Class container for the Varona's methods. More...

#include <Varona.hh>

Inherits Optimist::RootFinder::RootFinder< Scalar, Varona< Scalar > >.

Public Types
using	Method
Public Types inherited from Optimist::RootFinder::RootFinder< Scalar, Varona< Scalar > >
using	Scalar
using	Input
using	Output
Public Types inherited from Optimist::SolverBase< Scalar, Scalar, Varona< Scalar > >
using	InputTrait
using	OutputTrait
using	Scalar
using	FirstDerivative
using	SecondDerivative

Public Member Functions
	Varona ()
constexpr std::string	name_impl () const
Method	method () const
void	method (Method t_method)
void	enable_4th_order_method ()
void	enable_8th_order_method ()
void	enable_16th_order_method ()
void	enable_32th_order_method ()
void	set_method (Method t_method)
template<typename FunctionLambda, typename FirstDerivativeLambda>
bool	solve_impl (FunctionLambda &&function, FirstDerivativeLambda &&first_derivative, Scalar x_ini, Scalar &x_sol)
Public Member Functions inherited from Optimist::RootFinder::RootFinder< Scalar, Varona< Scalar > >
	RootFinder ()
constexpr std::string	name () const
Integer	jacobian_evaluations () const
Integer	max_jacobian_evaluations () const
Integer	hessian_evaluations () const
Integer	max_hessian_evaluations () const
bool	solve (FunctionLambda &&function, const Input &x_ini, Output &x_sol)
Public Member Functions inherited from Optimist::SolverBase< Scalar, Scalar, Varona< Scalar > >
	SolverBase ()
void	reset_bounds (const Integer n=InputTrait::IsDynamic ? 0 :InputTrait::Dimension)
const Scalar &	lower_bound () const
const Scalar &	upper_bound () const
void	bounds (const Scalar &t_lower_bound, const Scalar &t_upper_bound)
constexpr Integer	input_dimension () const
constexpr Integer	output_dimension () const
Integer	function_evaluations () const
void	max_function_evaluations (const Integer t_max_function_evaluations)
Integer	iterations () const
Integer	max_iterations () const
Scalar	alpha () const
Integer	relaxations () const
Integer	max_relaxations () const
Scalar	tolerance () const
void	verbose_mode (bool t_verbose)
void	enable_verbose_mode ()
void	disable_verbose_mode ()
void	damped_mode (bool t_damped)
void	enable_damped_mode ()
void	disable_damped_mode ()
std::string	task () const
bool	converged () const
std::ostream &	ostream () const
bool	solve (FunctionLambda &&function, const Scalar &x_ini, Scalar &x_sol)
bool	rootfind (const FunctionBase< FunctionInput, FunctionOutput, DerivedFunction > &function, const Scalar &x_ini, Scalar &x_sol)
bool	optimize (const FunctionBase< FunctionInput, FunctionOutput, DerivedFunction > &function, const Scalar &x_ini, Scalar &x_sol)
constexpr std::string	name () const

Static Public Attributes
static constexpr bool	RequiresFunction {true}
static constexpr bool	RequiresFirstDerivative {true}
static constexpr bool	RequiresSecondDerivative {false}
Static Public Attributes inherited from Optimist::RootFinder::RootFinder< Scalar, Varona< Scalar > >
static constexpr bool	IsRootFinder
static constexpr bool	IsOptimizer

Protected Member Functions
template<typename FunctionLambda>
void	compute_step (FunctionLambda &&function, Scalar x_old, Scalar function_old, Scalar first_derivative_old, Scalar &step_old)
Protected Member Functions inherited from Optimist::RootFinder::RootFinder< Scalar, Varona< Scalar > >
bool	evaluate_jacobian (JacobianLambda &&jacobian, const Input &x, FirstDerivative &out)
bool	evaluate_hessian (HessianLambda &&hessian, const Input &x, SecondDerivative &out)
Protected Member Functions inherited from Optimist::SolverBase< Scalar, Scalar, Varona< Scalar > >
Integer	first_derivative_evaluations () const
Integer	max_first_derivative_evaluations () const
Integer	second_derivative_evaluations () const
Integer	max_second_derivative_evaluations () const
void	reset_counters ()
bool	evaluate_function (FunctionLambda &&function, const Scalar &x, Scalar &out)
bool	evaluate_first_derivative (FirstDerivativeLambda &&function, const Scalar &x, FirstDerivative &out)
bool	evaluate_second_derivative (SecondDerivativeLambda &&function, const Scalar &x, SecondDerivative &out)
bool	damp (FunctionLambda &&function, const Scalar &x_old, const Scalar &function_old, const Scalar &step_old, Scalar &x_new, Scalar &function_new, Scalar &step_new)
void	header ()
void	bottom ()
void	info (Scalar residuals, const std::string &notes="-")

Static Protected Member Functions
static Scalar	Q (Scalar t)
static Scalar	W (Scalar t, Scalar s)
static Scalar	H (Scalar t, Scalar s, Scalar u)
static Scalar	J (Scalar t, Scalar s, Scalar u, Scalar v)

Private Attributes
Method	m_method {Method::ORDER_4}

Additional Inherited Members
Protected Attributes inherited from Optimist::SolverBase< Scalar, Scalar, Varona< Scalar > >
Scalar	m_lower_bound
Scalar	m_upper_bound
Integer	m_function_evaluations
Integer	m_first_derivative_evaluations
Integer	m_second_derivative_evaluations
Integer	m_max_function_evaluations
Integer	m_max_first_derivative_evaluations
Integer	m_max_second_derivative_evaluations
Integer	m_iterations
Integer	m_max_iterations
Scalar	m_alpha
Integer	m_relaxations
Integer	m_max_relaxations
Scalar	m_tolerance
bool	m_verbose
bool	m_damped
std::ostream *	m_ostream
std::string	m_task
bool	m_converged

Detailed Description

template<typename Scalar>
class Optimist::RootFinder::Varona< Scalar >

Template Parameters

Scalar Floating-point number type.

Member Typedef Documentation

◆ Method

template<typename Scalar>

using Optimist::RootFinder::Varona< Scalar >::Method

Initial value:

enum class Method : Integer {
       ORDER_4  = 41,
       ORDER_8  = 8,
       ORDER_16 = 16,
       ORDER_32 = 32
     }

Varona solver type enumeration.

Constructor & Destructor Documentation

◆ Varona()

template<typename Scalar>

Optimist::RootFinder::Varona< Scalar >::Varona ( )

inline

Class constructor for the Varona's solvers.

Member Function Documentation

◆ compute_step()

template<typename Scalar>

template<typename FunctionLambda>

void Optimist::RootFinder::Varona< Scalar >::compute_step	(	FunctionLambda &&	function,
		Scalar	x_old,
		Scalar	function_old,
		Scalar	first_derivative_old,
		Scalar &	step_old )

inlineprotected

Compute the step using the Varona's methods.

Parameters

[in]	function	Function lambda.
[in]	x_old	Old point.
[in]	function_old	Old function value.
[in]	first_derivative_old	Old first derivative value.
[out]	step_old	Old step.

◆ enable_16th_order_method()

template<typename Scalar>

void Optimist::RootFinder::Varona< Scalar >::enable_16th_order_method ( )

inline

Enable the Varona's 16-th order method.

◆ enable_32th_order_method()

template<typename Scalar>

void Optimist::RootFinder::Varona< Scalar >::enable_32th_order_method ( )

inline

Enable the Varona's 32-th order method.

◆ enable_4th_order_method()

template<typename Scalar>

void Optimist::RootFinder::Varona< Scalar >::enable_4th_order_method ( )

inline

Enable the Varona's 4-th order method.

◆ enable_8th_order_method()

template<typename Scalar>

void Optimist::RootFinder::Varona< Scalar >::enable_8th_order_method ( )

inline

Enable the Varona's 8-th order method.

◆ H()

template<typename Scalar>

Scalar Optimist::RootFinder::Varona< Scalar >::H	(	Scalar	t,
		Scalar	s,
		Scalar	u )

inlinestaticprotected

Compute the \( H \) function for the Varona's methods.

Parameters

[in]	t	Input value.
[in]	s	Input value.
[in]	u	Input value.

Returns: The \( H \) function value.

◆ J()

template<typename Scalar>

Scalar Optimist::RootFinder::Varona< Scalar >::J	(	Scalar	t,
		Scalar	s,
		Scalar	u,
		Scalar	v )

inlinestaticprotected

Compute the \( J \) function for the Varona's methods.

Parameters

[in]	t	Input value.
[in]	s	Input value.
[in]	u	Input value.
[in]	v	Input value.

Returns: The \( J \) function value.

◆ method() [1/2]

template<typename Scalar>

Method Optimist::RootFinder::Varona< Scalar >::method ( ) const

inline

Get the enumeration type of the Varona solver method.

Returns: The Varona solver enumeration type.

◆ method() [2/2]

template<typename Scalar>

void Optimist::RootFinder::Varona< Scalar >::method ( Method t_method )

inline

Set the enumeration type of the Varona solver method.

Parameters

[in] t_method The Varona solver enumeration type.

◆ name_impl()

template<typename Scalar>

std::string Optimist::RootFinder::Varona< Scalar >::name_impl ( ) const

inlineconstexpr

Get the Varona solver name.

Returns: The Varona solver name.

◆ Q()

template<typename Scalar>

Scalar Optimist::RootFinder::Varona< Scalar >::Q ( Scalar t )

inlinestaticprotected

Compute the \( Q \) function for the Varona's methods.

Parameters

[in] t Input value.

Returns: The \( Q \) function value.

◆ set_method()

template<typename Scalar>

void Optimist::RootFinder::Varona< Scalar >::set_method ( Method t_method )

inline

Set the Varona solver type.

Parameters

[in] t_method The Varona solver type enumeration.

◆ solve_impl()

template<typename Scalar>

template<typename FunctionLambda, typename FirstDerivativeLambda>

bool Optimist::RootFinder::Varona< Scalar >::solve_impl	(	FunctionLambda &&	function,
		FirstDerivativeLambda &&	first_derivative,
		Scalar	x_ini,
		Scalar &	x_sol )

inline

Solve the nonlinear equation \( f(x) = 0 \), with \( f: \mathbb{R} \rightarrow \mathbb{R} \).

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.

Returns: The convergence boolean flag.

◆ W()

template<typename Scalar>

Scalar Optimist::RootFinder::Varona< Scalar >::W	(	Scalar	t,
		Scalar	s )

inlinestaticprotected

Compute the \( W \) function for the Varona's methods.

Parameters

[in]	t	Input value.
[in]	s	Input value.

Returns: The \( W \) function value.

Member Data Documentation

◆ m_method

template<typename Scalar>

Method Optimist::RootFinder::Varona< Scalar >::m_method {Method::ORDER_4}

private

Varona solver type.

◆ RequiresFirstDerivative

template<typename Scalar>

bool Optimist::RootFinder::Varona< Scalar >::RequiresFirstDerivative {true}

staticconstexpr

◆ RequiresFunction

template<typename Scalar>

bool Optimist::RootFinder::Varona< Scalar >::RequiresFunction {true}

staticconstexpr

◆ RequiresSecondDerivative

template<typename Scalar>

bool Optimist::RootFinder::Varona< Scalar >::RequiresSecondDerivative {false}

staticconstexpr

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

core/include/Optimist/RootFinder/Varona.hh

Public Types

Public Member Functions

Static Public Attributes

Protected Member Functions

Static Protected Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ Method

Constructor & Destructor Documentation

◆ Varona()

Member Function Documentation

◆ compute_step()

◆ enable_16th_order_method()

◆ enable_32th_order_method()

◆ enable_4th_order_method()

◆ enable_8th_order_method()

◆ H()

◆ J()

◆ method() [1/2]

◆ method() [2/2]

◆ name_impl()

◆ Q()

◆ set_method()

◆ solve_impl()

◆ W()

Member Data Documentation

◆ m_method

◆ RequiresFirstDerivative

◆ RequiresFunction

◆ RequiresSecondDerivative