I want to loop a value into a vector, how do I do this?

I am trying to loop through my script in order to get several values of one variable (D_N), and then putting all these values into an empty vector. So far I have made:

N = 10;
M = 5;
B = zeros(M,N); % empty vector to contain x_t.
F = zeros(M,1); % empty vector to contain d_N.
for m=1:M % This creates more random walks.
  x_t(1) = 0;
  for n = 1:N % end position of the random walk.                                                                                                                                                                                                                                                                                                   
    A = sign(randn);
    x_t(n+1) = x_t(n) + A;
    B(m,n) = x_t(n); % vector containing all of x_t.
  end
  plot(x_t);
  hold on
  C = B(:,end) % takes the last elements in the B vector.
  D = C.^2 % ^2 on each of the elements in C.
  D_N = sqrt(mean(D)) % This is what I want to loop several times.
end
F(m,1) = D_N % This is where I want to put all the values from the looped D_N.

For some reason putting a third for-loop makes my script behave oddly. Anyone know how to do this?

[Jan]

Please edit the question and add more details: Which 3rd loop do you mean? What is "odd"? What do you observe and expect instead?

Answer 1

[Jan]

Your D_N is overwritten in each iteration. Perhaps you want:

   D_N(:, m) = sqrt(mean(D))

Are you sure with sign(randn)? There are cheaper methods to obtain a +/-1 and the very rare case of 0.

You can replace:

    x_t(1) = 0;
    for n = 1:N
        A = sign(randn);
        x_t(n+1) = x_t(n) + A;
        B(m,n) = x_t(n); % vector containing all of x_t.
    end

by

B(m, :) = [0, cumsum(1 - 2 * randi([0,1], 1, N - 1))];

Answer 2

[dpb]

You've got the assignment to F(m) outside the loop on m...

    ...
    C = B(:,end) % takes the last elements in the B vector.
    D = C.^2 % ^2 on each of the elements in C.
    D_N = sqrt(mean(D)) % This is what I want to loop several times.
  end
  F(m,1) = D_N % This is where I want to put all the values from the looped D_N.

should be

    ...
    C = B(:,end) % takes the last elements in the B vector.
    D = C.^2 % ^2 on each of the elements in C.
    D_N = sqrt(mean(D)) % This is what I want to loop several times.
    F(m,1) = D_N % This is where I want to put all the values from the looped D_N. 
  end

which could be shortened to just

    ...
    F(m)= rms(B(:,end));
  end

without all the intermediaries you don't use and the builtin rms function. Also, don't need the second explicit subscript on F as you've already preallocated it as a column vector.

NB, however, you're doing all this for every m where B only has elements for those rows to which the loop has yet traversed...that's a lot of overhead for what are still all zeros until the loop finishes and recomputing the same thing for every row that has already been done. What you're really looking for is

x_t=zeros(1,N);
for m=1:M % This creates more random walks.
  for n = 0:N-1  % your code built N+1 elements
    x_t(n+1) = x_t(n) + sign(randn);
    B(m,n) = x_t(n); % vector containing all of x_t.
  end
  plot(x_t);
  hold on
end
F=rms(B(:,end));  % wait 'til end to compute the end vector of distance

which does the full array assignment to F -- with this syntax you don't need (or want) the variable m.

Also note you could remove the intermediary loop on m,n by building a random array of that size via

x=randn(M,N-1);                     % mxn-1 rand normals.
B=cumsum([zeros(M,1) sign(x)],2);   % accumulate +/-1 
F=rms(B(:,end));

[dpb]

ADDENDUM: Jan's comment on sign(randn) is very good one, btw, outside the code structure...