如何对2D矩阵的每一行对外部乘积矩阵的求值向量化? [英] How to vectorize the evaluation of outer product matrix for every row of the 2D matrix?

问题描述

我正在尝试加快评估外部产品矩阵的过程.我有一个名为 a 的4 * n矩阵.我想通过公式

I am trying to speed the process in evaluation the outer product matrix. I have a 4*n matrix named a. I want to evaluate the outer product matrix for every row of a, by the formula:

K = a*a';

如果我使用 for 循环对该过程进行编码，则如下所示:

If I code this process using a for loop, it is as below:

K=zeros(4,4,size(a,2));
for i=1:size(a,2)
    K(:,:,i) = a(:,i)*a(:,i)';
end

我发现了另一种使用 cellfun 的方法，该方法比以前更慢.

I have found another method, using cellfun, which is even slower than before.

acell = num2cell(a, 1);
b = cellfun(@(x)(x*x'),acell,'UniformOutput',false);
K = reshape(cell2mat(b),4,4,[]);

是否有实现这些过程的好方法，例如矢量化?

Is there any good way to implement these process, such as vectorization?

推荐答案

您可以使用 kron 重复n次矩阵，因此无需预先分配，然后使用 a(:).'，最后重新塑形以添加第3维.

You can use kron to repeat the matrix n time, so no need to preallocation, then perform an element wise multiplication with a(:).', finally reshape to add a 3rd dimension.

%Dummy 2D matrix 4x3
a = [1 4 7
     2 5 8
     3 6 9
     4 7 10]
%Size of the first dimension  
n = size(a,1);
%Repeat the matrix n time
p = kron(a,ones(1,n)).*a(:).'
%Reshape to A = 4x4x3
A = reshape(p,n,n,[])

您失去了for循环方法的可读性，但应该提高性能.

You loose the readability of the for loop method but you should increase the performance.

这篇关于如何对2D矩阵的每一行对外部乘积矩阵的求值向量化?的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！