Running for loop on an equation

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.

Answer 1

[Torsten]

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))

[aliza mustafa]

Sorry, I want to run it for 1,2, .. 10. (Not from 0 to 10). So, for it, how can I do this?

[Torsten]

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]

Thank you so much for your guidance.

Answer 2

[Davide Masiello]

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.