## Friday, June 3, 2011

### Curve Fitting in Matlab

One of my friends was doing analysis of some sampled data. He wanted to fit them into a curve to derive the equation. He said Excel could fit up to polynomial of order 6 and he wanted a higher order one. So, he asked my help to write a Matlab program. He also wanted the plotted curve besides the calculated coefficients. The program and sample data are shown below. That is good for me because I also need to fit data occasionally and I can reuse it later :)
See d.txt and cf.m.
%--------------------------------------
%Curve fitting
%2011-Jun-03
%Programmer: Yan Naing Aye
%--------------------------------------
clc;
close all;
clear all;
%--------------------------------------
%get data from file that can be edited
X=d(:,1);
Y=d(:,2);
%--------------------------------------
%define order
N=2;
%--------------------------------------
%curve fitting
p=polyfit(X,Y,N);
%generate curve fitted data
[nr nc]=size(X);
YA=zeros(nr,1);
for i=0:N
YA=YA+p(i+1)*X.^(N-i);
end
%--------------------------------------
%Plot Y vs X
figure;
plot(X,Y,' rd','LineWidth',2,...
'MarkerEdgeColor','k',...
'MarkerFaceColor','g',...
'MarkerSize',6)
hold on;
plot(X,YA,'b','LineWidth',2,...
'MarkerEdgeColor','k',...
'MarkerFaceColor','g',...
'MarkerSize',6)
hold off;
grid on;
Title('Y vs X')
xlabel('X');
ylabel('Y');
legend('Sampled data','Fitted curve',...
'Location','NW')
%--------------------------------------


### Monte Carlo integration

As I am reading about Particle Filter, just for fun, I wrote a Matlab program that performs Monte Carlo integration using uniform distribution. The equation and the program are as follows.
clc;
close all;
clear all;
%--------------------------------------
%Monte Carlo Integration
%--------------------------------------
%--------------------------------------
%limits
LowerLimit=1;
UpperLimit=3;
%--------------------------------------
%generate uniformly distributed random
%numbers within the range
n=10000;
x=LowerLimit+(UpperLimit-LowerLimit)*rand(n,1);
%--------------------------------------
%Probability distribution function for
%uniformly distributed random numbers
q=1/(UpperLimit-LowerLimit);
%--------------------------------------
%function to integrate
f=3.*x.*x;
i=mean(f./q)
%--------------------------------------