dtzrzf(3P) Sun Performance Library dtzrzf(3P)NAMEdtzrzf - reduce the M-by-N ( M<=N ) real upper trapezoidal matrix A to
upper triangular form by means of orthogonal transformations
SYNOPSIS
SUBROUTINE DTZRZF(M, N, A, LDA, TAU, WORK, LWORK, INFO)
INTEGER M, N, LDA, LWORK, INFO
DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*)
SUBROUTINE DTZRZF_64(M, N, A, LDA, TAU, WORK, LWORK, INFO)
INTEGER*8 M, N, LDA, LWORK, INFO
DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*)
F95 INTERFACE
SUBROUTINE TZRZF([M], [N], A, [LDA], TAU, [WORK], [LWORK], [INFO])
INTEGER :: M, N, LDA, LWORK, INFO
REAL(8), DIMENSION(:) :: TAU, WORK
REAL(8), DIMENSION(:,:) :: A
SUBROUTINE TZRZF_64([M], [N], A, [LDA], TAU, [WORK], [LWORK], [INFO])
INTEGER(8) :: M, N, LDA, LWORK, INFO
REAL(8), DIMENSION(:) :: TAU, WORK
REAL(8), DIMENSION(:,:) :: A
C INTERFACE
#include <sunperf.h>
void dtzrzf(int m, int n, double *a, int lda, double *tau, int *info);
void dtzrzf_64(long m, long n, double *a, long lda, double *tau, long
*info);
PURPOSEdtzrzf 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 trian‐
gular matrix.
ARGUMENTS
M (input) The number of rows of the matrix A. M >= 0.
N (input) The number of columns of the matrix A. N >= 0.
A (input/output)
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)
The leading dimension of the array A. LDA >= max(1,M).
TAU (output)
The scalar factors of the elementary reflectors.
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input)
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)
= 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 trans‐
formation 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 ).
6 Mar 2009 dtzrzf(3P)
