How to directly construct a sparse transition probability matrix

Dear community,

I am new to Matlab. I am trying to construct a sparse probability transition matrix. A small example of the full probability transition matrix is matrix P. Matrix A represents my states and the row number gives an index for a particular state.

For the first four source states in matrix A, I search in the same matrix for the index of their corresponding destination states based on some conditions.

The indices of a source state and in this case two destination states, provide the row and column indices for my probability transition matrix P.

My first question is: is this approach with using find the most time-efficient one?

My second question is: how can I directly construct a sparse probability transition matrix Q? In my current code the loop does not work for Q. Q should look like:

Q =
 (1,5)       0.8000
 (2,6)       0.8000
 (3,7)       0.8000
 (1,8)       0.2000
 (4,8)       0.8000
 (2,9)       0.2000
 (3,10)      0.2000
 (4,11)      0.2000

My code for constructing full matrix P:

A = [1 1 1 ; 1 1 2; 1 2 1; 1 2 2;...
    2 1 1 ; 2 1 2 ; 2 2 1; 2 2 2;...
    2 2 3 ; 2 3 2 ; 2 3 3; 3 3 3]

P = zeros(12,12)

 for i = 1:4
      a=A(i,1)
      b=A(i,2)
      c=A(i,3)

      d = find(A(:,1)==a+1 & A(:,2)==b & A(:,3)==c)
      e = find(A(:,1)==a+1 & A(:,2)==b+1 & A(:,3)==c+1)

      P(i,d)=0.8
      P(i,e)=0.2

end

Followed by my attempt to directly construct a sparse matrix Q instead of full matrix P:

Q=spalloc(12,12,8)

for i = 1:4
      a=A(i,1)
      b=A(i,2)
      c=A(i,3)

      d = find(A(:,1)==a+1 & A(:,2)==b & A(:,3)==c)
      e = find(A(:,1)==a+1 & A(:,2)==b+1 & A(:,3)==c+1)

      Q=sparse(i, [d e], [0.8 0.2], 12, 12) % here is an error

end

Any help is greatly appreciated!

Answer 1

[Martine van den Boomen]

I found a solution by using a cell array. It works, and I post the answer as it may be helpful for others, but I am not sure whether my approach is the most efficient one.

Q=spalloc(12,12,8)

out=cell(1,4)  
for i = 1:4

        a=A(i,1)
        b=A(i,2)
        c=A(i,3)

        d = find(A(:,1)==a+1 & A(:,2)==b & A(:,3)==c)
        e = find(A(:,1)==a+1 & A(:,2)==b+1 & A(:,3)==c+1)

        out{i}=[i i; d e ; 0.8 0.2]   

end
vecmat = cell2mat(out(1:4)) 
Q=sparse(vecmat(1,:), vecmat(2,:), vecmat(3,:), 12, 12)