向量化此循环 [英] Vectorize this loop

问题描述

我在MATLAB中有以下循环:

I have the following loop in MATLAB:

n = 20000
rho=0.9;
sigma=[0.1 0.2 0.3];
epsilon = normrnd(0,1, 3, n);
z =  NaN(1,n);
z(1,1) = 0;
for i=2:n
   z(1,i) = rho * z(1,i-1) + sigma* epsilon(:,i);
end

我尝试通过以下方式向量化它:

I tried vectorizing it by doing:

z(1,2:end) = rho * z(1,1:end-1) + sigma * epsilon

它没有用.我知道问题是该位:z(1,2:end) = rho * z(1,1:end-1)不是递归的.

It didn't work. I understand that the problem is that this bit: z(1,2:end) = rho * z(1,1:end-1) is not recursive.

我该如何解决?

推荐答案

在一个充满 crazy fast parallel processors and almost-free memory latency machines 的世界末日世界中，像bsxfun和matrix multiplication这样的矢量化工具可以轻松生成20,000个内核，一个迷失的灵魂，拼命试图将这样的问题向量化，可能会冒险进入这样的情况-

In a post apocalyptic world filled with crazy fast parallel processors and almost-free memory latency machines, where vectorizing tools like bsxfun and matrix multiplication could easily spawn across 20,000 cores, one lost soul desperately trying to vectorize such a problem could venture into something like this -

parte1 = tril(rho.^(bsxfun(@minus,(0:n-2)',0:n-2)));
parte2 = sigma*epsilon(:,2:end);
z = [0 parte2*parte1.']

总的来说，它不应该提高内存效率，因此不太可能很快..现在，但是它旨在演示一种跟踪并应用递归的方法一个向量化的解决方案.

In all seriousness, it's not supposed to be memory-efficient and thus, isn't likely to be fast .. now, but is meant to demonstrate a way to trace the recursion and apply it for a vectorized solution.

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