Finding the vertices of a hypercube

New to Julia
1

I defined a data structure to represent a hypercube. It is defined by the min and max bounds on each dimension.

struct HyperCube 
    min_bounds::Array{Float32}
    max_bounds::Array{Float32}
end

Now, I want to define a function that returns all the vertices.
In Python, I would have done:
return list(product(*zip(self.min_bounds, self.max_bounds)))

I am wondering what would be the most elegant way to do this in Julia.

3

Thanks for the response. It is missing the zip part. The Python implementation would return the below list for the example:

[(1, 2, 3),
 (1, 2, 6),
 (1, 5, 3),
 (1, 5, 6),
 (4, 2, 3),
 (4, 2, 6),
 (4, 5, 3),
 (4, 5, 6)]

Please note that, in HyperCube([1, 2, 3], [4, 5, 6]) , there are three dimensions. The cube covers [1,4] in the first dimension, [2,5] in the second dimension, and so on.

4

I was stuck for sometime on how to do the Python’s f(*args) in Julia and then figured out:

collect(Iterators.product(zip(box.min_bounds, box.max_bounds)...))

I hope this works.

5

Note that you want Vector not Array here. Otherwise it’s an abstract type since you don’t appreciate the number of dimensions.

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6

Iterators.product returns multi-dimensional object. You can add vec to flatten it

julia> vec(collect(Iterators.product(zip(box.min_bounds, box.max_bounds)...)))
8-element Vector{Tuple{Float32, Float32, Float32}}:
 (1.0, 2.0, 3.0)
 (4.0, 2.0, 3.0)
 (1.0, 5.0, 3.0)
 (4.0, 5.0, 3.0)
 (1.0, 2.0, 6.0)
 (4.0, 2.0, 6.0)
 (1.0, 5.0, 6.0)
 (4.0, 5.0, 6.0)
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7

If you are worried about performance, I would also strongly consider using SVector from StaticArrays.jl here, at least if you are in low (< 20) dimensions, and anywhere you are using low-dimensional vectors in a fixed number of dimensions. (e.g. HCubature.jl does something similar for hypercubes.)

4 Likes
8

Apologies.

1 Like
9

Did you mean to have the struct definition as below?

struct HyperCube
    min_bounds::Vector{Float32}
    max_bounds::Vector{Float32}
end
1 Like
10

Yes. Exactly. Vector{Float32} is an alias for Array{Float32,1}

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