Re: [eigen] Eigen "views"

[Christoph Hertzberg <chtz@xxxxxxxxxxxxxxxxxxxxxxxx>]

On 16.08.2011 08:41, Gael Guennebaud wrote:
> there are some major differences though:
>
> With PermutationMatrix you can do transposed products.
>
> With such views you can repeat a row (or column) multiple times,
> remove some, etc.
>
> The conclusion is that though there is a non null intersection none of
> them is a subset of the other one.

Maybe I'm missing something, but I would say this means that permutation 
matrices _are_ a subset of views. I guess internally you store 
permutation matrices exactly as you would store views, i.e. by a vector 
of indexes, don't you?

I would even say that (in a limited way) transposed products with views 
are also possible. Having a permutation matrix P, with corresponding 
indexes p (P = I(:,p);) one can write in Matlab notation:

B = A*P,  or B     = A(:,p);
B = A*P', or B(:,p)= A;
B = P*A,  or B(p,:)= A;
B = P'*A, or B     = A(p,:);

assuming all dimensions agree, and I did not mix anything up.
That means at least the expressions A*P and P'*A are equivalent if P is 
just a view.
The question would be what should happen with expressions such as
B(:,p) = ...;
if indexes in p are not unique. Matlab, as it seems, then uses the last 
corresponding entry of p, i.e., it basically just overwrites the 
row/column every time.


Christoph


--
----------------------------------------------
Dipl.-Inf. Christoph Hertzberg
Cartesium 0.051
Universität Bremen
Enrique-Schmidt-Straße 5
28359 Bremen

Tel: (+49) 421-218-64252
----------------------------------------------