SRC/clatrz.f(3)

NAME
SRC/clatrz.f

SYNOPSIS

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

Function/Subroutine Documentation

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

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

Purpose:

     CLATRZ 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 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 array, dimension (M)
              The scalar factors of the elementary reflectors.

    WORK

              WORK is COMPLEX 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 clatrz.f.

Author

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