Comparison of Numerical Analysis Software: History
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The following tables provide a comparison of numerical analysis software.

  • numerical analysis

1. Applications

1.1. General

  Creator Development started First public release Latest stable version Stable release date Cost (United States dollar ) License Notes
ADMB David Fournier, ADMB Project 1989 1990 12.0 21 December 2017 Free BSD 3-clause (aka new) License Automatic differentiation makes it well suited to complex minimization problems
Analytica Lumina Decision Systems 1982 (Demos)   4.6 May 2015 Free (Analytica Free 101), $995 (Professional), $2795 (Enterprise) Proprietary A numerical modeling environment with a declarative and visual programming language based on influence diagrams.
Ch SoftIntegration   1 October 2001 7.5.1 2 December 2015 $399 (commercial) / $199 (academic) / Free (student) Proprietary C/C++ based numerical computing and graphical plotting[1]
DADiSP DSP Development 1984 1987 6.7 B02 17 January 2017 $1995 (commercial) / $129 (academic) / Free (student) Proprietary Numeric computations for science and engineering featuring a spreadsheet like interface.
DataMelt Sergei V. Chekanov (jwork.org) 2005 2005 1.4 12 March 2016 Free Free for non-commercial use Mathematics, symbolic calculations, algebra, data analysis, data mining, interactive 2D/3D graphics, Java scriptable, used for science and engineering, Cross-platform (written in Java)
Dyalog APL Dyalog Ltd. 1981 1983 17.0 23 July 2018 £850/year or 2% royalty (free for non-commercial use) Proprietary A modern dialect of APL, enhanced with features for functional and object-oriented programming.
Euler Math Toolbox René Grothmann 1987 1988 2018-09-21 21 September 2018 Free GPL Also a computer algebra system through interface with Maxima
Fityk Marcin Wojdyr   2002 1.3.1 19 December 2016 $115 (1.x binaries) / Free (source code and 0.x binaries) GPL interactive graphics, scriptable, specialized in curve fitting and peak fitting, 2D only
FlexPro Weisang GmbH n/a 1991 2017 2017 Not free (commercial) / Free (academic) Proprietary Dynamic, interactive 2D/3D diagrams, programmable, VBA, high performances, multicore compatible, large data sets.
FreeMat Samit Basu   2004 4.2 30 June 2013 Free GPL Codeless interface to external C, C++, and Fortran code. Mostly compatible with MATLAB.
GAUSS Aptech Systems   1984 17 22 December 2016 Not free Proprietary  
GNU Data Language Marc Schellens   2004 0.9.7 21 January 2017 Free GPL Aimed as a drop-in replacement for IDL/PV-WAVE
GNU MCSim Frederic Y. Bois & Don Maszle 1991 1993 6.0.0 24 February 2018 Free GPL General simulation and Monte Carlo sampling software
GNU Octave John W. Eaton 1988 1993 4.4.0 1 May 2018 Free GPL General numerical computing package with lots of extension modules. Syntax mostly compatible with MATLAB
IGOR Pro WaveMetrics 1986 1988 7.00 26 July 2016 $995 (commercial) $225 upgrade / $499 (academic) $175 upgrade / $85 (student) Proprietary interactive graphics, programmable, 2D/3D, used for science and engineering, large data sets.
J Jsoftware 1989 1990 J805 19 December 2016 Free GPL online access to: J Application Library (JAL)
Julia Jeff Bezanson, Stefan Karpinski, Viral B. Shah, and other[2] contributors 2009 2012 1.0.0 8 August 2018 Free MIT License Direct calls of C functions (no wrappers needed). Designed for cloud parallel computing with LLVM JIT as a backend. Lightweight "green" threading (coroutines). Efficient support for Unicode. Shell-like capabilities for managing other processes. Lisp-like macros and other metaprogramming facilities.
LabVIEW National Instruments 1985 1986 2016 August 2016 $1249 (commercial) / $79.95 (student) Proprietary Graphical, and textual through formula nodes, mathscript and .m file scripts[3]
Maple Maplesoft 1980 1982 2017 25 May 2017 $2275 (commercial) / $99 (student) Proprietary Mainly a computer algebra system
Mathcad Parametric Technology Corporation 1985 1986 15.0 ; Prime 4.0[4] 2 March 2015 $1195 (commercial) / $99 (student) Proprietary  
Mathematica Wolfram Research 1986 1988 13.0.1 (February 17, 2022; 8 months ago (2022-02-17)) [±][5] 8 March 2018 Free (Raspberry Pi[6]), Free Cloud Access, $2495 (commercial) / $145 (student) / $295 (personal)[7] Proprietary Also computer algebra system
mathlayer Quant Advisory Limited 2015 2015 1.1.3.8 March 2017 Free CC BY 4.0 Windows only. Designed to be embedded.
MATLAB MathWorks the late 1970s 1984 R2018a September 2017 $2150 (standard) / $500 (education) / $149 (home) / $49 (student) Proprietary Numerical computation and simulation with extended 2D/3D visualization.
Maxima MIT Project MAC and Bill Schelter et al. 1967 1982 5.41.0 3 October 2017 Free GPL Mainly a computer algebra system
MLAB Civilized Software, Inc. 1970 (in SAIL), 1985 (in C) 1972 (on DEC-10), 1988 (on PCs), 1993 (on MACs) 2015 2015 $2250 (standard) / $50 (student) Proprietary Numerical and Statistical computation for Scientific Applications, e.g. Chemical Kinetics. ODE Solving and Curve-Fitting. Symbolic Differentiation, Survival Analysis, Cluster Analysis, 2D/3D Graphics.
Origin OriginLab   1991 2016 22 May 2017 $1095 (std.)/$1800 (Pro)
$550 (std., academic)
$850 (Pro, academic)
$69/yr. (Pro, student)		 Proprietary Integrated data analysis graphing software for science and engineering. Flexible multi-layer graphing framework. 2D, 3D and statistical graph types. Built-in digitizing tool. Analysis with auto recalculation and report generation. Built-in scripting and programming languages.
Perl Data Language Karl Glazebrook late 1990s c. 1997 2.012 14 June 2015 Free Artistic License Used for astrophysics, solar physics, oceanography, biophysics, and simulation. 2D plotting via PGPLOT, PLPlot bindings; 3D via GL.
PSPP Ben Pfaff 1990s 1990s 0.8.5 20 June 2015 Free GPL v.3 or later FOSS alternative to IBM SPSS. Analysis of sampled data, frequencies, cross-tabs comparison of means (t-tests and one-way ANOVA); linear regression, logistic regression, reliability (Cronbach's Alpha, not failure or Weibull), and re-ordering data, non-parametric tests, factor analysis, cluster analysis, principal components analysis, chi-square analysis and more
R R Foundation 1997 1997 3.3.2 31 October 2016 Free GPL Primarily for statistics, but there are many interfaces to open-source numerical software
SageMath William Stein   2005 9.5 (30 January 2022; 9 months ago (2022-01-30)) [±][8] 17 October 2018 Free GPL Programmable, includes computer algebra, 2D+3D plotting. Interfaces to many open-source and proprietary software. Web based interface HTTP or HTTPS
SAS Anthony Barr and James Goodnight 1966 1972 9.4 10 July 2014 Not free Proprietary  
SequenceL Texas Multicore Technologies 1989 2012 2.4 10 February 2016 Free (Community Edition), $2495 (Professional Edition) Proprietary Functional programming language and tools. Delivers high performance on multicore hardware with ease of programming, and code clarity/readability. Designed to work with other languages, including C, C++, C#, Java, Fortran, Python, etc. Can be compiled to multithreaded C++ (and optionally OpenCL) code with no explicit indications from the programmer of how or what to parallelize. A platform-specific runtime manages the threads safely.
S-Lang John E. Davis   1992 2.3.0 18 September 2014 Free GPL, Artistic License (1.x only) Available as a standalone (slsh) and embedded interpreter (jed, slrn, ...)
Scilab Scilab Enterprises Was:Inria 1990 1994 6.0.1 15 February 2018 Free CeCILL license Programmable, direct support of 2D+3D plotting. Interfaces to many other software packages. Interfacing to external modules written in C, Java, Python or other languages. Language syntax similar to MATLAB. Used for numerical computing in engineering and physics.
SPSS Normal H. Nie, Dale H. Bent, and C. Hadlai Hull   1968 23.0 3 March 2015 Not free Proprietary  
Sysquake Calerga   1998 5.0 2013 free / $2500 (Pro, commercial) / $1000 (Pro, academic) Proprietary interactive graphics
TK Solver Universal Technical Systems, Inc. late 1970s 1982 5.0.141 2011 $399 commercial / $49 (student) Proprietary Numerical computation and rule-based application development
VisSim Visual Solutions   1989 10.1 January 2011 $495-$2800 (commercial)
free view only version
$50-$250/free v3.0 (academic)		 Proprietary Visual Language for simulation and Model Based Design. Used in business, science and engineering. Performs complex scalar or matrix based ODE solving with parametric optimization. Has 2D and 3D plotting, 3D animation, and state transition built in.
Yorick n/a n/a n/a 9 January 2015 Free GPL Programmable, callable 2D+3D plotting. Language syntax similar to C. Interfacing to other software packages via C calls.

1.2. Operating System Support

The operating systems the software can run on natively (without emulation).

  Windows macOS Linux BSD Unix DOS Android SaaS
ADMB Yes Yes Yes No No No No No
Analytica Yes No No No No No No No
Ch Yes Yes Yes Yes Yes No No No
Dyalog APL Yes Yes Yes No Yes No[9] No No
DADiSP Yes No No No Yes No No No
DataMelt Yes Yes Yes Yes Yes No Yes No
Euler Math Toolbox Yes No Yes No No No No No
FlexPro Yes No No No No No No No
FreeMat Yes Yes Yes Yes Yes No No No
GAUSS Yes Yes Yes No Yes No No No
GNU Data Language Yes Yes Yes Yes Yes No No No
GNU MCSim Yes Yes Yes Yes Yes Yes Yes Yes
GNU Octave Yes Yes Yes Yes Yes Yes Yes Yes
IGOR Pro Yes Yes No No No No No No
Julia Yes Yes Yes Yes No No No No
LabVIEW Yes Yes Yes No Yes No No No
Maple Yes Yes Yes No Yes No No No
Mathematica Yes Yes Yes Yes Yes No No Yes
MATLAB Yes Yes Yes Yes Yes No No No
MLAB Yes Yes Yes No No Yes No No
Origin Yes No No No No No No No
Perl Data Language Yes Yes Yes Yes Yes Yes No No
R Yes Yes Yes Yes Yes No No No
SageMath Yes Yes Yes No Yes No No Yes
SAS Yes No Yes No Yes No No No
SequenceL Yes Yes Yes No No No No No
S-Lang Yes Yes Yes Yes Yes Yes No No
Scilab Yes Yes Yes Yes Yes Yes No No
Sysquake Yes Yes Yes No No No No No
TK Solver Yes No No No No No No No
The Unscrambler Yes No No No No No No No
VisSim Yes Yes Yes No Yes No No No

1.3. Language Features

Colors indicate features available as

basic system capabilities
official or officially supported extensions and libraries
third-party software components or not supported
  Standalone executables creation support Symbolic computation support OOP support GUI creation support Multi-dimensional arrays as primitive data type Centralized extension library website Can call code in other languages Can be called from other languages
Analytica No No Yes Yes Yes Yes COM, Excel Excel, COM, .NET
Dyalog APL Yes[10] Yes Yes[11] Win32, .NET, WPF, HTML/JS Yes Yes COM, .NET, WebServices, Shared Libraries, DLLs, NAG, R, JavaScript[12] COM, .NET, WebServices[12]
GNU Data Language No No Yes GUI Widgets since v.0.9 but still incomplete Yes No C, Python Python
GNU MCSim Yes No No XMCSim with TCL/TK and wish No No C R
GNU Octave Yes with mkoctfile only with GiNaC extension Yes[13] GUI Octave code can be used[14] Yes Yes[15] C++, Fortran,[16] Perl,[17] Tcl[18] Java,[19] Perl,[17] C++[20]
J No Yes Yes Yes Yes Yes JavaScript JavaScript
Julia No No Yes Yes Yes Yes
C, Fortran
Python, C++, Java, MATLAB
C/C++
LabVIEW
Professional System version
With add-on[21]
No
Yes[22]
GOOP[23]
G#[24]
Yes Yes Yes[25]
C/C++,[26] DLLs, Python,[27] Perl, Tcl,[28] MATLAB, ActiveX, C#/.NET
With add-ons. I.e.[29]
Yes[30]
Maple No Yes Yes[31] Yes Yes Yes[32] C, C#, Fortran MATLAB,[33] Excel,[34] VisualBasic, Java, and C[35]
Mathematica Yes[36] Yes Yes Yes Yes Yes[37] Java, .NET, C++, Fortran, CUDA, OpenCL, R, Python
Java, .NET, C++
Excel,[38] LabVIEW[39]
Haskell,[40] AppleScript,[41] Racket,[42] Visual Basic,[43] Python[44][45]Clojure[46] MATLAB[47]
MATLAB with extension[48] with extension library[49] Yes[50] Yes Yes Yes[51]
Through MEX[52] files: C, C++, Fortran. Also compiled Java and ActiveX components.
Mathematica[47]
.NET,[53] Java,[54] Excel[55]
MLAB No Yes No Yes Yes No No No
PDL Yes[56] No Yes[57] Yes[58] Yes Yes[59] C via perlXS; C, Python, F77, etc. via Inline Perl, C[60]
R No Yes and extended via Ryacas package Yes[61] Via the tcltk library Yes Yes[62]
C, C++, Fortran[63]
MATLAB[64]
Python[65]
Excel[66]
Python[67]
SAS[68]
SageMath No Yes Yes No Yes Yes[69] Many languages[70][71][72] Yes (any language that can call Python)
SAS No No DS2 and SCL Yes No No
C, Java
R (requires IML)
No
DataMelt Yes Yes Yes Yes Yes Yes Java Yes (any language that can call Java)
TK Solver with extension No Yes with extension Yes Yes .NET Excel Unknown

2. Libraries

2.1. General

  Creator Language First public release Latest stable version Cost (United States dollar ) License Notes
ALGLIB Sergey Bochkanov C++, C#, FreePascal 2006 3.12.0 / August 2017 Dual licensed GPL/commercial General purpose numerical analysis library. Cross-platform (Windows, *nix).
Armadillo NICTA C++ 2009 3.900 / 2013 Free MPL C++ template library for linear algebra; includes various decompositions and factorisations; syntax (API) is similar to MATLAB.
DataMelt jwork.org (S.Chekanov) Java, Android 2005 12 March 2016 Free Free for non-commercial use General numerical calculations, statistics and interactive 2D/3D graphics for data and function presentation
Extreme Optimization Numerical Libraries Extreme Optimization C# 2003 6.0 / many frequent updates Non-free Proprietary Math and statistical libraries for the .NET Framework
GNU Scientific Library GNU Project C 1996 2.3 / December 2016 Free GPL General purpose numerical analysis library. Targets GNU/Linux, can be built on almost any *nix OS with Ansi C compiler.
ILNumerics H. Kutschbach C#, PowerShell 2007 1.3.14 / August 2008 Non-free Proprietary aims .Net/mono, 2D/3D plottings (beta)
IMSL Numerical Libraries Rogue Wave Software C, Java, C#, Fortran, Python 1970 many components Not free Proprietary General purpose numerical analysis library.
Math.NET Numerics C. Rüegg, M. Cuda, et al. C#, F#, C, PowerShell 2009 3.20 / July 2017 Free MIT/X11 General purpose numerical analysis and statistics library for the .NET Framework and Mono, with optional support for native providers.
NAG Numerical Library The Numerical Algorithms Group C, Fortran 1971 many components Not free Proprietary General purpose numerical analysis library.
NMath CenterSpace Software C# 2003 6.2 / March 2016 $995 Proprietary Math and statistical libraries for the .NET Framework
SciPy scipy.org community Python 2001 1.0.0 / 25 October 2017 Free BSD Adds numerical programming capabilities to the Python programming language. Related to NumPy, and therefore connected to the previous Numeric and Numarray packages for Python
SuanShu NM Limited Java and C# 2010 many components Non-free Proprietary Math and statistical libraries for Java

2.2. Operating System Support

The operating systems the software can run on natively (without emulation).

  Windows macOS Linux BSD Unix DOS Android
ALGLIB Yes Yes Yes Yes Yes No Yes
GNU Scientific Library Yes Yes Yes Yes Yes No Yes
ILNumerics Yes Yes Yes Yes Yes No No
IMSL Numerical Libraries Yes Yes Yes No Yes No No
Math.NET Numerics Yes Yes Yes Yes Yes No No
NAG Numerical Library Yes Yes Yes No Yes Yes No
NMath Yes No No No No No No
DataMelt Yes Yes Yes Yes Yes No Yes
SciPy (Python packages) Yes Yes Yes Yes Yes Yes No
SuanShu Yes Yes Yes Yes Yes Yes Yes

The content is sourced from: https://handwiki.org/wiki/Software:Comparison_of_numerical_analysis_software

References

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