Struct EigResidual 

pub struct EigResidual {
    values: Vec<Complex>,
    vectors: DMatrix<Complex>,
    pivots: Vec<usize>,
    scale: f64,
    vectors_lu: OnceLock<Result<Lu>>,
}

What eig saves for its derivatives: the right eigensystem, with unit vectors whose largest component is real and positive.

Fields

values: Vec<Complex>

vectors: DMatrix<Complex>

pivots: Vec<usize>

scale: f64

vectors_lu: OnceLock<Result<Lu>>

Factor the eigenvectors only when a derivative needs their inverse; every later direction and cotangent shares the same factors.

Implementations

impl EigResidual

pub fn state_size(n: usize) -> Result<usize>

Byte count for the native saved state of an n × n eigensystem.

impl EigResidual

fn vectors_lu(&self) -> Result<&Lu>

pub fn values(&self) -> &[Complex]

The eigenvalues in the solver’s order, which the pullback reads.

pub const fn vectors(&self) -> &DMatrix<Complex>

The right eigenvectors, one column per eigenvalue, which the pullback reads.

fn tied_pivot(&self, column: usize) -> bool

Whether the phase pivot is tied with another largest component.

fn eigenbasis_tangent( &self, operator: &DMatrix<Complex>, ) -> Result<DMatrix<Complex>>

Express the perturbation in the eigenbasis; its diagonal is the eigenvalue derivative and its off-diagonal entries determine eigenvectors.

fn check_value_order(&self, weights: Option<&[Complex]>) -> Result<()>

An ordered spectrum switches modes when real parts cross. Only equal loss weights across a tied group make that change irrelevant.

pub fn pushforward_values( &self, operator: &DMatrix<Complex>, ) -> Result<Vec<Complex>>

Eigenvalue tangents with no eigenvector phase constraint. Distinct real parts keep eigvals’ ordering fixed; tied phase pivots are supported.

pub fn pullback_values(&self, values: &[Complex]) -> Result<DMatrix<Complex>>

Pullback of eigvals, allowing equal weights at ordering ties.

pub fn pushforward( &self, operator: &DMatrix<Complex>, ) -> Result<(Vec<Complex>, DMatrix<Complex>)>

Eigenpair tangents with the same unit norm and real-positive pivot phase as the primal. Repeated eigenvalues and tied phase pivots have no pushforward of the complete eigenpair output. Use Self::pushforward_values when only eigenvalues are needed.

pub fn pullback( &self, values: &[Complex], vectors: DMatrix<Complex>, ) -> Result<DMatrix<Complex>>

The operator gradient from the eigenvalue and eigenvector cotangents, with the phase of each vector fixed at its pivot.

Repeated eigenvalues support equal eigenvalue weights and zero vector cotangents within each repeated group. Individual modes there have no pullback.

Trait Implementations

impl Debug for EigResidual

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl SavedState for EigResidual

fn save_state(&self) -> Result<Vec<u8>>

Copy the saved numerical state into its fixed byte layout.

fn from_state(bytes: &[u8]) -> Result<Self>

Restore numerical state from bytes produced by this extension.