I’ve just finished PolyhedralCubature.jl, a package allowing to evaluate the multiple integral of a function over a convex polytope, given by linear inequalities such as:
It remains to improve the doc. I also implemented this method in R and Python.
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Thanks. I didn’t look at the output yet ^^
It would be nice to remove the dependency on Polyhedra.jl. Perhaps you could obtain the v-representation yourself? Or is it too much work?
It’s a hard problem of computational geometry I think. Why would it be nice to remove this package?
This would be a nice to have.
I have such a feature in R and Python, but not in Julia yet.
It would be nice for users who cannot afford a heavy dependency. For example, we have similar integration features in our GeoStats.jl stack and would benefit from a well-tested package for integration over polytopes.
In Python and R, I get the V-representation with the help of the C library cddlib. I think it is also used by Polyhedra, via CDDLib.jl. I’m not aware of another available implementation.
Got it. I wish I had the time to read the original papers describing the methods. I am assuming that it is an optimization problem that can be formulated and solved with native Julia packages.
Perhaps. And I don’t need the sense V -> H. Moreover I need H -> V in the polytope case only, without rays and lines. So maybe that’s not so difiicult.
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