SRC/clatrz.f(3)            Library Functions Manual            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
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                 SRC/clatrz.f(3)