Abstract base class for defining mathematical functions used in root-finding algorithms. More...

#include <Utils_zeros.hh>

Public Member Functions
virtual Real	eval (Real x) const =0

virtual Real	eval_D (Real x) const =0

virtual Real	eval_DD (Real x) const =0

virtual Real	eval_DDD (Real x) const =0

Real	operator() (Real x) const

Real	D (Real x) const

Real	DD (Real x) const

Real	DDD (Real x) const

Detailed Description

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

Abstract base class for defining mathematical functions used in root-finding algorithms.

This class serves as a base interface for user-defined functions that can be evaluated and differentiated. It allows for the implementation of various numerical methods to find the roots of the equation \( f(x) = 0 \). Users must inherit from this class and implement the virtual methods to define their specific functions.

The class provides methods to evaluate the function itself as well as its first, second, and third derivatives, which are essential for many root-finding algorithms such as Newton-Raphson and Halley methods.

Template Parameter:

Real: A numeric type representing the data type of the function's input and output, such as float, double, etc.

Usage Example: To create a custom function, derive from this class and implement the required methods. Here is an example for the function \( f(x) = x^2 - 2 \):

class Fun1 : public Zeros_base_fun<double> {
public:
    double eval(double x) const override { return x*x - 2; }
    double eval_D(double x) const override { return 2*x; }
    double eval_DD(double x) const override { return 2; }
    double eval_DDD(double x) const override { return 0; }
};

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

/Users/enricobertolazzi/Ricerca/PINS/PINS-submodules/UtilsLite/src/Utils_zeros.hh

Public Member Functions

Detailed Description