# Crate linxal [−] [src]

# 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.

# Uasge

linxal is available as a crate through cargo. Add the following line
to your Cargo.toml, in the `dependencies`

section:

```
[dependencies]
...
linxal = "0.5"
```

In your `lib.rs`

or `main.rs`

file, use

```
extern crate linxal;
use linxal::prelude::*;
```

The `linxal::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`

.

#[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:

#[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:

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:

#[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); }

## Modules

eigenvalues |
Contains methods for solving eigenvalues, including general and symmetric/Hermitian eigenvalue problems. |

factorization |
Traits and functions for computing matrix factoriations. |

generate |
Generate random matrices. |

least_squares |
This module contains the |

permute | |

prelude |
Common traits, structures, and macros for most user-end applications |

properties |
Module for testing various matrix properties, such as being diagonal or unitary. |

solve_linear |
Containts traits and methods to solve sets of linear equations. |

svd |
Solve singular value decomposition problems. |

types |
Globally-used traits, structs, and enums |

util |

## Macros

assert_eq_within_tol |
Assert that two ndarrays are logically equivalent, within tolerance. |