Utils::Trichotomy< Real > Class Template Reference

Class for minimize the function \( f(x) \) without the usew of derivative. More...

#include <Utils_Trichotomy.hh>

Public Member Functions
	Trichotomy ()=default
	~Trichotomy ()=default
Real	eval (Real a, Real b, Trichotomy_base_fun< Real > *fun)
template<typename PFUN>
Real	eval2 (Real a, Real b, PFUN pfun)
Real	search (Real x, Real delta, Trichotomy_base_fun< Real > *fun)
template<typename PFUN>
Real	search2 (Real x, Real delta, PFUN pfun)
Integer	used_iter () const
Integer	num_fun_eval () const
Real	tolerance () const
bool	converged () const
void	set_max_iterations (Integer mit)
void	set_max_fun_evaluation (Integer mfev)

Detailed Description

template<typename Real>
class Utils::Trichotomy< Real >

Class for minimize the function \( f(x) \) without the usew of derivative.

Note

The used algorithm is described in: A new zero-order 1-D optimization algorithm: trichotomy method, by Alena Antonova, Olga Ibryaeva, link

Usage Example

To use this class, first wrap your function in a derived class. For instance, for the function \( f(x) = x^2 - 2 \), you can define:

class Fun1 : public Trichotomy_base_fun<double> {
public:
  double eval(double x) const override { return x*x - 2; }
};

Next, instantiate the function and the solver. Then, call the desired method to find the root:

Trichotomy<real_type> solver;
Fun1 f;
real_type a=-1,b=2;
real_type x_solution = solver.eval2(a,b,f);

If the method converges, x_solution will contain the computed solution.

Constructor & Destructor Documentation

Trichotomy()

template<typename Real>

Utils::Trichotomy< Real >::Trichotomy ( )

default

~Trichotomy()

template<typename Real>

Utils::Trichotomy< Real >::~Trichotomy ( )

default

Member Function Documentation

converged()

template<typename Real>

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

inline

Returns

true if the last computation was successfull

eval()

template<typename Real>

Real Utils::Trichotomy< Real >::eval ( Real a, Real b, Trichotomy_base_fun< Real > * fun )

inline

Find the minimum of a function wrapped in the class Trichotomy_base_fun<Real> starting from guess interval [a,b]

Parameters

a	lower bound search interval
b	upper bound search interval
fun	the pointer to base class Trichotomy_base_fun<Real> wrapping the user function

eval2()

template<typename Real>

template<typename PFUN>

Real Utils::Trichotomy< Real >::eval2 ( Real a, Real b, PFUN pfun )

inline

Find the minimum of a function pfun starting from guess interval [a,b]

Parameters

a	lower bound search interval
b	upper bound search interval
pfun	the pointer to base class Trichotomy_base_fun<Real> wrapping the user function

num_fun_eval()

template<typename Real>

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

inline

Returns

the number of evaluation used in the last computation

search()

template<typename Real>

Real Utils::Trichotomy< Real >::search ( Real x, Real delta, Trichotomy_base_fun< Real > * fun )

inline

Find the minimum of a function wrapped in the class Trichotomy_base_fun<Real> starting from guess interval [x-delta,x+delta]

Parameters

x	center of the search interval
delta	ray of th eseaerch interval
fun	the pointer to base class Trichotomy_base_fun<Real> wrapping the user function

search2()

template<typename Real>

template<typename PFUN>

Real Utils::Trichotomy< Real >::search2 ( Real x, Real delta, PFUN pfun )

inline

Find the minimum of a function object starting from guess interval [x-delta,x+delta]

Parameters

x	center of the search interval
delta	ray of th eseaerch interval
pfun	the function object

set_max_fun_evaluation()

template<typename Real>

void Utils::Trichotomy< 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::Trichotomy< Real >::set_max_iterations

(

Integer

mit

)

Fix the maximum number of iteration.

Parameters

mit	the maximum number of iteration

tolerance()

template<typename Real>

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

inline

Returns

the tolerance set for computation

used_iter()

template<typename Real>

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

inline

Returns

the number of iterations used in the last computation

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

• /Users/enricobertolazzi/Ricerca/PINS/PINS-submodules/UtilsLite/src/Utils_Trichotomy.hh
• /Users/enricobertolazzi/Ricerca/PINS/PINS-submodules/UtilsLite/src/Utils_Trichotomy.cc