List of numerical-analysis software

Last updated March 15, 2024

Listed here are notable end-user computer applications intended for use with numerical or data analysis:

Numerical-software packages

Analytica is a widely used proprietary tool for building and analyzing numerical models. It is a declarative and visual programming language based on influence diagrams.
FlexPro is a program for data analysis and presentation of measurement data. It provides a rich Excel-like user interface and its built-in vector programming language FPScript has a syntax similar to MATLAB.
FreeMat, an open-source MATLAB-like environment with a GPL license.
GNU Octave is a high-level language, primarily intended for numerical computations. It provides a convenient command-line interface for solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with MATLAB. The 4.0 and newer releases of Octave include a GUI. A number of independently developed Linux programs (Cantor, KAlgebra) also offer GUI front-ends to Octave. An active community provides technical support to users.
Igor Pro is proprietary software for performing complex numerical calculations, statistical analysis, and producing publication-quality graphics. It comes with its own programming language, in which numerical algorithms can be implemented.
Jacket, a proprietary GPU Toolbox for MATLAB, enabling some MATLAB computations to be offloaded to the GPU for acceleration and data visualization purposes.
jLab, a research platform for building an open-source MATLAB-like environment in pure Java and Groovy. Currently supports interpreted j-Scripts (MATLAB-like) and compiled GroovySci (extension to Groovy) scripts that provides direct interfacing to Java code and scripting access to many popular Java scientific libraries (e.g. Weka and JSci) and application Wizards.
Julia (programming language) is a high-level dynamic language with a surface similarity to MATLAB. Packages such as DataFrames.jl are available.
LabVIEW offers both textual and graphical-programming approaches to numerical analysis. Its text-based programming language MathScript uses .m-file-script syntax providing some compatibility with MATLAB and its clones.
LAPACK provides Fortran 90 routines for solving systems of simultaneous linear equations, least-squares solutions of linear systems of equations, eigenvalue problems, and singular value problems and the associated matrix factorizations (LU, Cholesky, QR, SVD, Schur, and generalized Schur).
MATLAB is a widely used proprietary software for performing numerical computations.^[1]^[2]^[3] It comes with its own programming language, in which numerical algorithms can be implemented.
GNU MCSim a simulation and numerical integration package, with fast Monte Carlo and Markov chain Monte Carlo capabilities.
ML.NET is a free-software machine-learning library for the C# programming language.^[4]^[5]
NAG Library is an extensive software library of highly optimized numerical-analysis routines for various programming environments.
O-Matrix is a proprietary licensed matrix programming language for mathematics, engineering, science, and financial analysis.
pandas is a BSD-licensed library providing data structures and data analysis tools for the Python programming language.
Perl Data Language provides large multidimensional arrays for the Perl programming language, and utilities for image processing and graphical plotting.
ScaLAPACK is a library of high-performance linear algebra routines for parallel distributed-memory machines that features functionality similar to LAPACK (solvers for dense and banded linear systems, least-squares problems, eigenvalue problems, and singular-value problem).
Scilab is advanced numerical analysis package similar to MATLAB or Octave.^[6]^[7] Comes with a complete GUI and Xcos which is alternative to Simulink. (free software, GPL-compatible CeCILL license)
Sysquake is a computing environment with interactive graphics for mathematics, physics and engineering. Like other applications from Calerga, it is based on a MATLAB-compatible language.
TK Solver is a mathematical modeling and problem-solving software system based on a declarative, rule-based language, commercialized by Universal Technical Systems, Inc.
Torch is a deep-learning library with support for manipulation, statistical analysis and presentation of Tensors.
XLfit, A plugin to Excel which provides curve-fitting and statistical analysis.

General-purpose computer algebra systems

Macsyma, a general-purpose computer algebra system, which has a free GPL-licensed version called Maxima.
Maple, a general-purpose commercial mathematics software package.
Mathcad offers a WYSIWYG interface and the ability to generate publication-quality mathematical equations.
Mathematica offers numerical evaluation, optimization and visualization of a very wide range of numerical functions. It also includes a programming language and computer algebra capabilities.^[8]^[9]^[10]^[11]
PARI/GP is a widely used computer algebra system designed for fast computations in number theory (factorizations, algebraic number theory, elliptic curves...), but also contains a large number of other useful functions to compute with mathematical entities such as matrices, polynomials, power series, algebraic numbers etc., and a lot of transcendental functions. PARI is also available as a C library to allow for faster computations.
SageMath is an open-source math software,^[12] with a unified Python interface which is available as a text interface or a graphical web-based one. Includes interfaces for open-source and proprietary general purpose CAS, and other numerical analysis programs, like PARI/GP, GAP, gnuplot, Magma, and Maple.
Speakeasy is an interactive numerical environment also featuring an interpreted programming language. Born in the mid '60s for matrix manipulation and still in continuous evolution, it pioneered the most common paradigms of this kind of tools, featuring dynamic typing of the structured data objects, dynamic allocation and garbage collection, operators overloading, dynamic linking of compiled or interpreted additional modules contributed by the community of the users and so on.
Trilinos is a collection of open-source object-oriented libraries for use in scientific and engineering applications. Trilinos is based on scalable, parallel linear-algebra algorithms.

Interface-oriented

Baudline is a time-frequency browser for numerical signals analysis and scientific visualization.
COMSOL Multiphysics is a finite-element analysis, solver and simulation software / FEA Software package for various physics and engineering applications, especially coupled phenomena, or multiphysics.
Dataplot is provided by NIST.
DADiSP is a commercial program focused on DSP that combines the numerical capability of MATLAB with a spreadsheet-like interface.
EJS is an open-source software tool, written in Java, for generating simulations.
Euler Mathematical Toolbox is a powerful numerical laboratory with a programming language that can handle real, complex and interval numbers, vectors and matrices. It can produce 2D/3D plots.
FEATool Multiphysics is a Matlab GUI toolbox for finite element FEM and PDE multiphysics simulations.
FEniCS Project is a collection of project for automated solutions to PDEs.
Hermes is a C++ library of advanced adaptive finite element algorithms to solve PDEs and multiphysics coupled problems.
Fityk is a curve fitting and data-analysis program. Primarily used for peak fitting and analyzing peak data.
FlexPro is a commercial program for interactive and automated analysis and presentation of mainly measurement data. It supports many binary instrument data formats and has its own vectorized programming language.
IGOR Pro, a software package with emphasis on time series, image analysis, and curve fitting. It comes with its own programming language and can be used interactively.
LabPlot is a data analysis and visualization application built on the KDE Platform.
MFEM is a free, lightweight, scalable C++ library for finite element methods.
Origin, a software package that is widely used for making scientific graphs. It comes with its own C/C++ compiler that conforms quite closely to ANSI standard.
PAW is a free data analysis package developed at CERN.
SPSS,^[13]^[14]^[15]^[16]^[17] an application for statistical analysis.
QtiPlot is a data analysis and scientific visualisation program, similar to Origin.
ROOT is a free object-oriented multi-purpose data-analysis package, developed at CERN.
Salome is a free software tool that provides a generic platform for pre- and post-processing for numerical simulation.
Shogun, an open-source large-scale machine-learning toolbox that provides several SVM implementations (like libSVM, SVMlight) under a common framework and interfaces to Octave, MATLAB, Python, R
Waffles is a free-software collection of command-line tools designed for scripting machine-learning operations in automated experiments and processes.
Weka is a suite of machine learning software written at the University of Waikato.

Language-oriented

acslX is a software application for modeling and evaluating the performance of continuous systems described by time-dependent, nonlinear differential equations.
ADMB is a software suite for non-linear statistical modeling based on C++ which uses automatic differentiation.
AMPL is a mathematical modeling language for describing and solving high complexity problems for large-scale optimization.
Ch, a commercial C/C++-based interpreted language with computational array for scientific numerical computation and visualization.^[18]
APMonitor: APMonitor is a mathematical modeling language for describing and solving representations of physical systems in the form of differential and algebraic equations.
Armadillo is C++ template library for linear algebra; includes various decompositions, factorisations, and statistics functions; its syntax (API) is similar to MATLAB.
Clojure with numeric libraries Neanderthal, ClojureCUDA, and ClojureCL to call optimized matrix and linear algebra functions on CPU and GPU.
Julia ^[19]^[20] is designed for cloud parallel scientific computing in mind on LLVM-based JIT as a backend. Lightweight “green” threading (coroutines). Direct calls of C functions from code (no wrappers or special APIs needed), support for Unicode. Powerful shell-like capabilities for managing other processes. Lisp-like macros and other metaprogramming facilities.
ELKI a software framework for development of data mining algorithms in Java.
GAUSS, a matrix programming language for mathematics and statistics.
GNU Data Language, a free compiler designed as a drop-in replacement for IDL.
IDL,^[21] a commercial interpreted language based on FORTRAN with some vectorization. Widely used in the solar physics, fusion, atmospheric sciences and medical communities. The GNU Data Language is a free alternative.
ILNumerics.Net, a C# math library that brings numeric computing functions for science, engineering and financial analysis to the .NET Framework.
KPP generates Fortran 90, FORTRAN 77, C, or Matlab code for the integration of ordinary differential equations (ODEs) resulting from chemical reaction mechanisms.
Madagascar, an open-source software package for multidimensional data analysis and reproducible computational experiments.
mlpack is an open-source library for machine learning, providing a simple and consistent API, while exploiting C++ language features to provide maximum performance and flexibility
NCAR Command Language is an interpreted language designed specifically for scientific data analysis and visualization.
O-Matrix - a matrix programming language for mathematics, engineering, science, and financial analysis.
OptimJ is a mathematical Java-based modeling language for describing and solving high-complexity problems for large-scale optimization.
Perl Data Language,^[22]^[23] also known as PDL, an array extension to Perl ver.5, used for data manipulation, statistics, numerical simulation and visualization.
Python ^[24]^[25] with well-known scientific computing packages: NumPy, SymPy and SciPy.^[26]^[27]^[28]
R is a widely used system with a focus on data manipulation and statistics which implements the S language.^[29] Many add-on packages are available (free software, GNU GPL license).
SAS,^[30] a system of software products for statistics. It includes SAS/IML,^[31] a matrix programming language.
VisSim is a visual block-diagram language for simulation of nonlinear dynamic systems and model-based embedded development. Its fast ODE engine supports real-time simulation of complex large-scale models. The highly efficient fixed-point code generator allows targeting of low-cost fixed-point embedded processors.
Wolfram Language which is used within many Wolfram technologies such as Mathematica and the Wolfram Cloud
World Programming System (WPS), supports mixing Python, R and SAS languages in a single-user program for statistical analysis and data manipulation
Yorick is an interpreted programming language designed for numerics, graph plotting and simulation.

Historically significant

Expensive Desk Calculator written for the TX-0 and PDP-1 in the late 1950s or early 1960s.
S is an (array-based) programming language with strong numerical support. R is an implementation of the S language.

Related Research Articles

<span class="mw-page-title-main">Numerical analysis</span> Study of algorithms using numerical approximation

Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis. It is the study of numerical methods that attempt to find approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts. Current growth in computing power has enabled the use of more complex numerical analysis, providing detailed and realistic mathematical models in science and engineering. Examples of numerical analysis include: ordinary differential equations as found in celestial mechanics, numerical linear algebra in data analysis, and stochastic differential equations and Markov chains for simulating living cells in medicine and biology.

Maple is a symbolic and numeric computing environment as well as a multi-paradigm programming language. It covers several areas of technical computing, such as symbolic mathematics, numerical analysis, data processing, visualization, and others. A toolbox, MapleSim, adds functionality for multidomain physical modeling and code generation.

SciPy is a free and open-source Python library used for scientific computing and technical computing.

NumPy is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. The predecessor of NumPy, Numeric, was originally created by Jim Hugunin with contributions from several other developers. In 2005, Travis Oliphant created NumPy by incorporating features of the competing Numarray into Numeric, with extensive modifications. NumPy is open-source software and has many contributors. NumPy is a NumFOCUS fiscally sponsored project.

LAPACK is a standard software library for numerical linear algebra. It provides routines for solving systems of linear equations and linear least squares, eigenvalue problems, and singular value decomposition. It also includes routines to implement the associated matrix factorizations such as LU, QR, Cholesky and Schur decomposition. LAPACK was originally written in FORTRAN 77, but moved to Fortran 90 in version 3.2 (2008). The routines handle both real and complex matrices in both single and double precision. LAPACK relies on an underlying BLAS implementation to provide efficient and portable computational building blocks for its routines.

Basic Linear Algebra Subprograms (BLAS) is a specification that prescribes a set of low-level routines for performing common linear algebra operations such as vector addition, scalar multiplication, dot products, linear combinations, and matrix multiplication. They are the de facto standard low-level routines for linear algebra libraries; the routines have bindings for both C and Fortran. Although the BLAS specification is general, BLAS implementations are often optimized for speed on a particular machine, so using them can bring substantial performance benefits. BLAS implementations will take advantage of special floating point hardware such as vector registers or SIMD instructions.

Computational science, also known as scientific computing, technical computing or scientific computation (SC), is a division of science that uses advanced computing capabilities to understand and solve complex physical problems. This includes

ScientificPython is an open source library of scientific tools for the Python programming language. Its development started in 1995.

Numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. It is a subfield of numerical analysis, and a type of linear algebra. Computers use floating-point arithmetic and cannot exactly represent irrational data, so when a computer algorithm is applied to a matrix of data, it can sometimes increase the difference between a number stored in the computer and the true number that it is an approximation of. Numerical linear algebra uses properties of vectors and matrices to develop computer algorithms that minimize the error introduced by the computer, and is also concerned with ensuring that the algorithm is as efficient as possible.

<span class="mw-page-title-main">Computational engineering</span>

Computational Engineering is an emerging discipline that deals with the development and application of computational models for engineering, known as Computational Engineering Models or CEM. Computational engineering uses computers to solve engineering design problems important to a variety of industries. At this time, various different approaches are summarized under the term Computational Engineering, including using computational geometry and virtual design for engineering tasks, often coupled with a simulation-driven approach In Computational Engineering, algorithms solve mathematical and logical models that describe engineering challenges, sometimes coupled with some aspect of AI, specifically Reinforcement Learning.

In computer programming, a scientific programming language can refer to two degrees of the same concept.

The FEniCS Project is a collection of free and open-source software components with the common goal to enable automated solution of differential equations. The components provide scientific computing tools for working with computational meshes, finite-element variational formulations of ordinary and partial differential equations, and numerical linear algebra.

Model order reduction (MOR) is a technique for reducing the computational complexity of mathematical models in numerical simulations. As such it is closely related to the concept of metamodeling, with applications in all areas of mathematical modelling.

<span class="mw-page-title-main">FEATool Multiphysics</span>

FEATool Multiphysics is a physics, finite element analysis (FEA), and partial differential equation (PDE) simulation toolbox. FEATool Multiphysics features the ability to model fully coupled heat transfer, fluid dynamics, chemical engineering, structural mechanics, fluid-structure interaction (FSI), electromagnetics, as well as user-defined and custom PDE problems in 1D, 2D (axisymmetry), or 3D, all within a graphical user interface (GUI) or optionally as script files. FEATool has been employed and used in academic research, teaching, and industrial engineering simulation contexts.

References

↑ Quarteroni, A., Saleri, F., & Gervasio, P. (2006). Scientific computing with MATLAB and Octave. Berlin: Springer.
↑ Gander, W., & Hrebicek, J. (Eds.). (2011). Solving problems in scientific computing using Maple and Matlab®. Springer Science & Business Media.
↑ Barnes, B., & Fulford, G. R. (2011). Mathematical modelling with case studies: a differential equations approach using Maple and MATLAB. Chapman and Hall/CRC.
↑ David Ramel (2018-05-08). "Open Source, Cross-Platform ML.NET Simplifies Machine Learning -- Visual Studio Magazine". Visual Studio Magazine. Retrieved 2018-05-10.
↑ Kareem Anderson (2017-05-09). "Microsoft debuts ML.NET cross-platform machine learning framework". On MSFT. Retrieved 2018-05-10.
↑ Bunks, C., Chancelier, J. P., Delebecque, F., Goursat, M., Nikoukhah, R., & Steer, S. (2012). Engineering and scientific computing with Scilab. Springer Science & Business Media.
↑ Thanki, R. M., & Kothari, A. M. (2019). Digital image processing using SCILAB. Springer International Publishing.
↑ Maeder, R. E. (1991). Programming in mathematica. Addison-Wesley Longman Publishing Co., Inc.
↑ Stephen Wolfram. (1999). The MATHEMATICA® book, version 4. Cambridge University Press.
↑ Shaw, W. T., & Tigg, J. (1993). Applied Mathematica: getting started, getting it done. Addison-Wesley Longman Publishing Co., Inc.
↑ Marasco, A., & Romano, A. (2001). Scientific Computing with Mathematica: Mathematical Problems for Ordinary Differential Equations; with a CD-ROM. Springer Science & Business Media.
↑ Zimmermann, P., Casamayou, A., Cohen, N., Connan, G., Dumont, T., Fousse, L., ... & Bray, E. (2018). Computational Mathematics with SageMath. SIAM.
↑ Wagner III, W. E. (2019). Using IBM® SPSS® statistics for research methods and social science statistics. Sage Publications.
↑ Pollock III, P. H., & Edwards, B. C. (2019). An IBM® SPSS® Companion to Political Analysis. Cq Press.
↑ Babbie, E., Wagner III, W. E., & Zaino, J. (2018). Adventures in social research: Data analysis using IBM SPSS statistics. Sage Publications.
↑ Aldrich, J. O. (2018). Using IBM® SPSS® Statistics: An interactive hands-on approach. Sage Publications.
↑ Stehlik-Barry, K., & Babinec, A. J. (2017). Data Analysis with IBM SPSS Statistics. Packt Publishing Ltd.
↑ Ch Scientific Numerical Computing
↑ Bezanson, J., Edelman, A., Karpinski, S., & Shah, V. B. (2017). Julia: A fresh approach to numerical computing. SIAM Review, 59(1), 65-98.
↑ Bezanson, J., Karpinski, S., Shah, V. B., & Edelman, A. (2012). Julia: A fast dynamic language for technical computing. arXiv preprint arXiv:1209.5145.
↑ Gumley, L. E. (2001). Practical IDL programming. Elsevier.
↑ Christiansen, T., Wall, L., & Orwant, J. (2012). Programming Perl: Unmatched power for text processing and scripting. " O'Reilly Media, Inc.".
↑ Srinivasan, S. (1997). Advanced perl programming. " O'Reilly Media, Inc.".
↑ Van Rossum, G. (2007, June). Python Programming Language. In USENIX annual technical conference (Vol. 41, p. 36).
↑ Sanner, M. F. (1999). Python: a programming language for software integration and development. J Mol Graph Model, 17(1), 57-61.
↑ Jones, E., Oliphant, T., & Peterson, P. (2001). SciPy: Open source scientific tools for Python.
↑ Bressert, E. (2012). SciPy and NumPy: an overview for developers. " O'Reilly Media, Inc.".
↑ Blanco-Silva, F. J. (2013). Learning SciPy for numerical and scientific computing. Packt Publishing Ltd.
↑ Ihaka, R., & Gentleman, R. (1996). R: a language for data analysis and graphics. Journal of computational and graphical statistics, 5(3), 299-314.
↑ Khattree, R., & Naik, D. N. (2018). Applied multivariate statistics with SAS software. SAS Institute Inc.
↑ SAS/IML

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[1] Quarteroni, A., Saleri, F., & Gervasio, P. (2006). Scientific computing with MATLAB and Octave. Berlin: Springer.

[gh-2] Gander, W., & Hrebicek, J. (Eds.). (2011). Solving problems in scientific computing using Maple and Matlab®. Springer Science & Business Media.

[bf-3] Barnes, B., & Fulford, G. R. (2011). Mathematical modelling with case studies: a differential equations approach using Maple and MATLAB. Chapman and Hall/CRC.

[visu_Open-4] David Ramel (2018-05-08). "Open Source, Cross-Platform ML.NET Simplifies Machine Learning -- Visual Studio Magazine". Visual Studio Magazine. Retrieved 2018-05-10.

[onms_Micr-5] Kareem Anderson (2017-05-09). "Microsoft debuts ML.NET cross-platform machine learning framework". On MSFT. Retrieved 2018-05-10.

[6] Bunks, C., Chancelier, J. P., Delebecque, F., Goursat, M., Nikoukhah, R., & Steer, S. (2012). Engineering and scientific computing with Scilab. Springer Science & Business Media.

[7] Thanki, R. M., & Kothari, A. M. (2019). Digital image processing using SCILAB. Springer International Publishing.

[8] Maeder, R. E. (1991). Programming in mathematica. Addison-Wesley Longman Publishing Co., Inc.

[9] Stephen Wolfram. (1999). The MATHEMATICA® book, version 4. Cambridge University Press.

[10] Shaw, W. T., & Tigg, J. (1993). Applied Mathematica: getting started, getting it done. Addison-Wesley Longman Publishing Co., Inc.

[11] Marasco, A., & Romano, A. (2001). Scientific Computing with Mathematica: Mathematical Problems for Ordinary Differential Equations; with a CD-ROM. Springer Science & Business Media.

[12] Zimmermann, P., Casamayou, A., Cohen, N., Connan, G., Dumont, T., Fousse, L., ... & Bray, E. (2018). Computational Mathematics with SageMath. SIAM.

[13] Wagner III, W. E. (2019). Using IBM® SPSS® statistics for research methods and social science statistics. Sage Publications.

[14] Pollock III, P. H., & Edwards, B. C. (2019). An IBM® SPSS® Companion to Political Analysis. Cq Press.

[15] Babbie, E., Wagner III, W. E., & Zaino, J. (2018). Adventures in social research: Data analysis using IBM SPSS statistics. Sage Publications.

[16] Aldrich, J. O. (2018). Using IBM® SPSS® Statistics: An interactive hands-on approach. Sage Publications.

[17] Stehlik-Barry, K., & Babinec, A. J. (2017). Data Analysis with IBM SPSS Statistics. Packt Publishing Ltd.

[18] Ch Scientific Numerical Computing

[19] Bezanson, J., Edelman, A., Karpinski, S., & Shah, V. B. (2017). Julia: A fresh approach to numerical computing. SIAM Review, 59(1), 65-98.

[20] Bezanson, J., Karpinski, S., Shah, V. B., & Edelman, A. (2012). Julia: A fast dynamic language for technical computing. arXiv preprint arXiv:1209.5145.

[21] Gumley, L. E. (2001). Practical IDL programming. Elsevier.

[22] Christiansen, T., Wall, L., & Orwant, J. (2012). Programming Perl: Unmatched power for text processing and scripting. " O'Reilly Media, Inc.".

[23] Srinivasan, S. (1997). Advanced perl programming. " O'Reilly Media, Inc.".

[24] Van Rossum, G. (2007, June). Python Programming Language. In USENIX annual technical conference (Vol. 41, p. 36).

[25] Sanner, M. F. (1999). Python: a programming language for software integration and development. J Mol Graph Model, 17(1), 57-61.

[26] Jones, E., Oliphant, T., & Peterson, P. (2001). SciPy: Open source scientific tools for Python.

[27] Bressert, E. (2012). SciPy and NumPy: an overview for developers. " O'Reilly Media, Inc.".

[28] Blanco-Silva, F. J. (2013). Learning SciPy for numerical and scientific computing. Packt Publishing Ltd.

[29] Ihaka, R., & Gentleman, R. (1996). R: a language for data analysis and graphics. Journal of computational and graphical statistics, 5(3), 299-314.

[30] Khattree, R., & Naik, D. N. (2018). Applied multivariate statistics with SAS software. SAS Institute Inc.

[31] SAS/IML

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