zlatrz(3S)

NAME
     ZLATRZ - factor 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

SYNOPSIS
     SUBROUTINE ZLATRZ( M, N, L, A, LDA, TAU, WORK )

         INTEGER        L, LDA, M, N

         COMPLEX*16     A( LDA, * ), TAU( * ), WORK( * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     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.

ARGUMENTS
     M       (input) INTEGER
             The number of rows of the matrix A.  M >= 0.

     N       (input) INTEGER
             The number of columns of the matrix A.  N >= 0.

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

     A       (input/output) 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     (input) INTEGER
             The leading dimension of the array A.  LDA >= max(1,M).

     TAU     (output) COMPLEX*16 array, dimension (M)
             The scalar factors of the elementary reflectors.

     WORK    (workspace) COMPLEX*16 array, dimension (M)

FURTHER DETAILS
     Based on contributions by
       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 )',   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 ).


SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

     This man page is available only online.