nag_zupgtr (f08gtc) generates the complex unitary matrix
, which was determined by
nag_zhptrd (f08gsc) when reducing a Hermitian matrix to tridiagonal form.
nag_zupgtr (f08gtc) is intended to be used after a call to
nag_zhptrd (f08gsc), which reduces a complex Hermitian matrix
to real symmetric tridiagonal form
by a unitary similarity transformation:
.
nag_zhptrd (f08gsc) represents the unitary matrix
as a product of
elementary reflectors.
The computed matrix
differs from an exactly unitary matrix 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 function. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.
The real analogue of this function is
nag_dopgtr (f08gfc).
This example computes all the eigenvalues and eigenvectors of the matrix
, where
using packed storage. Here
is Hermitian and must first be reduced to tridiagonal form by
nag_zhptrd (f08gsc). The program then calls
nag_zupgtr (f08gtc) to form
, and passes this matrix to
nag_zsteqr (f08jsc) which computes the eigenvalues and eigenvectors of
.