Computes the `k` eigenvectors of the sparse graph Laplacian `L_conn_i_sparse`
corresponding to the smallest, non-trivial eigenvalues.
Eigenvectors for eigenvalues numerically close to zero are discarded based on a dynamic tolerance.
Usage
compute_spectral_sketch_sparse(L_conn_i_sparse, k, eigenvalue_tol = 1e-08)
Arguments
- L_conn_i_sparse
A sparse graph Laplacian matrix (`Matrix::dgCMatrix`, `V_p x V_p`).
Must be symmetric.
- k
An integer, the desired spectral rank. Must be `k >= 0`.
- eigenvalue_tol
Numeric floor used when dynamically determining the
tolerance for filtering near-zero eigenvalues. Defaults to `1e-8`.
Value
A list containing two elements:
- `vectors`: A dense matrix `U_orig_i` (`V_p x k_actual`) of eigenvectors.
`k_actual` may be less than `k` if not enough informative eigenvectors are found.
- `values`: A vector of eigenvalues corresponding to the eigenvectors.