F08GGF (DOPMTR) multiplies an arbitrary real matrix
C by the real orthogonal matrix
Q which was determined by
F08GEF (DSPTRD) when reducing a real symmetric matrix to tridiagonal form.
F08GGF (DOPMTR) 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 elementary reflectors.
This routine may be used to form one of the matrix products
overwriting the result on
C (which may be any real rectangular matrix).
Golub G H and Van Loan C F (1996)
Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore
The computed result differs from the exact result by a matrix
E such that
where
ε is the
machine precision.
The complex analogue of this routine is
F08GUF (ZUPMTR).
This example computes the two smallest eigenvalues, and the associated eigenvectors, of the matrix
A, where
using packed storage. Here
A is symmetric and must first be reduced to tridiagonal form
T by
F08GEF (DSPTRD). The program then calls
F08JJF (DSTEBZ) to compute the requested eigenvalues and
F08JKF (DSTEIN) to compute the associated eigenvectors of
T. Finally F08GGF (DOPMTR) is called to transform the eigenvectors to those of
A.