f08fgf multiplies an arbitrary real matrix
by the real orthogonal matrix
which was determined by
f08fef when reducing a real symmetric matrix to tridiagonal form.
f08fgf is intended to be used after a call to
f08fef, which reduces a real symmetric matrix
to symmetric tridiagonal form
by an orthogonal similarity transformation:
.
f08fef represents the orthogonal matrix
as a product of elementary reflectors.
This routine may be used to form one of the matrix products
overwriting the result on
(which may be any real rectangular matrix).
The computed result differs from the exact result by a matrix
such that
where
is the
machine precision.
Please consult the
X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.
The complex analogue of this routine is
f08fuf.
This example computes the two smallest eigenvalues, and the associated eigenvectors, of the matrix
, where
Here
is symmetric and must first be reduced to tridiagonal form
by
f08fef. The program then calls
f08jjf to compute the requested eigenvalues and
f08jkf to compute the associated eigenvectors of
. Finally
f08fgf is called to transform the eigenvectors to those of
.