work)

ZLATRZ factors an upper trapezoidal matrix by means of unitary transformations.

Purpose:

     ZLATRZ factors the M-by-(M+L) complex upper trapezoidal matrix
     [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R  0 ) * Z by means
     of unitary transformations, where  Z is an (M+L)-by-(M+L) unitary
     matrix and, R and A1 are M-by-M upper triangular matrices.

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 >= 0.

    L

              L is INTEGER
              The number of columns of the matrix A containing the
              meaningful part of the Householder vectors. N-M >= L >= 0.

    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 N-L+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 (M)

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 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 l element vector. tau and z( k )
      are chosen to annihilate the elements of the kth row of A2.
      The scalar tau is returned in the kth element of TAU and the vector
      u( k ) in the kth row of A2, such that the elements of z( k ) are
      in  a( k, l + 1 ), ..., a( k, n ). The elements of R are returned in
      the upper triangular part of A1.
      Z is given by
         Z =  Z( 1 ) * Z( 2 ) * ... * Z( m ).

Definition at line 139 of file zlatrz.f.

Author

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