Class container for the Bracketing algorithms. More...

#include <Bracketing.hh>

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

Public Types
using	FunctionWrapper = typename RootFinder<Real, 1, DerivedSolver>::FunctionWrapper
using	FirstDerivativeWrapper = typename RootFinder<Real, 1, DerivedSolver>::FirstDerivativeWrapper
using	SecondDerivativeWrapper = typename RootFinder<Real, 1, DerivedSolver>::SecondDerivativeWrapper
Public Types inherited from Optimist::RootFinder::RootFinder< Real, 1, DerivedSolver >
using	FunctionWrapper = typename SolverBase<Real, 1, 1, DerivedSolver>::FunctionWrapper
using	FirstDerivativeWrapper = typename SolverBase<Real, 1, 1, DerivedSolver>::FirstDerivativeWrapper
using	SecondDerivativeWrapper = typename SolverBase<Real, 1, 1, DerivedSolver>::SecondDerivativeWrapper
using	Vector
using	Matrix
using	Tensor
using	JacobianWrapper
using	HessianWrapper

Public Member Functions
	Bracketing ()
std::string	name_impl () const
void	tolerance_bracketing (Real t_tolerance)
bool	solve_impl (FunctionWrapper function, Real, Real &x_sol)
Real	find_root (FunctionWrapper function)
Public Member Functions inherited from Optimist::RootFinder::RootFinder< Real, 1, DerivedSolver >
	RootFinder ()
std::string	name () const
bool	solve (FunctionWrapper function, Real x_ini, Real &x_sol)
bool	solve (FunctionWrapper function, FirstDerivativeWrapper first_derivative, Real x_ini, Real &x_sol)
bool	solve (FunctionWrapper function, FirstDerivativeWrapper first_derivative, SecondDerivativeWrapper second_derivate, Real x_ini, Real &x_sol)
Integer	jacobian_evaluations () const
Integer	max_jacobian_evaluations () const
Integer	hessian_evaluations () const
Integer	max_hessian_evaluations () const
Public Member Functions inherited from Optimist::SolverBase< Real, N, N, DerivedSolver, false >
	SolverBase ()
const InputType &	lower_bound () const
const InputType &	upper_bound () const
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	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 (FunctionWrapper function, const InputType &x_ini, InputType &x_sol)
bool	rootfind (FunctionBase< Real, FunInDim, FunOutDim, DerivedFunction, ForceEigen &&FunOutDim==1 > const &function, const InputType &x_ini, InputType &x_sol)
bool	optimize (FunctionBase< Real, FunInDim, FunOutDim, DerivedFunction, ForceEigen &&FunOutDim==1 > const &function, const InputType &x_ini, InputType &x_sol)
std::string	name () const
Public Member Functions inherited from Optimist::SolverBase< Real, 1, 1, DerivedSolver >
	SolverBase ()
const InputType &	lower_bound () const
const InputType &	upper_bound () const
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	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 (FunctionWrapper function, const InputType &x_ini, InputType &x_sol)
bool	rootfind (FunctionBase< Real, FunInDim, FunOutDim, DerivedFunction, false &&FunOutDim==1 > const &function, const InputType &x_ini, InputType &x_sol)
bool	optimize (FunctionBase< Real, FunInDim, FunOutDim, DerivedFunction, false &&FunOutDim==1 > const &function, const InputType &x_ini, InputType &x_sol)
std::string	name () const

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

Protected Attributes
Real	m_tolerance_bracketing {100*EPSILON}
Real	m_mu {0.5}
Real	m_interval_shink {0.025}
Real	m_a {0.0}
Real	m_fa {0.0}
Real	m_b {0.0}
Real	m_fb {0.0}
Real	m_c {0.0}
Real	m_fc {0.0}
Real	m_d {0.0}
Real	m_fd {0.0}
Real	m_e {0.0}
Real	m_fe {0.0}
Protected Attributes inherited from Optimist::SolverBase< Real, N, N, DerivedSolver, 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
Protected Attributes inherited from Optimist::SolverBase< Real, 1, 1, DerivedSolver >
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

Additional Inherited Members
Protected Types inherited from Optimist::SolverBase< Real, N, N, DerivedSolver, false >
using	InputType
using	OutputType
using	TraceType
using	FirstDerivativeType
using	SecondDerivativeType
using	FunctionWrapper
using	FirstDerivativeWrapper
using	SecondDerivativeWrapper
Protected Types inherited from Optimist::SolverBase< Real, 1, 1, DerivedSolver >
using	InputType
using	OutputType
using	TraceType
using	FirstDerivativeType
using	SecondDerivativeType
using	FunctionWrapper
using	FirstDerivativeWrapper
using	SecondDerivativeWrapper
Protected Member Functions inherited from Optimist::RootFinder::RootFinder< Real, 1, DerivedSolver >
void	evaluate_jacobian (JacobianWrapper jacobian, const Vector &x, Matrix &out)
void	evaluate_hessian (HessianWrapper hessian, const Vector &x, Matrix &out)
Protected Member Functions inherited from Optimist::SolverBase< Real, N, N, DerivedSolver, 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 ()
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 Member Functions inherited from Optimist::SolverBase< Real, 1, 1, DerivedSolver >
Integer	first_derivative_evaluations () const
Integer	max_first_derivative_evaluations () const
Integer	second_derivative_evaluations () const
Integer	max_second_derivative_evaluations () const
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="-")

Detailed Description

template<typename Real, typename DerivedSolver>
class Optimist::RootFinder::Bracketing< Real, DerivedSolver >

The Bracketing algorithms allow to find the roots of a scalar function \(f(x)\) in a given interval \([a, b]\).

Template Parameters

Real	Scalar number type.

Member Typedef Documentation

◆ FirstDerivativeWrapper

template<typename Real, typename DerivedSolver>

using Optimist::RootFinder::Bracketing< Real, DerivedSolver >::FirstDerivativeWrapper = typename RootFinder<Real, 1, DerivedSolver>::FirstDerivativeWrapper

◆ FunctionWrapper

template<typename Real, typename DerivedSolver>

using Optimist::RootFinder::Bracketing< Real, DerivedSolver >::FunctionWrapper = typename RootFinder<Real, 1, DerivedSolver>::FunctionWrapper

◆ SecondDerivativeWrapper

template<typename Real, typename DerivedSolver>

using Optimist::RootFinder::Bracketing< Real, DerivedSolver >::SecondDerivativeWrapper = typename RootFinder<Real, 1, DerivedSolver>::SecondDerivativeWrapper

Constructor & Destructor Documentation

◆ Bracketing()

template<typename Real, typename DerivedSolver>

Optimist::RootFinder::Bracketing< Real, DerivedSolver >::Bracketing ( )

inline

Class constructor for the Algorithm 748.

Member Function Documentation

◆ find_root()

template<typename Real, typename DerivedSolver>

Real Optimist::RootFinder::Bracketing< Real, DerivedSolver >::find_root ( FunctionWrapper function )

inline

Finds either an exact solution or an approximate solution of the equation \(f(x) = 0\) in the interval \([a, b]\).

Parameters

[in] function Function wrapper.

Returns: The approximate root.

◆ name_impl()

template<typename Real, typename DerivedSolver>

std::string Optimist::RootFinder::Bracketing< Real, DerivedSolver >::name_impl ( ) const

inline

Get the Algorithm 748 solver name.

Returns: The Algorithm 748 solver name.

◆ solve_impl()

template<typename Real, typename DerivedSolver>

bool Optimist::RootFinder::Bracketing< Real, DerivedSolver >::solve_impl	(	FunctionWrapper	function,
		Real	,
		Real &	x_sol )

inline

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

Parameters

[in]	function	Function wrapper.
[in]	x_ini	Initialization point (not used).
[out]	x_sol	Solution point.

Returns: The convergence boolean flag.

◆ tolerance_bracketing()

template<typename Real, typename DerivedSolver>

void Optimist::RootFinder::Bracketing< Real, DerivedSolver >::tolerance_bracketing ( Real t_tolerance )

inline

Set the tolerance for the Algorithm 748 solver.

Parameters

[in] t_tolerance The input value at which the tolerance is computed.

Note: To accurately find polynomial roots, the tolerance should be set to \( 100\epsilon(0) \).

Member Data Documentation

◆ m_a

template<typename Real, typename DerivedSolver>

Real Optimist::RootFinder::Bracketing< Real, DerivedSolver >::m_a {0.0}

protected

◆ m_b

template<typename Real, typename DerivedSolver>

Real Optimist::RootFinder::Bracketing< Real, DerivedSolver >::m_b {0.0}

protected

◆ m_c

template<typename Real, typename DerivedSolver>

Real Optimist::RootFinder::Bracketing< Real, DerivedSolver >::m_c {0.0}

protected

◆ m_d

template<typename Real, typename DerivedSolver>

Real Optimist::RootFinder::Bracketing< Real, DerivedSolver >::m_d {0.0}

protected

◆ m_e

template<typename Real, typename DerivedSolver>

Real Optimist::RootFinder::Bracketing< Real, DerivedSolver >::m_e {0.0}

protected

◆ m_fa

template<typename Real, typename DerivedSolver>

Real Optimist::RootFinder::Bracketing< Real, DerivedSolver >::m_fa {0.0}

protected

◆ m_fb

template<typename Real, typename DerivedSolver>

Real Optimist::RootFinder::Bracketing< Real, DerivedSolver >::m_fb {0.0}

protected

◆ m_fc

template<typename Real, typename DerivedSolver>

Real Optimist::RootFinder::Bracketing< Real, DerivedSolver >::m_fc {0.0}

protected

◆ m_fd

template<typename Real, typename DerivedSolver>

Real Optimist::RootFinder::Bracketing< Real, DerivedSolver >::m_fd {0.0}

protected

◆ m_fe

template<typename Real, typename DerivedSolver>

Real Optimist::RootFinder::Bracketing< Real, DerivedSolver >::m_fe {0.0}

protected

◆ m_interval_shink

template<typename Real, typename DerivedSolver>

Real Optimist::RootFinder::Bracketing< Real, DerivedSolver >::m_interval_shink {0.025}

protected

Interval shrinking factor.

◆ m_mu

template<typename Real, typename DerivedSolver>

Real Optimist::RootFinder::Bracketing< Real, DerivedSolver >::m_mu {0.5}

protected

Parameter \( \mu \).

◆ m_tolerance_bracketing

template<typename Real, typename DerivedSolver>

Real Optimist::RootFinder::Bracketing< Real, DerivedSolver >::m_tolerance_bracketing {100*EPSILON}

protected

Tolerance for the Algorithm 748 solver.

◆ requires_first_derivative

template<typename Real, typename DerivedSolver>

bool Optimist::RootFinder::Bracketing< Real, DerivedSolver >::requires_first_derivative {DerivedSolver::requires_first_derivative}

staticconstexpr

◆ requires_function

template<typename Real, typename DerivedSolver>

bool Optimist::RootFinder::Bracketing< Real, DerivedSolver >::requires_function {DerivedSolver::requires_function}

staticconstexpr

◆ requires_second_derivative

template<typename Real, typename DerivedSolver>

bool Optimist::RootFinder::Bracketing< Real, DerivedSolver >::requires_second_derivative {DerivedSolver::requires_second_derivative}

staticconstexpr

Basic constants.

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

include/Optimist/RootFinder/Bracketing.hh

Public Types

Public Member Functions

Static Public Attributes

Protected Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ FirstDerivativeWrapper

◆ FunctionWrapper

◆ SecondDerivativeWrapper

Constructor & Destructor Documentation

◆ Bracketing()

Member Function Documentation

◆ find_root()

◆ name_impl()

◆ solve_impl()

◆ tolerance_bracketing()

Member Data Documentation

◆ m_a

◆ m_b

◆ m_c

◆ m_d

◆ m_e

◆ m_fa

◆ m_fb

◆ m_fc

◆ m_fd

◆ m_fe

◆ m_interval_shink

◆ m_mu

◆ m_tolerance_bracketing

◆ requires_first_derivative

◆ requires_function

◆ requires_second_derivative