% fitting world population data to exponential model
% this time we are minimizing sum of squares of the
% population sizes
% we use the Matlab function fmins

clear all
popdt=[-10000     1;  
 -8000     5;  
 -6500     5;  
 -5000     5;  
 -4000     7;  
 -3000    14;  
 -2000    27;  
 -1000    50;  
  -500   100;  
  -400   162; 
  -200   150;  
     1   170;  
   200   190;  
   400   190;  
   500   190;  
   600   200;  
   700   207;  
   800   220;  
   900   226;  
  1000   254;  
  1100   301;  
  1200   360;  
  1250   400;  
  1300   360;  
  1340   443;  
  1400   350;  
  1500   425;  
  1600   545;  
  1650   470;  
  1700   600;  
  1750   629;  
  1800   813; 
  1850 1128; 
  1900 1550; 
  1910 1750; 
  1920 1860; 
  1930 2070; 
  1940 2300; 
  1950 2400];

tim=popdt(:,1);
popul=popdt(:,2);


% find quadratic fit parameters
% [0.0006 5] is our initial guess of 
% parameters which follows from least squares 
% for logarithms
% QPAR - is the vestor of parameters
% QPAR(1) - r
% QPAR(2) - log(N_0)


QPAR=fmins('wp_fun',[0.0006 5])


% now let us see how our estimates compare to data
for kk=1:length(tim)
   qppl(kk)=exp(QPAR(1)*tim(kk)+QPAR(2));
end

plot(tim,log(qppl),tim,log(popul),'or')
pause

% or
plot(tim,qppl,tim,popul,'or')