Interval package

The GNU Octave interval package for real-valued interval arithmetic.

Distribution

Latest version at Octave Forge
- pkg install -forge interval
- function reference
- package documentation (user manual)
MacPorts for Mac OS X
FreshPorts for FreeBSD

Development status

Completeness
- All required IEEE 1788 functions are implemented, the standard is currently in recirculation ballot phase and quite stable.
- Planned: more solvers
  - fsolve,
  - and possibly roots
  - Algorithms can be migrated from the C-XSC Toolbox (C++ code) from [1] (see nlinsys.cpp, and cpzero.cpp respectively).
- Planned: Improvement of the user documentation
  - Explain interval arithmetic concepts with examples from the package
Quality
- Includes tests for all functions, many tests for basic functions
- No known bugs. The package is quite new and still has a small user base, so there might be hidden bugs. Also some advanced functions need more testing.
Portability
- Runs in GNU Octave 3.8.2 and 4.0 release candidates
- Known to run under GNU/Linux, Microsoft Windows, Mac OS X and FreeBSD

Compatibility

The interval package's main goal is to be compliant with IEEE 1788, so it is compatible with other standard-conforming implementations (on the set of operations described by the standard document).

This interval package is not meant to be a replacement for INTLAB and any compatibility with it is pure coincidence. Since both are compatible with GNU Octave, they happen to agree on many function names and programs written for INTLAB may possibly run with this interval package as well. Some fundamental differences that I am currently aware of:

INTLAB is non-free software, it grants none of the four essential freedoms of free software
INTLAB is not conforming to IEEE 1788 and the parsing of intervals from strings uses a different format—especially for the uncertain form
INTLAB supports intervals with complex numbers and sparse interval matrices, but no empty intervals
INTLAB uses inferior accuracy for most arithmetic operations, because it focuses on speed
Basic operations can be found in both packages, but the availability of special functions depends

Code: In GNU Octave the interval package can also be run alongside INTLAB.

 # INTLAB intervals
 A1 = infsup (2, 3);
 B1 = hull (-4, A1);
 C1 = midrad (0, 2);
 # Interval package intervals
 pkg load interval
 A2 = infsup (2, 3);
 B2 = hull (-4, A2);
 C2 = midrad (0, 2);
 pkg unload interval
 
 # Computation with INTLAB
 A1 + B1 * C1
 # Computation without INTLAB
 A2 + B2 * C2

Similar software

For C++ there is an open source interval library libieeep1788 by Marco Nehmeier (member of IEEE P1788). It aims to be standard compliant with IEEE 1788 and is designed in a modular way, supporting several interval data types and different flavors of interval arithmetic [2]. The GNU Octave interval package shares several unit tests with libieeep1788.

For C++, Pascal and Fortran there is a free interval library XSC. It is not standard compliant with IEEE 1788. Some parts of the GNU Octave interval package have been derived from C-XSC.

For MATLAB there is a proprietary interval arithmetic toolbox INTLAB by Siegfried Rump. It had been free of charge for academic use in the past, but no longer is. Its origin dates back to 1999, so it is well tested and comprises a lot of functionality, especially for vector / matrix operations. INTLAB is compatible with GNU Octave since Version 9 [3].