nag_dopgtr (f08gfc) generates the real orthogonal matrix
, which was determined by
nag_dsptrd (f08gec) when reducing a symmetric matrix to tridiagonal form.
nag_dopgtr (f08gfc) is intended to be used after a call to
nag_dsptrd (f08gec), which reduces a real symmetric matrix
to symmetric tridiagonal form
by an orthogonal similarity transformation:
.
nag_dsptrd (f08gec) represents the orthogonal matrix
as a product of
elementary reflectors.
The computed matrix
differs from an exactly orthogonal 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 complex analogue of this function is
nag_zupgtr (f08gtc).
This example computes all the eigenvalues and eigenvectors of the matrix
, where
using packed storage. Here
is symmetric and must first be reduced to tridiagonal form by
nag_dsptrd (f08gec). The program then calls
nag_dopgtr (f08gfc) to form
, and passes this matrix to
nag_dsteqr (f08jec) which computes the eigenvalues and eigenvectors of
.