f08ntf generates the complex unitary matrix
which was determined by
f08nsf when reducing a complex general matrix
to Hessenberg form.
f08ntf is intended to be used following a call to
f08nsf, which reduces a complex general matrix
to upper Hessenberg form
by a unitary similarity transformation:
.
f08nsf represents the matrix
as a product of
elementary reflectors. Here
and
are values determined by
f08nvf when balancing the matrix; if the matrix has not been balanced,
and
.
This routine may be used to generate
explicitly as a square matrix.
has the structure:
where
occupies rows and columns
to
.
The computed matrix
differs from an exactly unitary matrix by a matrix
such that
where
is the
machine precision.
Background information to multithreading can be found in the
Multithreading documentation.
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
f08nff.
This example computes the Schur factorization of the matrix
, where
Here
is general and must first be reduced to Hessenberg form by
f08nsf. The program then calls
f08ntf to form
, and passes this matrix to
f08psf which computes the Schur factorization of
.