Daniel@0: function [T,Z] = mk_stochastic(T)
Daniel@0: % MK_STOCHASTIC Ensure the argument is a stochastic matrix, i.e., the sum over the last dimension is 1.
Daniel@0: % [T,Z] = mk_stochastic(T)
Daniel@0: %
Daniel@0: % If T is a vector, it will sum to 1.
Daniel@0: % If T is a matrix, each row will sum to 1.
Daniel@0: % If T is a 3D array, then sum_k T(i,j,k) = 1 for all i,j.
Daniel@0: 
Daniel@0: % Set zeros to 1 before dividing
Daniel@0: % This is valid since S(j) = 0 iff T(i,j) = 0 for all j
Daniel@0: 
Daniel@0: if (ndims(T)==2) & (size(T,1)==1 | size(T,2)==1) % isvector
Daniel@0:   [T,Z] = normalise(T);
Daniel@0: elseif ndims(T)==2 % matrix
Daniel@0:   Z = sum(T,2); 
Daniel@0:   S = Z + (Z==0);
Daniel@0:   norm = repmat(S, 1, size(T,2));
Daniel@0:   T = T ./ norm;
Daniel@0: else % multi-dimensional array
Daniel@0:   ns = size(T);
Daniel@0:   T = reshape(T, prod(ns(1:end-1)), ns(end));
Daniel@0:   Z = sum(T,2);
Daniel@0:   S = Z + (Z==0);
Daniel@0:   norm = repmat(S, 1, ns(end));
Daniel@0:   T = T ./ norm;
Daniel@0:   T = reshape(T, ns);
Daniel@0: end