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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