如何在Julia中乘以多维数组/矩阵 [英] How to multiply multi-dimensional arrays/matrices in Julia

问题描述

将两个多维数组(例如，一维数组和3维数组)相乘:

Multiplying two multi-dimensional arrays, say, a 1-dimensional with a 3-dimensional array:

[1 2] * reshape(1:8,2,2,2)

给我错误消息:

LoadError: MethodError: `*` has no method matching *(::Array{Int64,2}, ::Array{Int64,3})
Closest candidates are:
  *(::Any, ::Any, !Matched::Any, !Matched::Any...)
  *{TA,TB}(::Union{DenseArray{TA,1},DenseArray{TA,2},SubArray{TA,1,A<:DenseArray{T,N},I<:Tuple{Vararg{Union{Colon,Int64,Range{Int64}}}},LD},SubArray{TA,2,A<:DenseArray{T,N},I<:Tuple{Vararg{Union{Colon,Int64,Range{Int64}}}},LD}}, !Matched::Base.LinAlg.AbstractTriangular{TB,S<:AbstractArray{T,2}})
  *{TA,TQ,N}(::Union{DenseArray{TA,N},SubArray{TA,N,A<:DenseArray{T,N},I<:Tuple{Vararg{Union{Colon,Int64,Range{Int64}}}},LD}}, !Matched::Union{Base.LinAlg.QRCompactWYQ{TQ,M<:AbstractArray{T,2}},Base.LinAlg.QRPackedQ{TQ,S<:AbstractArray{T,2}}})
  ...
while loading In[167], in expression starting on line 1

 in Ac_mul_B at operators.jl:157

使用多维矩阵代数的数学定义对矩阵/数组进行(1 x 2)*(2 x 2 x 2)乘法.

using the math definition of multi-dimensional matrix algebra for a (1 by 2) * (2 by 2 by 2) multiplication of matrices/arrays.

更一般的示例可以是A * B = C，表示sum_k A_ {i，j，k} B_ {k，l，m} = C_ {i，j，l，m}，其中A是3 -index矩阵，或者张量(如果愿意)，B是3索引矩阵，而生成的C是4索引矩阵/张量，但是，通常，可以有任意数量的维度，并且维度可以具有任何大小(在合理范围内).查看有关矩阵产品或

A somewhat more general example can be A*B = C meaning sum_k A_{i,j,k} B_{k,l,m} = C_{i,j,l,m}, where A is a 3-index matrix, or tensor if you like, B is a 3-index one, and the resulting C is a four index matrix/tensor, but, in general, there can be any number of dimensions and a dimension can have any size (within reason). See more info on the definition of a matrix product or tensor contraction.

Julia中此乘法的正确语法是什么?

What is the right syntax of this multiplication in Julia?

推荐答案

您可以使用reshape将多维数组转换为矩阵， 将它们相乘，然后将结果转换回多维数组.

You can use reshape to convert the multi-dimensional arrays into matrices, multiply them, and convert the result back to a multi-dimensional array.

A = [1 2]
B = reshape(1:8,2,2,2)
reshape( reshape(A,2,1)' * reshape(B,2,4), 2, 2 )

(在此示例中，由于A已经是矩阵，因此实际上无需重塑形状.)

(In this example, since A is already a matrix, there is actually no need to reshape it.)

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