# Running for loop on an equation

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aliza mustafa on 1 Oct 2022
Commented: aliza mustafa on 1 Oct 2022
Hi everyone,
I have the equation:
(1)
I have:
and
I have to compute for 0, 1, 2, ... 10.
I did it this way in MATLAB:
S = [1/2, 1/3, 1/2, 1/3, 1/3, 1/2;
1/2, 0, 0, 0, 0, 0;
0, 1/3, 1/2, 0, 0, 0;
0, 0, 0, 0, 1/3, 0;
0, 1/3, 0, 1/3, 0, 0;
0, 0, 0, 1/3, 1/3, 1/2];
u_0 = [0, 0, 1, 0, 0 ,0]';
for i = 0:10
u_k = S.*u_i;
I am stuck here. How can I write the equation (1) in matlab? Any help will be highly appreciated. Thanks alot in advance.

Torsten on 1 Oct 2022
Edited: Torsten on 1 Oct 2022
S = [1/2, 1/3, 1/2, 1/3, 1/3, 1/2;
1/2, 0, 0, 0, 0, 0;
0, 1/3, 1/2, 0, 0, 0;
0, 0, 0, 0, 1/3, 0;
0, 1/3, 0, 1/3, 0, 0;
0, 0, 0, 1/3, 1/3, 1/2];
u_0 = [0, 0, 1, 0, 0 ,0]';
u = zeros(6,10);
u(:,1) = u_0;
for i = 2:11
u(:,i) = S*u(:,i-1);
end
u
u = 6×11
0 0.5000 0.5000 0.4583 0.4444 0.4433 0.4441 0.4444 0.4445 0.4445 0.4444 0 0 0.2500 0.2500 0.2292 0.2222 0.2216 0.2220 0.2222 0.2222 0.2222 1.0000 0.5000 0.2500 0.2083 0.1875 0.1701 0.1591 0.1535 0.1507 0.1494 0.1488 0 0 0 0 0.0278 0.0278 0.0285 0.0278 0.0278 0.0278 0.0278 0 0 0 0.0833 0.0833 0.0856 0.0833 0.0834 0.0833 0.0833 0.0833 0 0 0 0 0.0278 0.0509 0.0633 0.0689 0.0715 0.0728 0.0734
%u./vecnorm(u)
%null(S-eye(6))
##### 3 CommentsShow 1 older commentHide 1 older comment
Torsten on 1 Oct 2022
To run it for 1,2,...,10, you must run the loop from 2 to 11. Think about it.
I corrected it above in my code.
aliza mustafa on 1 Oct 2022
Thank you so much for your guidance.

Davide Masiello on 1 Oct 2022
Edited: Davide Masiello on 1 Oct 2022
I suspect you want to do something like this
S = [ 1/2, 1/3, 1/2, 1/3, 1/3, 1/2;...
1/2, 0, 0, 0, 0, 0;...
0, 1/3, 1/2, 0, 0, 0;...
0, 0, 0, 0, 1/3, 0;...
0, 1/3, 0, 1/3, 0, 0;...
0, 0, 0, 1/3, 1/3, 1/2;...
];
u = zeros(6,11);
u(:,1) = [0, 0, 1, 0, 0 ,0]';
for col = 2:11
u(:,col) = S*u(:,col-1);
end
u
u = 6×11
0 0.5000 0.5000 0.4583 0.4444 0.4433 0.4441 0.4444 0.4445 0.4445 0.4444 0 0 0.2500 0.2500 0.2292 0.2222 0.2216 0.2220 0.2222 0.2222 0.2222 1.0000 0.5000 0.2500 0.2083 0.1875 0.1701 0.1591 0.1535 0.1507 0.1494 0.1488 0 0 0 0 0.0278 0.0278 0.0285 0.0278 0.0278 0.0278 0.0278 0 0 0 0.0833 0.0833 0.0856 0.0833 0.0834 0.0833 0.0833 0.0833 0 0 0 0 0.0278 0.0509 0.0633 0.0689 0.0715 0.0728 0.0734
Beware of the fact that, to call , you must write
u(:,n+1)
This is because, unlike C, Matlab's indexing starts from 1 rather than 0.