f08awc generates all or part of the complex unitary matrix
from an
factorization computed by
f08avc.
f08awc is intended to be used after a call to
f08avc, which performs an
factorization of a complex matrix
. The unitary matrix
is represented as a product of elementary reflectors.
Usually
is determined from the
factorization of a
matrix
with
. The whole of
may be computed by
:
nag_lapackeig_zunglq(order,n,n,p,&a,pda,tau,&fail)
(note that the array
a must have at least
rows)
or its leading
rows by
:
nag_lapackeig_zunglq(order,p,n,p,&a,pda,tau,&fail)
The rows of
returned by the last call form an orthonormal basis for the space spanned by the rows of
; thus
f08avc followed by
f08awc can be used to orthogonalize the rows of
.
The information returned by the
factorization functions also yields the
factorization of the leading
rows of
, where
. The unitary matrix arising from this factorization can be computed by
:
nag_lapackeig_zunglq(order,n,n,k,&a,pda,tau,&fail)
or its leading
rows by
:
nag_lapackeig_zunglq(order,k,n,k,&a,pda,tau,&fail)
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 function. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.
The real analogue of this function is
f08ajc.
This example forms the leading
rows of the unitary matrix
from the
factorization of the matrix
, where
The rows of
form an orthonormal basis for the space spanned by the rows of
.