Why does my random walk simulation come out so weird?

Question

Kevin Nelson 2023-9-25

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2025567-why-does-my-random-walk-simulation-come-out-so-weird

编辑： William Rose 2023-9-25

在 MATLAB Online 中打开

Why does my graph come out so weird? I've provided the code:

clearvars

N = 1000;

M = 500;

P = cumsum(full(sparse(1:N, randi(M,1,N), [0 2*randi([0 1],1,N-1)-1], N, M))) ;

figure (2);

hold on ;

for S=1:size(P,2)

plot(1:size(P,1),P(:,S),'.-');

end

title('Random walk 2')

xlabel('#Step') ;

ylabel('Distance') ;

hold off;

I was told I'm plotting along the wrong dimension of S, but what does that mean? When I alter it, the graph either crashes or gives ,e a straight line.

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

William Rose 2023-9-25

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2025567-why-does-my-random-walk-simulation-come-out-so-weird#answer_1317847

@Kevin Nelson,

Your formula introduces an increaing probability of "stay the same on each step" as M, the number of walks, grows. Is that your intent? I doubt it. Here are plots of what happ[ens with your code when N=100, and M=1, M=2, and M=5. Notice the increase in the probability of making a "step" of 0, and M grows.

You can fix it by modifying (simplifying) your cumsum() statement.

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

William Rose 2023-9-25

编辑：William Rose 2023-9-25

在 MATLAB Online 中打开

@Kevin Nelson,

[edit: add explanation of code with and without 0 as a step option]

The line

P = cumsum(full(sparse(1:N, randi(M,1,N), [0 2*randi([0 1],1,N-1)-1], N, M))) ;

causes (M-1)/M of the random steps (which would otherwise be +1 or -1) to become zero.

Therefore, when M=1, none of the steps get reset to zero, and all steps are therefore +1 or -1. When M=5, you get 4/5=80% zeros. When M=500, as in your original example, you get 499/500=99.8% zeros. This is why your random walks look weird.

If the above behavior is not desired, and if you want random steps of -1, 0, or +1 at every time point of every walk, then do:

P=cumsum(zeros(1,M);randi([-1 1],N-1,M));

Try it. It yields a nice looking set of random walks. See below for N=300,M=20 and N=1000,M=500.