f08ftf generates the complex unitary matrix
, which was determined by
f08fsf when reducing a Hermitian matrix to tridiagonal form.
f08ftf is intended to be used after a call to
f08fsf, which reduces a complex Hermitian matrix
to real symmetric tridiagonal form
by a unitary similarity transformation:
.
f08fsf represents the unitary matrix
as a product of
elementary reflectors.
The computed matrix
differs from an exactly unitary matrix by a matrix
such that
where
is the
machine precision.
Please consult the
X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.
The real analogue of this routine is
f08fff.
This example computes all the eigenvalues and eigenvectors of the matrix
, where
Here
is Hermitian and must first be reduced to tridiagonal form by
f08fsf. The program then calls
f08ftf to form
, and passes this matrix to
f08jsf which computes the eigenvalues and eigenvectors of
.