Variable and Polyhedron dimension
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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)?
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
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 -----BEGIN PGP SIGNATURE----- Version: GnuPG/MacGPG2 v2.0.22 (Darwin) Comment: GPGTools - https://gpgtools.org Comment: Using GnuPG with Thunderbird - http://www.enigmail.net/
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participants (2)
-
Enea Zaffanella -
Stefan Schupp