clatrz man page on Scientific

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CLATRZ(1)		 LAPACK routine (version 3.2)		     CLATRZ(1)

NAME
       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

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

	   INTEGER	  L, LDA, M, N

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

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.

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 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 array, dimension (M)
	       The scalar factors of the elementary reflectors.

       WORK    (workspace) COMPLEX 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	transā€
       formation 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 ).

 LAPACK routine (version 3.2)	 November 2008			     CLATRZ(1)
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