function[c,l]=lagran(x,y)
%x為n個節點的橫坐標所組成的向量,y為縱坐標組成的向量
%c為所得插值函數的系數組成的向量
%conv為多項式乘多項式函數
w=length(x);
n=w-1;
l=zeros(w,w);
for k=1:n+1
    v=1;
    for j=1:n+1
        if k~=j
            v=conv(v,poly(x(j)))/(x(k)-x(j));
        end
    end
    l(k,:)=v;
end
c=y*l;

x=[-5:.1:5];
y1=1./(1+x.^2);
y2=0.0385;
y3=-0.0385*x.^2+1.0000;
y4=0.0053*x.^4-0.1711*x+1.0000;
y5=0.0001*x.^8-0.0050*x.^6-0.0020*x.^5+0.0776*x.^4+0.0257*x.^3-0.4524*x.^2-0.0947*x+1.0000
figure(1)
plot(x,y1,'k-',x,y2,'b--',x,y3,'r--',x,y4,'g--',x,y5,'y--')
grid on
legend('原函數曲線','插值多項式曲線')
title('lagran插值多項式與原函數')