在Matlab中，如何计算两个矩阵之间的快速外部积? [英] How to compute a fast outer product between two matrices, in Matlab?

问题描述

我有两个n×m矩阵，A和B.我想创建一个新的矩阵C，类似于:

I have two n-by-m matrices, A and B. I want to create a new matrix C which is something like:

for i = 1:n
    C = C + outerProduct(A(i,:), B(i,:));
end

即C是一个大小为m x m的矩阵，是A和B行的所有外部乘积之和.

i.e. C is a matrix of size m x m, the sum of all outer products of the rows of A and B.

有没有for循环的快速方法(假设for循环在Matlab中非常慢)?

Is there a fast way to do it without a for loop (given that for loops are notoriously slow in Matlab)?

推荐答案

您正在执行的操作(行外部乘积的总和)等效于A的转置版本与B的乘积:

The operation you are performing (the sum of the row outer products) is equivalent to the multiplication of a transposed version of A with B:

C = A.'*B;

您可以使用以下示例查看此信息:

You can see this using the following example:

>> mat = magic(5);  %# A sample 5-by-5 matrix
>> A = mat(1:4,:);  %# Create a 4-by-5 matrix
>> B = mat(2:5,:);  %# Create another 4-by-5 matrix

>> C = zeros(5);  %# Initialize C to be 5-by-5
>> for i = 1:4, C = C + A(i,:).'*B(i,:); end;  %'# Calculate C as you are now

>> isequal(C, A.'*B)  %'# Test for equality with the shorter solution

ans =

     1  %# Equal!

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