composeQ.m

function [Q] = composeQ(R,PI)
%COMPOSEQ - computes normalized rate matrix Q from R matrix (general reversible model)
%
% [Q] = composeQ(R,PI)

% Molecular Biology and Evolution Toolbox (MBEToolbox)
% Author: James Cai
% Email: jcai@tamu.edu
% Website: http://bioinformatics.org/mbetoolbox/
% 
% $LastChangedDate: 2013-01-05 12:04:29 -0600 (Sat, 05 Jan 2013) $
% $LastChangedRevision: 327 $
% $LastChangedBy: jcai $


narginchk(2, 2);

if (trace(R)~=0)
	error('error in R');
end

[x,y]=size(PI);
if ~(x==y), PI=diag(PI); end

Q=R*PI;
% Make it a valid rate matrix (make sum of rows = 0)
Q=Q+diag(-1*sum(Q,2));	% Markov Q requires sum(Q,2)==0


% Scale/normalize rate matrix to one expected substitution per unit time
%Q=Q*length(Q);		% rescale Q, x4 for nt, x20 for aa, x61 for codon
%Q=Q./abs(trace(Q));
Q=(Q./abs(trace(Q)))*length(Q);