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clatrz.f(3)				      LAPACK				      clatrz.f(3)

       clatrz.f -

       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 (integerM, integerN, integerL, complex, dimension( lda, * )A, integerLDA,
       complex, dimension( * )TAU, complex, dimension( * )WORK)
       CLATRZ factors an upper trapezoidal matrix by means of unitary transformations.


	    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.


		     M is INTEGER
		     The number of rows of the matrix A.  M >= 0.


		     N is INTEGER
		     The number of columns of the matrix A.  N >= 0.


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


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


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


		     WORK is COMPLEX 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

       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 ) )


		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 141 of file clatrz.f.

       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      clatrz.f(3)
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