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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)

Check Out this Related Man Page

STZRQF(l)								 )								 STZRQF(l)

NAME

       STZRQF - routine is deprecated and has been replaced by routine STZRZF

SYNOPSIS

       SUBROUTINE STZRQF( M, N, A, LDA, TAU, INFO )

	   INTEGER	  INFO, LDA, M, N

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

PURPOSE

       This  routine is deprecated and has been replaced by routine STZRZF.  STZRQF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A to
       upper triangular form by means of orthogonal transformations.

       The upper trapezoidal matrix A is factored as

	  A = ( R  0 ) * Z,

       where Z is an N-by-N orthogonal matrix and R is an M-by-M upper triangular matrix.

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 >= M.

       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 M+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.

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value

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 )',   u( k ) = (   1    ),
						      (   0    )
						      ( z( k ) )

       tau is a scalar and z( k ) is an ( n - m ) element vector.  tau and z( k ) are chosen to annihilate the elements of the kth row of X.

       The scalar tau is returned in the kth element of TAU and the vector u( k ) in the kth row of A, such that the elements of z( k ) are in	a(
       k, m + 1 ), ..., a( k, n ). The elements of R are returned in the upper triangular part of A.

       Z is given by

	  Z =  Z( 1 ) * Z( 2 ) * ... * Z( m ).

LAPACK version 3.0						   15 June 2000 							 STZRQF(l)
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