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

data analysis Data analysis is the process of inspecting, Data cleansing, cleansing, Data transformation, transforming, and Data modeling, modeling data with the goal of discovering useful information, informing conclusions, and supporting decision-making. Da ...

Numerical-software packages

* Analytica is a widely used

proprietary software Proprietary software is computer software, software that grants its creator, publisher, or other rightsholder or rightsholder partner a legal monopoly by modern copyright and intellectual property law to exclude the recipient from freely sharing t ...

tool for building and analyzing numerical models. It is a declarative and visual programming language based on influence diagrams. * FlexPro is a program to analyze and present measurement data. It has a rich Excel-like user interface and a built-in vector programming language FPScript has a syntax similar to

MATLAB MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementat ...

. * FreeMat, an open-source MATLAB-like environment with a

GNU General Public License The GNU General Public Licenses (GNU GPL or simply GPL) are a series of widely used free software licenses, or ''copyleft'' licenses, that guarantee end users the freedom to run, study, share, or modify the software. The GPL was the first ...

(GPL). *

GNU Octave GNU Octave is a scientific programming language for scientific computing and numerical computation. Octave helps in solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly ...

is a

high-level programming language A high-level programming language is a programming language with strong Abstraction (computer science), abstraction from the details of the computer. In contrast to low-level programming languages, it may use natural language ''elements'', be ea ...

, intended for mainly numerical computing. It has a convenient

command-line interface A command-line interface (CLI) is a means of interacting with software via command (computing), commands each formatted as a line of text. Command-line interfaces emerged in the mid-1960s, on computer terminals, as an interactive and more user ...

to solve linear and nonlinear problems numerically, and to perform other numerical experiments using a language that is compatible mostly with MATLAB. The 4.0 and newer releases of Octave include a GUI. Several independently developed

Linux Linux ( ) is a family of open source Unix-like operating systems based on the Linux kernel, an kernel (operating system), operating system kernel first released on September 17, 1991, by Linus Torvalds. Linux is typically package manager, pac ...

programs ( Cantor, KAlgebra) also offer GUI front-ends to Octave. An active community provides technical support to users. * Igor Pro is proprietary software to perform complex numerical calculations, statistical analysis, and produce 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 computations to be offloaded to the GPU for acceleration and data visualization. * jLab, a research platform to build an open-source MATLAB-like environment in pure

Java Java is one of the Greater Sunda Islands in Indonesia. It is bordered by the Indian Ocean to the south and the Java Sea (a part of Pacific Ocean) to the north. With a population of 156.9 million people (including Madura) in mid 2024, proje ...

and

Groovy ''Groovy'' (or, less commonly, ''groovie'' or ''groovey'') is a slang colloquialism popular during the 1960s and 1970s. It is roughly synonymous with words such as "excellent", "fashionable", or "amazing", depending on context. History The word ...

. Supports interpreted j-Scripts (MATLAB-like) and compiled GroovySci (extension to Groovy) scripts that give direct interfacing to Java code and scripting access to many popular Java scientific libraries (e.g., Weka and JSci) and application Wizards. * Julia 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

and its clones. * LAPACK has 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). *

is a widely used proprietary software to perform numerical computations.Gander, W., & Hrebicek, J. (Eds.). (2011). Solving problems in scientific computing using Maple and Matlab.

Springer Science & Business Media Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in ...

.Barnes, B., & Fulford, G. R. (2011). Mathematical modelling with case studies: a differential equations approach using Maple and MATLAB. Chapman and Hall/CRC. It comes with its own programming language, in which numerical algorithms can be implemented. * MCSim a simulation and numerical integration package, with fast Monte Carlo and Markov chain Monte Carlo abilities. * ML.NET is a

free software Free software, libre software, libreware sometimes known as freedom-respecting software is computer software distributed open-source license, under terms that allow users to run the software for any purpose as well as to study, change, distribut ...

machine learning Machine learning (ML) is a field of study in artificial intelligence concerned with the development and study of Computational statistics, statistical algorithms that can learn from data and generalise to unseen data, and thus perform Task ( ...

library A library is a collection of Book, books, and possibly other Document, materials and Media (communication), media, that is accessible for use by its members and members of allied institutions. Libraries provide physical (hard copies) or electron ...

for the C# programming language. * NAG Numerical Libraries 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 has large multidimensional arrays for the

Perl Perl is a high-level, general-purpose, interpreted, dynamic programming language. Though Perl is not officially an acronym, there are various backronyms in use, including "Practical Extraction and Reporting Language". Perl was developed ...

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 Scilab is a free and open-source, cross-platform numerical computational package and a high-level, numerically oriented programming language. It can be used for signal processing, statistical analysis, image enhancement, fluid dynamics simul ...

is advanced numerical analysis package similar to MATLAB or Octave. Comes with a complete GUI and Xcos which is alternative to Simulink. (

, GPL-compatible

CeCILL CeCILL (from CEA CNRS INRIA Logiciel Libre) is a free software license adapted to both international and French legal matters, in the spirit of and retaining compatibility with the GNU General Public License (GPL). It was jointly developed by ...

license) * Sysquake is a computing environment with

interactive Across the many fields concerned with interactivity, including information science, computer science, human-computer interaction, communication, and industrial design, there is little agreement over the meaning of the term "interactivity", but mo ...

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 for 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 ''Acer'' is a genus of trees and shrubs commonly known as maples. The genus is placed in the soapberry family Sapindaceae.Stevens, P. F. (2001 onwards). Angiosperm Phylogeny Website. Version 9, June 2008 nd more or less continuously updated si ...

, 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 abilities. * 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, 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 The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical s ...

. * DADiSP is a commercial program focused on

digital signal processing Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner are a ...

(DSP) that combines the numerical ability of MATLAB with a

spreadsheet A spreadsheet is a computer application for computation, organization, analysis and storage of data in tabular form. Spreadsheets were developed as computerized analogs of paper accounting worksheets. The program operates on data entered in c ...

-like interface. * Easy Java Simulations (EJS) is an

open-source software Open-source software (OSS) is Software, computer software that is released under a Open-source license, license in which the copyright holder grants users the rights to use, study, change, and Software distribution, distribute the software an ...

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

GUI toolbox for finite element FEM and PDE multiphysics simulations. * FEniCS Project is a collection of project for automated solutions to

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to ho ...

s (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 LabPlot is a free and open-source, cross-platform computer program for interactive scientific plotting, curve fitting, nonlinear regression, data processing and data analysis. LabPlot is available, under the GPL-2.0-or-later license, for Win ...

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

package developed at

CERN The European Organization for Nuclear Research, known as CERN (; ; ), is an intergovernmental organization that operates the largest particle physics laboratory in the world. Established in 1954, it is based in Meyrin, western suburb of Gene ...

. * SPSS, an application for statistical analysis. * QtiPlot is a data analysis and scientific visualisation program, similar to Origin. *

ROOT In vascular plants, the roots are the plant organ, organs of a plant that are modified to provide anchorage for the plant and take in water and nutrients into the plant body, which allows plants to grow taller and faster. They are most often bel ...

is a free object-oriented multi-purpose data-analysis package, developed at

. * Salome is a free software tool that is a generic platform for pre- and post-processing for numerical simulation. *

Shogun , officially , was the title of the military aristocracy, rulers of Japan during most of the period spanning from 1185 to 1868. Nominally appointed by the Emperor of Japan, Emperor, shoguns were usually the de facto rulers of the country, exc ...

, an open-source large-scale

toolbox that gives several SVM implementations (like libSVM, SVMlight) under a common framework and interfaces to MATLAB, Octave, Python, R *

Waffles A waffle is a dish made from leavened Batter (cooking), batter or dough that is cooked between two plates that are patterned to give a characteristic size, shape, and surface impression. There are many variations based on the type of waffle iron ...

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

software written at the

University of Waikato The University of Waikato (), established in 1964, is a Public university, public research university located in Hamilton, New Zealand, Hamilton, New Zealand. An additional campus is located in Tauranga. The university performs research in nume ...

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 AMPL (A Mathematical Programming Language) is an algebraic modeling language to describe and solve high-complexity problems for large-scale mathematical computing (e.g. large-scale optimization and scheduling-type problems). It was developed ...

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. * APMonitor: APMonitor is a mathematical modeling language for describing and solving representations of physical systems in the form of differential and algebraic equations. *

Armadillo Armadillos () are New World placental mammals in the order (biology), order Cingulata. They form part of the superorder Xenarthra, along with the anteaters and sloths. 21 extant species of armadillo have been described, some of which are dis ...

is C++ template library for linear algebra; includes various decompositions, factorisations, and statistics functions; its syntax (application programming interface (

API An application programming interface (API) is a connection between computers or between computer programs. It is a type of software interface, offering a service to other pieces of software. A document or standard that describes how to build ...

) is similar to MATLAB. *

Clojure Clojure (, like ''closure'') is a dynamic programming language, dynamic and functional programming, functional dialect (computing), dialect of the programming language Lisp (programming language), Lisp on the Java (software platform), Java platfo ...

with numeric libraries Neanderthal, ClojureCUDA, and ClojureCL to call optimized matrix and linear algebra functions on CPU and GPU. * Julia is designed for cloud parallel scientific computing in mind on

LLVM LLVM, also called LLVM Core, is a target-independent optimizer and code generator. It can be used to develop a Compiler#Front end, frontend for any programming language and a Compiler#Back end, backend for any instruction set architecture. LLVM i ...

-based just-in-time compilation (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 abilities to manage other processes.

Lisp Lisp (historically LISP, an abbreviation of "list processing") is a family of programming languages with a long history and a distinctive, fully parenthesized Polish notation#Explanation, prefix notation. Originally specified in the late 1950s, ...

-like macros and other metaprogramming facilities. * Environment for DeveLoping KDD-Applications Supported by Index-Structures ( ELKI) a

software framework In computer programming, a software framework is a software abstraction that provides generic functionality which developers can extend with custom code to create applications. It establishes a standard foundation for building and deploying soft ...

for developing

data mining Data mining is the process of extracting and finding patterns in massive data sets involving methods at the intersection of machine learning, statistics, and database systems. Data mining is an interdisciplinary subfield of computer science and ...

algorithms in

. *

GAUSS Johann Carl Friedrich Gauss (; ; ; 30 April 177723 February 1855) was a German mathematician, astronomer, Geodesy, geodesist, and physicist, who contributed to many fields in mathematics and science. He was director of the Göttingen Observat ...

, a matrix programming language for mathematics and statistics. * GNU Data Language, a free compiler designed as a drop-in replacement for IDL. * IDL, a commercial interpreted language based on FORTRAN with some vectorization. Widely used in the solar physics, fusion power,

atmospheric science Atmospheric science is the study of the Atmosphere of Earth, Earth's atmosphere and its various inner-working physical processes. Meteorology includes atmospheric chemistry and atmospheric physics with a major focus on weather forecasting. Clima ...

s and

medical Medicine is the science and Praxis (process), practice of caring for patients, managing the Medical diagnosis, diagnosis, prognosis, Preventive medicine, prevention, therapy, treatment, Palliative care, palliation of their injury or disease, ...

communities. The GNU Data Language is a free alternative. * ILNumerics, a C# math library that brings numeric computing functions for science, engineering and financial analysis to the

.NET The .NET platform (pronounced as "''dot net"'') is a free and open-source, managed code, managed computer software framework for Microsoft Windows, Windows, Linux, and macOS operating systems. The project is mainly developed by Microsoft emplo ...

framework. * Kinetic PreProcessor (KPP) generates Fortran 90, FORTRAN 77, C, or

code for the integration of

ordinary differential equations In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with any other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives ...

(ODEs) resulting from chemical reaction mechanisms. *

Madagascar Madagascar, officially the Republic of Madagascar, is an island country that includes the island of Madagascar and numerous smaller peripheral islands. Lying off the southeastern coast of Africa, it is the world's List of islands by area, f ...

, an open-source software package for multidimensional data analysis and reproducible computational experiments. *

mlpack mlpack is a free, open-source and header-only software library for machine learning and artificial intelligence written in C++, built on top of the Armadillo library and thensmallennumerical optimization library. mlpack has an emphasis on scal ...

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 The US National Center for Atmospheric Research (NCAR ) is a US federally funded research and development center (FFRDC) managed by the nonprofit University Corporation for Atmospheric Research (UCAR) and funded by the National Science Foundatio ...

is an interpreted language designed specifically for scientific

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, also known as PDL, an array extension to

ver.5, used for data manipulation, statistics, numerical simulation and visualization. * Python with well-known scientific computing packages: NumPy, SymPy and SciPy. * R is a widely used system with a focus on data manipulation and statistics which implements the S language. Many add-on packages are available (

, GNU

GPL license The GNU General Public Licenses (GNU GPL or simply GPL) are a series of widely used free software licenses, or ''copyleft'' licenses, that guarantee end users the freedom to run, study, share, or modify the software. The GPL was the first ...

). * SAS, a system of software products for statistics. It includes SAS/IML,SAS/IML
/ref> 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

programming language A programming language is a system of notation for writing computer programs. Programming languages are described in terms of their Syntax (programming languages), syntax (form) and semantics (computer science), semantics (meaning), usually def ...

s in a single-user program for statistical analysis and data manipulation *

Yorick Yorick is an unseen character in William Shakespeare's play ''Hamlet''. He is the dead court jester whose Human skull, skull is exhumed by the The Gravediggers, First Gravedigger in Act 5, Scene 1, of the play. The sight of Yorick's skull evokes ...

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.

References