Matlab FOR循环迭代时间增加

Question

我正在尝试跨越某个多变量函数的值 f(nu,delta,Omega,kappa,Gamma)。代码如下：

% PREALLOCATE RESULT MATRIX

N = 10;
d = 0.1;

M = zeros(4*N/d+(2*N+1)/d,6);

% SET UP LOOP INDICES

i=1;
increm=1;

% LOOP OVER MULTIPLE VARIABLE

for nu=d:d:N
    for delta=-N:d:N
        for Omega=d:d:N
            for kappa=d:d:N
                tic
                for Gamma=d:d:N

                % CALCULATE THE FUNCTION 

                mss = ((Gamma+kappa).*((Gamma+kappa).^2+4.*(delta+(-1).*nu).^2).^(-1)+( ...
                  -1).*(Gamma+kappa).*((Gamma+kappa).^2+4.*(delta+nu).^2).^(-1)+( ...
                  kappa.^2+4.*(delta+(-1).*nu).^2).^(-1).*(((2.*Gamma+kappa).^2+4.*( ...
                  delta+(-1).*nu).^2).*(kappa.*(Gamma+kappa).*(2.*Gamma+kappa)+4.*(( ...
                  -1).*Gamma+kappa).*(delta+(-1).*nu).^2)+4.*(kappa.*(2.*Gamma+ ...
                  kappa).^2+4.*(4.*Gamma+kappa).*(delta+(-1).*nu).^2).*Omega.^2).*( ...
                  16.*(delta+(-1).*nu).^4+4.*(delta+(-1).*nu).^2.*((Gamma+kappa).^2+ ...
                  (2.*Gamma+kappa).^2+(-8).*Omega.^2)+((Gamma+kappa).*(2.*Gamma+ ...
                  kappa)+4.*Omega.^2).^2).^(-1)+(-1).*(kappa.^2+4.*(delta+nu).^2).^( ...
                  -1).*(((2.*Gamma+kappa).^2+4.*(delta+nu).^2).*(kappa.*(Gamma+ ...
                  kappa).*(2.*Gamma+kappa)+4.*((-1).*Gamma+kappa).*(delta+nu).^2)+ ...
                  4.*(kappa.*(2.*Gamma+kappa).^2+4.*(4.*Gamma+kappa).*(delta+nu).^2) ...
                  .*Omega.^2).*(16.*(delta+nu).^4+4.*(delta+nu).^2.*((Gamma+kappa) ...
                  .^2+(2.*Gamma+kappa).^2+(-8).*Omega.^2)+((Gamma+kappa).*(2.*Gamma+ ...
                  kappa)+4.*Omega.^2).^2).^(-1)).^(-1).*((Gamma+kappa).*((Gamma+ ...
                  kappa).^2+4.*(delta+nu).^2).^(-1)+(kappa.^2+4.*(delta+nu).^2).^( ...
                  -1).*(((2.*Gamma+kappa).^2+4.*(delta+nu).^2).*(kappa.*(Gamma+ ...
                  kappa).*(2.*Gamma+kappa)+4.*((-1).*Gamma+kappa).*(delta+nu).^2)+ ...
                  4.*(kappa.*(2.*Gamma+kappa).^2+4.*(4.*Gamma+kappa).*(delta+nu).^2) ...
                  .*Omega.^2).*(16.*(delta+nu).^4+4.*(delta+nu).^2.*((Gamma+kappa) ...
                  .^2+(2.*Gamma+kappa).^2+(-8).*Omega.^2)+((Gamma+kappa).*(2.*Gamma+ ...
                  kappa)+4.*Omega.^2).^2).^(-1));

                % STORE THE RESULT

                M(i,:) = [mss nu delta Omega kappa Gamma];

                i = i+increm;

                end
            end
            toc
        end
    end
end

save M

但是，预分配无助于每次迭代花费更长的时间。当我运行代码并过早中断它时，迭代需要

Elapsed time is 0.003354 seconds.
Elapsed time is 0.006374 seconds.
Elapsed time is 0.009043 seconds.
Elapsed time is 0.012092 seconds.
Elapsed time is 0.015287 seconds.
Elapsed time is 0.019239 seconds.
Elapsed time is 0.023898 seconds.
Elapsed time is 0.035345 seconds.
Elapsed time is 0.046675 seconds.
Elapsed time is 0.056000 seconds.
Elapsed time is 0.066323 seconds.
Elapsed time is 0.072178 seconds.
Elapsed time is 0.075174 seconds.
Elapsed time is 0.081095 seconds.
Elapsed time is 0.095016 seconds.
Elapsed time is 0.095214 seconds.
Elapsed time is 0.100089 seconds.
Elapsed time is 0.104286 seconds.
Elapsed time is 0.109454 seconds.
Elapsed time is 0.115368 seconds.
Elapsed time is 0.124278 seconds.
Elapsed time is 0.131521 seconds.
Elapsed time is 0.135023 seconds.
Elapsed time is 0.137370 seconds.
Elapsed time is 0.145331 seconds.
Elapsed time is 0.163449 seconds.
Elapsed time is 0.162654 seconds.
Elapsed time is 0.159628 seconds.
Elapsed time is 0.166585 seconds.

我不明白变量本身的变化是如何导致这种情况的，因为唯一的变化量是 d，这应该不会比计算 mss 的新值更难之前的互动。

Answer 1

您没有预先分配足够大的数组！

如果你执行以下嵌套循环

for ii=1:3
   for jj = 1:4
       doSomething()
   end
end

doSomething 被执行 3*4=12 次。使用您的分配方案，您将分配 3+4=7 次。

换句话说，将您的预分配更改为

M = zeros((N/d)^4*(2*N+1)/d,6);

一切都会好起来的。