% Script for projection of matrix over time
function proj(mat,k,vector,time)
% mat = matrix without headings
% k = number of stages
% vector = population vector at the beginning
% time = no. of steps for the projection

% 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);

% Reads the population vector
fid=fopen(vector,'r');
vect=fscanf(fid,'%f',[k,1]);
fclose(fid);

vec(:,1)=vect;
% Calculates no. of individuals in time 1
suma(1)=sum(vec(:,1));

% Projection over time
for i=2:time
   vec(:,i)=b*vec(:,i-1);
   suma(i)=sum(vec(:,i));
   lambda(i)=suma(i)/suma(i-1);
end   

% Plots the result
figure;
plot(suma);
figure;
plot(lambda);