Class container for the Halley's method. More...

#include <Halley.hh>

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

Public Member Functions
	Halley ()
constexpr std::string	name_impl () const
template<typename FunctionLambda, typename FirstDerivativeLambda, typename SecondDerivativeLambda>
bool	solve_impl (FunctionLambda &&function, FirstDerivativeLambda &&first_derivative, SecondDerivativeLambda &&second_derivative, Scalar x_ini, Scalar &x_sol)
Public Member Functions inherited from Optimist::RootFinder::RootFinder< Scalar, Halley< 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, Halley< 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 {true}
Static Public Attributes inherited from Optimist::RootFinder::RootFinder< Scalar, Halley< Scalar > >
static constexpr bool	IsRootFinder
static constexpr bool	IsOptimizer

Additional Inherited Members
Public Types inherited from Optimist::RootFinder::RootFinder< Scalar, Halley< Scalar > >
using	Scalar
using	Input
using	Output
Public Types inherited from Optimist::SolverBase< Scalar, Scalar, Halley< Scalar > >
using	InputTrait
using	OutputTrait
using	Scalar
using	FirstDerivative
using	SecondDerivative
Protected Member Functions inherited from Optimist::RootFinder::RootFinder< Scalar, Halley< 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, Halley< 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="-")
Protected Attributes inherited from Optimist::SolverBase< Scalar, Scalar, Halley< 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::Halley< Scalar >

Template Parameters

Scalar Floating-point number type.

Constructor & Destructor Documentation

◆ Halley()

template<typename Scalar>

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

inline

Class constructor for the Halley solver.

Member Function Documentation

◆ name_impl()

template<typename Scalar>

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

inlineconstexpr

Get the Halley solver name.

Returns: The Halley solver name.

◆ solve_impl()

template<typename Scalar>

template<typename FunctionLambda, typename FirstDerivativeLambda, typename SecondDerivativeLambda>

bool Optimist::RootFinder::Halley< Scalar >::solve_impl	(	FunctionLambda &&	function,
		FirstDerivativeLambda &&	first_derivative,
		SecondDerivativeLambda &&	second_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.
SecondDerivativeLambda	Second derivative lambda type.

Parameters

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

Returns: The convergence boolean flag.

Member Data Documentation

◆ RequiresFirstDerivative

template<typename Scalar>

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

staticconstexpr

◆ RequiresFunction

template<typename Scalar>

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

staticconstexpr

◆ RequiresSecondDerivative

template<typename Scalar>

bool Optimist::RootFinder::Halley< Scalar >::RequiresSecondDerivative {true}

staticconstexpr

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

core/include/Optimist/RootFinder/Halley.hh

Public Member Functions

Static Public Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Halley()

Member Function Documentation

◆ name_impl()

◆ solve_impl()

Member Data Documentation

◆ RequiresFirstDerivative

◆ RequiresFunction

◆ RequiresSecondDerivative