f01rdf
f01rdf
© Numerical Algorithms Group, 2002.
Purpose
H
F01RDF Operations with unitary matrices, compute QB or Q B after
factorization by F01RCF
Synopsis
[b,ifail] = f01rdf(a,theta,b<,trans,wheret,ifail>)
Description
The unitary matrix Q is assumed to be given by
H
Q=(Q Q ...Q ) ,
n n-1 1
Q being given in the form
k
(I 0 )
Q =(0 T ),
k ( k)
where
H
T =I-(gamma) u u ,
k k k k
((zeta) )
( k)
u =(z ),
k ( k )
(gamma) is a scalar for which Re (gamma) =1.0, (zeta) is a real
k k k
scalar and z is an (m-k) element vector.
k
z must be supplied in the kth column of A in elements
k
a ,...,a and (theta) , given by
k+1,k m,k k
(theta) =((zeta) ,Im (gamma) ),
k k k
must be supplied either in a or in THETA(k), depending upon
k,k
the parameter WHERET.
To obtain Q explicitly B may be set to I and pre-multiplied by Q.
H
This is more efficient than obtaining Q . Alternatively, F01REF
may be used to obtain Q overwritten on A.
Parameters
f01rdf
Required Input Arguments:
a (:,:) complex
theta (:) complex
b (:,:) complex
Optional Input Arguments: <Default>
trans (1) string 'n'
wheret (1) string 's'
ifail integer -1
Output Arguments:
b (:,:) complex
ifail integer