Sparse optimizations for UniformABW sampling

[lucaperju]

optimized the complexity of the reflection when the A matrix is sparse

Sampled 1000 points from the same order polytope with the same seed using both sparse and dense abw, here are the last 2 points:
Dense:
0.947133 0.13444 0.417853 0.499325 0.995814 0.775422 0.728527 0.715522 0.0377974 0.428896
0.708553 0.119995 0.224509 0.549352 0.919391 0.649939 0.648627 0.55607 0.0863634 0.500581

Sparse:
0.947133 0.13444 0.417853 0.499325 0.995814 0.775422 0.728527 0.715522 0.0377974 0.428896
0.708553 0.119995 0.224509 0.549352 0.919391 0.649939 0.648627 0.55607 0.0863634 0.500581

points_sparse.txt
points_dense.txt

[TolisChal]

Do we need these lines?

[TolisChal]

Does it make sense to rename it to BoundaryOracleHeap?

[TolisChal]

since be the vector b doesn't change, why don't you initialize the b_data before the loop?

[TolisChal]

Could you please add a few lines of comments to briefly explain what does this data structure does?
You could add what is the improvement it gives regarding the previous implementation.
Don't be afraid to add some equations to help your explanation, e.g., how Av and Ar are updated now etc.

[TolisChal]

Hi @lucaperju! This is a really high quality PR! Thanks a lot!

1. I left a few comments on your changes.
2. Could you please copy paste in the description of this PR the results of an example that shows that the new implementation gives the same result with the previous one? For example, fix the seed and sample 1000 points from a 10-th dimensional order polytope with the current implementation and this new implementation. Print the last 10 points sampled from each polytope to the description of this PR. Also attach the txt files that contain the samples and add a script (in any programming language) that does an epsilon equality check for all points. Does this make sense?

[codecov]

Codecov Report

Attention: Patch coverage is 75.23810% with 26 lines in your changes missing coverage. Please review.

Project coverage is 57.32%. Comparing base (d424f3e) to head (fe5641d).

Files	Patch %	Lines
...random_walks/uniform_accelerated_billiard_walk.hpp	74.69%	4 Missing and 17 partials ⚠️
include/convex_bodies/hpolytope.h	77.27%	0 Missing and 5 partials ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##           develop     #329      +/-   ##
===========================================
+ Coverage    56.95%   57.32%   +0.37%     
===========================================
  Files          114      114              
  Lines         7155     7241      +86     
  Branches      3215     3236      +21     
===========================================
+ Hits          4075     4151      +76     
+ Misses         978      976       -2     
- Partials      2102     2114      +12     

Files	Coverage Δ
include/preprocess/rounding_util_functions.hpp	58.62% <ø> (ø)
...andom_walks/gaussian_accelerated_billiard_walk.hpp	61.47% <ø> (ø)
include/convex_bodies/hpolytope.h	76.64% <77.27%> (+1.24%)	⬆️
...random_walks/uniform_accelerated_billiard_walk.hpp	64.84% <74.69%> (+8.84%)	⬆️

... and 2 files with indirect coverage changes

[TolisChal]

please use scientifuc notation of const double eps = 1e-XY