function lagranline(x,y,xi)
%x為向量，全部的插值節點；
%y為向量，插值節點處的函數值；
%xi為標量，自變量x;
%yi為xi處的函數估計值
n=length(x);m=lenth(y);
if n~m
    error('the length of x and y must be equal');
    return;
end
for k=1:n-1
    if x(k)<=xi&xi<=x(k+1)
        yi=(xi-x(k+1))/(x(k)-x(k+1))*y(k)+(xi-x(k))/(x(k+1)-x(k))*y(k+1);
        return ;
    end
end
a=-5;b=5;n=8;h=(b-a)/n;
x=a: h: b; y =1./(1+x.^2);
x1=a:0.01:b; y1=1./(1+x1.^2);
m=length(x1); z=zeros(1,m);
for i=1:m
z(i)=lagranline(x,y,x1(i));
end
plot(x,y,’o’,x1,y1.’k:’,x1,z,’k-’);