Oracles + python

[van51]

Added membership and boundary oracles, as well as python support for them and HPolytopes.

[vissarion]

Thanks for the PR!

I tried to compiled it locally but with no success. After adding a few missing includes in the python\compile script by first adding the corresponding libraries to external i.e. -I../external/faiss -I../external/Eigen -I/usr/include/python2.7 -I../external/pybind11/include I got a linking error /usr/bin/ld: cannot find -lfaiss.

Is faiss needed to use the new functionality? When removing it from compile script (remove -DUSE_FAISS and -lfaiss from g++ command I got the following errors

volesti_pybind11.cpp:60:22: error: ‘Polytope {aka class HPolytope<point<Cartesian<float> > >}’ has no member named ‘contains_point’
             return p.contains_point((NT* ) point_info.ptr);
                      ^~~~~~~~~~~~~~
In file included from volesti_pybind11.cpp:7:0:
volume_approximation/include/convex_bodies/polytopes.h: In instantiation of ‘Point HPolytope<Point>::compute_boundary_intersection(Point&, Point&, float, int) [with Point = point<Cartesian<float> >]’:
volesti_pybind11.cpp:99:100:   required from here
volume_approximation/include/convex_bodies/polytopes.h:227:46: error: ‘get_nearest_facet’ was not declared in this scope
             long nn_index = get_nearest_facet(x0.data());

A clear way of checking if your new feature compiles/passes tests is to add some commands here: https://github.com/van51/volume_approximation/blob/R_volesti/.circleci/config.yml and see if it compiles/passes the tests. In my machine all old tests are passed so there are no regressions, which is good.

[van51]

FAISS is needed for this functionality. I didn't want to add it to the externals directory as it would make the repo much larger unnecessarily. So for now I just assumed that it would be installed in the user's system. Alternatives would be:

• To use it as a submodule (same could be done for some other libs in externals as well)
• To have a download script

[vissarion]

Thanks for the python2 support!

With the following diff I managed to compile and run the tests locally

diff --git a/python/compile b/python/compile
index 60fb188..33ec222 100755
--- a/python/compile
+++ b/python/compile
@@ -4,7 +4,8 @@ IFS=$'\n'
 names=($(readlink -f ../include/*/))
 # Restore IFS
 IFS=$SAVEIFS
-includes='-I../include -I../external/LPsolve_src/run_headers -I../external/boost -I../external '
+includes='-I../include -I../external/LPsolve_src/run_headers -I../external/boost -I../external 
+-I../external/Eigen '
 for (( i=0; i<${#names[@]}; i++ ))
 do
     includes+="-I${names[$i]} "
diff --git a/python/volesti_pybind11.cpp b/python/volesti_pybind11.cpp
index 998bf50..7e18fab 100644
--- a/python/volesti_pybind11.cpp
+++ b/python/volesti_pybind11.cpp
@@ -3,7 +3,7 @@
 #include "cartesian_kernel.h"
 #include "solve_lp.h"
 #include "pybind11/numpy.h"
-#include <eigen3/Eigen/Eigen>
+#include <Eigen/Eigen>
 #include "polytopes.h"
 #include <iostream>

Did you assume eigen3 installation? There is also a comment on the code.
I am ok with merging when those minor fixes are done. @TolisChal what do you think?

[vissarion]

Why not iterators?