F08GUF (ZUPMTR) multiplies an arbitrary complex matrix
C by the complex unitary matrix
Q which was determined by
F08GSF (ZHPTRD) when reducing a complex Hermitian matrix to tridiagonal form.
F08GUF (ZUPMTR) 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 elementary reflectors.
This routine may be used to form one of the matrix products
overwriting the result on
C (which may be any complex 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 real analogue of this routine is
F08GGF (DOPMTR).
This example computes the two smallest eigenvalues, and the associated eigenvectors, of the matrix
A, where
using packed storage. Here
A is Hermitian and must first be reduced to tridiagonal form
T by
F08GSF (ZHPTRD). The program then calls
F08JJF (DSTEBZ) to compute the requested eigenvalues and
F08JXF (ZSTEIN) to compute the associated eigenvectors of
T. Finally F08GUF (ZUPMTR) is called to transform the eigenvectors to those of
A.