Fitting a curve to a function

An example MatLab code to fit a curve to a piecewise linear function with the fixed end points.

%Fitting a curve to a piecewise linear function using least square method
%with the fixed start and end points

%clear command windows
clc;

%clear workspace
clear all;
%--------------------------------------------------------------------------
%Read curves
load Curve.dat;

%find lower left and upper right corners 
xD=Curve(1,:);
yD=Curve(2,:);
x0=min(xD); x1=max(xD); 
y0=min(yD);  y1=max(yD);
n=5;%order n i.e, the number of segments
FS=x1-x0;
global xs;
global yB;
global yE;
xs=(0:FS/n:FS);
yB=y0;
yE=y1;
%initialize coefficients (y values) to find 
%excluding the first and the last one
ys_initial=xs(2:n);
% options = optimset('MaxFunEvals',1000,'MaxIter',1000);
% LowerBoundC=y0;
% UpperBoundC=y1;
% ys =lsqcurvefit(@LineSeg,ys_initial,xD,yD,LowerBoundC,UpperBoundC,options);
ys =lsqcurvefit(@LineSeg,ys_initial,xD,yD);
%fixed start and end points
ys=[y0 ys y1];
%--------------------------------------------------------------------------
%Plot 
hFig1 = figure(1);
set(hFig1, 'Position', [600 100 500 300])
plot(xD,yD,':g','LineWidth',3,...
                'MarkerEdgeColor','b',...
                'MarkerFaceColor','b',...
                'MarkerSize',2)
hold on;             
plot(xs,ys,'-rs','LineWidth',1,...
     'MarkerEdgeColor','r',...
     'MarkerFaceColor','r',...
     'MarkerSize',4)
hold off;        
grid on;
%--------------------------------------------------------------------------

LineSeg.m

function [y] = LineSeg(ys,x)

global xs
global yB
global yE
L=length(x);
y=zeros(1,L);
ys=[yB ys yE];
LS=length(ys);
for i=1:L
    xt=x(i);
    %--------------------------
    %find segment
    for j=2:LS
        if(xs(j)>=xt) 
            break;
        end
    end    
    %interpolate
    x2=xs(j);
    y2=ys(j);
    y1=ys(j-1);
    x1=xs(j-1);
    y(i)=y1+(y2-y1)/(x2-x1)*(xt-x1);
    %--------------------------
end 

Image Retrieval

This is a MatLab program which receives a test image and find the most similar images in the database.

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
load('d.txt');
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')
%--------------------------------------