Matlab代码优化和删除循环 [英] Matlab code optimization and removing loops

问题描述

如果有人可以帮助我优化这段代码，我不能独自删除此循环-欢迎.

I can't remove this loops by myself, if anybody can help me with optimization this piece of code - welcome.

M = length(w);
expt = exp(-t .* (phis * w'));
G = zeros(M, M);
for i = 1 : M
    for j = 1 : M
        last = 2 * reg_coef * eye(M);
        G(i,j) = last(i, j) + mean(expt .* t .^2 .* phis(:,i) .* phis(:,j) ./ (1 + expt) .^ 2);
    end
end

• w -大小为(1xM)
• phis -大小为(NxM)
• t -大小为(Nx1)
• w - size is (1xM)
• phis - size is (NxM)
• t - size is (Nx1)

推荐答案

通过编写简洁的代码，您可以做得更好-确保分配正确，确保从循环等中删除重复的计算.

You can do alot better by just writing cleaner code - ensure that you allocate properly, ensure that you remove duplicate calculations from loops etc:

您还可以看到生成的矩阵G是对称的，因此通过仅计算上三角形并随后将其作为转置填充下三角形，即可立即获得2x加速.

You can also see that the resulting matrix G is symmetric, so you get an immediate 2x speed-up by only calculating the upper triangle and filling in the lower triangle afterwards as a transpose.

至少对于我的MATLAB，通过使用临时数组将对mean()的调用向量化，可以实现另一个大大的加速.

At least with my MATLAB another big speed-up is achieved by vectorising the call to mean() through the use of a temporary array.

N = 100;
M = 100;

w = rand(1,M);
t = rand(N,1);
phis = rand(N,M);
reg_coeff = rand(1,1);

expt = exp(-t .* (phis * w'));

%% Initial version
tic
for i = 1 : M
   for j = 1 : M
      last = 2 * reg_coeff * eye(M,M);
      G1(i,j) = last(i,j) + mean(expt .* t .^ 2 .* phis(:,i) .* phis(:,j) ./ (1 + expt) .^ 2);
   end
end
t1 = toc;

%% Faster version
tic
coeff = expt .* t .^ 2 ./ (1 + expt) .^ 2;
G2 = zeros(M,M);
TT = zeros(M,M);
for i = 1 : M
   for j = i : M % only form upper triangle
      TT(:,j) = coeff .* phis(:,i) .* phis(:,j);
   end
   G2(i,i:M) = mean(TT(:,i:M),1); % vectorise call to mean()
end
G2 = 2 * reg_coeff * eye(M,M) + G2 + triu(G2,+1)';
t2 = toc;

%% Compare versions
speed = t1/t2
error = max(max(abs(G2 - G1)))

对于这种100x100情况，我的机器上的加速速度约为41.0.

For this 100x100 case the speed-up was around 41.0 on my machine.

希望这会有所帮助.

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