Class container for the generic root-finding/optimization problem solver. More...

#include <SolverBase.hh>

Public Types
using	InputType
using	OutputType
using	TraceType = typename std::vector<InputType>
using	FirstDerivativeType
using	SecondDerivativeType

Public Member Functions
	SolverBase ()
template<typename FunctionLambda>
	SolverBase (FunctionLambda &&function, InputType const &x_ini, InputType &x_sol)
template<typename FunctionLambda, typename FirstDerivativeLambda>
	SolverBase (FunctionLambda &&function, FirstDerivativeLambda &&first_derivative, InputType const &x_ini, InputType &x_sol)
template<typename FunctionLambda, typename FirstDerivativeLambda, typename SecondDerivativeLambda>
	SolverBase (FunctionLambda &&function, FirstDerivativeLambda &&first_derivative, SecondDerivativeLambda &&second_derivative, InputType const &x_ini, InputType &x_sol)
InputType const &	lower_bound () const
void	lower_bound (InputType const &t_lower_bound)
InputType const &	upper_bound () const
void	upper_bound (InputType const &t_upper_bound)
void	bounds (InputType const &t_lower_bound, InputType const &t_upper_bound)
constexpr Integer	input_dimension () const
constexpr Integer	output_dimension () const
Integer	function_evaluations () const
void	max_function_evaluations (Integer t_max_function_evaluations)
Integer	max_function_evaluations () const
Integer	iterations () const
Integer	max_iterations () const
void	max_iterations (Integer t_max_iterations)
Real	alpha () const
void	alpha (Real t_alpha)
Integer	relaxations () const
Integer	max_relaxations () const
void	max_relaxations (Integer t_max_relaxations)
Real	tolerance () const
void	tolerance (Real t_tolerance)
void	verbose_mode (bool t_verbose)
bool	verbose_mode () const
void	enable_verbose_mode ()
void	disable_verbose_mode ()
void	damped_mode (bool t_damped)
bool	damped_mode () const
void	enable_damped_mode ()
void	disable_damped_mode ()
std::string	task () const
void	task (std::string t_task)
bool	converged () const
const TraceType &	trace () const
std::ostream &	ostream () const
void	ostream (std::ostream &t_ostream)
template<typename FunctionLambda>
bool	solve (FunctionLambda &&function, InputType const &x_ini, InputType &x_sol)
template<typename FunctionLambda, typename FirstDerivativeLambda>
bool	solve (FunctionLambda &&function, FirstDerivativeLambda &&first_derivative, InputType const &x_ini, InputType &x_sol)
template<typename FunctionLambda, typename FirstDerivativeLambda, typename SecondDerivativeLambda>
bool	solve (FunctionLambda &&function, FirstDerivativeLambda &&first_derivative, SecondDerivativeLambda &&second_derivative, InputType const &x_ini, InputType &x_sol)
template<Integer FunInDim, Integer FunOutDim, typename DerivedFunction>
bool	rootfind (FunctionBase< Real, FunInDim, FunOutDim, DerivedFunction, ForceEigen &&FunOutDim==1 > const &function, InputType const &x_ini, InputType &x_sol)
template<Integer FunInDim, Integer FunOutDim, typename DerivedFunction>
bool	optimize (FunctionBase< Real, FunInDim, FunOutDim, DerivedFunction, ForceEigen &&FunOutDim==1 > const &function, InputType const &x_ini, InputType &x_sol)
std::string	name () const

Protected Member Functions
Integer	first_derivative_evaluations () const
Integer	max_first_derivative_evaluations () const
void	max_first_derivative_evaluations (Integer first_derivative_evaluations)
Integer	second_derivative_evaluations () const
Integer	max_second_derivative_evaluations () const
void	max_second_derivative_evaluations (Integer second_derivative_evaluations)
template<Integer FunInDim, Integer FunOutDim, typename DerivedFunction>
bool	solve (FunctionBase< Real, FunInDim, FunOutDim, DerivedFunction, ForceEigen &&FunOutDim==1 > const &function, InputType const &x_ini, InputType &x_sol, bool is_optimization)
void	reset ()
template<typename FunctionLambda>
bool	evaluate_function (FunctionLambda &&function, InputType const &x, OutputType &out)
template<typename FirstDerivativeLambda>
bool	evaluate_first_derivative (FirstDerivativeLambda &&function, InputType const &x, FirstDerivativeType &out)
template<typename SecondDerivativeLambda>
bool	evaluate_second_derivative (SecondDerivativeLambda &&function, InputType const &x, SecondDerivativeType &out)
void	store_trace (InputType const &x)
template<typename FunctionLambda>
bool	damp (FunctionLambda &&function, InputType const &x_old, InputType const &function_old, InputType const &step_old, InputType &x_new, InputType &function_new, InputType &step_new)
void	header ()
void	bottom ()
void	info (Real residuals, std::string const &notes="-")

Protected Attributes
InputType	m_lower_bound
InputType	m_upper_bound
Integer	m_function_evaluations {0}
Integer	m_first_derivative_evaluations {0}
Integer	m_second_derivative_evaluations {0}
Integer	m_max_function_evaluations {1000}
Integer	m_max_first_derivative_evaluations {1000}
Integer	m_max_second_derivative_evaluations {1000}
Integer	m_iterations {0}
Integer	m_max_iterations {100}
Real	m_alpha {0.8}
Integer	m_relaxations {0}
Integer	m_max_relaxations {10}
Real	m_tolerance {EPSILON_LOW}
bool	m_verbose {false}
bool	m_damped {true}
std::ostream *	m_ostream {&std::cout}
std::string	m_task {"Undefined"}
bool	m_converged {false}
TraceType	m_trace

Detailed Description

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>
class Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >

Solver

The solvers implemented in Optimist are derived from the Solver class, which provides a common interface for solving nonlinear systems of equations. The Solver class is an abstract base class that defines the methods and attributes required by the derived classes. The derived classes implement the specific algorithms for solving the nonlinear systems of equations.

This class provides a base class for developing solvers that handle a generic function \(\mathbf{f}(\mathbf{x}): \mathbb{R}^{n} \rightarrow \mathbb{R}^{m}\). In general, the derived classes are designed to solve root-finding problems of the form

\[ \mathbf{f}(\mathbf{x}) = \mathbf{0} \text{,} \quad \text{with} \quad \mathbf{f}: \mathbb{R}^{n} \rightarrow \mathbb{R}^{n} \text{,} \]

as well as optimization problems of the form

\[ \min_{\mathbf{x}} f(\mathbf{x}) \text{,} \quad f: \mathbb{R}^{n} \rightarrow \mathbb{R} \text{.} \]

If \(n > 1\) the solver is a multi-dimensional solver, otherwise, it is a scalar solver. The linear algebra operations are performed using the Eigen library, which provides a high-level interface for matrix operations. Otherwise, for \(n = 1\), the base type changes to Real, a scalar type defined in the Optimist library.

Template Parameters

Real	Scalar number type.
SolInDim	The root-finding/optimization problem input dimension.
SolOutDim	The root-finding/optimization problem output dimension.
DerivedSolver	Derived solver class.
ForceEigen	Force the use of Eigen types for input and output.

Member Typedef Documentation

◆ FirstDerivativeType

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

using Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::FirstDerivativeType

Initial value:

std::conditional_t<ForceEigen || (SolInDim > 1) || (SolOutDim > 1),

Eigen::Matrix<Real, SolOutDim, SolInDim>, Real>

◆ InputType

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

using Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::InputType

Initial value:

typename std::conditional_t<ForceEigen || (SolInDim > 1),

Eigen::Vector<Real, SolInDim>, Real>

◆ OutputType

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

using Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::OutputType

Initial value:

typename std::conditional_t<ForceEigen || (SolOutDim > 1),

Eigen::Vector<Real, SolOutDim>, Real>

◆ SecondDerivativeType

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

using Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::SecondDerivativeType

Initial value:

 std::conditional_t<ForceEigen || (SolInDim > 1) || (SolOutDim > 1),
      std::conditional_t<SolInDim == 1 || SolOutDim == 1, Eigen::Matrix<Real, SolInDim, SolInDim>,
      std::vector<Eigen::Matrix<Real, SolInDim, SolInDim>>>, Real>

◆ TraceType

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

using Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::TraceType = typename std::vector<InputType>

Constructor & Destructor Documentation

◆ SolverBase() [1/4]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::SolverBase ( )

inline

Class constructor for the nonlinear solver.

◆ SolverBase() [2/4]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

template<typename FunctionLambda>

Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::SolverBase	(	FunctionLambda &&	function,
		InputType const &	x_ini,
		InputType &	x_sol )

inline

Class constructor for the nonlinear solver.

Template Parameters

FunctionLambda Function lambda type.

Parameters

[in]	function	Function lambda.
[in]	x_ini	Initialization point.
[out]	x_sol	Solution point.

◆ SolverBase() [3/4]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

template<typename FunctionLambda, typename FirstDerivativeLambda>

Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::SolverBase	(	FunctionLambda &&	function,
		FirstDerivativeLambda &&	first_derivative,
		InputType const &	x_ini,
		InputType &	x_sol )

inline

Class constructor for the nonlinear solver.

Template Parameters

FunctionLambda	Function lambda type.
FirstDerivativeLambda	First derivative lambda type.

Parameters

[in]	function	Function lambda.
[in]	first_derivative	First derivative lambda.
[in]	x_ini	Initialization point.
[out]	x_sol	Solution point.

◆ SolverBase() [4/4]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

template<typename FunctionLambda, typename FirstDerivativeLambda, typename SecondDerivativeLambda>

Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::SolverBase	(	FunctionLambda &&	function,
		FirstDerivativeLambda &&	first_derivative,
		SecondDerivativeLambda &&	second_derivative,
		InputType const &	x_ini,
		InputType &	x_sol )

inline

Class constructor for the nonlinear solver.

Template Parameters

FunctionLambda	Function lambda type.
FirstDerivativeLambda	First derivative lambda type.
SecondDerivativeLambda	Second derivative lambda type.

Parameters

[in]	function	Function lambda.
[in]	first_derivative	First derivative lambda.
[in]	second_derivative	The second derivative lambda.
[in]	x_ini	Initialization point.
[out]	x_sol	Solution point.

Member Function Documentation

◆ alpha() [1/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

Real Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::alpha ( ) const

inline

Get relaxation factor \( \alpha \).

Returns: The relaxation factor \( \alpha \).

◆ alpha() [2/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

void Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::alpha ( Real t_alpha )

inline

Set relaxation factor \( \alpha \).

Parameters

[in] t_alpha The relaxation factor \( \alpha \).

◆ bottom()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

void Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::bottom ( )

inlineprotected

Print the table bottom solver information.

Note: This has to be properly placed in the derived classes.

◆ bounds()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

void Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::bounds	(	InputType const &	t_lower_bound,
		InputType const &	t_upper_bound )

inline

Set the bounds.

Parameters

[in]	t_lower_bound	The lower bound.
[in]	t_upper_bound	The upper bound.

◆ converged()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

bool Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::converged ( ) const

inline

Get the convergence boolean flag.

Returns: The convergence boolean flag.

◆ damp()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

template<typename FunctionLambda>

bool Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::damp	(	FunctionLambda &&	function,
		InputType const &	x_old,
		InputType const &	function_old,
		InputType const &	step_old,
		InputType &	x_new,
		InputType &	function_new,
		InputType &	step_new )

inlineprotected

Damp the step using the affine invariant criterion.

Template Parameters

FunctionLambda Function lambda type.

Parameters

[in]	function	Function lambda.
[in]	x_old	Old point.
[in]	function_old	Old function value.
[in]	step_old	Old step.
[in]	x_new	New point.
[in]	function_new	New function value.
[out]	step_new	New step.

Returns: The damping boolean flag, true if the damping is successful, false otherwise.

◆ damped_mode() [1/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

bool Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::damped_mode ( ) const

inline

Get the damped mode boolean flag.

Returns: The damped mode boolean flag.

◆ damped_mode() [2/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

void Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::damped_mode ( bool t_damped )

inline

Set the damped mode boolean flag.

Parameters

[in] t_damped The damped mode boolean flag.

◆ disable_damped_mode()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

void Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::disable_damped_mode ( )

inline

Disable solver's damped mode.

◆ disable_verbose_mode()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

void Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::disable_verbose_mode ( )

inline

Disable solver's verbose mode.

◆ enable_damped_mode()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

void Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::enable_damped_mode ( )

inline

Enable solver's damped mode.

◆ enable_verbose_mode()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

void Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::enable_verbose_mode ( )

inline

Enable solver's verbose mode.

◆ evaluate_first_derivative()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

template<typename FirstDerivativeLambda>

bool Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::evaluate_first_derivative	(	FirstDerivativeLambda &&	function,
		InputType const &	x,
		FirstDerivativeType &	out )

inlineprotected

Evaluate the first derivative.

Template Parameters

FirstDerivativeLambda First derivative lambda type.

Parameters

[in]	function	First derivative lambda.
[in]	x	Input point.
[out]	out	First derivative value.

Returns: The boolean flag for successful evaluation.

◆ evaluate_function()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

template<typename FunctionLambda>

bool Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::evaluate_function	(	FunctionLambda &&	function,
		InputType const &	x,
		OutputType &	out )

inlineprotected

Evaluate the function.

Template Parameters

FunctionLambda Function lambda type.

Parameters

[in]	function	Function lambda.
[in]	x	Input point.
[out]	out	Function value.

Returns: The boolean flag for successful evaluation.

◆ evaluate_second_derivative()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

template<typename SecondDerivativeLambda>

bool Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::evaluate_second_derivative	(	SecondDerivativeLambda &&	function,
		InputType const &	x,
		SecondDerivativeType &	out )

inlineprotected

Evaluate the second derivative.

Parameters

[in]	function	Second derivative lambda.
[in]	x	Input point.
[out]	out	Second derivative value.

Returns: The boolean flag for successful evaluation.

◆ first_derivative_evaluations()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

Integer Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::first_derivative_evaluations ( ) const

inlineprotected

Get the number of function derivative evaluations.

Returns: The number of function derivative evaluations.

◆ function_evaluations()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

Integer Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::function_evaluations ( ) const

inline

Get the number of function evaluations.

Returns: The number of function evaluations.

◆ header()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

void Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::header ( )

inlineprotected

Print the table header solver information.

Note: This has to be properly placed in the derived classes.

◆ info()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

void Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::info	(	Real	residuals,
		std::string const &	notes = "-" )

inlineprotected

Print the solver information during the algorithm iterations.

Note: This has to be properly placed in the derived classes.

◆ input_dimension()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

Integer Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::input_dimension ( ) const

inlineconstexpr

Get the input dimension of the function.

Returns: The input dimension of the function.

◆ iterations()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

Integer Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::iterations ( ) const

inline

Get the number of algorithm iterations.

◆ lower_bound() [1/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

InputType const & Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::lower_bound ( ) const

inline

Get the lower bound.

Returns: The lower bound.

◆ lower_bound() [2/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

void Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::lower_bound ( InputType const & t_lower_bound )

inline

Set the lower bound.

Parameters

[in] t_lower_bound The lower bound.

◆ max_first_derivative_evaluations() [1/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

Integer Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::max_first_derivative_evaluations ( ) const

inlineprotected

Get the number of maximum allowed first derivative evaluations.

Returns: The number of maximum allowed first derivative evaluations.

◆ max_first_derivative_evaluations() [2/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

void Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::max_first_derivative_evaluations ( Integer first_derivative_evaluations )

inlineprotected

Set the number of maximum allowed first derivative evaluations.

Parameters

[in] first_derivative_evaluations The number of maximum allowed first derivative evaluations.

◆ max_function_evaluations() [1/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

Integer Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::max_function_evaluations ( ) const

inline

Get the number of maximum allowed function evaluations.

Returns: The number of maximum allowed function evaluations.

◆ max_function_evaluations() [2/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

void Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::max_function_evaluations ( Integer t_max_function_evaluations )

inline

Set the number of maximum allowed function evaluations.

Parameters

[in] t_max_function_evaluations The number of maximum allowed function evaluations.

◆ max_iterations() [1/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

Integer Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::max_iterations ( ) const

inline

Get the number of maximum allowed iterations.

Returns: The number of maximum allowed iterations.

◆ max_iterations() [2/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

void Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::max_iterations ( Integer t_max_iterations )

inline

Set the number of maximum allowed iterations.

Parameters

[in] t_max_iterations The number of maximum allowed iterations.

◆ max_relaxations() [1/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

Integer Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::max_relaxations ( ) const

inline

Get the number of maximum allowed relaxations.

Returns: The number of maximum allowed relaxations.

◆ max_relaxations() [2/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

void Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::max_relaxations ( Integer t_max_relaxations )

inline

Set the number of maximum allowed relaxations.

Parameters

[in] t_max_relaxations The number of maximum allowed relaxations.

◆ max_second_derivative_evaluations() [1/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

Integer Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::max_second_derivative_evaluations ( ) const

inlineprotected

Get the number of maximum allowed second derivative evaluations.

Returns: The number of maximum allowed second derivative evaluations.

◆ max_second_derivative_evaluations() [2/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

void Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::max_second_derivative_evaluations ( Integer second_derivative_evaluations )

inlineprotected

Set the number of maximum allowed second derivative evaluations.

Parameters

[in] second_derivative_evaluations The number of maximum allowed second derivative evaluations.

◆ name()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

std::string Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::name ( ) const

inline

Get the solver name.

Returns: The solver name.

◆ optimize()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

template<Integer FunInDim, Integer FunOutDim, typename DerivedFunction>

bool Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::optimize	(	FunctionBase< Real, FunInDim, FunOutDim, DerivedFunction, ForceEigen &&FunOutDim==1 > const &	function,
		InputType const &	x_ini,
		InputType &	x_sol )

inline

Solve the optimization problem given a function class.

Parameters

[in]	function	Function class.
[in]	x_ini	Initialization point.
[out]	x_sol	Solution point.

Template Parameters

FunInDim	The function output dimension.
FunOutDim	The function output dimension.
DerivedFunction	Derived function class.

Returns: True if the problem is solved, false otherwise.

◆ ostream() [1/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

std::ostream & Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::ostream ( ) const

inline

Get the output stream for verbose mode.

Returns: The output stream for verbose mode.

◆ ostream() [2/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

void Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::ostream ( std::ostream & t_ostream )

inline

Set the output stream for verbose mode.

Parameters

[in] t_ostream The output stream for verbose mode.

◆ output_dimension()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

Integer Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::output_dimension ( ) const

inlineconstexpr

Get the output dimension of the function.

Returns: The output dimension of the function.

◆ relaxations()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

Integer Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::relaxations ( ) const

inline

Get the number of algorithm relaxations.

Returns: The number of algorithm relaxations.

◆ reset()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

void Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::reset ( )

inlineprotected

Reset solver internal counters and variables.

◆ rootfind()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

template<Integer FunInDim, Integer FunOutDim, typename DerivedFunction>

bool Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::rootfind	(	FunctionBase< Real, FunInDim, FunOutDim, DerivedFunction, ForceEigen &&FunOutDim==1 > const &	function,
		InputType const &	x_ini,
		InputType &	x_sol )

inline

Solve the root-finding problem given a function class.

Parameters

[in]	function	Function class.
[in]	x_ini	Initialization point.
[out]	x_sol	Solution point.

Template Parameters

FunInDim	The function output dimension.
FunOutDim	The function output dimension.
DerivedFunction	Derived function class.

Returns: True if the problem is solved, false otherwise.

◆ second_derivative_evaluations()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

Integer Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::second_derivative_evaluations ( ) const

inlineprotected

Get the number of second derivative evaluations.

Returns: The number of second derivative evaluations.

◆ solve() [1/4]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

template<Integer FunInDim, Integer FunOutDim, typename DerivedFunction>

bool Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::solve	(	FunctionBase< Real, FunInDim, FunOutDim, DerivedFunction, ForceEigen &&FunOutDim==1 > const &	function,
		InputType const &	x_ini,
		InputType &	x_sol,
		bool	is_optimization )

inlineprotected

Solve the root-finding/optimization problem given a function class.

Parameters

[in]	function	Function class.
[in]	x_ini	Initialization point.
[out]	x_sol	Solution point.
[in]	is_optimization	Boolean flag for optimization.

Template Parameters

FunInDim	The function output dimension.
FunOutDim	The function output dimension.
DerivedFunction	Derived function class.

Returns: True if the problem is solved, false otherwise.

◆ solve() [2/4]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

template<typename FunctionLambda, typename FirstDerivativeLambda>

bool Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::solve	(	FunctionLambda &&	function,
		FirstDerivativeLambda &&	first_derivative,
		InputType const &	x_ini,
		InputType &	x_sol )

inline

Solve the root-finding/optimization problem given the function, and its first derivative.

Template Parameters

FunctionLambda	First derivative lambda type.
FirstDerivativeLambda	Function lambda type.

Parameters

[in]	function	Function lambda.
[in]	first_derivative	First derivative lambda
[in]	x_ini	Initialization point.
[out]	x_sol	Solution point.

Returns: True if the problem is solved, false otherwise.

◆ solve() [3/4]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

template<typename FunctionLambda, typename FirstDerivativeLambda, typename SecondDerivativeLambda>

bool Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::solve	(	FunctionLambda &&	function,
		FirstDerivativeLambda &&	first_derivative,
		SecondDerivativeLambda &&	second_derivative,
		InputType const &	x_ini,
		InputType &	x_sol )

inline

Solve the root-finding/optimization problem given the function, and its first and second derivatives.

Template Parameters

FunctionLambda	Function lambda type.
FirstDerivativeLambda	First derivative lambda type.
SecondDerivativeLambda	Second derivative lambda type.

Parameters

[in]	function	Function lambda.
[in]	first_derivative	First derivative lambda.
[in]	second_derivative	The second derivative lambda.
[in]	x_ini	Initialization point.
[out]	x_sol	Solution point.

Returns: True if the problem is solved, false otherwise.

◆ solve() [4/4]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

template<typename FunctionLambda>

bool Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::solve	(	FunctionLambda &&	function,
		InputType const &	x_ini,
		InputType &	x_sol )

inline

Solve the root-finding/optimization problem given the function, and without derivatives.

Template Parameters

FunctionLambda Function lambda type.

Parameters

[in]	function	Function lambda.
[in]	x_ini	Initialization point.
[out]	x_sol	Solution point.

Returns: True if the problem is solved, false otherwise.

◆ store_trace()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

void Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::store_trace ( InputType const & x )

inlineprotected

Update the history of the solver with the current point and function value.

Parameters

[in] x The point \( \mathbf{x} \).

◆ task() [1/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

std::string Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::task ( ) const

inline

Get the task name.

Returns: The task name.

◆ task() [2/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

void Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::task ( std::string t_task )

inline

Set the task name.

Parameters

[in] t_task The task name.

◆ tolerance() [1/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

Real Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::tolerance ( ) const

inline

Get the tolerance \( \epsilon \).

Returns: The tolerance \( \epsilon \).

◆ tolerance() [2/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

void Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::tolerance ( Real t_tolerance )

inline

Set the tolerance \( \epsilon \) for which the nonlinear solver stops, i.e., \( \left\| \mathbf{F}(\mathbf{x}) \right\|_{2} < \epsilon \).

Parameters

[in] t_tolerance The tolerance \( \epsilon \).

◆ trace()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

const TraceType & Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::trace ( ) const

inline

Get the trace of input values during the algorithm iterations.

Returns: The trace of input values.

◆ upper_bound() [1/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

InputType const & Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::upper_bound ( ) const

inline

Get the upper bound.

Returns: The upper bound.

◆ upper_bound() [2/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

void Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::upper_bound ( InputType const & t_upper_bound )

inline

Set the upper bound.

Parameters

[in] t_upper_bound The upper bound.

◆ verbose_mode() [1/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

bool Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::verbose_mode ( ) const

inline

Get the verbose mode boolean flag.

Returns: The verbose mode boolean flag.

◆ verbose_mode() [2/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

void Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::verbose_mode ( bool t_verbose )

inline

Set the verbose mode boolean flag.

Parameters

[in] t_verbose The verbose mode boolean flag.

Member Data Documentation

◆ m_alpha

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

Real Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::m_alpha {0.8}

protected

Relaxation factor \( \alpha \).

◆ m_converged

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

bool Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::m_converged {false}

protected

Convergence boolean flag.

◆ m_damped

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

bool Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::m_damped {true}

protected

Damped mode boolean flag.

◆ m_first_derivative_evaluations

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

Integer Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::m_first_derivative_evaluations {0}

protected

First derivative evaluations.

◆ m_function_evaluations

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

Integer Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::m_function_evaluations {0}

protected

Function evaluations.

◆ m_iterations

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

Integer Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::m_iterations {0}

protected

Algorithm iterations.

◆ m_lower_bound

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

InputType Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::m_lower_bound

protected

Lower bound.

◆ m_max_first_derivative_evaluations

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

Integer Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::m_max_first_derivative_evaluations {1000}

protected

Maximum allowed first derivative evaluations.

◆ m_max_function_evaluations

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

Integer Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::m_max_function_evaluations {1000}

protected

Maximum allowed function evaluations.

◆ m_max_iterations

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

Integer Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::m_max_iterations {100}

protected

Maximum allowed algorithm iterations.

◆ m_max_relaxations

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

Integer Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::m_max_relaxations {10}

protected

Maximum allowed algorithm relaxations.

◆ m_max_second_derivative_evaluations

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

Integer Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::m_max_second_derivative_evaluations {1000}

protected

Maximum allowed second derivative evaluations.

◆ m_ostream

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

std::ostream* Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::m_ostream {&std::cout}

protected

Output stream for verbose mode.

◆ m_relaxations

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

Integer Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::m_relaxations {0}

protected

Algorithm relaxations.

◆ m_second_derivative_evaluations

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

Integer Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::m_second_derivative_evaluations {0}

protected

Second derivative evaluations.

◆ m_task

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

std::string Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::m_task {"Undefined"}

protected

Task name.

◆ m_tolerance

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

Real Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::m_tolerance {EPSILON_LOW}

protected

Solver tolerance \( \epsilon \) for convergence.

◆ m_trace

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

TraceType Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::m_trace

protected

Trace for points \( \mathbf{x} \) values.

◆ m_upper_bound

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

InputType Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::m_upper_bound

protected

Upper bound.

◆ m_verbose

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver, bool ForceEigen = false>

bool Optimist::SolverBase< Real, SolInDim, SolOutDim, DerivedSolver, ForceEigen >::m_verbose {false}

protected

Verbose mode boolean flag.

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

include/Optimist/SolverBase.hh

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Solver

Member Typedef Documentation

◆ FirstDerivativeType

◆ InputType

◆ OutputType

◆ SecondDerivativeType

◆ TraceType

Constructor & Destructor Documentation

◆ SolverBase() [1/4]

◆ SolverBase() [2/4]

◆ SolverBase() [3/4]

◆ SolverBase() [4/4]

Member Function Documentation

◆ alpha() [1/2]

◆ alpha() [2/2]

◆ bottom()

◆ bounds()

◆ converged()

◆ damp()

◆ damped_mode() [1/2]

◆ damped_mode() [2/2]

◆ disable_damped_mode()

◆ disable_verbose_mode()

◆ enable_damped_mode()

◆ enable_verbose_mode()

◆ evaluate_first_derivative()

◆ evaluate_function()

◆ evaluate_second_derivative()

◆ first_derivative_evaluations()

◆ function_evaluations()

◆ header()

◆ info()

◆ input_dimension()

◆ iterations()

◆ lower_bound() [1/2]

◆ lower_bound() [2/2]

◆ max_first_derivative_evaluations() [1/2]

◆ max_first_derivative_evaluations() [2/2]

◆ max_function_evaluations() [1/2]

◆ max_function_evaluations() [2/2]

◆ max_iterations() [1/2]

◆ max_iterations() [2/2]

◆ max_relaxations() [1/2]

◆ max_relaxations() [2/2]

◆ max_second_derivative_evaluations() [1/2]

◆ max_second_derivative_evaluations() [2/2]

◆ name()

◆ optimize()

◆ ostream() [1/2]

◆ ostream() [2/2]

◆ output_dimension()

◆ relaxations()

◆ reset()

◆ rootfind()

◆ second_derivative_evaluations()

◆ solve() [1/4]

◆ solve() [2/4]

◆ solve() [3/4]

◆ solve() [4/4]

◆ store_trace()

◆ task() [1/2]

◆ task() [2/2]

◆ tolerance() [1/2]

◆ tolerance() [2/2]

◆ trace()

◆ upper_bound() [1/2]

◆ upper_bound() [2/2]

◆ verbose_mode() [1/2]

◆ verbose_mode() [2/2]

Member Data Documentation

◆ m_alpha

◆ m_converged

◆ m_damped

◆ m_first_derivative_evaluations

◆ m_function_evaluations