slatrz(l) [redhat man page]

SLATRZ(l)								 )								 SLATRZ(l)

NAME

       SLATRZ - factor the M-by-(M+L) real upper trapezoidal matrix [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z, by means of orthogo-
       nal transformations

SYNOPSIS

       SUBROUTINE SLATRZ( M, N, L, A, LDA, TAU, WORK )

	   INTEGER	  L, LDA, M, N

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

PURPOSE

       SLATRZ factors the M-by-(M+L) real upper trapezoidal matrix [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z, by means of  orthogo-
       nal transformations. Z is an (M+L)-by-(M+L) orthogonal 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) REAL 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 orthogonal 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) REAL array, dimension (M)
	       The scalar factors of the elementary reflectors.

       WORK    (workspace) REAL 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 							 SLATRZ(l)

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)