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zlatrz(3) [centos man page]

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

NAME

       zlatrz.f -

SYNOPSIS

   Functions/Subroutines
       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.

       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.

       Parameters:
	   M

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

	   N

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

	   L

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

	   A

		     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

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

	   TAU

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

	   WORK

		     WORK is COMPLEX*16 array, dimension (M)

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Contributors:
	   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 ) )

	     where

		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.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

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

Check Out this Related Man Page

CLATRZ(l)								 )								 CLATRZ(l)

NAME

       CLATRZ  -  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 uni-
       tary 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 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 ).

LAPACK version 3.0						   15 June 2000 							 CLATRZ(l)
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