Class container for the scalar Newton-Raphson method. More...

#include <NewtonRaphson.hh>

Inherits Optimist::RootFinder::RootFinder< Real, 1, NewtonRaphson< Real > >.

Public Member Functions
	NewtonRaphson ()
std::string	name_impl () const
template<typename FunctionLambda, typename FirstDerivativeLambda>
bool	solve_impl (FunctionLambda &&function, FirstDerivativeLambda &&first_derivative, Real x_ini, Real &x_sol)
Public Member Functions inherited from Optimist::RootFinder::RootFinder< Real, 1, NewtonRaphson< Real > >
	RootFinder ()
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, Vector const &x_ini, Vector &x_sol)
Public Member Functions inherited from Optimist::SolverBase< Real, N, N, NewtonRaphson< Real >, false >
	SolverBase ()
InputType const &	lower_bound () const
InputType const &	upper_bound () const
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	iterations () const
Integer	max_iterations () const
Real	alpha () const
Integer	relaxations () const
Integer	max_relaxations () const
Real	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
const TraceType &	trace () const
std::ostream &	ostream () const
bool	solve (FunctionLambda &&function, InputType const &x_ini, InputType &x_sol)
bool	rootfind (FunctionBase< Real, FunInDim, FunOutDim, DerivedFunction, ForceEigen &&FunOutDim==1 > const &function, InputType const &x_ini, InputType &x_sol)
bool	optimize (FunctionBase< Real, FunInDim, FunOutDim, DerivedFunction, ForceEigen &&FunOutDim==1 > const &function, InputType const &x_ini, InputType &x_sol)
std::string	name () const

Static Public Attributes
static constexpr bool	requires_function {true}
static constexpr bool	requires_first_derivative {true}
static constexpr bool	requires_second_derivative {false}
Static Public Attributes inherited from Optimist::RootFinder::RootFinder< Real, 1, NewtonRaphson< Real > >
static constexpr bool	is_rootfinder
static constexpr bool	is_optimizer

Additional Inherited Members
Public Types inherited from Optimist::RootFinder::RootFinder< Real, 1, NewtonRaphson< Real > >
using	Vector
using	Matrix
using	Tensor
Public Types inherited from Optimist::SolverBase< Real, N, N, NewtonRaphson< Real >, false >
using	InputType
using	OutputType
using	TraceType
using	FirstDerivativeType
using	SecondDerivativeType
Protected Member Functions inherited from Optimist::RootFinder::RootFinder< Real, 1, NewtonRaphson< Real > >
bool	evaluate_jacobian (JacobianLambda &&jacobian, Vector const &x, Matrix &out)
bool	evaluate_hessian (HessianLambda &&hessian, Vector const &x, Matrix &out)
Protected Member Functions inherited from Optimist::SolverBase< Real, N, N, NewtonRaphson< Real >, false >
Integer	first_derivative_evaluations () const
Integer	max_first_derivative_evaluations () const
Integer	second_derivative_evaluations () const
Integer	max_second_derivative_evaluations () const
void	reset ()
bool	evaluate_function (FunctionLambda &&function, InputType const &x, OutputType &out)
bool	evaluate_first_derivative (FirstDerivativeLambda &&function, InputType const &x, FirstDerivativeType &out)
bool	evaluate_second_derivative (SecondDerivativeLambda &&function, InputType const &x, SecondDerivativeType &out)
void	store_trace (InputType const &x)
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 inherited from Optimist::SolverBase< Real, N, N, NewtonRaphson< Real >, false >
InputType	m_lower_bound
InputType	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
Real	m_alpha
Integer	m_relaxations
Integer	m_max_relaxations
Real	m_tolerance
bool	m_verbose
bool	m_damped
std::ostream *	m_ostream
std::string	m_task
bool	m_converged
TraceType	m_trace

Detailed Description

template<typename Real>
class Optimist::RootFinder::NewtonRaphson< Real >

Newton-Raphson method

Newton-Raphson method, including its damped variant with an affine-invariant step, is based on the linearization of the function \(f(x)\) around the current iterate \(x_k\), which leads to the linear system

\[ f^{\prime}_{x}(x_k) h_k = -f(x_k) \text{.} \]

The advancing step \(h_k\) is then computed as

\[ x_{k+1} = x_k + \alpha_k h_k \text{,} \]

where \(\alpha_k\) is a damping coefficient that ensures affine-invariant criteria is satisfied.

Template Parameters

Real	Scalar number type.

Constructor & Destructor Documentation

◆ NewtonRaphson()

template<typename Real>

Optimist::RootFinder::NewtonRaphson< Real >::NewtonRaphson ( )

inline

Class constructor for the Newton solver.

Member Function Documentation

◆ name_impl()

template<typename Real>

std::string Optimist::RootFinder::NewtonRaphson< Real >::name_impl ( ) const

inline

Get the Newton solver name.

Returns: The Newton solver name.

◆ solve_impl()

template<typename Real>

template<typename FunctionLambda, typename FirstDerivativeLambda>

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

inline

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

Template Parameters

FunctionLambda	Function lambda.
FirstDerivativeLambda	First derivative lambda.

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.

Member Data Documentation

◆ requires_first_derivative

template<typename Real>

bool Optimist::RootFinder::NewtonRaphson< Real >::requires_first_derivative {true}

staticconstexpr

◆ requires_function

template<typename Real>

bool Optimist::RootFinder::NewtonRaphson< Real >::requires_function {true}

staticconstexpr

◆ requires_second_derivative

template<typename Real>

bool Optimist::RootFinder::NewtonRaphson< Real >::requires_second_derivative {false}

staticconstexpr

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

include/Optimist/RootFinder/NewtonRaphson.hh

Public Member Functions

Static Public Attributes

Additional Inherited Members

Detailed Description

Newton-Raphson method

Constructor & Destructor Documentation

◆ NewtonRaphson()

Member Function Documentation

◆ name_impl()

◆ solve_impl()

Member Data Documentation

◆ requires_first_derivative

◆ requires_function

◆ requires_second_derivative