Class to solve linear equations with 2nd order total generalized variation (TGV) regularization [3] using the alternating direction method of multipliers (ADMM) [2]. More...

#include <num_collect/regularization/tgv2_admm.h>

Inheritance diagram for num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >:

Collaboration diagram for num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, 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	derivative_matrix_type = DerivativeMatrix
	Type of matrices to compute derivatives.
using	this_type = tgv2_admm<Coeff, DerivativeMatrix, Data>
	This type.
Public Types inherited from num_collect::regularization::regularized_solver_base< tgv2_admm< Coeff, DerivativeMatrix, Data >, Data >
using	data_type
	Type of data.
using	scalar_type
	Type of scalars.

Public Member Functions
	tgv2_admm ()
	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 DerivativeMatrix &first_derivative_matrix, const DerivativeMatrix &second_derivative_matrix, 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) -> this_type &
	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) -> this_type &
	Set the tolerance of update rate of the solution.
auto	update_rate () const noexcept -> scalar_type
	Get the rate of the norm of the update of the solution in the last iteration.
Public Member Functions inherited from num_collect::regularization::iterative_regularized_solver_base< tgv2_admm< Coeff, DerivativeMatrix, 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< tgv2_admm< Coeff, DerivativeMatrix, 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< tgv2_admm< Coeff, DerivativeMatrix, 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< tgv2_admm< Coeff, DerivativeMatrix, Data > >
	iteration_logger_mixin ()=default
	Constructor.
void	configure_iteration_logger (num_collect::logging::iterations::iteration_logger< tgv2_admm< Coeff, DerivativeMatrix, Data > > &iteration_logger) const
	Configure an iteration logger.
auto	initialize_iteration_logger () -> num_collect::logging::iterations::iteration_logger< tgv2_admm< Coeff, DerivativeMatrix, Data > > &
	Get the iteration logger.

Private Member Functions
void	update_p (const scalar_type &param, const data_type &solution)
	Update p_.
void	update_s (const scalar_type &param, const data_type &solution)
	Update s_.
void	update_solution (const scalar_type &param, data_type &solution)
	Update the solution.
void	update_t (const scalar_type &param, const data_type &solution)
	Update t_.
void	update_u (const scalar_type &param, const data_type &solution)
	Update u_.
void	update_z (const scalar_type &param, const data_type &solution)
	Update z_.

Private Attributes
const coeff_type *	coeff_ {nullptr}
	Coefficient matrix to compute data vector.
linear::impl::operator_conjugate_gradient< data_type >	conjugate_gradient_solution_ {}
	Conjugate gradient solver for update of the solution.
linear::impl::operator_conjugate_gradient< data_type >	conjugate_gradient_z_ {}
	Conjugate gradient solver for update of the 1st order derivative.
scalar_type	constraint_coeff_ {default_constraint_coeff}
	Coefficient of the constraint for the derivative.
const data_type *	data_ {nullptr}
	Data vector.
const derivative_matrix_type *	first_derivative_matrix_ {nullptr}
	Matrix to compute the first order derivative.
index_type	iterations_ {}
	Number of iterations.
index_type	max_iterations_ {default_max_iterations}
	Maximum number of iterations.
data_type	p_ {}
	Lagrange multiplier for the 1st order derivative constraint.
data_type	p_update_ {}
	Update of p_.
data_type	previous_s_ {}
	Previous value of s_.
data_type	previous_solution_ {}
	Previous solution.
data_type	previous_t_ {}
	Previous value of t_.
data_type	previous_z_ {}
	Previous value of z_.
scalar_type	rate_of_cg_tol_rate_to_tol_update_rate_
	Rate of the ratio of the rate of tolerance in CG method to the tolerance of update rate of the solution.
data_type	residual_ {}
	Residual vector.
data_type	s_ {}
	Component of the 1st order derivative for regularization.
const derivative_matrix_type *	second_derivative_matrix_ {nullptr}
	Matrix to compute the second order derivative.
scalar_type	second_derivative_ratio_ {default_second_derivative_ratio}
	Ratio of regularization term for the 2nd order derivative.
data_type	t_ {}
	2nd order derivative of the solution.
data_type	temp_data_ {}
	Temporary vector with the size of data.
data_type	temp_solution_ {}
	Temporary vector for the update of the solution.
data_type	temp_t_ {}
	Temporary vector for the update of the 2nd order derivative.
data_type	temp_z_ {}
	Temporary vector for the update of the 1st order derivative.
scalar_type	tol_update_rate_ {default_tol_update_rate}
	Tolerance of update rate of the solution.
data_type	u_ {}
	Lagrange multiplier for the 2nd order derivative constraint.
data_type	u_update_ {}
	Update of u_.
scalar_type	update_rate_ {}
	Rate of norm of the update of the variables in the last iteration.
data_type	z_ {}
	Component of the 1st order derivative.

Static Private Attributes
static constexpr auto	default_constraint_coeff
	Default coefficient of the constraint for the derivative.
static constexpr index_type	default_max_iterations = 100000
	Default maximum number of iterations.
static constexpr auto	default_rate_of_cg_tol_rate_to_tol_update_rate
	Default value of the ratio of the rate of tolerance in CG method to the tolerance of update rate of the solution.
static constexpr auto	default_second_derivative_ratio
	Default ratio of regularization term for the 2nd order derivative.
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< tgv2_admm< Coeff, DerivativeMatrix, Data >, Data >
	iterative_regularized_solver_base (logging::log_tag_view tag)
	Constructor.
Protected Member Functions inherited from num_collect::regularization::implicit_regularized_solver_base< tgv2_admm< Coeff, DerivativeMatrix, Data >, Data >
	implicit_regularized_solver_base (logging::log_tag_view tag)
	Constructor.
auto	derived () noexcept -> tgv2_admm< Coeff, DerivativeMatrix, Data > &
	Access derived object.
Protected Member Functions inherited from num_collect::regularization::regularized_solver_base< tgv2_admm< Coeff, DerivativeMatrix, Data >, Data >
	regularized_solver_base (logging::log_tag_view tag)
	Constructor.
auto	derived () noexcept -> tgv2_admm< Coeff, DerivativeMatrix, Data > &
	Access derived object.

Detailed Description

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>
requires ((base::concepts::sparse_matrix<Coeff> || base::concepts::dense_matrix<Coeff>) && (base::concepts::sparse_matrix<DerivativeMatrix> || base::concepts::dense_matrix<DerivativeMatrix>))
class num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >

Class to solve linear equations with 2nd order total generalized variation (TGV) regularization [3] using the alternating direction method of multipliers (ADMM) [2].

Template Parameters

Coeff	Type of coefficient matrices.
DerivativeMatrix	Type of matrices to compute derivatives.
Data	Type of data vectors.

This class minimizes the following evaluation function [20] :

\[E(\boldsymbol{x}, \boldsymbol{z}) = \| A \boldsymbol{x} - \boldsymbol{y} \|_2^2 + \lambda (\| D \boldsymbol{x} - \boldsymbol{z} \|_1 + \alpha \| E \boldsymbol{z} \|_1) \]

where variables are defined as follows:

\(A\) is a coefficient matrix.
\(\boldsymbol{x}\) is a solution vector.
\(\boldsymbol{y}\) is a data vector.
\(\boldsymbol{z}\) is a component of the 1st order derivative of the solution which is used to compute the 2nd order derivative.
\(\lambda\) is a regularization parameter.
\(D\) is a matrix to compute the 1st order derivatives.
\(E\) is a matrix to compute the 2nd order derivative from the 1st order derivative.

For solving the above problem using ADMM, this class solves the following optimization problem:

\[\begin{aligned} \text{minimize} \hspace{1em} & \|A \boldsymbol{x} - \boldsymbol{y}\|_2^2 + \lambda \left( \|\boldsymbol{s}\|_1 + \alpha \|\boldsymbol{t}\|_1 \right) \\ \text{s.t.} \hspace{1em} & D \boldsymbol{x} - \boldsymbol{z} = \boldsymbol{s} \\ & E \boldsymbol{z} = \boldsymbol{t} \end{aligned} \]

where additional variables are defined as follows:

\(\boldsymbol{s}\) is a component of the 1st order derivative of the solution for regularization.
\(\boldsymbol{t}\) is the 2nd order derivative of the solution.

This class uses the following augmented Lagrangian function:

\[ L_{\rho}(\boldsymbol{x}, \boldsymbol{z}, \boldsymbol{s}, \boldsymbol{t}, \boldsymbol{p}, \boldsymbol{u}) \equiv \|A \boldsymbol{x} - \boldsymbol{y}\|_2^2 + \lambda \left( \|\boldsymbol{s}\|_1 + \alpha \|\boldsymbol{t}\|_1 \right) + \boldsymbol{p}^\top (D \boldsymbol{x} - \boldsymbol{z} - \boldsymbol{s}) + \boldsymbol{u}^\top (E \boldsymbol{z} - \boldsymbol{t}) + \frac{\rho}{2} \|D \boldsymbol{x} - \boldsymbol{z} - \boldsymbol{s}\|_2^2 + \frac{\rho}{2} \|E \boldsymbol{z} - \boldsymbol{t}\|_2^2 \]

where additional variables are defined as follows:

\(\boldsymbol{p}\) is a Lagrange multiplier for the 1st order derivative constraint.
\(\boldsymbol{u}\) is a Lagrange multiplier for the 2nd order derivative constraint.
\(\rho\) is a coefficient of the quadratic term for the constraints.

This class uses the following update rules:

\[\begin{aligned} \boldsymbol{x}_{k+1} & = (2 A^\top A + \rho D^\top D)^{-1} \left( 2 A^\top \boldsymbol{y} - D^\top \boldsymbol{p}_k + \rho D^\top \boldsymbol{z}_k + \rho D^\top \boldsymbol{s}_k \right) \\ \boldsymbol{z}_{k+1} & = (\rho I + \rho E^\top E)^{-1} \left( \boldsymbol{p}_k - E^\top \boldsymbol{u}_k + \rho D \boldsymbol{x}_{k+1} - \rho \boldsymbol{s}_k + \rho E^\top \boldsymbol{t}_k \right) \\ \boldsymbol{s}_{k+1} & = \mathcal{T}_{\lambda/\rho} \left( D \boldsymbol{x}_{k+1} - \boldsymbol{z}_{k+1} + \frac{\boldsymbol{p}_k}{\rho} \right) \\ \boldsymbol{t}_{k+1} & = \mathcal{T}_{\lambda/\rho \alpha} \left( E \boldsymbol{z}_{k+1} + \frac{\boldsymbol{u}_k}{\rho} \right) \\ \boldsymbol{p}_{k+1} & = \boldsymbol{p}_k + \rho (D \boldsymbol{x}_{k+1} - \boldsymbol{z}_{k+1} - \boldsymbol{s}_{k+1}) \\ \boldsymbol{u}_{k+1} & = \boldsymbol{u}_k + \rho (E \boldsymbol{z}_{k+1} - \boldsymbol{t}_{k+1}) \end{aligned} \]

where \(\mathcal{T}_\lambda\) is the thresholding operator implemented in num_collect::regularization::impl::apply_shrinkage_operator function.

This class uses the following variable names:

In Formula	In C++
\(\boldsymbol{x}\)	solution
\(\boldsymbol{y}\)	data
\(\boldsymbol{z}\)	z
\(\boldsymbol{s}\)	s
\(\boldsymbol{t}\)	t
\(\boldsymbol{p}\)	p
\(\boldsymbol{u}\)	u
\(A\)	coeff
\(D\)	first_derivative_matrix
\(E\)	second_derivative_matrix
\(\lambda\)	param
\(\alpha\)	second_derivative_ratio
\(\rho\)	constraint_coeff

Examples: regularization/image_denoising_tgv2_admm.cpp.

Definition at line 179 of file tgv2_admm.h.

Member Typedef Documentation

◆ base_type

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

using num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::base_type = iterative_regularized_solver_base<this_type, Data>

Type of the base class.

Definition at line 186 of file tgv2_admm.h.

◆ coeff_type

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

using num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::coeff_type = Coeff

Type of coefficient matrices.

Definition at line 192 of file tgv2_admm.h.

◆ derivative_matrix_type

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

using num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::derivative_matrix_type = DerivativeMatrix

Type of matrices to compute derivatives.

Definition at line 195 of file tgv2_admm.h.

◆ this_type

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

using num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::this_type = tgv2_admm<Coeff, DerivativeMatrix, Data>

This type.

Definition at line 183 of file tgv2_admm.h.

Constructor & Destructor Documentation

◆ tgv2_admm()

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::tgv2_admm ( )

inline

Constructor.

Definition at line 200 of file tgv2_admm.h.

Member Function Documentation

◆ calculate_data_for()

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

void num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, 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 345 of file tgv2_admm.h.

◆ change_data()

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

void num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::change_data ( const data_type & data )

inline

Change data.

Parameters

[in] data New data.

Definition at line 342 of file tgv2_admm.h.

◆ compute()

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

void num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::compute	(	const Coeff &	coeff,
		const DerivativeMatrix &	first_derivative_matrix,
		const DerivativeMatrix &	second_derivative_matrix,
		const Data &	data )

inline

Compute internal parameters.

Parameters

[in]	coeff	Coefficient matrix.
[in]	first_derivative_matrix	Matrix to compute the first derivative.
[in]	second_derivative_matrix	Matrix to compute the second derivative from the first order derivative.
[in]	data	Data vector.

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

Examples: regularization/image_denoising_tgv2_admm.cpp.

Definition at line 220 of file tgv2_admm.h.

◆ configure_iteration_logger()

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

void num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, 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 318 of file tgv2_admm.h.

◆ data_size()

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

auto num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::data_size ( ) const -> index_type

inlinenodiscard

Get the size of data.

Returns: Size of data.

Definition at line 350 of file tgv2_admm.h.

◆ init()

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

void num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, 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 231 of file tgv2_admm.h.

◆ is_stop_criteria_satisfied()

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

auto num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, 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 310 of file tgv2_admm.h.

◆ iterate()

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

void num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, 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 296 of file tgv2_admm.h.

◆ iterations()

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

auto num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::iterations ( ) const -> index_type

inlinenodiscardnoexcept

Get the number of iterations.

Returns: Value.

Definition at line 376 of file tgv2_admm.h.

◆ max_iterations() [1/2]

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

auto num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::max_iterations ( ) const -> index_type

inlinenodiscard

Get the maximum number of iterations.

Returns: Value.

Definition at line 404 of file tgv2_admm.h.

◆ max_iterations() [2/2]

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

auto num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::max_iterations ( index_type value ) -> this_type&

inline

Set the maximum number of iterations.

Parameters

[in] value Value.

Returns: This object.

Definition at line 414 of file tgv2_admm.h.

◆ param_search_region()

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

auto num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, 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 353 of file tgv2_admm.h.

◆ regularization_term()

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

auto num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::regularization_term ( const data_type & solution ) const -> scalar_type

inlinenodiscard

Calculate the regularization term.

Parameters

[in] solution Solution.

Returns: Result.

Definition at line 336 of file tgv2_admm.h.

◆ residual_norm()

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

auto num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, 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 330 of file tgv2_admm.h.

◆ residual_norm_rate()

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

auto num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, 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 395 of file tgv2_admm.h.

◆ tol_update_rate() [1/2]

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

auto num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::tol_update_rate ( ) const -> scalar_type

inlinenodiscard

Get the tolerance of update rate of the solution.

Returns: Value.

Definition at line 426 of file tgv2_admm.h.

◆ tol_update_rate() [2/2]

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

auto num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::tol_update_rate ( scalar_type value ) -> this_type&

inline

Set the tolerance of update rate of the solution.

Parameters

[in] value Value.

Returns: This object.

Definition at line 436 of file tgv2_admm.h.

◆ update_p()

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

void num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::update_p	(	const scalar_type &	param,
		const data_type &	solution )

inlineprivate

Update p_.

Parameters

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

Definition at line 544 of file tgv2_admm.h.

◆ update_rate()

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

auto num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::update_rate ( ) const -> scalar_type

inlinenodiscardnoexcept

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

Returns: Value.

Definition at line 386 of file tgv2_admm.h.

◆ update_s()

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

void num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::update_s	(	const scalar_type &	param,
		const data_type &	solution )

inlineprivate

Update s_.

Parameters

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

Definition at line 511 of file tgv2_admm.h.

◆ update_solution()

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

void num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::update_solution	(	const scalar_type &	param,
		data_type &	solution )

inlineprivate

Update the solution.

Parameters

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

Definition at line 451 of file tgv2_admm.h.

◆ update_t()

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

void num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::update_t	(	const scalar_type &	param,
		const data_type &	solution )

inlineprivate

Update t_.

Parameters

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

Definition at line 526 of file tgv2_admm.h.

◆ update_u()

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

void num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::update_u	(	const scalar_type &	param,
		const data_type &	solution )

inlineprivate

Update u_.

Parameters

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

Definition at line 561 of file tgv2_admm.h.

◆ update_z()

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

void num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::update_z	(	const scalar_type &	param,
		const data_type &	solution )

inlineprivate

Update z_.

Parameters

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

Definition at line 482 of file tgv2_admm.h.

Member Data Documentation

◆ coeff_

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

const coeff_type* num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::coeff_ {nullptr}

private

Coefficient matrix to compute data vector.

Definition at line 574 of file tgv2_admm.h.

◆ conjugate_gradient_solution_

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

linear::impl::operator_conjugate_gradient<data_type> num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::conjugate_gradient_solution_ {}

private

Conjugate gradient solver for update of the solution.

Definition at line 641 of file tgv2_admm.h.

◆ conjugate_gradient_z_

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

linear::impl::operator_conjugate_gradient<data_type> num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::conjugate_gradient_z_ {}

private

Conjugate gradient solver for update of the 1st order derivative.

Definition at line 645 of file tgv2_admm.h.

◆ constraint_coeff_

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

scalar_type num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::constraint_coeff_ {default_constraint_coeff}

private

Coefficient of the constraint for the derivative.

Definition at line 659 of file tgv2_admm.h.

◆ data_

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

const data_type* num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::data_ {nullptr}

private

Data vector.

Definition at line 583 of file tgv2_admm.h.

◆ default_constraint_coeff

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

auto num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::default_constraint_coeff

staticconstexprprivate

Initial value:

=

static_cast<scalar_type>(1)

num_collect::regularization::regularized_solver_base< tgv2_admm< Coeff, DerivativeMatrix, Data >, Data >::scalar_type

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

Definition regularized_solver_base.h:46

Default coefficient of the constraint for the derivative.

Definition at line 655 of file tgv2_admm.h.

◆ default_max_iterations

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

index_type num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::default_max_iterations = 100000

staticconstexprprivate

Default maximum number of iterations.

Definition at line 662 of file tgv2_admm.h.

◆ default_rate_of_cg_tol_rate_to_tol_update_rate

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

auto num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::default_rate_of_cg_tol_rate_to_tol_update_rate

staticconstexprprivate

Initial value:

=

static_cast<scalar_type>(1e-2)

Default value of the ratio of the rate of tolerance in CG method to the tolerance of update rate of the solution.

Definition at line 675 of file tgv2_admm.h.

◆ default_second_derivative_ratio

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

auto num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::default_second_derivative_ratio

staticconstexprprivate

Initial value:

=

static_cast<scalar_type>(1)

Default ratio of regularization term for the 2nd order derivative.

Definition at line 648 of file tgv2_admm.h.

◆ default_tol_update_rate

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

auto num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::default_tol_update_rate

staticconstexprprivate

Initial value:

=

static_cast<scalar_type>(1e-4)

Default tolerance of update rate of the solution.

Definition at line 668 of file tgv2_admm.h.

◆ first_derivative_matrix_

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

const derivative_matrix_type* num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::first_derivative_matrix_ {nullptr}

private

Matrix to compute the first order derivative.

Definition at line 577 of file tgv2_admm.h.

◆ iterations_

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

index_type num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::iterations_ {}

private

Number of iterations.

Definition at line 586 of file tgv2_admm.h.

◆ max_iterations_

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

index_type num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::max_iterations_ {default_max_iterations}

private

Maximum number of iterations.

Definition at line 665 of file tgv2_admm.h.

◆ p_

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

data_type num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::p_ {}

private

Lagrange multiplier for the 1st order derivative constraint.

Definition at line 598 of file tgv2_admm.h.

◆ p_update_

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

data_type num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::p_update_ {}

private

Update of p_.

Definition at line 628 of file tgv2_admm.h.

◆ previous_s_

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

data_type num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::previous_s_ {}

private

Previous value of s_.

Definition at line 622 of file tgv2_admm.h.

◆ previous_solution_

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

data_type num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::previous_solution_ {}

private

Previous solution.

Definition at line 616 of file tgv2_admm.h.

◆ previous_t_

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

data_type num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::previous_t_ {}

private

Previous value of t_.

Definition at line 625 of file tgv2_admm.h.

◆ previous_z_

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

data_type num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::previous_z_ {}

private

Previous value of z_.

Definition at line 619 of file tgv2_admm.h.

◆ rate_of_cg_tol_rate_to_tol_update_rate_

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

scalar_type num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::rate_of_cg_tol_rate_to_tol_update_rate_

private

Initial value:

{

default_rate_of_cg_tol_rate_to_tol_update_rate}

num_collect::regularization::tgv2_admm::default_rate_of_cg_tol_rate_to_tol_update_rate

static constexpr auto default_rate_of_cg_tol_rate_to_tol_update_rate

Default value of the ratio of the rate of tolerance in CG method to the tolerance of update rate of t...

Definition tgv2_admm.h:675

Rate of the ratio of the rate of tolerance in CG method to the tolerance of update rate of the solution.

Definition at line 679 of file tgv2_admm.h.

◆ residual_

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

data_type num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::residual_ {}

private

Residual vector.

Definition at line 634 of file tgv2_admm.h.

◆ s_

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

data_type num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::s_ {}

private

Component of the 1st order derivative for regularization.

Definition at line 592 of file tgv2_admm.h.

◆ second_derivative_matrix_

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

const derivative_matrix_type* num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::second_derivative_matrix_ {nullptr}

private

Matrix to compute the second order derivative.

Definition at line 580 of file tgv2_admm.h.

◆ second_derivative_ratio_

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

scalar_type num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::second_derivative_ratio_ {default_second_derivative_ratio}

private

Ratio of regularization term for the 2nd order derivative.

Definition at line 652 of file tgv2_admm.h.

◆ t_

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

data_type num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::t_ {}

private

2nd order derivative of the solution.

Definition at line 595 of file tgv2_admm.h.

◆ temp_data_

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

data_type num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::temp_data_ {}

private

Temporary vector with the size of data.

Definition at line 607 of file tgv2_admm.h.

◆ temp_solution_

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

data_type num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::temp_solution_ {}

private

Temporary vector for the update of the solution.

Definition at line 604 of file tgv2_admm.h.

◆ temp_t_

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

data_type num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::temp_t_ {}

private

Temporary vector for the update of the 2nd order derivative.

Definition at line 613 of file tgv2_admm.h.

◆ temp_z_

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

data_type num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::temp_z_ {}

private

Temporary vector for the update of the 1st order derivative.

Definition at line 610 of file tgv2_admm.h.

◆ tol_update_rate_

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

scalar_type num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::tol_update_rate_ {default_tol_update_rate}

private

Tolerance of update rate of the solution.

Definition at line 672 of file tgv2_admm.h.

◆ u_

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

data_type num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::u_ {}

private

Lagrange multiplier for the 2nd order derivative constraint.

Definition at line 601 of file tgv2_admm.h.

◆ u_update_

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

data_type num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::u_update_ {}

private

Update of u_.

Definition at line 631 of file tgv2_admm.h.

◆ update_rate_

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

scalar_type num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::update_rate_ {}

private

Rate of norm of the update of the variables in the last iteration.

Definition at line 637 of file tgv2_admm.h.

◆ z_

template<typename Coeff, typename DerivativeMatrix, base::concepts::dense_vector Data>

data_type num_collect::regularization::tgv2_admm< Coeff, DerivativeMatrix, Data >::z_ {}

private

Component of the 1st order derivative.

Definition at line 589 of file tgv2_admm.h.

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

include/num_collect/regularization/tgv2_admm.h

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Static Private Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ base_type

◆ coeff_type

◆ derivative_matrix_type

◆ this_type

Constructor & Destructor Documentation

◆ tgv2_admm()

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_p()

◆ update_rate()

◆ update_s()

◆ update_solution()

◆ update_t()

◆ update_u()

◆ update_z()

Member Data Documentation

◆ coeff_

◆ conjugate_gradient_solution_

◆ conjugate_gradient_z_

◆ constraint_coeff_

◆ data_

◆ default_constraint_coeff

◆ default_max_iterations

◆ default_rate_of_cg_tol_rate_to_tol_update_rate

◆ default_second_derivative_ratio

◆ default_tol_update_rate

◆ first_derivative_matrix_

◆ iterations_

◆ max_iterations_

◆ p_

◆ p_update_

◆ previous_s_

◆ previous_solution_

◆ previous_t_

◆ previous_z_

◆ rate_of_cg_tol_rate_to_tol_update_rate_

◆ residual_

◆ s_

◆ second_derivative_matrix_

◆ second_derivative_ratio_

◆ t_

◆ temp_data_

◆ temp_solution_

◆ temp_t_

◆ temp_z_

◆ tol_update_rate_

◆ u_

◆ u_update_

◆ update_rate_

◆ z_