#342 - Add caching lazy MinkowskiSum

[schillic]

Closes #342.

[schillic]

julia> using LazySets

julia> cms = CacheMinkowskiSum(5);

julia> X1 = BallInf(ones(3), 3.);

julia> X2 = BallInf(ones(3), 5.);

julia> X3 = Ball1(ones(3), 5.);

julia> d = ones(3);

julia> a = array(cms);

julia> 

julia> push!(a, X1);

julia> @time σ(d, cms);
  0.000027 seconds (25 allocations: 1.500 KiB)

julia> @time σ(d, cms);
  0.000012 seconds (12 allocations: 608 bytes)

julia> @time σ(d, cms);
  0.000011 seconds (12 allocations: 608 bytes)

julia> 

julia> push!(a, X2);

julia> @time σ(d, cms);
  0.000019 seconds (27 allocations: 1.656 KiB)

julia> @time σ(d, cms);
  0.000012 seconds (12 allocations: 608 bytes)

julia> @time σ(d, cms);
  0.000010 seconds (12 allocations: 608 bytes)

julia> 

julia> for i = 1 : 1000
           push!(a, X3);
       end

julia> @time σ(d, cms);
  0.000160 seconds (3.02 k allocations: 329.469 KiB)

julia> @time σ(d, cms);
  0.000023 seconds (13 allocations: 624 bytes)

julia> @time σ(d, cms);
  0.000015 seconds (13 allocations: 624 bytes)

julia> 

julia> for i = 1 : 1000
           push!(a, X3);
       end

julia> @time σ(d, cms);
  0.000159 seconds (3.03 k allocations: 329.484 KiB)

julia> @time σ(d, cms);
  0.000028 seconds (13 allocations: 624 bytes)

julia> @time σ(d, cms);
  0.000011 seconds (13 allocations: 624 bytes)

julia> msa = MinkowskiSumArray(5);

julia> a2 = array(msa);

julia> push!(a2, X1);

julia> push!(a2, X2);

julia> for i = 1 : 1000
           push!(a2, X3);
       end

julia> @time σ(d, msa);
  0.000162 seconds (3.02 k allocations: 329.547 KiB)

julia> @time σ(d, msa);
  0.000150 seconds (3.02 k allocations: 329.547 KiB)

julia> @time σ(d, msa);
  0.000152 seconds (3.02 k allocations: 329.547 KiB)

julia> for i = 1 : 1000
           push!(a2, X3);
       end

julia> @time σ(d, msa);
  0.000274 seconds (6.02 k allocations: 657.672 KiB)

julia> @time σ(d, msa);
  0.000257 seconds (6.02 k allocations: 657.672 KiB)

julia> @time σ(d, msa);
  0.000989 seconds (6.02 k allocations: 657.672 KiB)

julia> @time σ(d, msa);
  0.000897 seconds (6.02 k allocations: 657.672 KiB)

[schillic]

Possible future work: Currently the sum stores all sets, which takes a lot of memory. In applications where we always query the same support vector(s) and then add a new set in a loop, we could also provide a variant that only stores the newest sets.

[mforets]

side comment: we are using floating points vectors as keys, we should be careful about tolerance matters.

[schillic]

That is true, but the directions are always constructed from the same sources at the moment, which is why we get the same numbers every time.

[mforets]

can we add that this is a dictionary whose keys are directions and whose values are tuples (l, s) where l is the number of elements in the array where this function was evaluated last time, and s is the value of the support vector that was obtained

[mforets]

IIUC, only the number of elements is checked, not the actual elements

[schillic]

added 👍

[mforets]

🏆

[mforets]

LGTM