f08afc generates all or part of the real orthogonal matrix
from a
factorization computed by
f08aec or
f08bfc.
f08afc is intended to be used after a call to
f08aec or
f08bfc.
which perform a
factorization of a real matrix
. The orthogonal matrix
is represented as a product of elementary reflectors.
Usually
is determined from the
factorization of an
matrix
with
. The whole of
may be computed by
:
nag_lapackeig_dorgqr(order,m,m,p,a,pda,tau,&fail)
(note that the array
a must have at least
columns)
or its leading
columns by
:
nag_lapackeig_dorgqr(order,m,p,p,a,pda,tau,&fail)
The columns of
returned by the last call form an orthonormal basis for the space spanned by the columns of
; thus
f08aec followed by
f08afc can be used to orthogonalize the columns of
.
The information returned by the
factorization functions also yields the
factorization of the leading
columns of
, where
. The orthogonal matrix arising from this factorization can be computed by
:
nag_lapackeig_dorgqr(order,m,m,k,a,pda,tau,&fail)
or its leading
columns by
:
nag_lapackeig_dorgqr(order,m,k,k,a,pda,tau,&fail)
The computed matrix
differs from an exactly orthogonal matrix by a matrix
such that
where
is the
machine precision.
Background information to multithreading can be found in the
Multithreading documentation.
Please consult the
X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.
The complex analogue of this function is
f08atc.
This example forms the leading
columns of the orthogonal matrix
from the
factorization of the matrix
, where
The columns of
form an orthonormal basis for the space spanned by the columns of
.