# State “i” goes to state “j”

I would like to have a code that given a state "i" in S, it give the set of states "j" which are accessible from "i".

Is that possible in mathematica?

My state space (S) is

StateSpace = {"1", "2", "3", "4", "5"}


and my transition matrix is

transitionmatrix = {{17/25, 3/25, 5/25, 0, 0}, {5/18, 5/18, 7/18, 1/18, 0}, {4/21,
9/21, 4/21, 0, 4/21}, {0, 0, 3/4, 1/4, 0}, {3/4, 1/4, 0, 0, 0}}


And i know that a state "i" goes to "j" if in the transition matrix the value (i,j) is higher than zero.

I would like something like this

If[transitionmatrix {i, j} > 0, t];


And then i will have

transitionmatrix{1,2}
true


(as 1 goes to 2)

-

This uses Pick twice, once to select rows of the transition matrix, and again to select elements of the state space corresponding to positive elements of the matrix:

accessibleStates[i_] := Union@Flatten[
Pick[StateSpace, #, _?Positive] & /@
Pick[transitionmatrix, StateSpace, i]]

accessibleStates["4"]
(* {"3", "4"} *)


You can use patterns, e.g.

accessibleStates["1" | "4"]
(* {"1", "2", "3", "4"} *)

-
Thanks exactly what i wanted :D really helpfull – Mariana da Costa Jun 10 '14 at 12:36
but i'm not understanding what the second one does (accessibleStates["1" | "4"]) – Mariana da Costa Jun 10 '14 at 12:38
I would guess it means states accessible from either 1 or 4. – Per Alexandersson Jun 10 '14 at 12:55
@MarianadaCosta, the symbol | is a shorthand for Alternatives, so as Paxinum said, "1"|"4" is a pattern which matches either "1" or "4". You may have no use for this, but I thought it worth mentioning. – Simon Woods Jun 10 '14 at 13:37
oh right, thanks (: – Mariana da Costa Jun 10 '14 at 14:24