stzrqf(3P) Sun Performance Library stzrqf(3P)NAMEstzrqf - routine is deprecated and has been replaced by routine STZRZF
SYNOPSIS
SUBROUTINE STZRQF(M, N, A, LDA, TAU, INFO)
INTEGER M, N, LDA, INFO
REAL A(LDA,*), TAU(*)
SUBROUTINE STZRQF_64(M, N, A, LDA, TAU, INFO)
INTEGER*8 M, N, LDA, INFO
REAL A(LDA,*), TAU(*)
F95 INTERFACE
SUBROUTINE TZRQF(M, N, A, [LDA], TAU, [INFO])
INTEGER :: M, N, LDA, INFO
REAL, DIMENSION(:) :: TAU
REAL, DIMENSION(:,:) :: A
SUBROUTINE TZRQF_64(M, N, A, [LDA], TAU, [INFO])
INTEGER(8) :: M, N, LDA, INFO
REAL, DIMENSION(:) :: TAU
REAL, DIMENSION(:,:) :: A
C INTERFACE
#include <sunperf.h>
void stzrqf(int m, int n, float *a, int lda, float *tau, int *info);
void stzrqf_64(long m, long n, float *a, long lda, float *tau, long
*info);
PURPOSEstzrqf routine is deprecated and has been replaced by routine STZRZF.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 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 >= M.
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) REAL array, dimension (M)
The scalar factors of the elementary reflectors.
INFO (output)
= 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 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 stzrqf(3P)
