删除四个嵌套循环在Matlab [英] Removing four nested loops in Matlab

问题描述

我有以下四个嵌套循环在Matlab：

I have the following four nested loops in Matlab:

timesteps = 5;
inputsize = 10;
additionalinputsize = 3;
outputsize = 7;

input = randn(timesteps, inputsize);
additionalinput = randn(timesteps, additionalinputsize);
factor = randn(inputsize, additionalinputsize, outputsize);

output = zeros(timesteps,outputsize);
for t=1:timesteps
    for i=1:inputsize
        for o=1:outputsize
            for a=1:additionalinputsize
                output(t,o) = output(t,o) + factor(i,a,o) * input(t,i) * additionalinput(t,a);
            end
        end
    end
end

有三种载体：一个输入向量，一个附加输入矢量和输出矢量。所有被连接的因素。每个向量在给定的时间步长值。我需要在每一个给定的时间步的所有组合输入，增加投入和因素的总和。后来，我需要从输出到输入来计算：

There are three vectors: One input vector, one additional input vector and an output vector. All the are connected by factors. Every vector has values at given timesteps. I need the sum of all combined inputs, additional inputs and factors at every given timestep. Later, I need to calculate from the output to the input:

result2 = zeros(timesteps,inputsize);
for t=1:timesteps
    for i=1:inputsize
        for o=1:outputsize
            for a=1:additionalinputsize
                result2(t,i) = result2(t,i) + factor(i,a,o) * output(t,o) * additionalinput(t,a);
            end
        end
    end
end

在第三种情况下，我需要求和每一个时间步的所有三个向量的乘积：

In a third case, I need the product of all three vectors summed over every timestep:

product = zeros(inputsize,additionalinputsize,outputsize)
for t=1:timesteps
    for i=1:inputsize
        for o=1:outputsize
            for a=1:additionalinputsize
                product(i,a,o) = product(i,a,o) + input(t,i) * output(t,o) * additionalinput(t,a);
            end
        end
    end
end

这两个code片段工作，但令人难以置信的慢。如何删除嵌套循环？

The two code snippets work but are incredibly slow. How can I remove the nested loops?

编辑：增加值，改变小事，所以片段是可执行

Added values and changed minor things so the snippets are executable

EDIT2：添加其他使用案例

Added other use case

推荐答案

第一部分

一个办法 -

t1 = bsxfun(@times,additionalinput,permute(input,[1 3 2]));
t2 = bsxfun(@times,t1,permute(factor,[4 2 1 3]));
t3 = permute(t2,[2 3 1 4]);
output = squeeze(sum(sum(t3)));

或轻微变种，以避免紧缩 -

Or a slight variant to avoid squeeze -

t1 = bsxfun(@times,additionalinput,permute(input,[1 3 2]));
t2 = bsxfun(@times,t1,permute(factor,[4 2 1 3]));
t3 = permute(t2,[1 4 2 3]);
output = sum(sum(t3,3),4); 

---

第二部分

t11 = bsxfun(@times,additionalinput,permute(output,[1 3 2]));
t22 = bsxfun(@times,permute(t11,[1 4 2 3]),permute(factor,[4 1 2 3]));
result2=sum(sum(t22,3),4);

---

第三部分

t11 = bsxfun(@times,permute(output,[4 3 2 1]),permute(additionalinput,[4 2 3 1]));
t22 = bsxfun(@times,permute(input,[2 4 3 1]),t11);
product = sum(t22,4);

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