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 

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')
%--------------------------------------