% Calculates lambda, sensitivity and elastivity
function lambda(mat,k)
% mat = set of transition matrices, one bellow each other, without any headings 
% k = number of stages
% Reads the transition matrix
fid=fopen(mat,'r');
b=fscanf(fid,'%f',[k,k]);

% Transpose the transition matrix - this is due to matlab way of reading
b=transpose(b);   
fclose(fid);

[W,d] = eig(b);
lambda = diag(d);
imax = find(lambda==max(lambda));
V=conj(inv(W));
% w = stable stage distribution
w = W(:,imax)
% v = reproductive value
v=real(V(imax,:))
% gets population growth rate - the dominant eigenvalue of the matrix
lambda1 = lambda(imax)
% calculates sensitivity of the matrix
sen = v'*w';
% calculates elasticity of the matrix
ela = sen.*b/max(eig(b));
% prints the results
fid=fopen('lambda','a');
fprintf(fid,'%10.7f\t%10.7f\n',lambda1,i);
fclose(fid);