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
Re-exports§
pub use self::least_squares::LeastSquaresOwned;pub use self::svd::SvdOwned;pub use self::svd::SvdRef;pub use self::tridiagonal::LUFactorizedTridiagonal;pub use self::tridiagonal::Tridiagonal;pub use self::flags::*;
Modules§
- alloc
- cholesky
- Factorize positive-definite symmetric/Hermitian matrices using Cholesky algorithm
- eig
- Eigenvalue problem for general matricies
- eigh
- Eigenvalue problem for symmetric/Hermitian matricies
- eigh_
generalized - Generalized eigenvalue problem for symmetric/Hermitian matrices
- error
- flags
- Charactor flags, e.g.
'T', used in LAPACK API - layout
- Memory layout of matrices
- least_
squares - Least squares
- opnorm
- Operator norm
- qr
- QR decomposition
- rcond
- Reciprocal conditional number
- solve
- Solve linear equations using LU-decomposition
- solveh
- Factorize symmetric/Hermitian matrix using Bunch-Kaufman diagonal pivoting method
- svd
- Singular-value decomposition
- svddc
- Compute singular value decomposition with divide-and-conquer algorithm
- triangular
- Linear problem for triangular matrices
- tridiagonal
- Implement linear solver using LU decomposition for tridiagonal matrix
Traits§
- Lapack
- Trait for primitive types which implements LAPACK subroutines