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

#include <Solver.hh>

Public Member Functions
	Solver ()

	Solver (FunctionWrapper function, const InputType &x_ini, InputType &x_sol)

	Solver (FunctionWrapper function, FirstDerivativeWrapper first_derivative, const InputType &x_ini, InputType &x_sol)

	Solver (FunctionWrapper function, FirstDerivativeWrapper first_derivative, SecondDerivativeWrapper second_derivative, const InputType &x_ini, InputType &x_sol)

const InputType &	lower_bound () const

void	lower_bound (const InputType &t_lower_bound)

const InputType &	upper_bound () const

void	upper_bound (const InputType &t_upper_bound)

void	bounds (const InputType &t_lower_bound, const InputType &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)

bool	solve (FunctionWrapper function, const InputType &x_ini, InputType &x_sol)

bool	solve (FunctionWrapper function, FirstDerivativeWrapper first_derivative, const InputType &x_ini, InputType &x_sol)

bool	solve (FunctionWrapper function, FirstDerivativeWrapper first_derivative, SecondDerivativeWrapper second_derivative, const InputType &x_ini, InputType &x_sol)

template<Integer FunInDim, Integer FunOutDim, typename DerivedFunction>
bool	rootfind (Function< Real, FunInDim, FunOutDim, DerivedFunction > const &function, const InputType &x_ini, InputType &x_sol)

template<Integer FunInDim, Integer FunOutDim, typename DerivedFunction>
bool	optimize (Function< Real, FunInDim, FunOutDim, DerivedFunction > const &function, const InputType &x_ini, InputType &x_sol)

std::string	name () const

Protected Types
using	InputType = typename std::conditional_t<SolInDim == 1, Real, Eigen::Vector<Real, SolInDim>>

using	OutputType = typename std::conditional_t<SolOutDim == 1, Real, Eigen::Vector<Real, SolOutDim>>

using	TraceType = typename std::vector<InputType>

using	FirstDerivativeType = std::conditional_t<SolInDim == 1 && SolOutDim == 1, Real, Eigen::Matrix<Real, SolOutDim, SolInDim>>

using	SecondDerivativeType

using	FunctionWrapper = typename std::function<void(const InputType &, OutputType &)>

using	FirstDerivativeWrapper = typename std::function<void(const InputType &, FirstDerivativeType &)>

using	SecondDerivativeWrapper = typename std::function<void(const InputType &, SecondDerivativeType &)>

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 (Function< Real, FunInDim, FunOutDim, DerivedFunction > const &function, const InputType &x_ini, InputType &x_sol, bool is_optimization)

void	reset ()

void	evaluate_function (FunctionWrapper function, const InputType &x, OutputType &out)

void	evaluate_first_derivative (FirstDerivativeWrapper function, const InputType &x, FirstDerivativeType &out)

void	evaluate_second_derivative (SecondDerivativeWrapper function, const InputType &x, SecondDerivativeType &out)

void	store_trace (const InputType &x)

bool	damp (FunctionWrapper 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>
class Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >

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.

Member Typedef Documentation

◆ FirstDerivativeType

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

using Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::FirstDerivativeType = std::conditional_t<SolInDim == 1 && SolOutDim == 1, Real, Eigen::Matrix<Real, SolOutDim, SolInDim>>

protected

First derivative type.

◆ FirstDerivativeWrapper

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

using Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::FirstDerivativeWrapper = typename std::function<void(const InputType &, FirstDerivativeType &)>

protected

First derivative type.

◆ FunctionWrapper

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

using Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::FunctionWrapper = typename std::function<void(const InputType &, OutputType &)>

protected

Function type.

◆ InputType

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

using Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::InputType = typename std::conditional_t<SolInDim == 1, Real, Eigen::Vector<Real, SolInDim>>

protected

Basic constants. Input type.

◆ OutputType

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

using Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::OutputType = typename std::conditional_t<SolOutDim == 1, Real, Eigen::Vector<Real, SolOutDim>>

protected

Output type.

◆ SecondDerivativeType

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

using Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::SecondDerivativeType

protected

Initial value:

 std::conditional_t<SolInDim == 1 && SolOutDim == 1, Real,
      std::conditional_t<SolInDim == 1 || SolOutDim == 1, Eigen::Matrix<Real, SolInDim, SolInDim>,
      std::vector<Eigen::Matrix<Real, SolInDim, SolInDim>>>>

Second derivative type.

◆ SecondDerivativeWrapper

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

using Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::SecondDerivativeWrapper = typename std::function<void(const InputType &, SecondDerivativeType &)>

protected

Second derivative type.

◆ TraceType

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

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

protected

Input trace type.

Constructor & Destructor Documentation

◆ Solver() [1/4]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::Solver ( )

inline

Class constructor for the nonlinear solver.

◆ Solver() [2/4]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::Solver	(	FunctionWrapper	function,
		const InputType &	x_ini,
		InputType &	x_sol )

inline

Class constructor for the nonlinear solver.

Parameters

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

◆ Solver() [3/4]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::Solver	(	FunctionWrapper	function,
		FirstDerivativeWrapper	first_derivative,
		const InputType &	x_ini,
		InputType &	x_sol )

inline

Class constructor for the nonlinear solver.

Parameters

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

◆ Solver() [4/4]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::Solver	(	FunctionWrapper	function,
		FirstDerivativeWrapper	first_derivative,
		SecondDerivativeWrapper	second_derivative,
		const InputType &	x_ini,
		InputType &	x_sol )

inline

Class constructor for the nonlinear solver.

Parameters

[in]	function	Function wrapper.
[in]	first_derivative	First derivative wrapper.
[in]	second_derivative	The second derivative wrapper.
[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>

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

inline

Get relaxation factor \( \alpha \).

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

◆ alpha() [2/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

void Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

void Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

void Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::bounds	(	const InputType &	t_lower_bound,
		const InputType &	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 Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::converged ( ) const

inline

Get the convergence boolean flag.

Returns: The convergence boolean flag.

◆ damp()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

bool Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::damp	(	FunctionWrapper	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.

Parameters

[in]	function	Function wrapper.
[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 Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

void Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

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

inline

Disable solver's damped mode.

◆ disable_verbose_mode()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

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

inline

Disable solver's verbose mode.

◆ enable_damped_mode()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

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

inline

Enable solver's damped mode.

◆ enable_verbose_mode()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

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

inline

Enable solver's verbose mode.

◆ evaluate_first_derivative()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

void Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::evaluate_first_derivative	(	FirstDerivativeWrapper	function,
		const InputType &	x,
		FirstDerivativeType &	out )

inlineprotected

Evaluate the first derivative.

Parameters

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

◆ evaluate_function()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

void Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::evaluate_function	(	FunctionWrapper	function,
		const InputType &	x,
		OutputType &	out )

inlineprotected

Evaluate the function.

Parameters

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

◆ evaluate_second_derivative()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

void Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::evaluate_second_derivative	(	SecondDerivativeWrapper	function,
		const InputType &	x,
		SecondDerivativeType &	out )

inlineprotected

Evaluate the second derivative.

Parameters

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

◆ first_derivative_evaluations()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

Integer Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

Integer Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

void Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

void Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

Integer Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

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

inline

Get the number of algorithm iterations.

◆ lower_bound() [1/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

const InputType & Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

void Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::lower_bound ( const InputType & 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>

Integer Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

void Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

Integer Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

void Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

Integer Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

void Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

Integer Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

void Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

Integer Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

void Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

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

inline

Get the solver name.

Returns: The solver name.

◆ optimize()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

template<Integer FunInDim, Integer FunOutDim, typename DerivedFunction>

bool Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::optimize	(	Function< Real, FunInDim, FunOutDim, DerivedFunction > const &	function,
		const InputType &	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.

◆ ostream() [1/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

std::ostream & Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

void Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

Integer Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

Integer Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

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

inlineprotected

Reset solver internal counters and variables.

◆ rootfind()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

template<Integer FunInDim, Integer FunOutDim, typename DerivedFunction>

bool Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::rootfind	(	Function< Real, FunInDim, FunOutDim, DerivedFunction > const &	function,
		const InputType &	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.

◆ second_derivative_evaluations()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

Integer Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

template<Integer FunInDim, Integer FunOutDim, typename DerivedFunction>

bool Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::solve	(	Function< Real, FunInDim, FunOutDim, DerivedFunction > const &	function,
		const InputType &	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.

◆ solve() [2/4]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

bool Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::solve	(	FunctionWrapper	function,
		const InputType &	x_ini,
		InputType &	x_sol )

inline

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

Parameters

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

◆ solve() [3/4]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

bool Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::solve	(	FunctionWrapper	function,
		FirstDerivativeWrapper	first_derivative,
		const InputType &	x_ini,
		InputType &	x_sol )

inline

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

Parameters

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

◆ solve() [4/4]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

bool Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::solve	(	FunctionWrapper	function,
		FirstDerivativeWrapper	first_derivative,
		SecondDerivativeWrapper	second_derivative,
		const InputType &	x_ini,
		InputType &	x_sol )

inline

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

Parameters

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

◆ store_trace()

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

void Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::store_trace ( const InputType & 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>

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

inline

Get the task name.

Returns: The task name.

◆ task() [2/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

void Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

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

inline

Get the tolerance \( \epsilon \).

Returns: The tolerance \( \epsilon \).

◆ tolerance() [2/2]

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

void Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

const TraceType & Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

const InputType & Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

void Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::upper_bound ( const InputType & 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 Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

void Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

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

protected

Relaxation factor \( \alpha \).

◆ m_converged

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

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

protected

Convergence boolean flag.

◆ m_damped

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

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

protected

Damped mode boolean flag.

◆ m_first_derivative_evaluations

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

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

protected

First derivative evaluations.

◆ m_function_evaluations

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

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

protected

Function evaluations.

◆ m_iterations

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

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

protected

Algorithm iterations.

◆ m_lower_bound

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

InputType Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::m_lower_bound

protected

Lower bound.

◆ m_max_first_derivative_evaluations

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

Integer Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::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>

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

protected

Maximum allowed function evaluations.

◆ m_max_iterations

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

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

protected

Maximum allowed algorithm iterations.

◆ m_max_relaxations

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

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

protected

Maximum allowed algorithm relaxations.

◆ m_max_second_derivative_evaluations

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

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

protected

Maximum allowed second derivative evaluations.

◆ m_ostream

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

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

protected

Output stream for verbose mode.

◆ m_relaxations

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

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

protected

Algorithm relaxations.

◆ m_second_derivative_evaluations

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

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

protected

Second derivative evaluations.

◆ m_task

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

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

protected

Task name.

◆ m_tolerance

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

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

protected

Solver tolerance \( \epsilon \) for convergence.

◆ m_trace

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

TraceType Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::m_trace

protected

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

◆ m_upper_bound

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

InputType Optimist::Solver< Real, SolInDim, SolOutDim, DerivedSolver >::m_upper_bound

protected

Upper bound.

◆ m_verbose

template<typename Real, Integer SolInDim, Integer SolOutDim, typename DerivedSolver>

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

protected

Verbose mode boolean flag.

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

include/Optimist/Solver.hh

Public Member Functions

Protected Types

Protected Member Functions

Protected Attributes

Detailed Description

Solver

Member Typedef Documentation

◆ FirstDerivativeType

◆ FirstDerivativeWrapper

◆ FunctionWrapper

◆ InputType

◆ OutputType

◆ SecondDerivativeType

◆ SecondDerivativeWrapper

◆ TraceType

Constructor & Destructor Documentation

◆ Solver() [1/4]

◆ Solver() [2/4]

◆ Solver() [3/4]

◆ Solver() [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