f08awf generates all or part of the complex unitary matrix
from an
factorization computed by
f08avf.
f08awf is intended to be used after a call to
f08avf, 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
:
Call zunglq(n,n,p,a,lda,tau,work,lwork,info)
(note that the array
a must have at least
rows)
or its leading
rows by
:
Call zunglq(p,n,p,a,lda,tau,work,lwork,info)
The rows of
returned by the last call form an orthonormal basis for the space spanned by the rows of
; thus
f08avf followed by
f08awf can be used to orthogonalize the rows of
.
The information returned by the
factorization routines also yields the
factorization of the leading
rows of
, where
. The unitary matrix arising from this factorization can be computed by
:
Call zunglq(n,n,k,a,lda,tau,work,lwork,info)
or its leading
rows by
:
Call zunglq(k,n,k,a,lda,tau,work,lwork,info)
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
f08ajf.
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
.