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.

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)

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

September 2012

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

  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 ).