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lib.rs
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lib.rs
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//! Linear Algebra eXtension (LAX)
//! ===============================
//!
//! ndarray-free safe Rust wrapper for LAPACK FFI
//!
//! Linear equation, Inverse matrix, Condition number
//! --------------------------------------------------
//!
//! As the property of $A$, several types of triangular factorization are used:
//!
//! - LU-decomposition for general matrix
//! - $PA = LU$, where $L$ is lower matrix, $U$ is upper matrix, and $P$ is permutation matrix
//! - Bunch-Kaufman diagonal pivoting method for nonpositive-definite Hermitian matrix
//! - $A = U D U^\dagger$, where $U$ is upper matrix,
//! $D$ is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
//!
//! | matrix type | Triangler factorization (TRF) | Solve (TRS) | Inverse matrix (TRI) | Reciprocal condition number (CON) |
//! |:--------------------------------|:------------------------------|:------------|:---------------------|:----------------------------------|
//! | General (GE) | [lu] | [solve] | [inv] | [rcond] |
//! | Symmetric (SY) / Hermitian (HE) | [bk] | [solveh] | [invh] | - |
//!
//! [lu]: solve/trait.Solve_.html#tymethod.lu
//! [solve]: solve/trait.Solve_.html#tymethod.solve
//! [inv]: solve/trait.Solve_.html#tymethod.inv
//! [rcond]: solve/trait.Solve_.html#tymethod.rcond
//!
//! [bk]: solveh/trait.Solveh_.html#tymethod.bk
//! [solveh]: solveh/trait.Solveh_.html#tymethod.solveh
//! [invh]: solveh/trait.Solveh_.html#tymethod.invh
//!
//! Eigenvalue Problem
//! -------------------
//!
//! Solve eigenvalue problem for a matrix $A$
//!
//! $$ Av_i = \lambda_i v_i $$
//!
//! or generalized eigenvalue problem
//!
//! $$ Av_i = \lambda_i B v_i $$
//!
//! | matrix type | Eigenvalue (EV) | Generalized Eigenvalue Problem (EG) |
//! |:--------------------------------|:----------------|:------------------------------------|
//! | General (GE) |[eig] | - |
//! | Symmetric (SY) / Hermitian (HE) |[eigh] |[eigh_generalized] |
//!
//! [eig]: eig/trait.Eig_.html#tymethod.eig
//! [eigh]: eigh/trait.Eigh_.html#tymethod.eigh
//! [eigh_generalized]: eigh/trait.Eigh_.html#tymethod.eigh_generalized
//!
//! Singular Value Decomposition (SVD), Least square problem
//! ----------------------------------------------------------
//!
//! | matrix type | Singular Value Decomposition (SVD) | SVD with divided-and-conquer (SDD) | Least square problem (LSD) |
//! |:-------------|:-----------------------------------|:-----------------------------------|:---------------------------|
//! | General (GE) | [svd] | [svddc] | [least_squares] |
//!
//! [svd]: svd/trait.SVD_.html#tymethod.svd
//! [svddc]: svddck/trait.SVDDC_.html#tymethod.svddc
//! [least_squares]: least_squares/trait.LeastSquaresSvdDivideConquer_.html#tymethod.least_squares
#[cfg(any(feature = "intel-mkl-system", feature = "intel-mkl-static"))]
extern crate intel_mkl_src as _src;
#[cfg(any(feature = "openblas-system", feature = "openblas-static"))]
extern crate openblas_src as _src;
#[cfg(any(feature = "netlib-system", feature = "netlib-static"))]
extern crate netlib_src as _src;
pub mod error;
pub mod layout;
mod cholesky;
mod eig;
mod eigh;
mod least_squares;
mod opnorm;
mod qr;
mod rcond;
mod solve;
mod solveh;
mod svd;
mod svddc;
mod triangular;
mod tridiagonal;
pub use self::cholesky::*;
pub use self::eig::*;
pub use self::eigh::*;
pub use self::least_squares::*;
pub use self::opnorm::*;
pub use self::qr::*;
pub use self::rcond::*;
pub use self::solve::*;
pub use self::solveh::*;
pub use self::svd::*;
pub use self::svddc::*;
pub use self::triangular::*;
pub use self::tridiagonal::*;
use cauchy::*;
pub type Pivot = Vec<i32>;
/// Trait for primitive types which implements LAPACK subroutines
pub trait Lapack:
OperatorNorm_
+ QR_
+ SVD_
+ SVDDC_
+ Solve_
+ Solveh_
+ Cholesky_
+ Eig_
+ Eigh_
+ Triangular_
+ Tridiagonal_
+ Rcond_
+ LeastSquaresSvdDivideConquer_
{
}
impl Lapack for f32 {}
impl Lapack for f64 {}
impl Lapack for c32 {}
impl Lapack for c64 {}
/// Upper/Lower specification for seveal usages
#[derive(Debug, Clone, Copy)]
#[repr(u8)]
pub enum UPLO {
Upper = b'U',
Lower = b'L',
}
impl UPLO {
pub fn t(self) -> Self {
match self {
UPLO::Upper => UPLO::Lower,
UPLO::Lower => UPLO::Upper,
}
}
/// To use Fortran LAPACK API in lapack-sys crate
pub fn as_ptr(&self) -> *const i8 {
self as *const UPLO as *const i8
}
}
#[derive(Debug, Clone, Copy)]
#[repr(u8)]
pub enum Transpose {
No = b'N',
Transpose = b'T',
Hermite = b'C',
}
impl Transpose {
/// To use Fortran LAPACK API in lapack-sys crate
pub fn as_ptr(&self) -> *const i8 {
self as *const Transpose as *const i8
}
}
#[derive(Debug, Clone, Copy)]
#[repr(u8)]
pub enum NormType {
One = b'O',
Infinity = b'I',
Frobenius = b'F',
}
impl NormType {
pub fn transpose(self) -> Self {
match self {
NormType::One => NormType::Infinity,
NormType::Infinity => NormType::One,
NormType::Frobenius => NormType::Frobenius,
}
}
/// To use Fortran LAPACK API in lapack-sys crate
pub fn as_ptr(&self) -> *const i8 {
self as *const NormType as *const i8
}
}
/// Create a vector without initialization
///
/// Safety
/// ------
/// - Memory is not initialized. Do not read the memory before write.
///
unsafe fn vec_uninit<T: Sized>(n: usize) -> Vec<T> {
let mut v = Vec::with_capacity(n);
v.set_len(n);
v
}