Matlab - How to perform a sparse eigendecomposition?

[poster]

I have a large n * n sparse matrix called L. constant k is a given value. I am supposed to do this:

perform a sparse eigendecomposition of the Laplacian L that computes
only the eigenvectors associated with the k smallest-magnitude
eigenvalues.

How can I do this?

This is what I have tried:

d = diag(eigs(L,k,'smallestabs'));

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And then I am supposed to do this:

Then project matrix V (vertex positions) onto the basis spanned by
these eigenvectors and reconstruct a filtered V called V_new (version
of the mesh).

P is not important here. I just want the new V based on the D matrix. Basically I want to calculate this:

I have tried this:

pd = padarray(diag(d),[n-k,n-k],0,'post');

V_new = V * pd * V'

But seems not to be working, because the resulting V_new is very different than V.

What is the right way to do this?

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