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## dlatrz()

subroutine dlatrz | ( | integer | m,
|  | integer | n,
|  | integer | l,
|  | double precision, dimension( lda, * ) | a,
|  | integer | lda,
|  | double precision, dimension( * ) | tau,
|  | double precision, dimension( * ) | work )

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

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

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

  [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 >= 0.
      !>

  [in]

  L

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

  [in,out]

  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.
      !>

  [in]

  LDA

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

  [out]

  TAU

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

  [out]

  WORK

      !>          WORK is DOUBLE PRECISION 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 )**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 ).
      !>