Question

我正在使用三个嵌套for循环的函数，这对于它的预期用途来说太慢了。瓶颈显然是循环部分 - 几乎100％的执行时间都花在了最里面的循环中该函数采用名为rM的2d矩阵作为输入，并返回一个名为ec的3d矩阵：

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

任何关于加速for循环的帮助都会受到赞赏......

Answer 1

问题是，内循环是最慢的，而它几乎不可能进行矢量化。因为每次迭代都直接依赖于前一次迭代。

外面的两个是可能的：

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)))

但令我惊讶的是，矢量化代码确实较慢。（但也许有人可以改进代码，所以我想我把它留给你了。）

Answer 2

我刚尝试对外循环进行矢量化，实际上注意到速度显着增加。当然，如果不知道输入的大小，很难判断脚本的速度，但我会说这是一个很好的起点：

% 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

给定的输出是：

因此，对于此riskVec和rM，它的速度是非矢量化解决方案的3倍。

Matlab - 加速嵌套For-Loops

2 个答案: