Julia:序列的向量化乘积

Question

学习从Python传递到Julia，我正在尝试转换我拥有的旧代码，也就是计算这个表达式的序列的乘积：

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我用Python语言编写了两个版本的代码，一个使用for循环实现，另一个使用广播。for循环版本为：

import numpy as np
A = np.arange(1.,5.,1)
G = np.array([[1.,2.],[3.,4.]])

def calcF(G,A):
    N = A.size
    print A
    print N
    F = []
    for l in range(N):
        F.append(G/A[l])
        print F[l]
        for j in range(N):
            if j != l:
                F[l]*=((G - A[l])/(G + A[j]))*((A[l] - A[j])/(A[l] + A[j]))
    return F

F= calcF(G,A)
print F

我从我的问题here的回答中了解到的矢量化版本是这个函数：

def calcF_vectorized(G,A):
    # Get size of A
    N = A.size

    # Perform "(G - A[l])/(G + A[j]))" in a vectorized manner
    p1 = (G - A[:,None,None,None])/(G + A[:,None,None])

    # Perform "((A[l] - A[j])/(A[l] + A[j]))" in a vectorized manner
    p2 = ((A[:,None] - A)/(A[:,None] + A))

    # Elementwise multiplications between the previously calculated parts
    p3 = p1*p2[...,None,None]

    # Set the escaped portion "j != l" output as "G/A[l]"
    p3[np.eye(N,dtype=bool)] = G/A[:,None,None]

    Fout = p3.prod(1)

    # If you need separate arrays just like in the question, split it
    return np.array_split(Fout,N)

我尝试天真地将Python for循环代码翻译成Julia：

function JuliacalcF(G,A)
    F = Array{Float64}[]
    for l in eachindex(A)
        push!(F,G/A[l])
        println(A[i])
        for j in eachindex(A)
            if j!=l
                F[l]*=((G - A[l])/(G + A[j]))*((A[l] - A[j])/(A[l] + A[j]))
            end
        end
    end
    #println(alpha)
    return F
end
A = collect(1.0:1.0:5.0)
G = Vector{Float64}[[1.,2.],[3.,4.]]
println(JuliacalcF(G,A))

但是，有没有办法像numpy广播矢量化版本那样聪明地做到这一点呢？

Answer 1

此外，还可以查看More-Dots和Loop Fusion，其中通过示例描述了矢量化。