DTZRZF doc

[themos]

Hello

Reading "Further details" in the source for DTZRZF, I think the explanation there is quite confusing and possibly wrong. I am just trying to understand how to build up Z from the elements of a on exit:

I would start with the column vectors u(k), k=1..m, each of length n, and specify their components as, from top to bottom:

0 of length (k-1), (if length is zero then this is absent)
1,
0 of length (m-k), (if length is zero then this is absent)
z of length(n-m) = a(k,m+1:n) (on exit)

Then , the Z(k) matrices are built up as 1 - tau(k)*u(k)*u(k)'
where ' means transposed.

And Z is built up as Z(1)*Z(2)*...*Z(m)

Best Regards
Themos Tsikas

[rodney]

Hello Themos,

You are correct, the "Further details" section for DTZRZF is not very clear, thanks for pointing this out.

The N-by-N matrix Z can be computed by:

Z = Z(1)*Z(2)* ... *Z(M)

where each N-by-N Z(k) is given by

Z(k) = I - tau(k)*v(k)*v(k)**T

where I is the N-by-N identity, v(k) is the kth row vector of the M-by-N matrix

V = ( I A(:,M+1:N) )

where this I is the M-by-M identity matrix, A(:,M+1:N) is the output stored in A on exit from DTZRZF,
and tau(k) is the kth element of the array TAU.

I hope this helps.

Rodney