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

#include <Greenstadt.hh>

Inherits Optimist::RootFinder::QuasiNewton< Real, N, Greenstadt< Real, N > >.

Public Types
using	Method = enum class Method : Integer {ONE = 1, TWO = 2}
using	Vector = typename QuasiNewton<Real, N, Greenstadt<Real, N>>::Vector
using	Matrix = typename QuasiNewton<Real, N, Greenstadt<Real, N>>::Matrix
using	FunctionWrapper = typename QuasiNewton<Real, N, Greenstadt<Real, N>>::FunctionWrapper
using	JacobianWrapper = typename QuasiNewton<Real, N, Greenstadt<Real, N>>::JacobianWrapper
Public Types inherited from Optimist::RootFinder::QuasiNewton< Real, N, Greenstadt< Real, N > >
using	Method
using	Vector
using	Matrix
using	FunctionWrapper
using	JacobianWrapper
Public Types inherited from Optimist::RootFinder::RootFinder< Real, N, Greenstadt< Real, N >, true >
using	Vector
using	Matrix
using	Tensor
using	FunctionWrapper
using	JacobianWrapper
using	HessianWrapper

Public Member Functions
	Greenstadt ()
std::string	name_impl () const
Method	method () const
void	method (Method t_method)
void	enable_one_method ()
void	enable_two_method ()
void	set_method (Method t_method)
void	update_impl (Vector const &, Vector const &, Matrix const &jacobian_old, Vector const &delta_x_new, Vector const &delta_function_new, Vector const &function_new, Matrix &jacobian_new)
Public Member Functions inherited from Optimist::RootFinder::QuasiNewton< Real, N, Greenstadt< Real, N > >
	QuasiNewton ()
std::string	name_impl () const
bool	solve_impl (FunctionWrapper function, JacobianWrapper jacobian, Vector const &x_ini, Vector &x_sol)
void	update (Vector const &delta_x_old, Vector const &delta_function_old, Matrix const &jacobian_old, Vector const &delta_x_new, Vector const &delta_function_new, Vector const &function_new, Matrix &jacobian_new)
Public Member Functions inherited from Optimist::RootFinder::RootFinder< Real, N, Greenstadt< Real, N >, true >
	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 (FunctionWrapper function, Vector const &x_ini, Vector &x_sol)
Public Member Functions inherited from Optimist::SolverBase< Real, N, N, Greenstadt< Real, N >, ForceEigen >
	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

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::QuasiNewton< Real, N, Greenstadt< Real, N > >
static constexpr bool	requires_function
static constexpr bool	requires_first_derivative
static constexpr bool	requires_second_derivative
Static Public Attributes inherited from Optimist::RootFinder::RootFinder< Real, N, Greenstadt< Real, N >, true >
static constexpr bool	is_rootfinder
static constexpr bool	is_optimizer
static constexpr bool	requires_function
static constexpr bool	requires_first_derivative
static constexpr bool	requires_second_derivative

Private Attributes
Method	m_method {Method::ONE}

Additional Inherited Members
Protected Types inherited from Optimist::SolverBase< Real, N, N, Greenstadt< Real, N >, ForceEigen >
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, N, Greenstadt< Real, N >, true >
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, Greenstadt< Real, N >, ForceEigen >
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 Attributes inherited from Optimist::SolverBase< Real, N, N, Greenstadt< Real, N >, ForceEigen >
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, Integer N>
class Optimist::RootFinder::Greenstadt< Real, N >

Greenstadt's method

Similarly to the Broyden's methods, Greenstadt's methods are quasi-Newton methods that approximates the Jacobian matrix \(\mathbf{Jf}_{\mathbf{x}}\) an update rule. The generic Greenstadt's method is defined as

\[ \mathbf{H}_k(\mathbf{x}_k) \mathbf{h}_k = -\mathbf{f}(\mathbf{x}_k) \text{,} \]

where \(\mathbf{H}_k\) is the (inverse) Jacobian approximation at the \(k\)-th iteration.

Based on the update rule, Greenstadt's method is classified into two methods: trivially method 1 and method 2. The update of the Jacobian approximation is performed as

\[ \mathbf{H}_{k+1}^{-1} = \mathbf{H}_k^{-1} - \displaystyle\frac{\mathbf{H}_k^{-1} \Delta\mathbf{f}_k - \Delta\mathbf{x}_k}{\mathbf{g} \Delta\mathbf{f}_k} \mathbf{g} \text{,} \]

where \(\Delta\mathbf{x}_k = \mathbf{x}_k - \mathbf{x}_{k-1}\), and \(\Delta\mathbf{f}_k = \mathbf{f}(\mathbf{x}_k) - \mathbf{f}(\mathbf{x}_{k-1})\). The quantity \(\mathbf{g}\) is \(\mathbf{g} = \mathbf{f}_k^\top\) for method 1 and \(\mathbf{g} = \mathbf{H}_{k\top}^{-1} \mathbf{H}_k^{-1} \Delta\mathbf{f}_k^{\top}\) for method 2. The choice of the method is based on the convergence history, switching between the methods to adapt to the problem's behavior.

For more details on the Greenstadt's methods refer to the reference: Spedicato E., Greenstadt J. On some classes of variationally derived Quasi-Newton methods for systems of nonlinear algebraic equations, Numerische Mathematik, 29 (1978), pp. 363-380.

Template Parameters

Real	Scalar number type.
N	Dimension of the root-finding problem.

Member Typedef Documentation

◆ FunctionWrapper

template<typename Real, Integer N>

using Optimist::RootFinder::Greenstadt< Real, N >::FunctionWrapper = typename QuasiNewton<Real, N, Greenstadt<Real, N>>::FunctionWrapper

◆ JacobianWrapper

template<typename Real, Integer N>

using Optimist::RootFinder::Greenstadt< Real, N >::JacobianWrapper = typename QuasiNewton<Real, N, Greenstadt<Real, N>>::JacobianWrapper

◆ Matrix

template<typename Real, Integer N>

using Optimist::RootFinder::Greenstadt< Real, N >::Matrix = typename QuasiNewton<Real, N, Greenstadt<Real, N>>::Matrix

◆ Method

template<typename Real, Integer N>

using Optimist::RootFinder::Greenstadt< Real, N >::Method = enum class Method : Integer {ONE = 1, TWO = 2}

Greenstadt solver type.

◆ Vector

template<typename Real, Integer N>

using Optimist::RootFinder::Greenstadt< Real, N >::Vector = typename QuasiNewton<Real, N, Greenstadt<Real, N>>::Vector

Constructor & Destructor Documentation

◆ Greenstadt()

template<typename Real, Integer N>

Optimist::RootFinder::Greenstadt< Real, N >::Greenstadt ( )

inline

Class constructor for the Greenstadt solver.

Member Function Documentation

◆ enable_one_method()

template<typename Real, Integer N>

void Optimist::RootFinder::Greenstadt< Real, N >::enable_one_method ( )

inline

Enable the Greenstadt1 solver method.

◆ enable_two_method()

template<typename Real, Integer N>

void Optimist::RootFinder::Greenstadt< Real, N >::enable_two_method ( )

inline

Enable the Greenstadt2 solver method.

◆ method() [1/2]

template<typename Real, Integer N>

Method Optimist::RootFinder::Greenstadt< Real, N >::method ( ) const

inline

Get the enumeration type of the Greenstadt solver method.

Returns: The Greenstadt solver enumeration type.

◆ method() [2/2]

template<typename Real, Integer N>

void Optimist::RootFinder::Greenstadt< Real, N >::method ( Method t_method )

inline

Set the enumeration type of the Greenstadt solver method.

Parameters

[in] t_method The Greenstadt solver method enumeration type.

◆ name_impl()

template<typename Real, Integer N>

std::string Optimist::RootFinder::Greenstadt< Real, N >::name_impl ( ) const

inline

Get the Greenstadt solver name.

Returns: The Greenstadt solver name.

◆ set_method()

template<typename Real, Integer N>

void Optimist::RootFinder::Greenstadt< Real, N >::set_method ( Method t_method )

inline

Set the Greenstadt solver method.

Parameters

[in] t_method The Greenstadt solver method enumeration type.

◆ update_impl()

template<typename Real, Integer N>

void Optimist::RootFinder::Greenstadt< Real, N >::update_impl	(	Vector const &	,
		Vector const &	,
		Matrix const &	jacobian_old,
		Vector const &	delta_x_new,
		Vector const &	delta_function_new,
		Vector const &	function_new,
		Matrix &	jacobian_new )

inline

Jacobian approximation update rule for the Greenstadt's method.

Parameters

[in]	delta_x_old	Old difference between points.
[in]	delta_function_old	Old difference between function values.
[in]	jacobian_old	Old jacobian approximation.
[in]	delta_x_new	New difference between points.
[in]	delta_function_new	New difference between function values.
[in]	function_new	New function value.
[out]	jacobian_new	New jacobian approximation.

Member Data Documentation

◆ m_method

template<typename Real, Integer N>

Method Optimist::RootFinder::Greenstadt< Real, N >::m_method {Method::ONE}

private

Greenstadt solver type.

◆ requires_first_derivative

template<typename Real, Integer N>

bool Optimist::RootFinder::Greenstadt< Real, N >::requires_first_derivative {true}

staticconstexpr

◆ requires_function

template<typename Real, Integer N>

bool Optimist::RootFinder::Greenstadt< Real, N >::requires_function {true}

staticconstexpr

◆ requires_second_derivative

template<typename Real, Integer N>

bool Optimist::RootFinder::Greenstadt< Real, N >::requires_second_derivative {false}

staticconstexpr

Basic constants.

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

include/Optimist/RootFinder/Greenstadt.hh

Public Types

Public Member Functions

Static Public Attributes

Private Attributes

Additional Inherited Members

Detailed Description

Greenstadt's method

Member Typedef Documentation

◆ FunctionWrapper

◆ JacobianWrapper

◆ Matrix

◆ Method

◆ Vector

Constructor & Destructor Documentation

◆ Greenstadt()

Member Function Documentation

◆ enable_one_method()

◆ enable_two_method()

◆ method() [1/2]

◆ method() [2/2]

◆ name_impl()

◆ set_method()

◆ update_impl()

Member Data Documentation

◆ m_method

◆ requires_first_derivative

◆ requires_function

◆ requires_second_derivative