batmat::linalg::micro_kernels::sterf Namespace Reference

Classes
struct	SterfOptions

Functions
template<class T, class Abi>
std::expected< index_t, index_t >	sterf (view< T, Abi, StorageOrder::ColMajor > diag, view< T, Abi, StorageOrder::ColMajor > subdiag, SterfOptions options) noexcept
	Eigenvalues of a symmetric tridiagonal matrix given by diag and subdiag, computed in-place using the Pal-Walker-Kahan variant of the implicit QR/QL method with Wilkinson shifts.
constexpr auto	default_tolerance (auto user_tol) noexcept
template<class T, class Abi>
datapar::simd< T, Abi >	safe_scaling_factor (datapar::simd< T, Abi > anorm) noexcept
template<class T, class Abi>
bool	all_zero (datapar::simd< T, Abi > x) noexcept
template<class T, class Abi>
bool	negligible_squared_e (datapar::simd< T, Abi > e0_sq, datapar::simd< T, Abi > d0, datapar::simd< T, Abi > d1, T ε_sq) noexcept
template<class T, class Abi>
std::pair< datapar::simd< T, Abi >, datapar::simd< T, Abi > >	stable_2x2_eigenvalues (datapar::simd< T, Abi > a, datapar::simd< T, Abi > b, datapar::simd< T, Abi > c) noexcept
	Eigenvalues of [a b; b c].
template<class T, class Abi>
void	solve_2x2_squared_e_inplace (uview< T, Abi, StorageOrder::ColMajor > d, uview< T, Abi, StorageOrder::ColMajor > e, index_t l) noexcept
template<class T, class Abi>
void	scale_diag_only (uview< T, Abi, StorageOrder::ColMajor > d, index_t l, index_t m, datapar::simd< T, Abi > factor) noexcept
template<class T, class Abi>
void	scale_squared_e (uview< T, Abi, StorageOrder::ColMajor > d, uview< T, Abi, StorageOrder::ColMajor > e, index_t l, index_t m, datapar::simd< T, Abi > factor) noexcept
template<class T, class Abi>
void	sterf_ql_sweep_squared_e_inplace (uview< T, Abi, StorageOrder::ColMajor > d, uview< T, Abi, StorageOrder::ColMajor > e, index_t l, index_t m) noexcept
template<class T, class Abi>
void	sterf_qr_sweep_squared_e_inplace (uview< T, Abi, StorageOrder::ColMajor > d, uview< T, Abi, StorageOrder::ColMajor > e, index_t l, index_t m) noexcept
template<class T, class Abi>
void	sterf_dynamic_step_squared_e_inplace (uview< T, Abi, StorageOrder::ColMajor > d, uview< T, Abi, StorageOrder::ColMajor > e, index_t l, index_t m) noexcept
template<class T, class Abi>
datapar::simd< T, Abi >	squared_block_norm_estimate_from_squared_e (uview< T, Abi, StorageOrder::ColMajor > d, uview< T, Abi, StorageOrder::ColMajor > e_sq, index_t l, index_t m) noexcept
template<class T, class Abi>
datapar::simd< T, Abi >	block_norm_estimate_from_squared_e (uview< T, Abi, StorageOrder::ColMajor > d, uview< T, Abi, StorageOrder::ColMajor > e_sq, index_t l, index_t m) noexcept

---

Class Documentation

batmat::linalg::micro_kernels::sterf::SterfOptions

struct batmat::linalg::micro_kernels::sterf::SterfOptions

Class Members
double	relative_tolerance = 0.0	If <= 0, machine epsilon is used.
index_t	max_iterations_per_eigenvalue = 64

Function Documentation

sterf()

template<class T, class Abi>

std::expected< index_t, index_t > batmat::linalg::micro_kernels::sterf::sterf ( view< T, Abi, StorageOrder::ColMajor > diag, view< T, Abi, StorageOrder::ColMajor > subdiag, SterfOptions options )

noexcept

Eigenvalues of a symmetric tridiagonal matrix given by diag and subdiag, computed in-place using the Pal-Walker-Kahan variant of the implicit QR/QL method with Wilkinson shifts.

Based on LAPACK 3.12.1's STERF: https://netlib.org/lapack//explore-html/d4/d9d/group__sterf_gad293bb81da1c7785b42796d1e197f08c.html

Definition at line 227 of file sterf.tpp.

default_tolerance()

auto batmat::linalg::micro_kernels::sterf::default_tolerance ( auto user_tol )

nodiscardconstexprnoexcept

Definition at line 16 of file sterf.tpp.

safe_scaling_factor()

template<class T, class Abi>

datapar::simd< T, Abi > batmat::linalg::micro_kernels::sterf::safe_scaling_factor ( datapar::simd< T, Abi > anorm )

nodiscardnoexcept

Definition at line 21 of file sterf.tpp.

all_zero()

template<class T, class Abi>

bool batmat::linalg::micro_kernels::sterf::all_zero ( datapar::simd< T, Abi > x )

nodiscardnoexcept

Definition at line 39 of file sterf.tpp.

negligible_squared_e()

template<class T, class Abi>

bool batmat::linalg::micro_kernels::sterf::negligible_squared_e ( datapar::simd< T, Abi > e0_sq, datapar::simd< T, Abi > d0, datapar::simd< T, Abi > d1, T ε_sq )

nodiscardnoexcept

Definition at line 45 of file sterf.tpp.

stable_2x2_eigenvalues()

template<class T, class Abi>

std::pair< datapar::simd< T, Abi >, datapar::simd< T, Abi > > batmat::linalg::micro_kernels::sterf::stable_2x2_eigenvalues ( datapar::simd< T, Abi > a, datapar::simd< T, Abi > b, datapar::simd< T, Abi > c )

nodiscardnoexcept

Eigenvalues of [a b; b c].

Definition at line 55 of file sterf.tpp.

solve_2x2_squared_e_inplace()

template<class T, class Abi>

void batmat::linalg::micro_kernels::sterf::solve_2x2_squared_e_inplace ( uview< T, Abi, StorageOrder::ColMajor > d, uview< T, Abi, StorageOrder::ColMajor > e, index_t l )

noexcept

Definition at line 70 of file sterf.tpp.

scale_diag_only()

template<class T, class Abi>

void batmat::linalg::micro_kernels::sterf::scale_diag_only ( uview< T, Abi, StorageOrder::ColMajor > d, index_t l, index_t m, datapar::simd< T, Abi > factor )

noexcept

Definition at line 81 of file sterf.tpp.

scale_squared_e()

template<class T, class Abi>

void batmat::linalg::micro_kernels::sterf::scale_squared_e ( uview< T, Abi, StorageOrder::ColMajor > d, uview< T, Abi, StorageOrder::ColMajor > e, index_t l, index_t m, datapar::simd< T, Abi > factor )

noexcept

Definition at line 88 of file sterf.tpp.

sterf_ql_sweep_squared_e_inplace()

template<class T, class Abi>

void batmat::linalg::micro_kernels::sterf::sterf_ql_sweep_squared_e_inplace ( uview< T, Abi, StorageOrder::ColMajor > d, uview< T, Abi, StorageOrder::ColMajor > e, index_t l, index_t m )

noexcept

Definition at line 98 of file sterf.tpp.

sterf_qr_sweep_squared_e_inplace()

template<class T, class Abi>

void batmat::linalg::micro_kernels::sterf::sterf_qr_sweep_squared_e_inplace ( uview< T, Abi, StorageOrder::ColMajor > d, uview< T, Abi, StorageOrder::ColMajor > e, index_t l, index_t m )

noexcept

Definition at line 139 of file sterf.tpp.

sterf_dynamic_step_squared_e_inplace()

template<class T, class Abi>

void batmat::linalg::micro_kernels::sterf::sterf_dynamic_step_squared_e_inplace ( uview< T, Abi, StorageOrder::ColMajor > d, uview< T, Abi, StorageOrder::ColMajor > e, index_t l, index_t m )

noexcept

Definition at line 180 of file sterf.tpp.

squared_block_norm_estimate_from_squared_e()

template<class T, class Abi>

datapar::simd< T, Abi > batmat::linalg::micro_kernels::sterf::squared_block_norm_estimate_from_squared_e ( uview< T, Abi, StorageOrder::ColMajor > d, uview< T, Abi, StorageOrder::ColMajor > e_sq, index_t l, index_t m )

nodiscardnoexcept

Definition at line 194 of file sterf.tpp.

block_norm_estimate_from_squared_e()

template<class T, class Abi>

datapar::simd< T, Abi > batmat::linalg::micro_kernels::sterf::block_norm_estimate_from_squared_e ( uview< T, Abi, StorageOrder::ColMajor > d, uview< T, Abi, StorageOrder::ColMajor > e_sq, index_t l, index_t m )

nodiscardnoexcept

Definition at line 215 of file sterf.tpp.