% 4-18-2008
% MATLAB data fitting examples
clear all;
close all;

% Load the data
load linefit.dat;
x = linefit(:,1);
y = linefit(:,2);

% These are the points we would like to interpolate to
xp = 0:0.1:7;

% Polynomial fits
P1 = polyfit(x,y,1);
yp1 = polyval(P1,xp);
P2 = polyfit(x,y,2);
yp2 = polyval(P2,xp);
P3 = polyfit(x,y,3);
yp3 = polyval(P3,xp);

% E_2 error
E_2_1 = sqrt( 1/length(x) * sum( abs(polyval(P1,x) - y).^2 ) )
E_2_2 = sqrt( 1/length(x) * sum( abs(polyval(P2,x) - y).^2 ) )
E_2_3 = sqrt( 1/length(x) * sum( abs(polyval(P3,x) - y).^2 ) )

% Piecewise defined fitting functions
yp4 = interp1(x,y,xp);  % Linear functions
yp5 = spline(x,y,xp);   % Cubic functions (splines)

figure(1)
plot(x,y,'o:')
hold on
plot(xp,yp1,'r')
plot(xp,yp2,'k')
plot(xp,yp3,'g')
plot(xp,yp4,'c')
plot(xp,yp5,'b')

% Load gaussian data
load gaussfit.dat;
x=gaussfit(:,1);
y=gaussfit(:,2);

% Interpolated points
xp=-3:0.01:2.5;

% Search for the minimum error with an initial guess of [1 1]
C=fminsearch('gafit',[1 1]);

figure(2)
plot(x,y,'o:');
hold on
plot(xp,C(1)*exp(-C(2).*xp.^2),'k')