#include <uni20/core/scalar_concepts.hpp>
#include <uni20/krylov/dense_subspace.hpp>
#include <uni20/krylov/matrix_free.hpp>
#include <algorithm>
#include <cmath>
#include <cstddef>
#include <limits>
#include <numeric>
#include <optional>
#include <span>
#include <stdexcept>
#include <type_traits>
#include <utility>
#include <vector>

Include dependency graph for symmetric_lanczos.hpp:

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Classes
struct	uni20::krylov::SymmetricCompressedLanczosFactorization< Scalar, Vector >
	Compressed symmetric Lanczos factorization after implicit restart. More...

struct	uni20::krylov::SymmetricQrShiftResult< Scalar >
	Result of applying implicit QR shifts to a symmetric tridiagonal projection. More...

struct	uni20::krylov::SymmetricRestartPlan< Scalar >
	Restart dimensions after implicit-restart edge-case adjustment. More...

struct	uni20::krylov::SymmetricRestartSelection< Scalar >
	Ritz-value selection state used by symmetric implicit restart logic. More...

Namespaces
namespace	uni20

namespace	uni20::krylov

Functions
template<uni20::Real Scalar>
SymmetricQrShiftResult< Scalar >	uni20::krylov::apply_symmetric_qr_shifts (std::vector< Scalar > diagonal, std::vector< Scalar > subdiagonal, std::vector< Scalar > const &shifts)
	Apply implicit shifted QR sweeps to a symmetric tridiagonal matrix.

template<uni20::LapackRealOrComplex Scalar, typename Vector , KrylovMatrixFreeOperator< Vector, Scalar > Ops>
SymmetricCompressedLanczosFactorization< uni20::make_real_t< Scalar >, Vector >	uni20::krylov::compress_symmetric_lanczos_restart (Ops &ops, std::vector< Vector > const &basis, Vector const &residual, SymmetricQrShiftResult< uni20::make_real_t< Scalar > > const &shifted, std::size_t retained_count)
	Compress a Lanczos factorization with the accumulated restart transform.

template<uni20::Real Scalar>
Scalar	uni20::krylov::map_symmetric_transformed_eigenvalue (Scalar transformed_value, SymmetricSpectralTransformOptions< Scalar > const &options)
	Map a native symmetric transformed Ritz value back to the original eigenvalue scale.

template<uni20::Real Scalar>
SymmetricRestartPlan< Scalar >	uni20::krylov::plan_symmetric_restart (SymmetricEigenParams< Scalar > const &params, std::vector< Scalar > const &values, std::vector< Scalar > const &residual_bounds, int converged_count)
	Adjust restart dimensions for implicit-restart edge cases.

template<uni20::Real Scalar>
SymmetricRestartSelection< Scalar >	uni20::krylov::select_symmetric_restart (std::vector< Scalar > const &values, std::vector< Scalar > const &residual_bounds, SymmetricEigenParams< Scalar > const &params, std::size_t shift_count, std::span< std::size_t const > protected_shift_indices={})
	Select wanted Ritz values and exact-shift candidates for symmetric restart.

template<uni20::LapackRealOrComplex Scalar, typename Vector , KrylovMatrixFreeOperator< Vector, Scalar > OpOps, KrylovMatrixFreeOperator< Vector, Scalar > BOps, typename MetricOps >
EigenResult< uni20::make_real_t< Scalar >, Vector >	uni20::krylov::symmetric_lanczos_restarted_generalized_transformed (OpOps &op_ops, BOps &b_ops, MetricOps &metric_ops, Vector const &initial, SymmetricEigenParams< uni20::make_real_t< Scalar > > const &params, SymmetricSpectralTransformOptions< uni20::make_real_t< Scalar > > const &options)
	Run restarted symmetric Lanczos on a transformed generalized operator with a `B` metric.

template<uni20::LapackRealOrComplex Scalar, typename Vector , KrylovMatrixFreeOperator< Vector, Scalar > OpOps, KrylovMatrixFreeOperator< Vector, Scalar > BOps>
EigenResult< uni20::make_real_t< Scalar >, Vector >	uni20::krylov::symmetric_lanczos_restarted_generalized_transformed (OpOps &op_ops, BOps &b_ops, Vector const &initial, SymmetricEigenParams< uni20::make_real_t< Scalar > > const &params, SymmetricSpectralTransformOptions< uni20::make_real_t< Scalar > > const &options)
	Run restarted symmetric Lanczos on a transformed generalized operator with default metric handling.

template<uni20::LapackRealOrComplex Scalar, typename Vector , KrylovMatrixFreeOperator< Vector, Scalar > Ops>
EigenResult< uni20::make_real_t< Scalar >, Vector >	uni20::krylov::symmetric_lanczos_restarted_standard (Ops &ops, Vector const &initial, SymmetricEigenParams< uni20::make_real_t< Scalar > > const &params)
	Run a native symmetric/Hermitian Lanczos solve with implicit restarts.

template<uni20::LapackRealOrComplex Scalar, typename Vector , KrylovMatrixFreeOperator< Vector, Scalar > Ops>
EigenResult< uni20::make_real_t< Scalar >, Vector >	uni20::krylov::symmetric_lanczos_restarted_transformed (Ops &op_ops, Vector const &initial, SymmetricEigenParams< uni20::make_real_t< Scalar > > const &params, SymmetricSpectralTransformOptions< uni20::make_real_t< Scalar > > const &options)
	Run restarted symmetric Lanczos on a caller-supplied transformed operator.

template<uni20::LapackRealOrComplex Scalar, typename Vector , KrylovMatrixFreeOperator< Vector, Scalar > Ops>
EigenResult< uni20::make_real_t< Scalar >, Vector >	uni20::krylov::symmetric_lanczos_standard (Ops &ops, Vector const &initial, SymmetricEigenParams< uni20::make_real_t< Scalar > > const &params)
	Run the native symmetric/Hermitian Lanczos full-projection solver.

Classes

Namespaces

Functions