IntervalRootFinding.jl

Find all roots of a function in a guaranteed way with Julia
Popularity
116 Stars
Updated Last
11 Months Ago
Started In
April 2017

IntervalRootFinding.jl

Build Status

coverage

This package provides guaranteed methods for finding roots of functions, i.e. solutions to the equation f(x) == 0 for a function f. To do so, it uses methods from interval analysis, using interval arithmetic from the IntervalArithmetic.jl package by the same authors.

Basic usage examples

The basic function is roots. A standard Julia function and an interval is provided and the roots function return a list of intervals containing all roots of the function located in the starting interval.

julia> using IntervalArithmetic, IntervalRootFinding

julia> f(x) = sin(x) - 0.1*x^2 + 1
f (generic function with 1 method)

julia> roots(f, -10..10)
4-element Array{Root{Interval{Float64}},1}:
 Root([3.14959, 3.1496], :unique)
 Root([-4.42654, -4.42653], :unique)
 Root([-1.08205, -1.08204], :unique)
 Root([-3.10682, -3.10681], :unique)

The :unique status tell us, in addition, that each listed region contains exactly one root. The other possible status is :unknown, which corresponds to intervals that may contain zero, one, or more roots - no guarantee is provided for these intervals.

These results are represented in the following plot, the region containing roots being in green. The inset show a close-up of one of the roots:

basic usage

The full documentation is available here.

Authors

  • Luis Benet, Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México (UNAM)
  • David P. Sanders, Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México (UNAM)

Acknowledgements

Financial support is acknowledged from DGAPA-UNAM PAPIME grants PE-105911 and PE-107114, and DGAPA-UNAM PAPIIT grants IN-117214 and IN-117117. LB acknowledges support through a Cátedra Moshinsky (2013).