function [p,dp,q,r,alp,dom,x,wint,wipr]=vanderpol(n)
dom=[0,2*pi];alpha=(dom(2)-dom(1))/2;beta=(dom(2)+dom(1))/2;
e1=ones(n,1)/2;e2=e1;e2(2)=1;X=spdiags([e1,e2],[-1,1],n,n);
X=alpha*X+beta*eye(n);
r=1;
alp='c';%the known eigenvalues, the eigenfunctions and their derivatives 
        % will be given in p,dp,q respectively
[x,wint]=pd(n,dom);
wipr=ones(n,1);
p=zeros(27,1);dp=zeros(n,27);q=dp;
for k=1:27 p(k)=floor(k/2);end;
for k=1:2:27 dp(:,k)=cos(p(k)*x);q(:,k)=-p(k)*sin(p(k)*x);end;
for k=2:2:26 dp(:,k)=sin(p(k)*x);q(:,k)=p(k)*cos(p(k)*x);end;
for i=1:length(p)
    p(i)=p(i)^2;
    I(i)=wip(dp(:,i),dp(:,i),wipr,wint,dom);
    dp(:,i)=dp(:,i)/sqrt(I(i));q(:,i)=q(:,i)/sqrt(I(i));
end