function yi=Lagrange(x,y,xi)

%x为向量，全部的插值节点

%y为向量，插值节点处的函数值

%xi为标量或向量，被估计函数的自变量；

%yi为xi处的函数估计值

n=length(x);m=length(y);

%插值点与它的函数值应有相同的个数

if n~=m

    error('The lengths of X and Y must be equal!');

    return;

end

yi=zeros(size(xi));

for k=1:n

    w=ones(size(xi));

    for j=[1:k-1 k+1:n]

        %输入的插值节点必须互异

        if abs(x(k)-x(j))<eps

            error('the DATA is error');

            return;

        end

        w=(xi-x(j))/(x(k)-x(j)).*w;

    end

    yi=yi+w*y(k);

end

function [coeff,dist,class]=dclass(x1,x2,x)

[N1,p]=size(x1);

[N2,p]=size(x2);

[N,p]=size(x);

meanx1=mean(x1);

meanx2=mean(x2);

covx1=(N1-1)*cov(x1);

covx2=(N2-1)*cov(x2);

mean=(meanx1+meanx2)./2;

cov=(covx1+covx2)./(N1+N2-2);

coeff=inv(cov)*(meanx1-meanx2)';

dist=[];

class=[];

for byk=1:N

    w=(x(byk,:)-mean)*coeff;

    if w>0

        r=1;

    else

        r=2;

    end

    dist=[dist,w];

    class=[class,r];

end

coeff=coeff';

function [Dy,dy,jdw,n]=diffext1(fun,x0,jdwc,max1)

h=1;j=1; n=1;jdW=1;xdW=1; x1=x0+h;x2=x0-h;

Dy(1,1)=(feval(fun,x1)- feval(fun,x2))/(2*h);

while((jdW>jdwc)&(j<max1))

j;x1=x0+2^(-j)*h;x2=x0-2^(-j)*h;

Dy(j+1,1)=(feval(fun,x1)-feval(fun,x2))/(2^(1-j)*h);

for k=1:j

k;Dy(j+1,k+1)= Dy(j+1,k)+( Dy(j+1,k)- Dy(j,k))/(4^k-1);

end

jdW=abs(Dy(j+1,j+1)-Dy(j+1,j)); j=j+1;

end

[n,n]=size(Dy);jdw=abs(Dy(n,n)-Dy(n,n-1));

dy= Dy(n,n);