felipeZ / eigenvalues

symmetric matrices algorithms to compute eigenvalue/eigenvector pairs

Eigenvalue Decomposition

This package contains some iterative algorithms for computing the eigenvalues/eigenvectors of a symmetric matrix H, implemented in Rust.

Matrix Representation

The library examples represent H using the nalgebra DMatrix type, but the matrix H does not need to be dense. Sparse or other representations are handled by implementing the Matrixoperations trait.

Available Algorithms:

• Davidson using either Diagonal-Preconditioned-Residue (DPR) or Generalized Jacobi Davidson (GJD). See Davidson Diagonalization Method
• Lanczos, see Hermitian Lanczos

Note:

The Davidson method is suitable for diagonal-dominant symmetric matrices that are quite common in certain scientific problems like electronic structure calculations. The Davidson method could be not practical for other kind of symmetric matrices.