Solver< T > Class Template Reference

Class Solver managing the solving process and creating the Stepper object. More...

#include <solver_def.hpp>

Collaboration diagram for Solver< T >:

Public Member Functions
	Solver (std::function< double(double)> fun, T initial_guess, const Method method, int max_iterations, double tolerance, bool aitken_mode, bool verbose)
	Constructor for Solver object.
	Solver (std::function< double(double)> fun, T initial_guess, const Method method, int max_iterations, double tolerance, bool aitken_mode, bool verbose, std::function< double(double)> derivative_or_function_g)
	Constructor for Solver object.
Eigen::MatrixX2d	solve ()
	Calls everything required to Solve with a method.

Private Member Functions
void	solver_step (int &iter, std::unique_ptr< StepperBase< T > > &stepper, double &err)
	Creates the stepper, calls the step computation, the error calculation and the results' saver.
void	save_results (int iter, Eigen::Vector2d result_to_save)
	Saves the result of a step in a defined row of the results' matrix.
Eigen::Vector2d	get_previous_result (int step_length)
	Returns a row of the results' matrix.
double	calculate_error (double x_prev, double x_next)
	Computes the error of the latest iteration.
void	save_starting_point ()
	Saves the actual initial guess in the top row of the results' matrix, no matter what type will be the Class argument initial_guess.
void	convert_stepper (std::unique_ptr< StepperBase< T > > &stepper)
	Converts the generic Abstract stepper into a typed one.
void	convert_stepper (std::unique_ptr< StepperBase< double > > &stepper)
void	convert_stepper (std::unique_ptr< StepperBase< Eigen::Vector2d > > &stepper)
void	save_starting_point ()
void	save_starting_point ()

Private Attributes
Method	method
	Method which will be used - defined thanks to.
int	max_iterations
	Stores the maximum iterations for the method.
double	tolerance
	Stores the tolerance below which the process ends.
bool	aitken_requirement
	True if Aitken acceleration is required, 0 otherwise.
bool	verbose
	Verbose mode flag.
std::function< double(double)>	derivative_or_function_g
	Stores the derivative or g_function of the function if needed.
Eigen::MatrixX2d	results
std::function< double(double)>	function
	Stores the function to find the root of and the starting guess for the process.
T	initial_guess
	Templated initial_guess for the method, whose type changes depending on the method itself.

Friends
class	SolverTester
	Friend class for unit testing purposes.

Detailed Description

template<typename T>
class Solver< T >

Class Solver managing the solving process and creating the Stepper object.

Constructor & Destructor Documentation

Solver() [1/2]

template<typename T >

Solver< T >::Solver	(	std::function< double(double)>	fun,
		T	initial_guess,
		const Method	method,
		int	max_iterations,
		double	tolerance,
		bool	aitken_mode,
		bool	verbose
	)

Constructor for Solver object.

Parameters

fun	The function to find the root of
initial_guess	The initial guess(es) or interval
method	The method which will be used for the Solution
max_iterations	Maximum iterations in which the method has to converge
tolerance	The tolerance below which the error/function will make the method converge
aitken_mode	Option to apply Aitken's acceleration
verbose	Option to give verbose output

Solver() [2/2]

template<typename T >

Solver< T >::Solver	(	std::function< double(double)>	fun,
		T	initial_guess,
		const Method	method,
		int	max_iterations,
		double	tolerance,
		bool	aitken_mode,
		bool	verbose,
		std::function< double(double)>	derivative_or_function_g
	)

Constructor for Solver object.

Parameters

fun	The function to find the root of
initial_guess	The initial guess(es) or interval
method	The method which will be used for the Solution
max_iterations	Maximum iterations in which the method has to converge
tolerance	The tolerance below which the error/function will make the method converge
aitken_mode	Option to apply Aitken's acceleration
verbose	Option to give verbose output
derivative_or_function_g	The derivative of the function (for Newton) or g_function (for Fixed Point)

Member Function Documentation

calculate_error()

template<typename T >

double Solver< T >::calculate_error ( double  x_prev, double  x_next  )

private

Computes the error of the latest iteration.

Parameters

x_next	The new guess x(i)
x_prev	The old guess x(i-1)

Returns

|x_next - x_prev|

convert_stepper() [1/3]

void Solver< double >::convert_stepper ( std::unique_ptr< StepperBase< double > > &  stepper )

private

convert_stepper() [2/3]

void Solver< Eigen::Vector2d >::convert_stepper ( std::unique_ptr< StepperBase< Eigen::Vector2d > > &  stepper )

private

convert_stepper() [3/3]

template<typename T >

void Solver< T >::convert_stepper ( std::unique_ptr< StepperBase< T > > &  stepper )

private

Converts the generic Abstract stepper into a typed one.

Parameters

stepper

The original abstract stepper to be converted

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get_previous_result()

template<typename T >

Eigen::Vector2d Solver< T >::get_previous_result ( int  step_length )

private

Returns a row of the results' matrix.

Parameters

step_length

tells how far to go up from the bottom row

Returns

2-dimensional vector storing x(end - step_length) and f(x(end - step_length))

save_results()

template<typename T >

void Solver< T >::save_results ( int  iter, Eigen::Vector2d  result_to_save  )

private

Saves the result of a step in a defined row of the results' matrix.

Parameters

iter	The row index in which to store the result
result_to_save	2-dimensional vector storing the new guess x(i) and the evaluation at it f(x(i))

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save_starting_point() [1/3]

void Solver< double >::save_starting_point ( )

private

save_starting_point() [2/3]

void Solver< Eigen::Vector2d >::save_starting_point ( )

private

save_starting_point() [3/3]

template<typename T >

void Solver< T >::save_starting_point ( )

private

Saves the actual initial guess in the top row of the results' matrix, no matter what type will be the Class argument initial_guess.

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solve()

template<typename T >

Eigen::MatrixX2d Solver< T >::solve

(

)

Calls everything required to Solve with a method.

Returns

Matrix storing in the first column x(i) for each iteration i, in the second column f(x(i))

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solver_step()

template<typename T >

void Solver< T >::solver_step ( int &  iter, std::unique_ptr< StepperBase< T > > &  stepper, double &  err  )

private

Creates the stepper, calls the step computation, the error calculation and the results' saver.

Parameters

iter	Reference to the current iteration, which will be increased once the step is computed
stepper	The stepper object previously created and specialized depending on the method
err	Reference to the error, which will be computed and updated to check convergence

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Friends And Related Symbol Documentation

SolverTester

template<typename T >

friend class SolverTester

friend

Friend class for unit testing purposes.

Member Data Documentation

aitken_requirement

template<typename T >

bool Solver< T >::aitken_requirement

private

True if Aitken acceleration is required, 0 otherwise.

derivative_or_function_g

template<typename T >

std::function<double(double)> Solver< T >::derivative_or_function_g

private

Stores the derivative or g_function of the function if needed.

function

template<typename T >

std::function<double(double)> Solver< T >::function

private

Stores the function to find the root of and the starting guess for the process.

initial_guess

template<typename T >

T Solver< T >::initial_guess

private

Templated initial_guess for the method, whose type changes depending on the method itself.

max_iterations

template<typename T >

int Solver< T >::max_iterations

private

Stores the maximum iterations for the method.

method

template<typename T >

Method Solver< T >::method

private

Method which will be used - defined thanks to.

Author

Saransh-ccp's Reader

results

template<typename T >

Eigen::MatrixX2d Solver< T >::results

private

Stores in the first column the points computed at each step, in the second the value of the function at those points.

tolerance

template<typename T >

double Solver< T >::tolerance

private

Stores the tolerance below which the process ends.

verbose

template<typename T >

bool Solver< T >::verbose

private

Verbose mode flag.

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

• libROOT/libROOT/solver_def.hpp
• libROOT/libROOT/solver.hpp