f08guf multiplies an arbitrary complex matrix
by the complex unitary matrix
which was determined by
f08gsf when reducing a complex Hermitian matrix to tridiagonal form.
f08guf is intended to be used after a call to
f08gsf, which reduces a complex Hermitian matrix
to real symmetric tridiagonal form
by a unitary similarity transformation:
.
f08gsf represents the unitary 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 complex rectangular matrix).
The computed result differs from the exact result 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 routine. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.
The real analogue of this routine is
f08ggf.
This example computes the two smallest eigenvalues, and the associated eigenvectors, of the matrix
, where
using packed storage. Here
is Hermitian and must first be reduced to tridiagonal form
by
f08gsf. The program then calls
f08jjf to compute the requested eigenvalues and
f08jxf to compute the associated eigenvectors of
. Finally
f08guf is called to transform the eigenvectors to those of
.