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