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`IntervalContractors.jl`

`IntervalContractors.jl`

provides contractors and reverse functions (also called backward functions or relational functions) for interval arithmetic.

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.

Functions like `sin!`

(currently non-exported) 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 IEEE-1788 2015 standard on interval arithmetic.

- David P. Sanders, Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México (UNAM)

*Applied Interval Analysis*, Luc Jaulin, Michel Kieffer, Olivier Didrit, Eric Walter (2001)IBEX library documentation: http://www.ibex-lib.org/doc/interval.html#backward-arithmetic

Financial support is acknowledged from DGAPA-UNAM PAPIIT grant IN-117117. 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.

04/30/2017

5 months ago

31 commits