F08FTF (ZUNGTR) generates the complex unitary matrix
Q, which was determined by
F08FSF (ZHETRD) when reducing a Hermitian matrix to tridiagonal form.
F08FTF (ZUNGTR) is intended to be used after a call to
F08FSF (ZHETRD), which reduces a complex Hermitian matrix
A to real symmetric tridiagonal form
T by a unitary similarity transformation:
A=QTQH.
F08FSF (ZHETRD) 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
F08FFF (DORGTR).
This example computes all the eigenvalues and eigenvectors of the matrix
A, where
Here
A is Hermitian and must first be reduced to tridiagonal form by
F08FSF (ZHETRD). The program then calls F08FTF (ZUNGTR) to form
Q, and passes this matrix to
F08JSF (ZSTEQR) which computes the eigenvalues and eigenvectors of
A.