dlatrz.f(3)

NAME
dlatrz.f -

SYNOPSIS

  Functions/Subroutines

subroutine dlatrz (M, N, L, A, LDA, TAU, WORK)
DLATRZ factors an upper trapezoidal matrix by means of orthogonal transformations.

Function/Subroutine Documentation

  subroutine dlatrz (integerM, integerN, integerL, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( * )TAU, double precision, dimension( * )WORK)

DLATRZ factors an upper trapezoidal matrix by means of orthogonal transformations.

Purpose:

     DLATRZ factors the M-by-(M+L) real upper trapezoidal matrix
     [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R  0 ) * Z, by means
     of orthogonal transformations.  Z is an (M+L)-by-(M+L) orthogonal
     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 DOUBLE PRECISION 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
              orthogonal 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 DOUBLE PRECISION array, dimension (M)
              The scalar factors of the elementary reflectors.

    WORK

              WORK is DOUBLE PRECISION array, dimension (M)

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    September 2012

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 )**T,   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 141 of file dlatrz.f.

Author

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