Added show option to DiscreteBelief and extended SparseCat

[dylan-asmar]

I found myself converting DiscreteBeliefs to SparseCat distributions often so I could visualize the distribution using the default UnicodePlots show function built-in. This change just extends the same show function to DiscreteBelief.

Current:

julia> b = DiscreteBelief(MiniHallway(), [0.1, 0.1, 0.123, 0.4, 0, 0, 0, 0, 0.177, 0.05, 0, 0, 0.05])
DiscreteBelief{MiniHallway, Int64}(MiniHallway(Deterministic{Int64}[Deterministic{Int64}(1), Deterministic{Int64}(2), Deterministic{Int64}(7), Deterministic{Int64}(4), Deterministic{Int64}(1), Deterministic{Int64}(10), Deterministic{Int64}(1), Deterministic{Int64}(8), Deterministic{Int64}(9), Deterministic{Int64}(10), Deterministic{Int64}(13), Deterministic{Int64}(8), Deterministic{Int64}(13)]), [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], [0.1, 0.1, 0.123, 0.4, 0.0, 0.0, 0.0, 0.0, 0.177, 0.05, 0.0, 0.0, 0.05])

New:

julia> b = DiscreteBelief(MiniHallway(), [0.1, 0.1, 0.123, 0.4, 0, 0, 0, 0, 0.177, 0.05, 0, 0, 0.05])
              MiniHallway DiscreteBelief         
      ┌                                        ┐ 
    1 ┤■■■■■■■■■ 0.1                             
    2 ┤■■■■■■■■■ 0.1                             
    3 ┤■■■■■■■■■■■ 0.123                         
    4 ┤■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■ 0.4   
    5 ┤ 0                                        
    6 ┤ 0                                        
    7 ┤ 0                                        
    8 ┤ 0                                        
    9 ┤■■■■■■■■■■■■■■■ 0.177                     
   10 ┤■■■■ 0.05                                 
   11 ┤ 0                                        
   12 ┤ 0                                        
   13 ┤■■■■ 0.05                                 
      └              

I have also found myself converting from DiscreteBeliefs to SparseCats for various reasons (probably not great ones outside of visualizations...but they existed). I added a constructor for SparseCat that accepts a DiscreteBelief as the input instead of the names and probabilities.

Current:

julia> SparseCat(b)
ERROR: MethodError: no method matching SparseCat(::DiscreteBelief{MiniHallway, Int64})

Closest candidates are:
  SparseCat(::Any, ::AbstractArray{<:Number})
   @ POMDPTools ~/.julia/packages/POMDPTools/7Rekv/src/POMDPDistributions/sparse_cat.jl:26
  SparseCat(::Any, ::AbstractArray)
   @ POMDPTools ~/.julia/packages/POMDPTools/7Rekv/src/POMDPDistributions/sparse_cat.jl:16
  SparseCat(::V, ::P) where {V, P}
   @ POMDPTools ~/.julia/packages/POMDPTools/7Rekv/src/POMDPDistributions/sparse_cat.jl:11

New:

julia> SparseCat(b)
                SparseCat distribution           
      ┌                                        ┐ 
    1 ┤■■■■■■■■■ 0.1                             
    2 ┤■■■■■■■■■ 0.1                             
    3 ┤■■■■■■■■■■■ 0.123                         
    4 ┤■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■ 0.4   
    9 ┤■■■■■■■■■■■■■■■ 0.177                     
   10 ┤■■■■ 0.05                                 
   13 ┤■■■■ 0.05                                 
      └                   

julia> SparseCat(b; check_zeros=false)
                SparseCat distribution           
      ┌                                        ┐ 
    1 ┤■■■■■■■■■ 0.1                             
    2 ┤■■■■■■■■■ 0.1                             
    3 ┤■■■■■■■■■■■ 0.123                         
    4 ┤■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■ 0.4   
    5 ┤ 0                                        
    6 ┤ 0                                        
    7 ┤ 0                                        
    8 ┤ 0                                        
    9 ┤■■■■■■■■■■■■■■■ 0.177                     
   10 ┤■■■■ 0.05                                 
   11 ┤ 0                                        
   12 ┤ 0                                        
   13 ┤■■■■ 0.05                                 
      └                 

Other changes in the files is just removing whitespace.

[zsunberg]

@dylan-asmar this is really great! Thank you for the contribution! Thanks especially for adding tests.

If you want to continue this, it might be nice to get convert(SparseCat, b) to work too.

(btw, in general it is better to avoid adding whitespace changes to PRs (unless the PR is about whitespace changes), but I know that sometimes editors do that automatically, so it is difficult to avoid)

[dylan-asmar]

@zsunberg , I was implementing convert like you mentioned, but stumbled upon

Conversion vs. Construction
Note that the behavior of convert(T, x) appears to be nearly identical to T(x). Indeed, it usually is. However, there is a key semantic difference: since convert can be called implicitly, its methods are restricted to cases that are considered "safe" or "unsurprising". convert will only convert between types that represent the same basic kind of thing (e.g. different representations of numbers, or different string encodings). It is also usually lossless; converting a value to a different type and back again should result in the exact same value.

in the Julia documentation. DiscreteBelief has a reference to the pomdp as one of its fields. Therefore, when we create a SparseCat out of it, it drops this information. So this process feels more like a construction to me than a conversion.

Thoughts?

[zsunberg]

@dylan-asmar This is a good question to ask.

I would consider conversion between DiscreteBelief and SparseCat to be conceptually lossless because the only function of the pomdp in DiscreteBeleif is looking up the state index (I think). According to the distribution interface (i.e. rand, pdf, etc.), the two distributions would behave exactly the same (except for maybe wrt the random number seed).

Unfortunately, right now it is impossible convert a SparseCat to a DiscreteBelief since you need a pomdp to construct the DiscreteBelief. However, it would be relatively easy to generalize DiscreteBelief to not need the pomdp by changing the pomdp field to a state index lookup function that defaults to s -> stateindex(pomdp, s). (there may be other factors that I am not seeing)

In any case, even if we don't modify DiscreteBelief, I think it does make sense to have a convert method for DiscreteBelief to SparseCat.