STZRZF (3)  Linux Manuals
NAME
stzrzf.f 
SYNOPSIS
Functions/Subroutines
subroutine stzrzf (M, N, A, LDA, TAU, WORK, LWORK, INFO)
STZRZF
Function/Subroutine Documentation
subroutine stzrzf (integerM, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( * )TAU, real, dimension( * )WORK, integerLWORK, integerINFO)
STZRZF
Purpose:

STZRZF reduces the MbyN ( 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 NbyN orthogonal matrix and R is an MbyM upper triangular matrix.
Parameters:

M
M is INTEGER The number of rows of the matrix A. M >= 0.
NN is INTEGER The number of columns of the matrix A. N >= M.
AA is REAL array, dimension (LDA,N) On entry, the leading MbyN upper trapezoidal part of the array A must contain the matrix to be factorized. On exit, the leading MbyM 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.
LDALDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
TAUTAU is REAL array, dimension (M) The scalar factors of the elementary reflectors.
WORKWORK is REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORKLWORK is 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.
INFOINFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value
Author:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
 April 2012
Contributors:
 A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
Further Details:

The NbyN matrix Z can be computed by Z = Z(1)*Z(2)* ... *Z(M) where each NbyN Z(k) is given by Z(k) = I  tau(k)*v(k)*v(k)**T with v(k) is the kth row vector of the MbyN matrix V = ( I A(:,M+1:N) ) I is the MbyM identity matrix, A(:,M+1:N) is the output stored in A on exit from DTZRZF, and tau(k) is the kth element of the array TAU.
Definition at line 152 of file stzrzf.f.
Author
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