Class for fast iterative shrinkage-thresholding algorithm (FISTA) [1] for L1-regularization of linear equations. More...

#include <num_collect/regularization/fista.h>

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

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

Public Types
using	base_type = iterative_regularized_solver_base<this_type, Data>
	Type of the base class.

using	coeff_type = Coeff
	Type of coefficient matrices.

using	this_type = fista<Coeff, Data>
	This type.

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

using	scalar_type
	Type of scalars.

Public Member Functions
	fista ()
	Constructor.

void	calculate_data_for (const data_type &solution, data_type &data) const
	Calculate data for a solution.

void	change_data (const data_type &data)
	Change data.

void	compute (const Coeff &coeff, const Data &data)
	Compute internal parameters.

void	configure_iteration_logger (logging::iterations::iteration_logger< this_type > &iteration_logger) const
	Configure an iteration logger.

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

void	init (const scalar_type &param, data_type &solution)
	Initialize.

auto	is_stop_criteria_satisfied (const data_type &solution) const -> bool
	Determine if stopping criteria of the algorithm are satisfied.

void	iterate (const scalar_type &param, data_type &solution)
	Iterate the algorithm once.

auto	iterations () const noexcept -> index_type
	Get the number of iterations.

auto	max_iterations () const -> index_type
	Get the maximum number of iterations.

auto	max_iterations (index_type value) -> fista &
	Set the maximum number of iterations.

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 data_type &solution) const -> scalar_type
	Calculate the regularization term.

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

auto	residual_norm_rate () const -> scalar_type
	Get the rate of the last residual norm.

auto	tol_update_rate () const -> scalar_type
	Get the tolerance of update rate of the solution.

auto	tol_update_rate (scalar_type value) -> fista &
	Set the tolerance of update rate of the solution.

auto	update () const noexcept -> scalar_type
	Get the norm of the update of the solution in the last iteration.

Public Member Functions inherited from num_collect::regularization::iterative_regularized_solver_base< fista< Coeff, Data >, Data >
void	init (const scalar_type &param, data_type &solution)
	Initialize.

auto	is_stop_criteria_satisfied (const data_type &solution) const -> bool
	Determine if stopping criteria of the algorithm are satisfied.

void	iterate (const scalar_type &param, data_type &solution)
	Iterate the algorithm once.

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

Public Member Functions inherited from num_collect::regularization::implicit_regularized_solver_base< fista< Coeff, Data >, Data >
void	calculate_data_for (const data_type &solution, data_type &data) const
	Calculate data for a solution.

void	change_data (const data_type &data)
	Change data.

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

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

Public Member Functions inherited from num_collect::regularization::regularized_solver_base< fista< 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.

Public Member Functions inherited from num_collect::logging::iterations::iteration_logger_mixin< fista< Coeff, Data > >
	iteration_logger_mixin ()=default
	Constructor.

void	configure_iteration_logger (num_collect::logging::iterations::iteration_logger< fista< Coeff, Data > > &iteration_logger) const
	Configure an iteration logger.

auto	initialize_iteration_logger () -> num_collect::logging::iterations::iteration_logger< fista< Coeff, Data > > &
	Get the iteration logger.

Private Attributes
const coeff_type *	coeff_ {nullptr}
	Coefficient matrix.

const data_type *	data_ {nullptr}
	Data vector.

scalar_type	inv_max_eigen_ {}
	Inverse of maximum eigenvalue of \( AA^T \) for coefficient matrix \( A \).

index_type	iterations_ {}
	Number of iterations.

index_type	max_iterations_ {default_max_iterations}
	Maximum number of iterations.

data_type	residual_ {}
	Residual vector.

scalar_type	t_ {}
	Parameter for step size of y_.

scalar_type	tol_update_rate_ {default_tol_update_rate}
	Tolerance of update rate of the solution.

scalar_type	update_ {}
	Norm of the update of the solution in the last iteration.

data_type	y_ {}
	Another vector to update in FISTA.

Static Private Attributes
static constexpr index_type	default_max_iterations = 1000
	Default maximum number of iterations.

static constexpr auto	default_tol_update_rate
	Default tolerance of update rate of the solution.

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

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

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

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

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

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

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

Detailed Description

template<typename Coeff, typename Data>
class num_collect::regularization::fista< Coeff, Data >

Class for fast iterative shrinkage-thresholding algorithm (FISTA) [1] for L1-regularization of linear equations.

This class execute fast iterative shrinkage-thresholding algorithm (FISTA) for L1-regularization of linear equations. This class is for large inferior-determined problems, and implemented with OpenMP.

Template Parameters

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

Definition at line 55 of file fista.h.

Member Typedef Documentation

◆ base_type

template<typename Coeff , typename Data >

using num_collect::regularization::fista< Coeff, Data >::base_type = iterative_regularized_solver_base<this_type, Data>

Type of the base class.

Definition at line 62 of file fista.h.

◆ coeff_type

template<typename Coeff , typename Data >

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

Type of coefficient matrices.

Definition at line 68 of file fista.h.

◆ this_type

template<typename Coeff , typename Data >

using num_collect::regularization::fista< Coeff, Data >::this_type = fista<Coeff, Data>

This type.

Definition at line 59 of file fista.h.

Constructor & Destructor Documentation

◆ fista()

template<typename Coeff , typename Data >

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

inline

Constructor.

Definition at line 73 of file fista.h.

Member Function Documentation

◆ calculate_data_for()

template<typename Coeff , typename Data >

void num_collect::regularization::fista< Coeff, Data >::calculate_data_for	(	const data_type &	solution,
		data_type &	data ) const

inline

Calculate data for a solution.

Parameters

[in]	solution	Solution.
[out]	data	Data.

Definition at line 209 of file fista.h.

◆ change_data()

template<typename Coeff , typename Data >

void num_collect::regularization::fista< Coeff, Data >::change_data ( const data_type & data )

inline

Change data.

Parameters

[in] data New data.

Definition at line 206 of file fista.h.

◆ compute()

template<typename Coeff , typename Data >

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

inline

Compute internal parameters.

Parameters

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

Note: Pointers to the arguments are saved in this object, so don't destruct those arguments.; Call this before init.

Definition at line 85 of file fista.h.

◆ configure_iteration_logger()

template<typename Coeff , typename Data >

void num_collect::regularization::fista< Coeff, Data >::configure_iteration_logger ( logging::iterations::iteration_logger< this_type > & iteration_logger ) const

inline

Configure an iteration logger.

Parameters

[in] iteration_logger Iteration logger.

Definition at line 182 of file fista.h.

◆ data_size()

template<typename Coeff , typename Data >

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

inlinenodiscard

Get the size of data.

Returns: Size of data.

Definition at line 214 of file fista.h.

◆ init()

template<typename Coeff , typename Data >

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

inline

Initialize.

Parameters

[in]	param	Regularization parameter.
[in,out]	solution	Solution. (Assumed to be the initial solution.)

Warning: Any required initializations (with compute functions) are assumed to have been done.

Definition at line 95 of file fista.h.

◆ is_stop_criteria_satisfied()

template<typename Coeff , typename Data >

auto num_collect::regularization::fista< Coeff, Data >::is_stop_criteria_satisfied ( const data_type & solution ) const -> bool

inlinenodiscard

Determine if stopping criteria of the algorithm are satisfied.

Parameters

[in] solution Solution.

Returns: If stopping criteria of the algorithm are satisfied.

Definition at line 175 of file fista.h.

◆ iterate()

template<typename Coeff , typename Data >

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

inline

Iterate the algorithm once.

Parameters

[in]	param	Regularization parameter.
[in,out]	solution	Solution. (Assumed to be the last solution.)

Warning: Any required initializations (with init functions) are assumed to have been done.

Definition at line 117 of file fista.h.

◆ iterations()

template<typename Coeff , typename Data >

auto num_collect::regularization::fista< Coeff, Data >::iterations ( ) const -> index_type

inlinenodiscardnoexcept

Get the number of iterations.

Returns: Value.

Definition at line 235 of file fista.h.

◆ max_iterations() [1/2]

template<typename Coeff , typename Data >

auto num_collect::regularization::fista< Coeff, Data >::max_iterations ( ) const -> index_type

inlinenodiscard

Get the maximum number of iterations.

Returns: Value.

Definition at line 262 of file fista.h.

◆ max_iterations() [2/2]

template<typename Coeff , typename Data >

auto num_collect::regularization::fista< Coeff, Data >::max_iterations ( index_type value ) -> fista&

inline

Set the maximum number of iterations.

Parameters

[in] value Value.

Returns: This object.

Definition at line 272 of file fista.h.

◆ param_search_region()

template<typename Coeff , typename Data >

auto num_collect::regularization::fista< 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 217 of file fista.h.

◆ regularization_term()

template<typename Coeff , typename Data >

auto num_collect::regularization::fista< Coeff, Data >::regularization_term ( const data_type & solution ) const -> scalar_type

inlinenodiscard

Calculate the regularization term.

Parameters

[in] solution Solution.

Returns: Result.

Definition at line 200 of file fista.h.

◆ residual_norm()

template<typename Coeff , typename Data >

auto num_collect::regularization::fista< Coeff, Data >::residual_norm ( const data_type & solution ) const -> scalar_type

inlinenodiscard

Calculate the squared norm of the residual.

Parameters

[in] solution Solution.

Returns: Result.

Definition at line 194 of file fista.h.

◆ residual_norm_rate()

template<typename Coeff , typename Data >

auto num_collect::regularization::fista< Coeff, Data >::residual_norm_rate ( ) const -> scalar_type

inlinenodiscard

Get the rate of the last residual norm.

Returns: Rate of the residual norm.

Definition at line 253 of file fista.h.

◆ tol_update_rate() [1/2]

template<typename Coeff , typename Data >

auto num_collect::regularization::fista< Coeff, Data >::tol_update_rate ( ) const -> scalar_type

inlinenodiscard

Get the tolerance of update rate of the solution.

Returns: Value.

Definition at line 284 of file fista.h.

◆ tol_update_rate() [2/2]

template<typename Coeff , typename Data >

auto num_collect::regularization::fista< Coeff, Data >::tol_update_rate ( scalar_type value ) -> fista&

inline

Set the tolerance of update rate of the solution.

Parameters

[in] value Value.

Returns: This object.

Definition at line 294 of file fista.h.

◆ update()

template<typename Coeff , typename Data >

auto num_collect::regularization::fista< Coeff, Data >::update ( ) const -> scalar_type

inlinenodiscardnoexcept

Get the norm of the update of the solution in the last iteration.

Returns: Value.

Definition at line 244 of file fista.h.

Member Data Documentation

◆ coeff_

template<typename Coeff , typename Data >

const coeff_type* num_collect::regularization::fista< Coeff, Data >::coeff_ {nullptr}

private

Coefficient matrix.

Definition at line 305 of file fista.h.

◆ data_

template<typename Coeff , typename Data >

const data_type* num_collect::regularization::fista< Coeff, Data >::data_ {nullptr}

private

Data vector.

Definition at line 308 of file fista.h.

◆ default_max_iterations

template<typename Coeff , typename Data >

index_type num_collect::regularization::fista< Coeff, Data >::default_max_iterations = 1000

staticconstexprprivate

Default maximum number of iterations.

Definition at line 332 of file fista.h.

◆ default_tol_update_rate

template<typename Coeff , typename Data >

auto num_collect::regularization::fista< Coeff, Data >::default_tol_update_rate

staticconstexprprivate

Initial value:

=

static_cast<scalar_type>(1e-4)

num_collect::regularization::regularized_solver_base< fista< Coeff, Data >, Data >::scalar_type

typename Eigen::NumTraits< typename data_type::Scalar >::Real scalar_type

Definition regularized_solver_base.h:46

Default tolerance of update rate of the solution.

Definition at line 338 of file fista.h.

◆ inv_max_eigen_

template<typename Coeff , typename Data >

scalar_type num_collect::regularization::fista< Coeff, Data >::inv_max_eigen_ {}

private

Inverse of maximum eigenvalue of \( AA^T \) for coefficient matrix \( A \).

Definition at line 314 of file fista.h.

◆ iterations_

template<typename Coeff , typename Data >

index_type num_collect::regularization::fista< Coeff, Data >::iterations_ {}

private

Number of iterations.

Definition at line 317 of file fista.h.

◆ max_iterations_

template<typename Coeff , typename Data >

index_type num_collect::regularization::fista< Coeff, Data >::max_iterations_ {default_max_iterations}

private

Maximum number of iterations.

Definition at line 335 of file fista.h.

◆ residual_

template<typename Coeff , typename Data >

data_type num_collect::regularization::fista< Coeff, Data >::residual_ {}

private

Residual vector.

Definition at line 326 of file fista.h.

◆ t_

template<typename Coeff , typename Data >

scalar_type num_collect::regularization::fista< Coeff, Data >::t_ {}

private

Parameter for step size of y_.

Definition at line 320 of file fista.h.

◆ tol_update_rate_

template<typename Coeff , typename Data >

scalar_type num_collect::regularization::fista< Coeff, Data >::tol_update_rate_ {default_tol_update_rate}

private

Tolerance of update rate of the solution.

Definition at line 342 of file fista.h.

◆ update_

template<typename Coeff , typename Data >

scalar_type num_collect::regularization::fista< Coeff, Data >::update_ {}

private

Norm of the update of the solution in the last iteration.

Definition at line 329 of file fista.h.

◆ y_

template<typename Coeff , typename Data >

data_type num_collect::regularization::fista< Coeff, Data >::y_ {}

private

Another vector to update in FISTA.

Definition at line 323 of file fista.h.

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

include/num_collect/regularization/fista.h

Public Types

Public Member Functions

Private Attributes

Static Private Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ base_type

◆ coeff_type

◆ this_type

Constructor & Destructor Documentation

◆ fista()

Member Function Documentation

◆ calculate_data_for()

◆ change_data()

◆ compute()

◆ configure_iteration_logger()

◆ data_size()

◆ init()

◆ is_stop_criteria_satisfied()

◆ iterate()

◆ iterations()

◆ max_iterations() [1/2]

◆ max_iterations() [2/2]

◆ param_search_region()

◆ regularization_term()

◆ residual_norm()

◆ residual_norm_rate()

◆ tol_update_rate() [1/2]

◆ tol_update_rate() [2/2]

◆ update()

Member Data Documentation

◆ coeff_

◆ data_

◆ default_max_iterations

◆ default_tol_update_rate

◆ inv_max_eigen_

◆ iterations_

◆ max_iterations_

◆ residual_

◆ t_

◆ tol_update_rate_

◆ update_

◆ y_