使用Matlab/Octave对两个矩阵的核心对应列的外部乘积之和进行矢量化 [英] Vectorize the sum of outer products of coresponding columns of two matrices using Matlab/Octave

问题描述

假设我有两个矩阵A和B，它们由列向量组成，如下所示.

Suppose I have two matrices A and B which are made up of column vectors as follows.

A = [a_1,a_2,...,a_N];
B = [b_1,b_2,...,b_N];

有什么方法可以将A中每一列的外部乘积之和与B中的相应列向量化.这是我的非向量化解决方案.

Is there any way to vectorize the calculation of the sum of outer products for every column in A with the corresponding column in B. Here is my non-vectorized solution.

S = zeros(size(A,1), size(B,1));
for n=1:N
    S = S + A(:,n)*B(:,n)';   % S = S + a_n * b_n'
end

任何帮助将不胜感激.

推荐答案

您不清楚N是什么，但是我假设N =列向量的数量-这意味着您只是在做A * B'

you are not clear on what N is, but I assume that N = number of column vectors - which means you are simply doing A * B'

A = rand(3,4);
B = rand(3,4);
N = size(A,2);
S = zeros(size(A,1), size(B,1));
for n=1:N
  S = S + A(:,n)*B(:,n)';   % S = S + a_n * b_n'
end
%Check that you are doing A*B'
S == A*B'
>> ans =

 1     1     1
 1     1     1
 1     1     1

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