7 unstable releases (3 breaking)
0.16.0 | Oct 4, 2022 |
---|---|
0.15.0 | Aug 30, 2022 |
0.2.0 | Jul 17, 2021 |
0.1.0 | Feb 13, 2021 |
#2133 in Algorithms
16,811 downloads per month
Used in 78 crates
(4 directly)
150KB
3.5K
SLoC
Linear Algebra eXtension (LAX)
ndarray-free safe Rust wrapper for LAPACK FFI for implementing ndarray-linalg crate. This crate responsibles for
- Linking to LAPACK shared/static libraries
- Dispatching to LAPACK routines based on scalar types by using
Lapack
trait
lib.rs
:
Safe Rust wrapper for LAPACK without external dependency.
[Lapack] trait
This crates provides LAPACK wrapper as a traits. For example, LU decomposition of general matrices is provided like:
pub trait Lapack {
fn lu(l: MatrixLayout, a: &mut [Self]) -> Result<Pivot>;
}
see [Lapack] for detail.
This trait is implemented for [f32], [f64], [c32] which is an alias to num::Complex<f32>
,
and [c64] which is an alias to num::Complex<f64>
.
You can use it like f64::lu
:
use lax::{Lapack, layout::MatrixLayout, Transpose};
let mut a = vec![
1.0, 2.0,
3.0, 4.0
];
let mut b = vec![1.0, 2.0];
let layout = MatrixLayout::C { row: 2, lda: 2 };
let pivot = f64::lu(layout, &mut a).unwrap();
f64::solve(layout, Transpose::No, &a, &pivot, &mut b).unwrap();
When you want to write generic algorithm for real and complex matrices, this trait can be used as a trait bound:
use lax::{Lapack, layout::MatrixLayout, Transpose};
fn solve_at_once<T: Lapack>(layout: MatrixLayout, a: &mut [T], b: &mut [T]) -> Result<(), lax::error::Error> {
let pivot = T::lu(layout, a)?;
T::solve(layout, Transpose::No, a, &pivot, b)?;
Ok(())
}
There are several similar traits as described below to keep development easy. They are merged into a single trait, [Lapack].
Linear equation, Inverse matrix, Condition number
According to the property input metrix, several types of triangular decomposition are used:
- [solve] module provides methods for LU-decomposition for general matrix.
- [solveh] module provides methods for Bunch-Kaufman diagonal pivoting method for symmetric/Hermitian indefinite matrix.
- [cholesky] module provides methods for Cholesky decomposition for symmetric/Hermitian positive dinite matrix.
Eigenvalue Problem
According to the property input metrix, there are several types of eigenvalue problem API
- [eig] module for eigenvalue problem for general matrix.
- [eigh] module for eigenvalue problem for symmetric/Hermitian matrix.
- [eigh_generalized] module for generalized eigenvalue problem for symmetric/Hermitian matrix.
Singular Value Decomposition
- [svd] module for singular value decomposition (SVD) for general matrix
- [svddc] module for singular value decomposition (SVD) with divided-and-conquer algorithm for general matrix
- [least_squares] module for solving least square problem using SVD
Dependencies
~73MB
~1M SLoC