diff toolboxes/FullBNT-1.0.7/KPMstats/mc_stat_distrib.m @ 0:cc4b1211e677 tip

initial commit to HG from
Changeset:
646 (e263d8a21543) added further path and more save "camirversion.m"

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+++ b/toolboxes/FullBNT-1.0.7/KPMstats/mc_stat_distrib.m	Fri Aug 19 13:07:06 2016 +0200
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+function pi = mc_stat_distrib(P)
+% MC_STAT_DISTRIB Compute stationary distribution of a Markov chain
+% function pi = mc_stat_distrib(P)
+% 
+% Each row of P should sum to one; pi is a column vector
+
+% Kevin Murphy, 16 Feb 2003
+
+% The stationary distribution pi satisfies pi P = pi
+% subject to sum_i pi(i) = 1,  0 <= pi(i) <= 1
+% Hence
+% (P'  0n   (pi  = (pi 
+%  1n  0)    1)     1)
+% or P2 pi2 = pi2.
+% Naively we can solve this using (P2 - I(n+1)) pi2 = 0(n+1)
+% or P3 pi2 = 0(n+1), i.e., pi2 = P3 \ zeros(n+1,1)
+% but this is singular (because of the sum-to-one constraint).
+% Hence we replace the last row of P' with 1s instead of appending ones to create P2, 
+% and similarly for pi.
+
+n = length(P);
+P4 = P'-eye(n);
+P4(end,:) = 1;
+pi = P4 \ [zeros(n-1,1);1];
+
+