Software I like: Numerical and symbolic computation

General | Finite-element | Discrete-element | Block-diagram | Electronics | Statistics | Symbolic

General numerical computation

These are open-source alternatives to MATLAB. Latest version numbers and dates are as of 2010 Jan 31, unless otherwise noted.

• GNU Octave: for Linux, Windows and Mac OS X. (As of 2022 Mar 25, the latest version is 6.4.0, dated 2021 Oct 30.) The Octave language is ‘quite similar’ to that of MATLAB. Discussions are held primarily at octave.discourse.group, with an optional mailing-list mode; there are also the old help-octave and octave-maintainers e-mail lists. See also Guidelines for reporting a new bug.

  See Any short texts … (2025 Mar 17) for suggestions for introductions to Octave.

  Some of the linear-algebra libraries used by Octave are compiled for 32-bit integers, but there is a Windows installer (e.g., octave-7.2.0-w64-64-installer.exe) with a version of Octave compiled with 64-bit integers, allowing larger arrays (ref).

  The following information is rather old.

  Octave-Forge is ‘a central location for the collaborative development of packages for GNU Octave’. A Windows installer is provided which includes all or most of the packages, including a Windows package which provides a COM interface and additional functionality under Windows, including ActiveX support with actxserver. There have been some moves toward absorbing Octave-Forge into the GNU Octave Web site (cf. blog post by Carnë Draug, 2012 Aug 2, and a mock-up of the proposed agora.octave.org).

  Various versions of Octave use gnuplot-x11, gnuplot-qt, fltk and qt as graphics backends. The command available_graphics_toolkits() lists which backends are available, and the command graphics_toolkit() can be used to ask about or set the default backend.

  GUI development is possible within Octave; it works best with qt, to some extent with fltk, and not at all with gnuplot (ref).

  See Henry Gomersall’s Squishing Matlab mex files into Octave for how to use a precompiled .mex file with Octave under Linux when you don't have the source code. A hint but no complete solution is offered for MS Windows.

• FreeMat: for Linux, Windows and Mac OS X (as of 2016 Aug 30, latest version = 4.2, dated 2013 Jun 30). Syntax is based on that of MATLAB.
• Scilab: for Linux, Windows and Mac OS X (latest version = 5.2, dated 2009 Dec 17)
  Scilab traces its history to the original, public-domain version of MATLAB. With the development of the Java-based Scilab 5, a fork based on Scilab 4 was launched and became ScicosLab.
• SciPy. A Python library, making use of the NumPy library. See here and here for comparisons with MATLAB and other software. Open-source, multi-platform. As of 2011 Jan 17, latest version is 0.9.0b1 dated 2010 Dec 12.
• rlabplus: for Linux (latest version = 2.2.11.9 dated 2009 May 28)
• JMathLib: supported primarily for Windows, but written in Java so should be portable (latest version = 0.9.4, 2009 Feb 22)

The following is a selection of the many available lists and discussions of MATLAB alternatives, some rather dated:

• Jean-Daniel Bonjour’s MATLAB et GNU Octave (including a list of alternatives to MATLAB, and a specific comparison of Octave to MATLAB).
• A comparative evaluation by Neeraj Sharma and Matthias Gobbert (2010)
• Neill Tucker's Matlab Alternatives (2010)
• EEGLAB and supercomputing applications using free alternatives to MATLAB (2011)
• Dave's Matlab Alternatives (2008)
• Gerald Recktenwald's Alternatives to the Commerical [sic] Version of MATLAB (2007)
• Ryan Morlok's Open Source MATLAB Alternatives (2006)

Finite-element modelling

See Finite-element software

Discrete-element modelling

This topic is here taken to include discrete particle modelling, agent-base modelling, molecular dynamics, and whatever else might fit.

• Yade ‘is an extensible open-source framework for discrete numerical models’
• molsim is an Octave wrapper for seplib, ‘a flexible lightweight stand alone and easy hackable molecular dynamics software package’
• Rule-based modelling
  • BioNetGen ‘is software designed for modular, structure-based modeling of biochemical reaction networks. It can be applied to many other types of modeling as well.’
  • Kappa ‘is a rule-based language for modeling systems of interacting agents. While its current development is primarily motivated by molecular systems biology, its range of applications is quite broad’.
  • PySB ‘is a framework for building mathematical models of biochemical systems as Python programs’ It uses a ‘simple and intuitive domain specific programming language … which is internally translated into BioNetGen or Kappa rules’.
• NetLogo ‘is a multi-agent programmable modeling environment’.

Block-diagram modelling

Modelica is a model-description language. See the on-line book Modelica by Example by Michael M. Tiller. Modelica is used in OpenModelica, Scicos and many other packages.

• OpenModelica: open-source, aims to be a complete reference implementation, not necessarily as efficient and scalable as the commercial implementations of Modelica. Includes a nice graphical connection editor.
  • Good for time-domain simulations; I don't know if there's any way to do frequency-domain calculations, although other Modelica implementations have been used for that.
  • Local copies of the documentation are in share/doc/, including the User Guide in the omc/ subdirectory.
  • The Modelica Standard Library, which can be downloaded as a .zip file from https://www.modelica.org/libraries/Modelica, is included (as a .zip file) in OpenModelica in lib/omlibrary/mslxx/. There is a linear systems library that does frequency responses, among other things.
    There's no built-in way of including extra libraries in OMEdit, but there's a work-around (that I don't understand).
  • Signal sources, for example, can be found in the Libraries panel at Modelica ► Blocks ► Sources.
  • For some errors, look at the file SanityCheckFail.mo. Under MS Windows it's in c:\Users\username\AppData\Local\Temp\OpenModelica\OMEdit\.
  • In the modelling tab, right-click on an object to change its parameters. To change the simulation parameters (e.g., total time), do Simulation ► Simulation Setup or click on the corresponding icon on the Simulation toolbar. If the Simulate box is checked, a simulation will be run when you click on OK.
  • By default, plots have time on the horizontal axis. To plot one variable against another, use the New Parametric Plot Window on the Plot toolbar. Select the variable for the horizontal axis followed by the variable for the vertical axis.
  • Graphical custom components can be created by specifying Icon and Diagram views using graphical annotations.
• JModelica.org is ‘an extensible Modelica-based open source platform for optimization, simulation and analysis of complex dynamic systems’, aiming both to be ‘industrially viable’ and to serve as an R&D platform for algorithm development. It is based on Java, Eclipse and Python.
• Scicos, a block-diagram modeller/simulator, was originally developed under Scilab. ‘Due to stability and performance problems with Scilab 5, Scicos is now only developed in and for ScicosLab.’ (Based on Scicos history)

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Electronics

• Wokwi ‘is an online Electronics simulator … to simulate Arduino, ESP32, STM32, and many other popular boards, parts and sensors.’ It is ‘free to use’, with a paid ‘Club’ that allows private projects to be unlisted, among other things.
• Autodesk Tinkercad ‘is a free web app for 3D design, electronics, and coding.’

Statistics

Some of the software listed above can be used for statistics. The following are popular specialized statistical packages. I haven’t used them myself.

• R ‘is a system for statistical computation and graphics. It consists of a language plus a run-time environment with graphics, a debugger, access to certain system functions, and the ability to run programs stored in script files’. It can be run from within Emacs. Alternative interfaces include R Commander and RStudio.
• PSPP ‘is a Free replacement for the proprietary program SPSS, and appears very similar to it with a few exceptions’.

Symbolic algebra

• Axiom (including original Axiom, OpenAxiom and FriCAS)
• Maxima