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//! # Description //! //! `linxal` is a linear algebra package on top of `ndarray`.It //! currently provides major drivers from LAPACK, but will also //! support other higher-level tasks in the future, such as linear //! regression, PCA, etc. //! //! The repository for `linxal` can be found //! [here](https://github.com/masonium/linxal). //! //! # Uasge //! //! linxal is available as a crate through cargo. Add the following line //! to your Cargo.toml, in the `dependencies` section: //! //! ```text //! [dependencies] //! ... //! linxal = "0.5" //! ``` //! //! In your `lib.rs` or `main.rs` file, use //! //! ```text //! extern crate linxal; //! use linxal::prelude::*; //! ``` //! //! The [`linxal::prelude`](./prelude) modules re-exports the most useful functionality. //! //! # Organization //! //! Most of the useful functionality for `linxal` comes in the form of //! traits, which are implemented in terms of scalars and provide //! functionality for matrices and vectors composed of the //! scalars. //! //! The `LinxalMatrix` trait, defined on two-dimensional `ndarray` //! arrays, contains most of the computational funcationality in //! `linxal`. //! //! ```rust //! #[macro_use] //! extern crate linxal; //! extern crate ndarray; //! //! use linxal::types::{c32, LinxalMatrix}; //! use ndarray::{arr1, arr2}; //! //! fn main() { //! let m = arr2(&[[1.0f32, 2.0], //! [-2.0, 1.0]]); //! //! let r = m.eigenvalues(); //! assert!(r.is_ok()); //! //! let r = r.unwrap(); //! let true_evs = arr1(&[c32::new(1.0, 2.0), c32::new(1.0, -2.0)]); //! assert_eq_within_tol!(true_evs, r, 0.01); //! //! let b = arr1(&[-1.0, 1.0]); //! let x = m.solve_linear(&b).unwrap(); //! let true_x = arr1(&[-0.6, -0.2]); //! assert_eq_within_tol!(x, true_x, 0.0001); //! } //! ``` //! //! Most functionality is implemented in terms of specific traits //! defined on scalars, representing computational routines. These //! traits typically have a `compute` function, and variants, which //! performs the describe behavior. //! //! For instance, the `Eigen` trait, implemented for single- and //! double-precision real and complex-valued scalars, allows one to //! compute eigenvalues and eigenvectors of square matrices with that //! type of scalar as elements. The above example can be implemented //! in terms of individual computational routines, as follows: //! //! ```rust //! #[macro_use] //! extern crate linxal; //! extern crate ndarray; //! //! use linxal::eigenvalues::{Eigen}; //! use linxal::solve_linear::{SolveLinear}; //! use linxal::types::{c32, LinxalScalar}; //! use ndarray::{arr1, arr2}; //! //! fn main() { //! let m = arr2(&[[1.0f32, 2.0], //! [-2.0, 1.0]]); //! //! let r = Eigen::compute(&m, false, false); //! assert!(r.is_ok()); //! //! let r = r.unwrap(); //! let true_evs = arr1(&[c32::new(1.0, 2.0), c32::new(1.0, -2.0)]); //! assert_eq_within_tol!(true_evs, r.values, 0.01); //! //! let b = arr1(&[-1.0, 1.0]); //! let x = SolveLinear::compute(&m, &b).unwrap(); //! let true_x = arr1(&[-0.6, -0.2]); //! assert_eq_within_tol!(x, true_x, 0.0001); //! } //! ``` //! //! # Details //! //! ## Prelude //! //! In practice, you can use the prelude to gain access to the most //! common features, rather than having to include computational //! traits individually. //! //! For instance, the previous example's `use`s could be replaced by: //! //! ```rust //! use linxal::prelude::*; //! ``` //! //! For reference, all tests and examples will include the specific //! required traits, but this precision is rarely necessary. //! //! ## Symmetric Algorithms //! //! Some traits and algorithms are designed only to work on symmetric //! or Hermititan matrices. Throught the library, 'Sym' or 'Symmetric' //! refers simply to symmetric matrices for real-valued matrices and //! Hermititan matrices for complex-valued matrices. //! //! Symmetric algorithms typically take a (`Symmetric`) enum //! argument. `Symmetric::Upper` indicates that the values of the //! matrix are stored in the upper-triangular portion of the //! matrix. `Symmetric::Lower` corresponds to the lower portion. For //! algorithms that take this argument, only that portion is read. So, //! for example: //! //! ```rust //! #[macro_use] //! extern crate linxal; //! extern crate ndarray; //! //! use ndarray::{arr1, arr2}; //! use linxal::types::{Symmetric}; //! use linxal::eigenvalues::{SymEigen}; //! //! fn main() { //! // `upper_only` is not symmetric, but the portion below the diagonal is never read. //! let upper_only = arr2(&[[1.0f32, 2.0], [-3.0, 1.0]]); //! //! // Since only the upper triangle is read by `SymEigen`, it is equivalent to `full`. //! let full = arr2(&[[1.0f32, 2.0], [2.0, 1.0]]); //! //! let upper_only_ev = SymEigen::compute_into(upper_only, Symmetric::Upper).unwrap(); //! let full_ev = SymEigen::compute_into(full, Symmetric::Upper).unwrap(); //! //! assert_eq_within_tol!(upper_only_ev, full_ev, 1e-5); //! } //! ``` //! #![macro_use] #[macro_use] extern crate ndarray; extern crate libc; extern crate lapack_sys; extern crate lapack; extern crate num_traits; extern crate rand; pub mod util; pub mod permute; pub mod eigenvalues; pub mod svd; pub mod solve_linear; pub mod least_squares; pub mod types; pub mod factorization; pub mod generate; pub mod properties; #[macro_use] pub mod prelude; mod impl_prelude;