F08GTF (ZUPGTR) generates the complex unitary matrix
Q, which was determined by
F08GSF (ZHPTRD) when reducing a Hermitian matrix to tridiagonal form.
F08GTF (ZUPGTR) is intended to be used after a call to
F08GSF (ZHPTRD), which reduces a complex Hermitian matrix
A to real symmetric tridiagonal form
T by a unitary similarity transformation:
A=QTQH.
F08GSF (ZHPTRD) represents the unitary matrix
Q as a product of
n-1 elementary reflectors.
Golub G H and Van Loan C F (1996)
Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore
The computed matrix
Q differs from an exactly unitary matrix by a matrix
E such that
where
ε is the
machine precision.
The real analogue of this routine is
F08GFF (DOPGTR).
This example computes all the eigenvalues and eigenvectors of the matrix
A, where
using packed storage. Here
A is Hermitian and must first be reduced to tridiagonal form by
F08GSF (ZHPTRD). The program then calls F08GTF (ZUPGTR) to form
Q, and passes this matrix to
F08JSF (ZSTEQR) which computes the eigenvalues and eigenvectors of
A.