#include <uni20/core/scalar_concepts.hpp>
#include <uni20/core/math.hpp>
#include <algorithm>
#include <cmath>
#include <complex>
#include <concepts>
#include <cstddef>
#include <limits>
#include <optional>
#include <stdexcept>
#include <string>
#include <type_traits>
#include <vector>

Include dependency graph for matrix_free.hpp:

This graph shows which files directly or indirectly include this file:

Classes
struct	uni20::krylov::EigenResult< Scalar, Vector >
	Matrix-free eigenvalue result with solver-owned vector objects. More...

struct	uni20::krylov::NonsymmetricArnoldiDiagnostics< Scalar >
	Optional diagnostic state for nonsymmetric Arnoldi solves. More...

struct	uni20::krylov::NonsymmetricEigenParams< Scalar >
	Parameters for a native nonsymmetric eigenvalue solve. More...

struct	uni20::krylov::NonsymmetricEigenResult< Scalar, Vector >
	Matrix-free nonsymmetric eigenvalue result. More...

struct	uni20::krylov::SymmetricEigenParams< Scalar >
	Common parameters for a symmetric or Hermitian eigenvalue solve. More...

struct	uni20::krylov::SymmetricLanczosDiagnostics< Scalar >
	Optional diagnostic state for symmetric Lanczos solves. More...

struct	uni20::krylov::SymmetricRestartCycleDiagnostics< Scalar >
	Diagnostic state for one symmetric Lanczos restart cycle. More...

struct	uni20::krylov::SymmetricTransformOptions< Scalar >
	Native symmetric transform options for mapping `OP` Ritz values. More...

Namespaces
namespace	uni20

namespace	uni20::krylov

Concepts
concept	uni20::krylov::KrylovVectorOps
	Concept for opaque vector-space operations required by Krylov solvers.

concept	uni20::krylov::KrylovOperator
	Concept for an output-first Krylov operator application `y <- OP*x`.

concept	uni20::krylov::KrylovMatrixFreeOperator
	Composite concept for current adapters that own vector ops and `OP*x`.

concept	uni20::krylov::MatrixFreeVectorOps
	Backward-compatible name for the combined vector/operator concept.

concept	uni20::krylov::KrylovMetricInnerProduct
	Optional customization point for backend-owned metric inner products.

concept	uni20::krylov::MetricInnerProductOps
	Backward-compatible name for direct metric inner-product customization.

concept	uni20::krylov::KrylovNorm
	Optional customization point for direct vector norms.

Typedefs
using	uni20::krylov::SymmetricSpectralTransform = SymmetricTransformKind
	Backward-compatible name for symmetric transform kinds.

template<uni20::Real Scalar>
using	uni20::krylov::SymmetricSpectralTransformOptions = SymmetricTransformOptions< Scalar >
	Backward-compatible name for symmetric transform options.

Enumerations
enum class	uni20::krylov::KrylovDiagnosticsLevel { uni20::krylov::None , uni20::krylov::Summary , uni20::krylov::Full }
	Amount of solver-internal diagnostic state to retain. More...

enum class	uni20::krylov::NonsymmetricStatus { uni20::krylov::Converged , uni20::krylov::NotConverged , uni20::krylov::ComplexPairEncountered , uni20::krylov::ComplexPromotionRecommended , uni20::krylov::RealSchurPairRequired , uni20::krylov::AmbiguousReality , uni20::krylov::Breakdown , uni20::krylov::InvalidInput }
	Native nonsymmetric solver status. More...

enum class	uni20::krylov::RealNonsymmetricPolicy { uni20::krylov::RequireRealEigenpairs , uni20::krylov::AllowRealSchurPairs , uni20::krylov::PromoteToComplexSuggested }
	Policy for real nonsymmetric solves when wanted Ritz values may be complex. More...

enum class	uni20::krylov::RitzReality { uni20::krylov::Real , uni20::krylov::Ambiguous , uni20::krylov::Complex }
	Numerical reality classification for a complex Ritz value from a real Arnoldi solve. More...

enum class	uni20::krylov::SpectrumPart { uni20::krylov::LargestMagnitude , uni20::krylov::SmallestMagnitude , uni20::krylov::LargestAlgebraic , uni20::krylov::SmallestAlgebraic , uni20::krylov::BothEnds , uni20::krylov::LargestReal , uni20::krylov::SmallestReal , uni20::krylov::LargestImaginary , uni20::krylov::SmallestImaginary }
	Spectrum selector for matrix-free eigenvalue solvers. More...

enum class	uni20::krylov::SymmetricTransformKind { uni20::krylov::Regular , uni20::krylov::GeneralizedInverse , uni20::krylov::ShiftInvert , uni20::krylov::Buckling , uni20::krylov::Cayley }
	Transform represented by the caller-supplied symmetric Krylov operator. More...

Functions
template<uni20::Complex C>
RitzReality	uni20::krylov::classify_ritz_reality (C theta, uni20::make_real_t< C > tolerance=uni20::make_real_t< C >{}, uni20::make_real_t< C > scale=uni20::make_real_t< C >{1}, uni20::make_real_t< C > ambiguity_factor=uni20::make_real_t< C >{10})
	Classify whether a complex Ritz value is numerically real.

template<uni20::Real Scalar> requires requires { uni20::numeric_limits<Scalar>::epsilon(); }
Scalar	uni20::krylov::default_complex_pair_tolerance ()
	Default imaginary-part tolerance for deciding whether a real Arnoldi Ritz value is real.

template<uni20::Real Scalar>
Scalar	uni20::krylov::default_complex_pair_tolerance (Scalar const &exemplar)
	Default reality tolerance using the exemplar's working precision.

int	uni20::krylov::default_nonsymmetric_krylov_dimension (int eigenvalue_count, std::size_t problem_dimension)
	Return the default nonsymmetric Arnoldi subspace dimension.

int	uni20::krylov::default_nonsymmetric_retained_ritz_count (int eigenvalue_count, int krylov_dimension)
	Return the default nonsymmetric retained Schur dimension.

int	uni20::krylov::default_symmetric_krylov_dimension (int eigenvalue_count, std::size_t problem_dimension)
	Return the default symmetric/Hermitian Krylov subspace dimension.

int	uni20::krylov::default_symmetric_retained_ritz_count (int eigenvalue_count, int krylov_dimension)
	Return the default symmetric/Hermitian retained Ritz count.

template<uni20::Real Scalar>
int	uni20::krylov::effective_nonsymmetric_krylov_dimension (NonsymmetricEigenParams< Scalar > const &params, std::size_t problem_dimension)
	Return the effective nonsymmetric Arnoldi subspace dimension.

template<uni20::Real Scalar>
int	uni20::krylov::effective_nonsymmetric_retained_ritz_count (NonsymmetricEigenParams< Scalar > const &params, int krylov_dimension)
	Return the effective nonsymmetric retained Ritz or Schur count.

template<uni20::Real Scalar>
int	uni20::krylov::effective_symmetric_krylov_dimension (SymmetricEigenParams< Scalar > const &params, std::size_t problem_dimension)
	Return the effective symmetric/Hermitian Krylov subspace dimension.

template<uni20::Real Scalar>
int	uni20::krylov::effective_symmetric_retained_ritz_count (SymmetricEigenParams< Scalar > const &params, int krylov_dimension)
	Return the effective symmetric/Hermitian retained Ritz count.

template<typename Scalar , typename Vector , typename MetricOps , typename BOps , typename InnerOps >
Scalar	uni20::krylov::metric_inner_product_or_apply (MetricOps &metric_ops, BOps &b_ops, InnerOps &inner_ops, Vector const &x, Vector const &y, Vector &scratch)
	Evaluate a metric inner product, using a backend override when available.

template<typename Scalar , typename Vector , typename Ops >
uni20::make_real_t< Scalar >	uni20::krylov::norm_or_inner_product (Ops &ops, Vector const &x)
	Evaluate a vector norm, using a backend override when available.

template<typename Ops , typename Vector >
std::size_t	uni20::krylov::validate_matrix_free_dimensions (Ops const &ops, Vector const &vector, char const *context)
	Validate that an initial/prototype vector matches the matrix-free problem dimension.

Classes

Namespaces

Concepts

Typedefs

Enumerations

Functions