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The GNU Octave interval package for real-valued interval arithmetic. | |||
The GNU Octave interval package for real-valued | |||
== Distribution == | == Distribution == | ||
* [ | * [http://octave.sourceforge.net/interval/index.html Latest version at Octave Forge] | ||
* [ | ** <code>pkg install -forge interval</code> | ||
* | ** [http://octave.sourceforge.net/interval/overview.html function reference] | ||
* [https:// | ** [http://octave.sourceforge.net/interval/package_doc/index.html package documentation] (user manual) | ||
* [ | * [https://trac.macports.org/browser/trunk/dports/math/octave-interval MacPorts] for Mac OS X | ||
* [http://www.freshports.org/math/octave-forge-interval/ FreshPorts] for FreeBSD | |||
== Development status == | == Development status == | ||
* Completeness | * Completeness | ||
** All required | ** All required IEEE 1788 functions are implemented, the standard is currently in recirculation ballot phase and quite stable. | ||
** | ** Planned: more solvers | ||
** | *** <code>polyval</code>, | ||
*** <code>fsolve</code>, | |||
*** and possibly <code>roots</code> | |||
*** Algorithms can be migrated from the C-XSC Toolbox (C++ code) from [http://www2.math.uni-wuppertal.de/wrswt/xsc/cxsc_new.html] (see rpeval.cpp, nlinsys.cpp, and cpzero.cpp respectively). | |||
** Planned: Improvement of the user documentation | |||
*** Explain interval arithmetic concepts with examples from the package | |||
* Quality | * 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 | * Portability | ||
** Runs in GNU Octave | ** Runs in GNU Octave 3.8.2 and 4.0 release candidates | ||
** Known to run under GNU/Linux, Microsoft Windows, | ** Known to run under GNU/Linux, Microsoft Windows, Mac OS X and FreeBSD | ||
== Compatibility == | == Compatibility == | ||
The interval package's main goal is to be compliant with IEEE | 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: | 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 [http://www.gnu.org/philosophy/free-sw.html four essential freedoms] of free software | * INTLAB is non-free software, it grants none of the [http://www.gnu.org/philosophy/free-sw.html four essential freedoms] of free software | ||
* INTLAB is not conforming to IEEE | * 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 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 | * 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 | * 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.|<syntaxhighlight lang="octave"> | |||
# INTLAB intervals | |||
A1 = infsup (2, 3); | |||
{{Code| | B1 = hull (-4, A1); | ||
C1 = midrad (0, 2); | |||
A1 = infsup (2, 3); | # Interval package intervals | ||
B1 = hull (-4, | pkg load interval | ||
C1 = midrad (0, 2); | 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 = infsup (2, 3); | A2 + B2 * C2 | ||
B2 = hull (-4, A2); | |||
C2 = midrad (0, 2); | |||
A2 + B2 * C2 | |||
</syntaxhighlight> | </syntaxhighlight> | ||
}} | }} | ||
== Similar software == | |||
== | |||
For C++ there is an open source interval library [https://github.com/nehmeier/libieeep1788/ 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 [http://www.youtube.com/watch?v=GOa9aWAZO_Q]. The GNU Octave interval package shares several unit tests with libieeep1788. | |||
For C++, Pascal and Fortran there is a free interval library [http://www2.math.uni-wuppertal.de/~xsc/xsc-sprachen.html 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 popular, nonfree interval arithmetic toolbox [http://www.ti3.tu-harburg.de/rump/intlab/ 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 [http://www.ti3.tuhh.de/rump/intlab/Octave/octave.html]. | |||
[[Category:Octave Forge]] | [[Category:Octave-Forge]] |