如何在不使用for循环的情况下求和不同大小的矩阵的各个部分? [英] How to sum parts of a matrix of different sizes, without using for loops?

问题描述

我有一个相对较大的矩阵NxN(N〜20,000)和一个Nx1向量，用于标识必须分组在一起的索引.

I have a relatively large matrix NxN (N~20,000) and a Nx1 vector identifying the indices that must be grouped together.

我想将矩阵的各个部分加在一起，原则上可以有不同数量的元素和不相邻的元素. 我很快写了一个双for循环，它可以正常工作，但是效率很低.探查器将这些循环识别为我的代码中的瓶颈之一.

I want to sum together parts of the matrix, which in principle can have a different number of elements and non-adjacent elements. I quickly wrote a double for-loop that works correctly but of course it is inefficient. The profiler identified these loops as one of the bottlenecks in my code.

我试图找到一种智能的矢量化方法来解决该问题.我研究了arrayfun，cellfun和bsxfun函数，并寻找解决类似问题的方法...但是我还没有找到最终的解决方案.

I tried to find a smart vectorization method to solve the problem. I explored the arrayfun, cellfun, and bsxfun functions, and looked for solutions to similar problems... but I haven't found a final solution yet.

这是带有两个for循环的测试代码:

This is the test code with the two for-loops:

M=rand(10); % test matrix
idxM=[1 2 2 3 4 4 4 1 4 2]; % each element indicates to which group each row/column of M belongs
nT=size(M,1);
sumM=zeros(max(idxM),max(idxM));
for t1=1:nT
    for t2=1:nT
        sumM(t1,t2) = sum(sum(M(idxM==t1,idxM==t2)));
    end
end

推荐答案

我想指出对其他论坛提供的答案感兴趣的人

I'd like to point those who are interested to this answer provided on another forum

S=sparse(1:N,idxM,1); sumM=S.'*(M*S);

S=sparse(1:N,idxM,1); sumM=S.'*(M*S);

信用(和有用的讨论):

Credits (and useful discussion):

https://www.mathworks.com/matlabcentral/answers/407634-how-to-sum-parts-of-a-matrix-of-different-sizes-without-using-for -循环

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