STZRZF(3S)STZRZF(3S)NAMESTZRZF - reduce the M-by-N ( M<=N ) real upper trapezoidal matrix A to
upper triangular form by means of orthogonal transformations
SYNOPSIS
SUBROUTINE STZRZF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
INTEGER INFO, LDA, LWORK, M, N
REAL 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.
PURPOSESTZRZF 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 >= 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 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.
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STZRZF(3S)STZRZF(3S)
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/output) REAL array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,M). For optimum
performance LWORK >= M*NB, where NB is the optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns this
value as the first entry of the WORK array, and no error message
related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
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 ( 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 ).
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STZRZF(3S)STZRZF(3S)SEE ALSOINTRO_LAPACK(3S), INTRO_SCSL(3S)
This man page is available only online.
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