ModalIntervalArithmetic.jl

Modal interval arithmetic using algorithms defined in Chapter 5 of the book Modal Interval Analysis: New Tools for Numerical Information, by Miguel Sainz.

Dependencies

ModalIntervalArithmetic.jl

Usage

Instantiate modal intervals of the form ModalInterval{T<:Real} <: Number using the following constructors

ModalInterval(a::Real, b::Real) constructs a modal interval [a, b]
ModalInterval{T}(a::Real) constructs a modal interval [a, a] representing a real number, cast to type T
ModalInterval(a::Real) constructs a modal interval [a, a] representing a real number
ModalInterval(X::Interval) constructs a proper modal interval from classical interval X
ModalInterval{T}(X::Interval) constructs a proper modal interval from classical interval X, with endpoints cast to type T
ModalInterval{T}(X::ModalInterval)

Julia operations are overloaded to support ModalInterval.

TODOs

• Extend modal intervals to additional unary/binary operations (trig., exp.).
• Implement AE-extensions of real functions.
• Automatic inner and outer roundings of intervals.

Related Works

Miguel Sainz et al. 2014. Modal Interval Analysis: New Tools for Numerical Information. Springer Lecture Notes in Mathematics, New York, NY. PDF:https://www.springer.com/gp/book/9783319017204