One Dimensional Root-Finding

The module vsl.roots contains functions for the root finding methods and related declarations.

Functions

fn brent (f func.Fn, x1, x2, tol f64) ?(f64, f64)

Find th root of f between x1 and x1 with an accuracy of order tol. The result will be the root and an upper bound of the error.

fn newton_bisection (f func.FnFdf, x_min, x_max, tol f64, n_max int) ?f64

Find th root of f between x_min and x_max with an accuracy of order tol and a maximum of n_max iterations. The result will be the found root.

Note that the function must also compute the first derivate of the function. This function relies on combining Newton's approach with a bisection technique.

fn newton (f func.FnFdf, x0, x_eps, fx_eps f64, n_max int) ?f64

Find the root of f starting from x0 using Newton’s method with descent direction given by the inverse of the derivative. The algorithm stops when one of the three following conditions is met:

• the maximum number of iterations n_max is reached
• the last improvement over x is smaller than x . x_eps
• at the current position |f(x)| < fx_eps

fn bisection(f func.Fn, xmin, xmax, epsrel, epsabs f64, n_max int) ?f64

Find the root of f between x_min and x_max with the accuracy |x_max - x_min| < epsrel * x_min + epsabs, or with the maximum number of iterations n_max.

On exit, the results is (x_max + x_min) / 2.

Usage example

module main

import vsl.func
import vsl.roots
import math

const (
	epsabs = 0.0001
	epsrel = 0.00001
	n_max  = 100
)

fn cos(x f64, _ []f64) f64 {
	return math.cos(x)
}

f := func.new_func(f: cos)
result := roots.bisection(f, 0.0, 3.0, epsrel, epsabs, n_max)?

result will be math.pi / 2.00