Why Is My Markov Chain Simulation Producing Unexpected Output?

[Jamin2112]

Homework Statement

Homework Equations

Seems pretty straightforward ...

The Attempt at a Solution

Here's what I put:


P = zeros(10,10);

P(1,2) = 1;

P(2,1) = 1/2;

P(2,3) = 1/2;

P(3,1) = 1/2;

P(3,4) = 1/2;

P(4,1) = 1/3;

P(4,2) = 1/3;

P(4,5) = 1/3;

P(5,1) = 1/2;

P(5,6) = 1/2;

P(6,1) = 1/4;

P(6,2) = 1/4;

P(6,3) = 1/4;

P(6,7) = 1/4;

P(7,1) = 1/2;

P(7,8) = 1/2;

P(8,1) = 1/4;

P(8,2) = 1/4;

P(8,4) = 1/4;

P(8,9) = 1/4;

P(9,1) = 1/3;

P(9,3) = 1/3;

P(9,10) = 1/3;

P(10,1) = 1/3;

P(10,2) = 1/3;

P(10,5) = 1/3;

A = P';

save A.dat A -ASCII

x0 = [.1 .1 .1 .1 .1 .1 .1 .1 .1 .1]';

for
i = 1:5
Q(:,i) = A^i * x0;
end

for i = 1:4
p10(i,1) = Q(10,i);
end

save p10.dat p10 -ASCII

b0 = x0;

i = 0;

tol = 10^(-8);

B(:,1) = A * b0 / norm(A*b0, 1);

while
norm(B(:,i+1)-B(:,i), 1) / norm(B(:,i+1)) > tol
i = i+1
B(:,i+1) = A * B(:,i) / nor * B(:,i), 1);
end

X = B(:,i);

save ssVect.dat X -ASCII

c = dim(max(B(:,i)))

save mostOften.dat c -ASCII

save counter.dat i -ASCII



But I'm getting weird output like

B =
0.0333 0.0083 0.0042 0.0010 0.0005
0.0083 0 0 0 0
0.0042 0 0 0 0
0.0010 0 0 0 0
0.0005 0 0 0 0

When B supposed to just be a vector ... What's going on here?

 

[mighty2000]

Hi there! It looks like there may be a few issues with your code. First, when you define P as a 10x10 matrix, you only need to specify the non-zero elements. So for example, instead of setting P(1,2) and P(2,1) to be non-zero, you can just set P(1,2) = 1/2. This will make your code cleaner and more efficient.

Second, when you define Q(:,i) = A^i * x0, you are creating a matrix where each column represents the state vector at a different time step. If you want to get the steady state vector, you should only calculate Q(:,end), which represents the state vector at the final time step.

Third, your while loop for calculating the steady state vector is missing a closing parenthesis after "nor". It should be "nor * B(:,i), 1)".

Lastly, the output for B is not a vector because you are saving it as a matrix in your code. To get the steady state vector, you should use X = B(:,end) instead of just X = B.

I hope this helps! Let me know if you have any other questions.