title: Fastest way to compute k largest eigenvalues and corresponding eigenvectors with numpy
body: <p>I have a large NxN dense symmetric matrix and want the eigenvectors corresponding to the k largest eigenvalues.  What's the best way to find them (preferably using numpy but perhaps in general using blas/atlas/lapack if that's the only way to go)?  In general N is much much larger then k (say N > 5000, k &lt; 10).</p>
  
  <p>Numpy seems to only have functions for finding the k largest eigenvalues if my starting matrix is sparse.</p>