Class to perform Tikhonov regularization. More...

#include <num_collect/regularization/tikhonov.h>

Inheritance diagram for num_collect::regularization::tikhonov< Coeff, Data >:

Collaboration diagram for num_collect::regularization::tikhonov< Coeff, Data >:

Public Types
using	base_type
	Type of base class.

using	coeff_type = Coeff
	Type of coefficient matrices.

Public Types inherited from num_collect::regularization::regularized_solver_base< tikhonov< Coeff, Data >, Data >
using	data_type
	Type of data.

using	scalar_type
	Type of scalars.

Public Member Functions
	tikhonov ()
	Constructor.

void	compute (const coeff_type &coeff, const data_type &data)
	Compute internal matrices.

auto	data_size () const -> index_type
	Get the size of data.

auto	first_derivative_of_regularization_term (const scalar_type &param) const -> scalar_type
	Calculate the first-order derivative of the Regularization term.

auto	first_derivative_of_residual_norm (const scalar_type &param) const -> scalar_type
	Calculate the first-order derivative of the squared norm of the residual.

auto	param_search_region () const -> std::pair< scalar_type, scalar_type >
	Get the default region to search for the optimal regularization parameter.

auto	regularization_term (const scalar_type &param) const -> scalar_type
	Calculate the regularization term.

auto	residual_norm (const scalar_type &param) const -> scalar_type
	Calculate the squared norm of the residual.

auto	second_derivative_of_regularization_term (const scalar_type &param) const -> scalar_type
	Calculate the send-order derivative of the Regularization term.

auto	second_derivative_of_residual_norm (const scalar_type &param) const -> scalar_type
	Calculate the second-order derivative of the squared norm of the residual.

auto	singular_values () const -> const typename Eigen::BDCSVD< coeff_type >::SingularValuesType &
	Get the singular values.

void	solve (const scalar_type &param, data_type &solution) const
	Solve for a regularization parameter.

auto	sum_of_filter_factor (const scalar_type &param) const -> scalar_type
	Calculate the sum of filter factors.

Public Member Functions inherited from num_collect::regularization::explicit_regularized_solver_base< tikhonov< Coeff, Data >, Data >
auto	first_derivative_of_regularization_term (const scalar_type &param) const -> scalar_type
	Calculate the first-order derivative of the Regularization term.

auto	first_derivative_of_residual_norm (const scalar_type &param) const -> scalar_type
	Calculate the first-order derivative of the squared norm of the residual.

auto	gcv (const scalar_type &param) const -> scalar_type
	Calculate GCV function.

auto	l_curve_curvature (const scalar_type &param) const
	Calculate the curvature of L-curve.

auto	regularization_term (const scalar_type &param) const -> scalar_type
	Calculate the regularization term.

auto	residual_norm (const scalar_type &param) const -> scalar_type
	Calculate the squared norm of the residual.

auto	second_derivative_of_regularization_term (const scalar_type &param) const -> scalar_type
	Calculate the send-order derivative of the Regularization term.

auto	second_derivative_of_residual_norm (const scalar_type &param) const -> scalar_type
	Calculate the second-order derivative of the squared norm of the residual.

void	solve (const scalar_type &param, data_type &solution) const
	Solve for a regularization parameter.

auto	sum_of_filter_factor (const scalar_type &param) const -> scalar_type
	Calculate the sum of filter factors.

Public Member Functions inherited from num_collect::regularization::regularized_solver_base< tikhonov< Coeff, Data >, Data >
auto	data_size () const -> index_type
	Get the size of data.

auto	param_search_region () const -> std::pair< scalar_type, scalar_type >
	Get the default region to search for the optimal regularization parameter.

void	solve (const scalar_type &param, data_type &solution)
	Solve for a regularization parameter.

Public Member Functions inherited from num_collect::logging::logging_mixin
	logging_mixin (log_tag_view tag)
	Constructor.

template<typename Child >
void	configure_child_algorithm_logger_if_exists (Child &child)
	Configure a logger of a child algorithm if exists.

auto	logger () const noexcept -> const num_collect::logging::logger &
	Access to the logger.

auto	logger () noexcept -> num_collect::logging::logger &
	Access to the logger.

Private Attributes
scalar_type	min_res_ {}
	Minimum residual.

data_type	rot_data_ {}
	Data in the space of singular values.

Eigen::BDCSVD< coeff_type >	svd_ {}
	SVD of the coefficient matrix.

Additional Inherited Members
Protected Member Functions inherited from num_collect::regularization::explicit_regularized_solver_base< tikhonov< Coeff, Data >, Data >
	explicit_regularized_solver_base (logging::log_tag_view tag)
	Constructor.

Protected Member Functions inherited from num_collect::regularization::regularized_solver_base< tikhonov< Coeff, Data >, Data >
	regularized_solver_base (logging::log_tag_view tag)
	Constructor.

auto	derived () const noexcept -> const tikhonov< Coeff, Data > &
	Access derived object.

auto	derived () noexcept -> tikhonov< Coeff, Data > &
	Access derived object.

Detailed Description

template<base::concepts::dense_matrix Coeff, base::concepts::dense_matrix Data>
class num_collect::regularization::tikhonov< Coeff, Data >

Class to perform Tikhonov regularization.

Template Parameters

Coeff	Type of coefficient matrices.
Data	Type of data vectors.

Definition at line 47 of file tikhonov.h.

Member Typedef Documentation

◆ base_type

template<base::concepts::dense_matrix Coeff, base::concepts::dense_matrix Data>

using num_collect::regularization::tikhonov< Coeff, Data >::base_type

Initial value:

explicit_regularized_solver_base<tikhonov<Coeff, Data>, Data>

num_collect::regularization::explicit_regularized_solver_base< tikhonov< Coeff, Data >, Data >::explicit_regularized_solver_base

explicit_regularized_solver_base(logging::log_tag_view tag)

Definition explicit_regularized_solver_base.h:177

Type of base class.

Definition at line 51 of file tikhonov.h.

◆ coeff_type

template<base::concepts::dense_matrix Coeff, base::concepts::dense_matrix Data>

using num_collect::regularization::tikhonov< Coeff, Data >::coeff_type = Coeff

Type of coefficient matrices.

Definition at line 58 of file tikhonov.h.

Constructor & Destructor Documentation

◆ tikhonov()

template<base::concepts::dense_matrix Coeff, base::concepts::dense_matrix Data>

num_collect::regularization::tikhonov< Coeff, Data >::tikhonov ( )

inline

Constructor.

Definition at line 67 of file tikhonov.h.

Member Function Documentation

◆ compute()

template<base::concepts::dense_matrix Coeff, base::concepts::dense_matrix Data>

void num_collect::regularization::tikhonov< Coeff, Data >::compute	(	const coeff_type &	coeff,
		const data_type &	data )

inline

Compute internal matrices.

Parameters

[in]	coeff	Coefficient matrix.
[in]	data	Data vector.

Definition at line 75 of file tikhonov.h.

◆ data_size()

template<base::concepts::dense_matrix Coeff, base::concepts::dense_matrix Data>

auto num_collect::regularization::tikhonov< Coeff, Data >::data_size ( ) const -> index_type

inlinenodiscard

Get the size of data.

Returns: Size of data.

Definition at line 211 of file tikhonov.h.

◆ first_derivative_of_regularization_term()

template<base::concepts::dense_matrix Coeff, base::concepts::dense_matrix Data>

auto num_collect::regularization::tikhonov< Coeff, Data >::first_derivative_of_regularization_term ( const scalar_type & param ) const -> scalar_type

inlinenodiscard

Calculate the first-order derivative of the Regularization term.

Parameters

[in] param Regularization parameter.

Returns: Result.

Definition at line 151 of file tikhonov.h.

◆ first_derivative_of_residual_norm()

template<base::concepts::dense_matrix Coeff, base::concepts::dense_matrix Data>

auto num_collect::regularization::tikhonov< Coeff, Data >::first_derivative_of_residual_norm ( const scalar_type & param ) const -> scalar_type

inlinenodiscard

Calculate the first-order derivative of the squared norm of the residual.

Parameters

[in] param Regularization parameter.

Returns: Result.

Definition at line 136 of file tikhonov.h.

◆ param_search_region()

template<base::concepts::dense_matrix Coeff, base::concepts::dense_matrix Data>

auto num_collect::regularization::tikhonov< Coeff, Data >::param_search_region ( ) const -> std::pair<scalar_type, scalar_type>

inlinenodiscard

Get the default region to search for the optimal regularization parameter.

Returns: Pair of minimum and maximum regularization parameters.

Definition at line 214 of file tikhonov.h.

◆ regularization_term()

template<base::concepts::dense_matrix Coeff, base::concepts::dense_matrix Data>

auto num_collect::regularization::tikhonov< Coeff, Data >::regularization_term ( const scalar_type & param ) const -> scalar_type

inlinenodiscard

Calculate the regularization term.

Parameters

[in] param Regularization parameter.

Returns: Result.

Definition at line 122 of file tikhonov.h.

◆ residual_norm()

template<base::concepts::dense_matrix Coeff, base::concepts::dense_matrix Data>

auto num_collect::regularization::tikhonov< Coeff, Data >::residual_norm ( const scalar_type & param ) const -> scalar_type

inlinenodiscard

Calculate the squared norm of the residual.

Parameters

[in] param Regularization parameter.

Returns: Result.

Definition at line 108 of file tikhonov.h.

◆ second_derivative_of_regularization_term()

template<base::concepts::dense_matrix Coeff, base::concepts::dense_matrix Data>

auto num_collect::regularization::tikhonov< Coeff, Data >::second_derivative_of_regularization_term ( const scalar_type & param ) const -> scalar_type

inlinenodiscard

Calculate the send-order derivative of the Regularization term.

Parameters

[in] param Regularization parameter.

Returns: Result.

Definition at line 183 of file tikhonov.h.

◆ second_derivative_of_residual_norm()

template<base::concepts::dense_matrix Coeff, base::concepts::dense_matrix Data>

auto num_collect::regularization::tikhonov< Coeff, Data >::second_derivative_of_residual_norm ( const scalar_type & param ) const -> scalar_type

inlinenodiscard

Calculate the second-order derivative of the squared norm of the residual.

Parameters

[in] param Regularization parameter.

Returns: Result.

Definition at line 166 of file tikhonov.h.

◆ singular_values()

template<base::concepts::dense_matrix Coeff, base::concepts::dense_matrix Data>

auto num_collect::regularization::tikhonov< Coeff, Data >::singular_values ( ) const -> const typename Eigen::BDCSVD<coeff_type>::SingularValuesType&

inlinenodiscard

Get the singular values.

Returns: Singular values.

Definition at line 102 of file tikhonov.h.

◆ solve()

template<base::concepts::dense_matrix Coeff, base::concepts::dense_matrix Data>

void num_collect::regularization::tikhonov< Coeff, Data >::solve	(	const scalar_type &	param,
		data_type &	solution ) const

inline

Solve for a regularization parameter.

Parameters

[in]	param	Regularization parameter.
[out]	solution	Solution.

Definition at line 86 of file tikhonov.h.

◆ sum_of_filter_factor()

template<base::concepts::dense_matrix Coeff, base::concepts::dense_matrix Data>

auto num_collect::regularization::tikhonov< Coeff, Data >::sum_of_filter_factor ( const scalar_type & param ) const -> scalar_type

inlinenodiscard

Calculate the sum of filter factors.

Parameters

[in] param Regularization parameter.

Returns: Result.

Definition at line 198 of file tikhonov.h.

Member Data Documentation

◆ min_res_

template<base::concepts::dense_matrix Coeff, base::concepts::dense_matrix Data>

scalar_type num_collect::regularization::tikhonov< Coeff, Data >::min_res_ {}

private

Minimum residual.

Definition at line 231 of file tikhonov.h.

◆ rot_data_

template<base::concepts::dense_matrix Coeff, base::concepts::dense_matrix Data>

data_type num_collect::regularization::tikhonov< Coeff, Data >::rot_data_ {}

private

Data in the space of singular values.

Definition at line 228 of file tikhonov.h.

◆ svd_

template<base::concepts::dense_matrix Coeff, base::concepts::dense_matrix Data>

Eigen::BDCSVD<coeff_type> num_collect::regularization::tikhonov< Coeff, Data >::svd_ {}

private

SVD of the coefficient matrix.

Definition at line 225 of file tikhonov.h.

The documentation for this class was generated from the following file:

include/num_collect/regularization/tikhonov.h

Public Types

Public Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ base_type

◆ coeff_type

Constructor & Destructor Documentation

◆ tikhonov()

Member Function Documentation

◆ compute()

◆ data_size()

◆ first_derivative_of_regularization_term()

◆ first_derivative_of_residual_norm()

◆ param_search_region()

◆ regularization_term()

◆ residual_norm()

◆ second_derivative_of_regularization_term()

◆ second_derivative_of_residual_norm()

◆ singular_values()

◆ solve()

◆ sum_of_filter_factor()

Member Data Documentation

◆ min_res_

◆ rot_data_

◆ svd_