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zlatrz.f(3)				      LAPACK				      zlatrz.f(3)

       zlatrz.f -

       subroutine zlatrz (M, N, L, A, LDA, TAU, WORK)
	   ZLATRZ factors an upper trapezoidal matrix by means of unitary transformations.

Function/Subroutine Documentation
   subroutine zlatrz (integerM, integerN, integerL, complex*16, dimension( lda, * )A, integerLDA,
       complex*16, dimension( * )TAU, complex*16, dimension( * )WORK)
       ZLATRZ factors an upper trapezoidal matrix by means of unitary transformations.


	    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.


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


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


		     WORK is COMPLEX*16 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 zlatrz.f.

       Generated automatically by Doxygen for LAPACK from the source code.

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