How large matrix can LAPACK support

[gyhuang]

Hello
My code is as simple as follows

LaSymmMatDouble A(N, N);
LaVectorDouble v(N);
LaGenMatDouble Eigenvectors(N, N);
LaEigSolve(A, v, Eigenvectors);

However, I find that N can not be more than 40000. I feel puzzled about this. From the Internet a lot of people said LAPACK supports large matrix. Also, it is a little bit slow to calculate eigenvectors.

My problem is simply to calculate eigenvectors and eigenvalue for matrix as large as 40000*40000. Any idea on this?

Thanks.