IntervalContractors
IntervalContractors.jl
About IntervalContractors.jl
provides contractors and reverse functions (also called backward functions or relational functions) for interval arithmetic.
Reverse functions
The reverse function of a function f
calculates the (interval hull of) its inverse function, f⁻¹
.
For example, sin_rev(Y::Interval, X::Interval)
calculates the (interval hull of) those x ∈ X
such that sin(x) ∈ Y
. This can also be thought of as an inverse function, calculating X_new := sin⁻¹(Y) ∩ X
.
The return value is (Y, X_new)
.
Functions such as mul_rev(C::Interval, A::Interval, B::Interval)
take three arguments, and correspond to C = A * B
; they return (C, A_new, B_new)
, with A_new
and B_new
similarly defined to be the corresponding inverse images of the multiplication operator in each component.
Contractors
Functions like sin!
(currently nonexported) are contractors for the set {(x, y): y = sin(x)}
.
The list of available functions may be found in the documentation.
These functions are designed to be used inside the IntervalConstraintProgramming.jl
library,
and (eventually) to satisfy the section on reverse functions in the IEEE1788 2015 standard on interval arithmetic.
Author
 David P. Sanders, Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México (UNAM)
References:

Applied Interval Analysis, Luc Jaulin, Michel Kieffer, Olivier Didrit, Eric Walter (2001)

IBEX library documentation: http://www.ibexlib.org/doc/interval.html#backwardarithmetic
Acknowledements
Financial support is acknowledged from DGAPAUNAM PAPIIT grant IN117117. The author thanks Luc Jaulin and Jordan Ninin for the IAMOOC online course, which introduced him to this subject, and Zenna Tavares for a helpful conversation.