Package smile.util.function

Interface DifferentiableFunction

All Superinterfaces:

Function, Serializable

All Known Implementing Classes:

Exp, Kurtosis, LogCosh

public interface DifferentiableFunction
extends Function

A differentiable function is a function whose derivative exists at each point in its domain.

Field Summary

Fields inherited from interface smile.util.function.Function

logger

Method Summary

Modifier and Type	Method	Description
double	g(double x)	Computes the gradient/derivative at x.
default double	g2(double x)	Compute the second-order derivative at x.
default double	root(double x1, double x2, double tol, int maxIter)	Newton's method (also known as the Newton–Raphson method).

Methods inherited from interface smile.util.function.Function

apply, f, inv

Method Details

g

double g(double x)

Computes the gradient/derivative at x.

Parameters:

x - a real number.

Returns:

the derivative.

g2

default double g2(double x)

Compute the second-order derivative at x.

Parameters:

x - a real number.

Returns:

the second-order derivative.

root

default double root(double x1,
 double x2,
 double tol,
 int maxIter)

Newton's method (also known as the Newton–Raphson method). This method finds successively better approximations to the roots of a real-valued function. Newton's method assumes the function to have a continuous derivative. Newton's method may not converge if started too far away from a root. However, when it does converge, it is faster than the bisection method, and is usually quadratic. Newton's method is also important because it readily generalizes to higher-dimensional problems. Newton-like methods with higher orders of convergence are the Householder's methods.

Specified by:

root in interface Function

Parameters:

x1 - the left end of search interval.

x2 - the right end of search interval.

tol - the desired accuracy (convergence tolerance).

maxIter - the maximum number of iterations.

Returns:

the root.