F08GFF (DOPGTR) generates the real orthogonal matrix
Q, which was determined by
F08GEF (DSPTRD) when reducing a symmetric matrix to tridiagonal form.
F08GFF (DOPGTR) is intended to be used after a call to
F08GEF (DSPTRD), which reduces a real symmetric matrix
A to symmetric tridiagonal form
T by an orthogonal similarity transformation:
A=QTQT.
F08GEF (DSPTRD) represents the orthogonal 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 orthogonal matrix by a matrix
E such that
where
ε is the
machine precision.
The complex analogue of this routine is
F08GTF (ZUPGTR).
This example computes all the eigenvalues and eigenvectors of the matrix
A, where
using packed storage. Here
A is symmetric and must first be reduced to tridiagonal form by
F08GEF (DSPTRD). The program then calls F08GFF (DOPGTR) to form
Q, and passes this matrix to
F08JEF (DSTEQR) which computes the eigenvalues and eigenvectors of
A.