[PPL-devel] Variable and Polyhedron dimension

[Enea Zaffanella]

On 04/04/2014 05:02 PM, Stefan Schupp wrote:
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> I am starting to use the PPL for a project dealing with state set
> representations for hybrid systems. I have a question regarding the
> dimension of polyhedra and variables. From what I can conclude, each
> variable can be assigned to a coordinate axis. Suppose I utilize 4
> variables with each assigned to a different dimension:
>
> Variable a(0);
> Variable b(1);
> Variable c(2);
> Variable d(3);
>
> When I construct a polytope with the first two variables, it has a
> dimension of 2, as intended. When creating the same polytope with
> other variables (e.g. c and d), I get a dimension > 2 (in this case
> 4). Is it intended to return the dimension of the variable assigned to
> the "latest/largest" coordinate axis, although the number of used
> variables/dimensions might be smaller than the returned value (the
> polytope still uses only 2 variables)?

Hello Stefan.

Variable are just "names" of space dimensions.
For a polyhedron or other PPL entity of space dimension k,
its set of space dimensions is { i \in N | i < k }.
So if you put Variable d (naming space dimension 3) in a 
constraint/generator,
you will obtain a constraint/generator having space dimension 4.
Namely,
    a + 3*b >= 0    is a constraint having space dimension 2
whereas
    c + 3*d >= 0    is a constraint having space dimension 4.
Also note that
    a + 0*d >= 0    would also have space dimension 4
(the fact that the coefficient for d is zero does not matter).

Hope this helps; if you need more details, take a look to the documentation.

Regads,
Enea.


> Best regards,
> Stefan
>
> - -- 
> Stefan Schupp M.Sc.
> RWTH Aachen University
> Computer Science Department, Informatik 2
> D-52056 Aachen, Germany
> http://www-i2.informatik.rwth-aachen.de/i2/schupp/
> Tel.: +49 241 80 21243
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