ZLATRZ(3S)ZLATRZ(3S)NAME
ZLATRZ - 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 unitary
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 ZLATRZ( M, N, L, A, LDA, TAU, WORK )
INTEGER L, LDA, M, N
COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
IMPLEMENTATION
These routines are part of the SCSL Scientific Library and can be loaded
using either the -lscs or the -lscs_mp option. The -lscs_mp option
directs the linker to use the multi-processor version of the library.
When linking to SCSL with -lscs or -lscs_mp, the default integer size is
4 bytes (32 bits). Another version of SCSL is available in which integers
are 8 bytes (64 bits). This version allows the user access to larger
memory sizes and helps when porting legacy Cray codes. It can be loaded
by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
only one of the two versions; 4-byte integer and 8-byte integer library
calls cannot be mixed.
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.
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*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.
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ZLATRZ(3S)ZLATRZ(3S)
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU (output) COMPLEX*16 array, dimension (M)
The scalar factors of the elementary reflectors.
WORK (workspace) COMPLEX*16 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 ).
SEE ALSOINTRO_LAPACK(3S), INTRO_SCSL(3S)
This man page is available only online.
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