在 Julia 中制作二维晶格

问题描述

让我们考虑 5 x 5 晶格，每个点的索引为 (1,1),(1,2),...(1,5),(2,1),...,(5,5)，并将这个格子称为 L.

Let us consider 5 x 5 lattice with each point indexed as (1,1),(1,2),...(1,5),(2,1),...,(5,5), and call this lattice L.

我想制作一个 5 x 5 矩阵，每个元素都有一个值，该值指示 L 的每个点，如下所示:

I want to make a 5 x 5 matrix with each element having a value which indicates each point of L like this:

5×5 Matrix{Vector{Int64}}:
 [1, 1]  [1, 2]  [1, 3]  [1, 4]  [1, 5]
 [2, 1]  [2, 2]  [2, 3]  [2, 4]  [2, 5]
 [3, 1]  [3, 2]  [3, 3]  [3, 4]  [3, 5]
 [4, 1]  [4, 2]  [4, 3]  [4, 4]  [4, 5]
 [5, 1]  [5, 2]  [5, 3]  [5, 4]  [5, 5]

我尝试了什么

我刚刚尝试了以下方法:

What I tried

I just tried the following:

X1 = [1,2,3,4,5]
X2 = copy(X1)
Lattice = Matrix{Vector{Int64}}(undef, length(X1), length(X2)) # what I want to make
for x1 in X1
    for x2 in X2
        Lattice[x1,x2] = [X1[x1],X2[x2]]
    end
end

Lattice

问题

• 还有其他方法可以使代码简单或简短吗?
• 如果增加像 50 x 50 这样的晶格尺寸，我担心性能会变差.还有更好的方法吗?
• 有什么更好的做法?

任何信息将不胜感激.

推荐答案

它不是向量矩阵，但 CartesianIndices 服务于这个目的.

It's not a Matrix of Vectors, but CartesianIndices serves this purpose.

L = zeros((5,5)) # example 5x5 Matrix

Li = CartesianIndices(size(L))
#=
5×5 CartesianIndices{2,Tuple{Base.OneTo{Int64},Base.OneTo{Int64}}}:
 CartesianIndex(1, 1)  …  CartesianIndex(1, 5)
 CartesianIndex(2, 1)     CartesianIndex(2, 5)
 CartesianIndex(3, 1)     CartesianIndex(3, 5)
 CartesianIndex(4, 1)     CartesianIndex(4, 5)
 CartesianIndex(5, 1)     CartesianIndex(5, 5)
=#

如果您必须拥有像您的帖子中那样的索引矩阵，您可以创建一个将 CartesianIndex 转换为 Vector 并通过 CartesianIndices 广播该方法的方法:

If you must have the indices matrix like in your post, you could make a method that converts a CartesianIndex to a Vector and broadcast that method over the CartesianIndices:

CItoVector(CI) = collect(Tuple(CI))

CItoVector.(Li)
#=
5×5 Array{Array{Int64,1},2}:
 [1, 1]  [1, 2]  [1, 3]  [1, 4]  [1, 5]
 [2, 1]  [2, 2]  [2, 3]  [2, 4]  [2, 5]
 [3, 1]  [3, 2]  [3, 3]  [3, 4]  [3, 5]
 [4, 1]  [4, 2]  [4, 3]  [4, 4]  [4, 5]
 [5, 1]  [5, 2]  [5, 3]  [5, 4]  [5, 5]
=#

但我建议坚持使用 CartesianIndices，因为它不分配内存，而且 CartesianIndex 是为数组索引量身定制的，这似乎是您的意图.

But I recommend sticking with CartesianIndices because it doesn't allocate memory, and CartesianIndex is tailor-made for array indexing, which seems to be your intent.

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