Crate lax

Expand description

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