Struct lax::eig::EigWork

#[non_exhaustive]
pub struct EigWork<T: Scalar> {
    pub n: i32,
    pub jobvr: JobEv,
    pub jobvl: JobEv,
    pub eigs: Vec<MaybeUninit<T::Complex>>,
    pub eigs_re: Option<Vec<MaybeUninit<T::Real>>>,
    pub eigs_im: Option<Vec<MaybeUninit<T::Real>>>,
    pub vc_l: Option<Vec<MaybeUninit<T::Complex>>>,
    pub vr_l: Option<Vec<MaybeUninit<T::Real>>>,
    pub vc_r: Option<Vec<MaybeUninit<T::Complex>>>,
    pub vr_r: Option<Vec<MaybeUninit<T::Real>>>,
    pub work: Vec<MaybeUninit<T>>,
    pub rwork: Option<Vec<MaybeUninit<T::Real>>>,
}

Eigenvalue problem for general matrix

To manage memory more strictly, use EigWork.

Right and Left eigenvalue problem

LAPACK can solve both right eigenvalue problem $$ AV_R = V_R \Lambda $$ where $V_R = \left( v_R^1, \cdots, v_R^n \right)$ are right eigenvectors and left eigenvalue problem $$ V_L^\dagger A = V_L^\dagger \Lambda $$ where $V_L = \left( v_L^1, \cdots, v_L^n \right)$ are left eigenvectors and eigenvalues $$ \Lambda = \begin{pmatrix} \lambda_1 & & 0 \\ & \ddots & \\ 0 & & \lambda_n \end{pmatrix} $$ which satisfies $A v_R^i = \lambda_i v_R^i$ and $\left(v_L^i\right)^\dagger A = \lambda_i \left(v_L^i\right)^\dagger$ for column-major matrices, although row-major matrices are not supported. Since a row-major matrix can be interpreted as a transpose of a column-major matrix, this transforms right eigenvalue problem to left one:

$$ A^\dagger V = V Λ ⟺ V^\dagger A = Λ V^\dagger $$

Fields (Non-exhaustive)

Non-exhaustive structs could have additional fields added in future. Therefore, non-exhaustive structs cannot be constructed in external crates using the traditional Struct { .. } syntax; cannot be matched against without a wildcard ..; and struct update syntax will not work.

n: i32

Problem size

jobvr: JobEv

Compute right eigenvectors or not

jobvl: JobEv

Compute left eigenvectors or not

eigs: Vec<MaybeUninit<T::Complex>>

Eigenvalues

eigs_re: Option<Vec<MaybeUninit<T::Real>>>

Real part of eigenvalues used in real routines

eigs_im: Option<Vec<MaybeUninit<T::Real>>>

Imaginary part of eigenvalues used in real routines

vc_l: Option<Vec<MaybeUninit<T::Complex>>>

Left eigenvectors

vr_l: Option<Vec<MaybeUninit<T::Real>>>

Left eigenvectors used in real routines

vc_r: Option<Vec<MaybeUninit<T::Complex>>>

Right eigenvectors

vr_r: Option<Vec<MaybeUninit<T::Real>>>

Right eigenvectors used in real routines

work: Vec<MaybeUninit<T>>

Working memory

rwork: Option<Vec<MaybeUninit<T::Real>>>

Working memory with T::Real

Implementations

impl<T> EigWork<T>

where T: Scalar, EigWork<T>: EigWorkImpl<Elem = T>,

pub fn new(calc_v: bool, l: MatrixLayout) -> Result<Self>

Create new working memory for eigenvalues compution.

pub fn calc(&mut self, a: &mut [T]) -> Result<EigRef<'_, T>>

Compute eigenvalues and vectors on this working memory.

pub fn eval(self, a: &mut [T]) -> Result<EigOwned<T>>

Compute eigenvalues and vectors by consuming this working memory.

Trait Implementations

impl EigWorkImpl for EigWork<c32>

type Elem = Complex<f32>

fn new(calc_v: bool, l: MatrixLayout) -> Result<Self>

fn calc<'work>( &'work mut self, a: &mut [Self::Elem], ) -> Result<EigRef<'work, Self::Elem>>

fn eval(self, a: &mut [Self::Elem]) -> Result<EigOwned<Self::Elem>>

impl EigWorkImpl for EigWork<c64>

type Elem = Complex<f64>

fn new(calc_v: bool, l: MatrixLayout) -> Result<Self>

fn calc<'work>( &'work mut self, a: &mut [Self::Elem], ) -> Result<EigRef<'work, Self::Elem>>

fn eval(self, a: &mut [Self::Elem]) -> Result<EigOwned<Self::Elem>>

impl EigWorkImpl for EigWork<f32>

type Elem = f32

fn new(calc_v: bool, l: MatrixLayout) -> Result<Self>

fn calc<'work>( &'work mut self, a: &mut [Self::Elem], ) -> Result<EigRef<'work, Self::Elem>>

fn eval(self, a: &mut [Self::Elem]) -> Result<EigOwned<Self::Elem>>

impl EigWorkImpl for EigWork<f64>

type Elem = f64

fn new(calc_v: bool, l: MatrixLayout) -> Result<Self>

fn calc<'work>( &'work mut self, a: &mut [Self::Elem], ) -> Result<EigRef<'work, Self::Elem>>

fn eval(self, a: &mut [Self::Elem]) -> Result<EigOwned<Self::Elem>>