Crate eigenvalues[−][src]
Eigenvalues decomposition
This crate contains implementations of several algorithm to diagonalize symmetric matrices.
Davidson Usage Example
// Use the Davidson method use eigenvalues::davidson::Davidson; use eigenvalues::{DavidsonCorrection, SpectrumTarget}; use nalgebra::{DMatrix, DVector}; // Generate random symmetric matrix let matrix = eigenvalues::utils::generate_diagonal_dominant(20, 0.005); let tolerance = 1e-4; // Compute the first 2 lowest eigenvalues/eigenvectors using the DPR method let eig = Davidson::new (matrix.clone(), 2, DavidsonCorrection::DPR, SpectrumTarget::Lowest, tolerance).unwrap(); println!("eigenvalues:{}", eig.eigenvalues); println!("eigenvectors:{}", eig.eigenvectors); // Compute the first 2 highest eigenvalues/eigenvectors using the GJD method let eig = Davidson::new (matrix, 2, DavidsonCorrection::GJD, SpectrumTarget::Highest, tolerance).unwrap(); println!("eigenvalues:{}", eig.eigenvalues); println!("eigenvectors:{}", eig.eigenvectors);
Lanczos Usage Example
use nalgebra as na; use eigenvalues::algorithms::lanczos::HermitianLanczos; use eigenvalues::utils::{generate_random_sparse_symmetric, sort_eigenpairs}; use eigenvalues::SpectrumTarget; // Generate sparse matrix let matrix = generate_random_sparse_symmetric(100, 5, 0.5); // Use 20 iterations to approximate the highest part of the spectrum let spectrum_target = SpectrumTarget::Highest; let lanczos = HermitianLanczos::new(matrix.clone(), 20, spectrum_target).unwrap(); let eig = sort_eigenpairs(na::linalg::SymmetricEigen::new(matrix.clone()), false); // Compare against reference println!("Computed eigenvalues:\n{}", lanczos.eigenvalues.rows(0, 3)); println!("Expected eigenvalues:\n{}", eig.eigenvalues.rows(0, 3));
Re-exports
pub use algorithms::davidson; |
pub use algorithms::lanczos; |
pub use algorithms::DavidsonCorrection; |
pub use algorithms::SpectrumTarget; |
pub use modified_gram_schmidt::MGS; |
Modules
algorithms | Algorithms to compute (some) eigenvalues/eigenvectors for symmetric matrices. |
matrix_operations | Common matrix operations for all the matrix representations. |
modified_gram_schmidt | Modified Gram-Schmidt (MGS) |
utils | Auxiliar functions to manipulate arrays |