Struct HermitianEigenproblem 

pub struct HermitianEigenproblem<'a> { /* private fields */ }

A finite Hermitian matrix pencil with an explicitly positive-definite metric.

Types retain exact basis identities and physical dimensions. Matrices describe the already constrained space; this owner never removes nullspace coordinates or regularizes a singular metric. The caller retains the constraint lineage. A standard problem supplies an explicit dimensionless identity metric.

Implementations

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impl HermitianEigenproblem<'_>

Signature links:HermitianEigenproblem

pub fn excluded_metric_projector( operator: &ValueLiteral, metric: &ValueLiteral, embedding: &ValueLiteral, tolerance: f64, ) -> Result<ValueLiteral, Diagnostic>

Signature links:excluded_metric_projectorValueLiteralValueLiteralValueLiteralf64ResultValueLiteralDiagnostic

Dimensionless complementary metric projector E = I - P (Pᴴ B P)⁻¹ Pᴴ B of an explicitly declared embedding.

The full original metric may be singular or indefinite; its pullback must be positive definite. E describes directions excluded by P and has rank full_extent - admitted_extent. It is generally an oblique projector in coefficient coordinates. This does not assert that A or B vanishes on those directions, or that they are physical gauge freedoms. Cholesky triangular solves avoid explicitly forming an inverse. tolerance checks the B-orthonormality of the lifted coordinate basis.

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impl HermitianEigenproblem<'_>

Signature links:HermitianEigenproblem

pub fn pullback( operator: &ValueLiteral, metric: &ValueLiteral, embedding: &ValueLiteral, ) -> Result<(ValueLiteral, ValueLiteral), Diagnostic>

Signature links:pullbackValueLiteralValueLiteralValueLiteralResultValueLiteralValueLiteralDiagnostic

Pull back complete Hermitian matrices along an explicit map u=Pq.

Returns (Pᴴ A P, Pᴴ B P) in P’s exact source basis. The restricted metric must have positive finite Cholesky pivots; the original metric may be singular or indefinite only outside this admitted space. No coordinates are chosen, deleted, shifted or regularized implicitly. This does not prove that reduced eigenvectors satisfy the original equation: lifted candidates still require original-pencil verification.

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impl HermitianEigenproblem<'_>

Signature links:HermitianEigenproblem

pub fn metric_projector( &self, modes: &[ValueLiteral], tolerance: f64, ) -> Result<ValueLiteral, Diagnostic>

Signature links:metric_projectorValueLiteralf64ResultValueLiteralDiagnostic

Construct the dimensionless metric projector P=U Uᴴ B of supplied modes.

Checks the exact mode types, nonzero vectors and B-orthonormality, using ||UᴴBU-I||_F <= tolerance. Tolerance is an explicit dimensionless numerical control in (0,1). A mode permutation, independent phases, or a unitary rotation within this subspace leaves the projector unchanged. This does not establish that the subspace is invariant under A; eigenpair residuals must be verified separately by the owning Plan.

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impl<'a> HermitianEigenproblem<'a>

Signature links:HermitianEigenproblem

pub fn check_operator(operator: &ValueLiteral) -> Result<(), Diagnostic>

Signature links:check_operatorValueLiteralResult()Diagnostic

Check one complete Hermitian endomorphism on its exact finite basis.

This checks the bound coefficients before any evolution scaling or solve. Both triangles and imaginary diagonal parts participate; no tolerance, dimension cap, or discarded triangle weakens this mathematical contract.

Errors

Rejects non-endomorphism types or any unequal conjugate coefficients.

pub fn new( operator: &'a ValueLiteral, metric: &'a ValueLiteral, ) -> Result<HermitianEigenproblem<'a>, Diagnostic>

Signature links:newValueLiteralValueLiteralResultHermitianEigenproblemDiagnostic

Check exact type correspondence, both full Hermitian matrices, and every Cholesky pivot of the metric. No dimension-specific formula or size cap is used. Numerically nonpositive/nonfinite pivots reject explicitly.

pub fn original_eigenpair_defects( operator: &'a ValueLiteral, metric: &'a ValueLiteral, eigenvalue: &ValueLiteral, mode: &ValueLiteral, ) -> Result<(f64, f64), Diagnostic>

Signature links:original_eigenpair_defectsValueLiteralValueLiteralValueLiteralValueLiteralResultf64f64Diagnostic

Verify a lifted mode against a complete original Hermitian pencil.

The original metric need not be positive definite outside the admitted space. This evaluates residual and normalization only; it does not admit a singular/indefinite pencil for execution or prove subspace membership.

pub fn original_metric_projector( operator: &'a ValueLiteral, metric: &'a ValueLiteral, modes: &[ValueLiteral], tolerance: f64, ) -> Result<ValueLiteral, Diagnostic>

Signature links:original_metric_projectorValueLiteralValueLiteralValueLiteralf64ResultValueLiteralDiagnostic

Verify B-orthonormal lifted modes and construct their original-space metric projector. Positivity outside their span is not established.

pub const fn operator(&self) -> &ValueLiteral

Signature links:operatorValueLiteral

Complete typed operator, in row-major component order.

pub const fn metric(&self) -> &ValueLiteral

Signature links:metricValueLiteral

Complete typed metric, in row-major component order.

pub const fn dimension(&self) -> usize

Signature links:dimensionusize

Number of coordinates of the exact admitted finite space.

pub const fn eigenvalue_type(&self) -> &ValueType

Signature links:eigenvalue_typeValueType

Real eigenvalue type, including the quotient dimension A/B.

pub const fn mode_type(&self) -> &ValueType

Signature links:mode_typeValueType

Mode type, including the metric normalization dimension B^-1/2.

pub fn eigenpair_defects( &self, eigenvalue: &ValueLiteral, mode: &ValueLiteral, ) -> Result<(f64, f64), Diagnostic>

Signature links:eigenpair_defectsValueLiteralValueLiteralResultf64f64Diagnostic

Independently measure a typed candidate against the original pencil.

Returns (relative residual, normalization defect) where the residual is ||Au-lambda Bu|| / (||Au|| + |lambda| ||Bu||) and the defect is |uᴴBu - 1|. A zero residual with zero denominator has relative residual zero. Both quantities are dimensionless; no acceptance tolerance is hidden here. Zero modes, wrong types and nonfinite arithmetic reject.

Trait Implementations

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impl<'a> Clone for HermitianEigenproblem<'a>

Signature links:CloneHermitianEigenproblem

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fn clone(&self) -> HermitianEigenproblem<'a>

Signature links:cloneHermitianEigenproblem

Returns a duplicate of the value.

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fn clone_from(&mut self, source: &Self)

Signature links:unstableSourceclone_from

Performs copy-assignment from source.

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impl<'a> Debug for HermitianEigenproblem<'a>

Signature links:DebugHermitianEigenproblem

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

Signature links:fmtFormatterResult()Error

Formats the value using the given formatter.