I need to get the eigenvectors of a sparse matrix. This is leading me to two issues/questions:

1) Is there a way to do eigen-decomposition for sparse matrices? Or do you always have to use dense matrices? It would be AWESOME to have a Lanczos method available.
2) Do DiagonalMatrix and SparseMatrix play nicely? I am getting errors when trying to add/subtract the two

More details: I have a sparse matrix which is formed from three matrices, two of which are Eigen::DiagonalMatrix and one which is Eigen::SparseMatrix as such:

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const Eigen::SparseMatrix<double> sparse_mat2 = diag1 * (diag2 - sparse_mat1) * diag1

That line is giving me fits saying that you cannot add/subtract diag2 and sparse_mat, which seems surprising to me.

My ultimate goal is to obtain k eigenvectors of sparse_mat2 corresponding to the k smallest eigenvalues. Is the only way to do this to convert all matrices to the dense form?

Check this project: https://github.com/yixuan/spectra

For sparse and diagonal interaction, such operations are not allowed because they are inherently inefficient unless we create a temporary, whereas in most cases the user can avoid this temporary by doing, e.g. (with 3.3-alpha1):

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#include <Eigen/Sparse>
using namespace Eigen;
int main() {
  DiagonalMatrix<double,Dynamic> diag1, diag2;
  SparseMatrix<double> sparse_mat1;
  sparse_mat1 -= diag2;
  const Eigen::SparseMatrix<double> sparse_mat2 = diag1 * (-sparse_mat1) * diag1;
}


Wow thanks so much for your response. These were exactly the two things that I needed!!