Algorithms for root-finding in mathematical functions. More...

Classes
class	Utils::Bracket_base_fun< Real >
	Abstract base class for defining mathematical functions used in the Bracket search algorithm. More...

class	Utils::AlgoBracket< Real >
	Class for solving \( f(x)=0 \) without the usew of derivative. More...

class	Utils::AlgoHNewton_base_fun< Real >
	Abstract base class for defining mathematical functions used in the zero search algorithm. More...

class	Utils::AlgoHNewton< Real >
	Class for solving \( f(x)=0 \) without the usew of derivative. More...

class	Utils::Sturm< Real >
	Class for managing and computing the Sturm sequence associated with a polynomial. More...

class	Utils::Zeros_base_fun< Real >
	Abstract base class for defining mathematical functions used in root-finding algorithms. More...

class	Utils::Zeros< Real >
	Class for solving the equation \( f(x) = 0 \) using various numerical methods. More...

Functions
virtual Real	Utils::Zeros_base_fun< Real >::eval (Real x) const =0

virtual Real	Utils::Zeros_base_fun< Real >::eval_D (Real x) const =0

virtual Real	Utils::Zeros_base_fun< Real >::eval_DD (Real x) const =0

virtual Real	Utils::Zeros_base_fun< Real >::eval_DDD (Real x) const =0

Real	Utils::Zeros_base_fun< Real >::operator() (Real x) const

Real	Utils::Zeros_base_fun< Real >::D (Real x) const

Real	Utils::Zeros_base_fun< Real >::DD (Real x) const

Real	Utils::Zeros_base_fun< Real >::DDD (Real x) const

	Utils::Zeros< Real >::Zeros ()=default

	Utils::Zeros< Real >::~Zeros ()=default

void	Utils::Zeros< Real >::set_max_iterations (Integer mit)

void	Utils::Zeros< Real >::set_max_fun_evaluation (Integer mfev)

void	Utils::Zeros< Real >::set_tolerance (Real tol)

Real	Utils::Zeros< Real >::solve_Newton (Real x_guess, Zeros_base_fun< Real > *fun)

Real	Utils::Zeros< Real >::solve_Chebyshev (Real x_guess, Zeros_base_fun< Real > *fun)

Real	Utils::Zeros< Real >::solve_Halley (Real x_guess, Zeros_base_fun< Real > *fun)

Real	Utils::Zeros< Real >::solve_Order4 (Real x_guess, Zeros_base_fun< Real > *fun)

Real	Utils::Zeros< Real >::solve_Order8 (Real x_guess, Zeros_base_fun< Real > *fun)

Real	Utils::Zeros< Real >::solve_Order16 (Real x_guess, Zeros_base_fun< Real > *fun)

Real	Utils::Zeros< Real >::solve_Order32 (Real x_guess, Zeros_base_fun< Real > *fun)

Integer	Utils::Zeros< Real >::used_iter () const

Integer	Utils::Zeros< Real >::num_fun_eval () const

Real	Utils::Zeros< Real >::tolerance () const

bool	Utils::Zeros< Real >::converged () const

Detailed Description

Algorithms for root-finding in mathematical functions.

This module implements a variety of efficient algorithms to compute the roots (zeros) of scalar functions, i.e., points where a function equals zero. It supports techniques ranging from simple bisection and secant methods to more advanced techniques like Newton-Raphson and Brent's method for solving nonlinear equations.

Function Documentation

◆ converged()

template<typename Real>

bool Utils::Zeros< Real >::converged ( ) const

inline

Returns: true if the last computation was successfull

◆ D()

template<typename Real>

Real Utils::Zeros_base_fun< Real >::D ( Real x ) const

inline

Evaluate the first derivative of \( f(x) \)

This operator provides a convenient way to evaluate the first derivative using the call operator.

Parameters

[in] x the point to evaluate \( f'(x) \)

Returns: the value of \( f'(x) \)

◆ DD()

template<typename Real>

Real Utils::Zeros_base_fun< Real >::DD ( Real x ) const

inline

Evaluate the second derivative of \( f(x) \)

This operator allows for an easy evaluation of the second derivative using the call operator.

Parameters

[in] x the point to evaluate \( f''(x) \)

Returns: the value of \( f''(x) \)

◆ DDD()

template<typename Real>

Real Utils::Zeros_base_fun< Real >::DDD ( Real x ) const

inline

Evaluate the third derivative of \( f(x) \)

This operator enables straightforward evaluation of the third derivative using the call operator.

Parameters

[in] x the point to evaluate \( f'''(x) \)

Returns: the value of \( f'''(x) \)

◆ eval()

template<typename Real>

virtual Real Utils::Zeros_base_fun< Real >::eval ( Real x ) const

pure virtual

Evaluate the function \( f(x) \)

Parameters

[in] x the point to evaluate \( f(x) \)

Returns: the value of \( f(x) \)

◆ eval_D()

template<typename Real>

virtual Real Utils::Zeros_base_fun< Real >::eval_D ( Real x ) const

pure virtual

Evaluate the first derivative of \( f(x) \)

Parameters

[in] x the point to evaluate \( f'(x) \)

Returns: the value of \( f'(x) \)

◆ eval_DD()

template<typename Real>

virtual Real Utils::Zeros_base_fun< Real >::eval_DD ( Real x ) const

pure virtual

Evaluate the second derivative of \( f(x) \)

Parameters

[in] x the point to evaluate \( f''(x) \)

Returns: the value of \( f''(x) \)

◆ eval_DDD()

template<typename Real>

virtual Real Utils::Zeros_base_fun< Real >::eval_DDD ( Real x ) const

pure virtual

Evaluate the third derivative of \( f(x) \)

Parameters

[in] x the point to evaluate \( f'''(x) \)

Returns: the value of \( f'''(x) \)

◆ num_fun_eval()

template<typename Real>

Integer Utils::Zeros< Real >::num_fun_eval ( ) const

inline

Returns: the number of evaluation used in the last computation

◆ operator()()

template<typename Real>

Real Utils::Zeros_base_fun< Real >::operator() ( Real x ) const

inline

Evaluate the function \( f(x) \)

This operator allows for a more intuitive usage of the function object, enabling the evaluation of the function using the call operator.

Parameters

[in] x the point to evaluate \( f(x) \)

Returns: the value of \( f(x) \)

◆ set_max_fun_evaluation()

template<typename Real>

void Utils::Zeros< Real >::set_max_fun_evaluation ( Integer mfev )

Fix the maximum number of evaluation.

Parameters

mfev	the maximum number of evaluation of \( f(x) \)

◆ set_max_iterations()

template<typename Real>

void Utils::Zeros< Real >::set_max_iterations ( Integer mit )

Fix the maximum number of iteration.

Parameters

mit	the maximum number of iteration

◆ set_tolerance()

template<typename Real>

void Utils::Zeros< Real >::set_tolerance ( Real tol )

Fix the requested tolerance for ieration stop. Stop when \( |f(x)| < \epsilon \)

Parameters

tol	the requested tolerance

◆ solve_Chebyshev()

template<typename Real>

Real Utils::Zeros< Real >::solve_Chebyshev	(	Real	x_guess,
		Zeros_base_fun< Real > *	fun )

Find the zero of a function wrapped in the class Zeros_base_fun<Real> starting from guess value x_guess.

Parameters

x_guess	starting value for iterative method
fun	the pointer to base class `Zeros_base_fun<Real>` wrapping the user function