Matlab - 加速嵌套For循環

Question

我正在處理一個帶有三個嵌套for循環的函數，對於其預期用途來說太慢了。瓶頸顯然是循環部分 - 幾乎100％的執行時間都花在最內層的循環中。
該函數採用名爲rM作爲輸入二維矩陣，並返回一個名爲ec 3D矩陣：

rows = size(rM, 1); 
cols = size(rM, 2); 

%preallocate. 
ec = zeros(rows+1, cols, numRiskLevels); 
ec(1, :, :) = 100; 

for risk = minRisk:stepRisk:maxRisk; 
    for c = 1:cols, 
     for r = 2:rows+1, 
      ec(r, c, risk) = ec(r-1, c, risk) * (1 + risk * rM(r-1, c)); 
     end 
    end 
end 

關於加快for循環任何幫助，將不勝感激......

Answer 1

的問題是，內循環最慢，而矢量化幾乎不可能。每次迭代都直接取決於前一次迭代。

外兩個是可能的：

clc; 
rM = rand(50); 

rows = size(rM, 1); 
cols = size(rM, 2); 

minRisk = 1; 
stepRisk = 1; 
maxRisk = 100; 
numRiskLevels = maxRisk/stepRisk; 

%preallocate. 
ec = zeros(rows+1, cols, numRiskLevels); 
ec(1, :, :) = 100; 

riskArray = (minRisk:stepRisk:maxRisk)'; 
tic 
for r = 2:rows+1 
    tmp = riskArray * rM(r-1, :); 
    tmp = permute(tmp, [3 2 1]); 
    ec(r, :, :) = ec(r-1, :, :) .* (1 + tmp); 
end 
toc 


%preallocate. 
ec2 = zeros(rows+1, cols, numRiskLevels); 
ec2(1, :, :) = 100; 
tic 
for risk = minRisk:stepRisk:maxRisk; 
    for c = 1:cols 
     for r = 2:rows+1 
      ec2(r, c, risk) = ec2(r-1, c, risk) * (1 + risk * rM(r-1, c)); 
     end 
    end 
end 
toc 

all(all(all(ec == ec2))) 

但我驚訝的是，量化代碼確實比較慢。 （但也許有人可以提高代碼的，所以我想我放在她給你的。）

Answer 2

我剛纔想矢量化外環，居然發現一個顯著的速度增加。當然，這是很難判斷的腳本的速度不知道（的大小）的投入，但我會說這是一個很好的起點：

% Here you can change the input parameters 
riskVec = 1:3:120; 
rM = rand(50); 


%preallocate and calculate non vectorized solution 
ec2 = zeros(size(rM,2)+1, size(rM,1), max(riskVec)); 
ec2(1, :, :) = 100; 
tic 
for risk = riskVec 
    for c = 1:size(rM,2) 
     for r = 2:size(rM,1)+1 
      ec2(r, c, risk) = ec2(r-1, c, risk) * (1 + risk * rM(r-1, c)); 
     end 
    end 
end 
t1=toc; 

%preallocate and calculate vectorized solution 
ec = zeros(size(rM,2)+1, size(rM,1), max(riskVec)); 
ec(1, :, :) = 100; 
tic 
for c = 1:size(rM,2) 
    for r = 2:size(rM,1)+1 
     ec(r, c, riskVec) = ec(r-1, c, riskVec) .* reshape(1 + riskVec * rM(r-1, c),[1 1 length(riskVec)]); 
    end 
end 
t2=toc; 

% Check whether the vectorization is done correctly and show the timing results 
if ec(:) == ec2(:) 
    t1 
    t2 
end 

給定輸出是：

t1 = 

    0.1288 


t2 = 

    0.0408 

因此，對於這個riskVec和rM，它大約是非矢量化解決方案的3倍。