implement faster issubset for CartesianIndices{N}

[xili-h]

No description provided.

[Seelengrab]

Do you have some benchmarks showing a performance improvement?

[xili-h]

Do you have some benchmarks showing a performance improvement?

[xili-h]

For 1D, it is also faster.

[LilithHafner]

Thanks for looking into this, @xili-h! This is a good specialization to have.

This clearly has higher performance than the generic fallback, especially because the indices themselves have O(1) subset checking.

However, there's a correctness problem: if the first argument is empty, then it is always a subset, even if some of its indices are not subsets because there are no elements to witness that axis being larger:

julia> a = CartesianIndices((0, 1))
CartesianIndices((0, 1))

julia> b = CartesianIndices((1,0))
CartesianIndices((1, 0))

julia> issubset(a, b)
true

julia> _issubset(a::CartesianIndices{N}, b::CartesianIndices{N}) where N =
           all(map(issubset, a.indices, b.indices))
_issubset (generic function with 2 methods)

julia> _issubset(a,b)
false

julia> _issubset2(a::CartesianIndices{N}, b::CartesianIndices{N}) where N =
           isempty(a) || all(map(issubset, a.indices, b.indices))
_issubset2 (generic function with 1 method)

julia> _issubset2(a,b)
true

As an aside, I prefer if you paste results as text rather than screenshots because that makes it easier for folks to copy your code and reproduce it locally.

[xili-h]

Thanks for looking into this, @xili-h! This is a good specialization to have.

This clearly has higher performance than the generic fallback, especially because the indices themselves have O(1) subset checking.

However, there's a correctness problem: if the first argument is empty, then it is always a subset, even if some of its indices are not subsets because there are no elements to witness that axis being larger:

julia> a = CartesianIndices((0, 1))
CartesianIndices((0, 1))

julia> b = CartesianIndices((1,0))
CartesianIndices((1, 0))

julia> issubset(a, b)
true

julia> _issubset(a::CartesianIndices{N}, b::CartesianIndices{N}) where N =
           all(map(issubset, a.indices, b.indices))
_issubset (generic function with 2 methods)

julia> _issubset(a,b)
false

julia> _issubset2(a::CartesianIndices{N}, b::CartesianIndices{N}) where N =
           isempty(a) || all(map(issubset, a.indices, b.indices))
_issubset2 (generic function with 1 method)

julia> _issubset2(a,b)
true

As an aside, I prefer if you paste results as text rather than screenshots because that makes it easier for folks to copy your code and reproduce it locally.

Thanks @LilithHafner. I have fix the problem base on your suggestion. I will paste results as text next time.

[LilithHafner]

Thanks!