stzrqf.f - Man Page
SRC/DEPRECATED/stzrqf.f
Synopsis
Functions/Subroutines
subroutine stzrqf (m, n, a, lda, tau, info)
STZRQF
Function/Subroutine Documentation
subroutine stzrqf (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, integer info)
STZRQF
Purpose:
This routine is deprecated and has been replaced by routine STZRZF.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 triangular matrix.
- Parameters
M
M is INTEGER The number of rows of the matrix A. M >= 0.
N
N is INTEGER The number of columns of the matrix A. N >= M.
A
A is 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.
LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
TAU
TAU is REAL array, dimension (M) The scalar factors of the elementary reflectors.
INFO
INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
- Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
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 )**T, 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 ).
Definition at line 137 of file stzrqf.f.
Author
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Referenced By
The man page stzrqf(3) is an alias of stzrqf.f(3).
Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK