slatrz (l)  Linux Manuals
slatrz: factors the Mby(M+L) real upper trapezoidal matrix [ A1 A2 ] = [ A(1:M,1:M) A(1:M,NL+1:N) ] as ( R 0 ) * Z, by means of orthogonal transformations
Command to display slatrz
manual in Linux: $ man l slatrz
NAME
SLATRZ  factors the Mby(M+L) real upper trapezoidal matrix [ A1 A2 ] = [ A(1:M,1:M) A(1:M,NL+1:N) ] as ( R 0 ) * Z, by means of orthogonal 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 Mby(M+L) real upper trapezoidal matrix
[ A1 A2 ] = [ A(1:M,1:M) A(1:M,NL+1:N) ] as ( R 0 ) * Z, by means
of orthogonal transformations. Z is an (M+L)by(M+L) orthogonal
matrix and, R and A1 are MbyM 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. NM >= L >= 0.
 A (input/output) REAL array, dimension (LDA,N)

On entry, the leading MbyN upper trapezoidal part of the
array A must contain the matrix to be factorized.
On exit, the leading MbyM upper triangular part of A
contains the upper triangular matrix R, and elements NL+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 Householderaqs 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 )aq, 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 ).
Pages related to slatrz
 slatrz (3)
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 slatrs (l)  solves one of the triangular systems A *x = s*b or Aaq*x = s*b with scaling to prevent overflow
 slatbs (l)  solves one of the triangular systems A *x = s*b or Aaq*x = s*b with scaling to prevent overflow, where A is an upper or lower triangular band matrix
 slatdf (l)  uses the LU factorization of the nbyn matrix Z computed by SGETC2 and computes a contribution to the reciprocal Difestimate by solving Z * x = b for x, and choosing the r.h.s
 slatps (l)  solves one of the triangular systems A *x = s*b or Aaq*x = s*b with scaling to prevent overflow, where A is an upper or lower triangular matrix stored in packed form
 slatzm (l)  routine i deprecated and has been replaced by routine SORMRZ
 sla_gbamv (l)  performs one of the matrixvector operations y := alpha*abs(A)*abs(x) + beta*abs(y),