Preface

Welcome to the user manual of the interval package for GNU Octave. This chapter presents background information and may safely be skipped. First-time users who want to cut right to the chase should read Getting Started, which teaches basic concepts and first steps with the package. Users who are not familiar with interval arithmetic should read Introduction to Interval Arithmetic first. Still feeling undecided? Look at the Examples and see how easy you can put this software to great use!

Development of the GNU Octave Interval Package started in September 2014. The IEEE standard for interval arithmetic, IEEE Std 1788-2015, had been drafted by its working group until July 2014 and was about to enter the balloting process. In January 2015 a first package release could be made, which contained the full set of functions required by the standard’s draft. On June 11 the standard finally became approved and this interval package can be seen as the first ever completed standard conforming interval arithmetic library.

The creation of the interval package has been straightforward, although the author had no previous experience with Octave. Octave is a great environment for getting things done and its active community helps a lot. In this spirit, the interval package wants to be an easy to use tool for experimenting with and quick prototyping of interval arithmetic algorithms and applications.

Originally it was intended to only implement the operations required by the standard document, but support for fundamental concepts of Octave as well as interval vectors and interval matrices have soon been added. Today the package contains many useful interval analysis algorithms and solvers, which, together with basic arithmetic functions, form a powerful and versatile library.

In 2017 the Google Summer of Code (GSoC) program has lead to support for N-dimensional arrays of intervals.

Like Octave, the interval package has nothing to do with music. Above picture is a pun and shows an “octave interval” between the notes d’ and d”. The frequencies of these notes can be enclosed by an interval which is a subset of [293, 588] Hz.