
dtzrzf.f(3) LAPACK dtzrzf.f(3)
NAME
dtzrzf.f 
SYNOPSIS
Functions/Subroutines
subroutine dtzrzf (M, N, A, LDA, TAU, WORK, LWORK, INFO)
DTZRZF
Function/Subroutine Documentation
subroutine dtzrzf (integerM, integerN, double precision, dimension( lda, * )A, integerLDA,
double precision, dimension( * )TAU, double precision, dimension( * )WORK, integerLWORK,
integerINFO)
DTZRZF
Purpose:
DTZRZF 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.
N
N is INTEGER
The number of columns of the matrix A. N >= M.
A
A is DOUBLE PRECISION 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.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU
TAU is DOUBLE PRECISION array, dimension (M)
The scalar factors of the elementary reflectors.
WORK
WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK
LWORK 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.
INFO
INFO 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 dtzrzf.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 dtzrzf.f(3) 
