Contents
stzrzf - reduce the M-by-N ( M<=N ) real upper trapezoidal
matrix A to upper triangular form by means of orthogonal
transformations
SUBROUTINE STZRZF(M, N, A, LDA, TAU, WORK, LWORK, INFO)
INTEGER M, N, LDA, LWORK, INFO
REAL A(LDA,*), TAU(*), WORK(*)
SUBROUTINE STZRZF_64(M, N, A, LDA, TAU, WORK, LWORK, INFO)
INTEGER*8 M, N, LDA, LWORK, INFO
REAL A(LDA,*), TAU(*), WORK(*)
F95 INTERFACE
SUBROUTINE TZRZF([M], [N], A, [LDA], TAU, [WORK], [LWORK], [INFO])
INTEGER :: M, N, LDA, LWORK, INFO
REAL, DIMENSION(:) :: TAU, WORK
REAL, DIMENSION(:,:) :: A
SUBROUTINE TZRZF_64([M], [N], A, [LDA], TAU, [WORK], [LWORK], [INFO])
INTEGER(8) :: M, N, LDA, LWORK, INFO
REAL, DIMENSION(:) :: TAU, WORK
REAL, DIMENSION(:,:) :: A
C INTERFACE
#include <sunperf.h>
void stzrzf(int m, int n, float *a, int lda, float *tau, int
*info);
void stzrzf_64(long m, long n, float *a, long lda, float
*tau, long *info);
stzrzf 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.
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
Based on contributions by
A. Petitet, Computer Science Dept., Univ. of Tenn., Knox-
ville, USA
The factorization is obtained by Householder's method. The
kth transformation matrix, Z( k ), which is used to intro-
duce 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 ).