矢量化三环-MATLAB

Question

我有下面这个非常低效的大循环。

P is a [2000 x 200 x 5] matrix
D is a [2000 x 200 x 5] matrix
S is a [200 x 1005] matrix
PS is a [2000 x 1000 x 5] matrix

我想计算以下循环：

for k=1:2000
   for n=1:200
      for t=1:5
          P(k,n,t) = sum(S(n,t+1:t+1000) .* PS(k,1:1000,t));
      end
   end
end

显然，这是非常低效的。我尝试了parfor，但我更喜欢矢量化的解决方案。我用bsxfun尝试了几件事，但都没能成功。

谢谢。

Answer 1

这里有一个使用powerful matrix-multiplication-的近似（几乎是因为我们还有一个循环，但只有5次迭代）矢量化方法

out = zeros(2000,200,5);
for t=1:size(P,3) %// size(P,3) = 5
    out(:,:,t) = PS(:,:,t)*S(:,t+1:t+1000).';
end

---

运行时测试和验证输出-

%// Inputs
D = rand(2000,200,5);
S = rand(200,1005);
PS = rand(2000,1000,5);
disp('--------------------- No Matrix-mult-fun')
tic
P = zeros(2000,200,5);
for k=1:2000
   for n=1:200
      for t=1:5
          P(k,n,t) = sum(S(n,t+1:t+1000) .* PS(k,1:1000,t));
      end
   end
end
toc
disp('--------------------- Fun fun Matrix-mult-fun')
tic
out = zeros(2000,200,5);
for t=1:size(P,3) %// size(P,3) = 5
    out(:,:,t) = PS(:,:,t)*S(:,t+1:t+1000).';
end
toc
error_val = max(abs(P(:)-out(:)))

输出-

--------------------- No Matrix-mult-fun
Elapsed time is 70.223008 seconds.
--------------------- Fun fun Matrix-mult-fun
Elapsed time is 0.624308 seconds.
error_val =
     1.08e-12