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List of numerical libraries
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<h2 id="multi-language">Multi-language</h2> <ul><li><a href="/facts/ALGLIB/fSduLPd2">ALGLIB</a> is an open source numerical analysis library which may be used from C++, C#, FreePascal, Delphi, VBA.</li> <li><a href="/facts/ArrayFire/EuQt0yYk">ArrayFire</a> is a high performance open source software library for parallel computing with an easy-to-use API.</li> <li><a href="/facts/IMSL_Numerical_Libraries/H6pg7hgj">IMSL Numerical Libraries</a> are libraries of numerical analysis functionality implemented in standard programming languages like C, Java, C# .NET, Fortran, and Python.</li> <li>The <a href="/facts/NAG_Numerical_Library/PKd05xdo">NAG Library</a> is a collection of mathematical and statistical routines for multiple programming languages (C, C++, Fortran, Visual Basic, Java, Python and C#) and packages (MATLAB, Excel, R, LabVIEW).</li> <li><a href="/facts/GNU_Octave/vVVq5evM">GNU Octave</a> is an open source high level programming language and library, including a command line interface and GUI, analogous to commercial alternatives such as Maple, MATLAB, Mathematica, etc. APIs, functions and libraries can be called from many platforms, including high level engineering programs, where functions are, in many cases, seamlessly interpreted and integrated in similar fashion to MATLAB. It also can be used with batch orientation.</li> <li><a href="/facts/Librsb/zJJ3HHkg">librsb</a> is an open source library for high performance sparse matrix computations providing multi-threaded primitives to build iterative solvers (implements also the Sparse <a href="/facts/BLAS/T8Jq1Jpq">BLAS</a> standard). It can be used from C, C++, Fortran, and a dedicated <a href="/facts/GNU_Octave/vVVq5evM">GNU Octave</a> package.</li></ul> <h2 id="c"><a href="/facts/C_(programming_language)/Ky2No763">C</a></h2> <ul><li><a href="/facts/BLOPEX/I131RpW0">BLOPEX</a> (Block Locally Optimal Preconditioned Eigenvalue Xolvers) is an <a href="/facts/Open_source/7X9rCdz4">open-source</a> <a href="/facts/Library_(computing)/xRzL3P7q">library</a> for the <a href="/facts/Scalability/jh7JomPa">scalable</a> (<a href="/facts/Parallel_computing/nQzcpzQt">parallel</a>) solution of eigenvalue problems.</li> <li><a href="/facts/Fastest_Fourier_Transform_in_the_West/Q7STPyIk">Fastest Fourier Transform in the West</a> (FFTW) is a software library for computing Fourier and related transforms.</li> <li><a href="/facts/GNU_Scientific_Library/WKX9L554">GNU Scientific Library</a>, a popular, free numerical analysis library implemented in <a href="/facts/C_(programming_language)/Ky2No763">C</a>.</li> <li><a href="/facts/GNU_Multi-Precision_Library/ldrpmQPR">GNU Multi-Precision Library</a> is a library for doing <a href="/facts/Arbitrary-precision_arithmetic/cXxc8yB2">arbitrary-precision arithmetic</a>.</li> <li><a href="/facts/Hypre/1ReEIya4">hypre</a> (High Performance Preconditioners) is an <a href="/facts/Open_source/7X9rCdz4">open-source</a> <a href="/facts/Library_(computing)/xRzL3P7q">library</a> of <a href="/facts/Source_code/o9J6Jv23">routines</a> for <a href="/facts/Scalability/jh7JomPa">scalable</a> (<a href="/facts/Parallel_computing/nQzcpzQt">parallel</a>) solution of linear systems and preconditioning.</li> <li><a href="/facts/LabWindows%2fCVI/j8RhSpLU">LabWindows/CVI</a> is an ANSI C <a href="/facts/Integrated_Development_Environment/jbEINSQf">IDE</a> that includes built-in libraries for analysis of raw measurement data, signal generation, windowing, filter functions, signal processing, linear algebra, array and complex operations, curve fitting and statistics.</li> <li><a href="/facts/Lis_(linear_algebra_library)/LxWHXaJQ">Lis</a> is a scalable parallel library for solving systems of linear equations and eigenvalue problems using iterative methods.</li> <li><a href="/facts/Intel_MKL/nwPPAUpe">Intel MKL</a> (Math Kernel Library) contains optimized math routines for science, engineering, and financial applications, and is written in C/C++ and Fortran. Core math functions include BLAS, LAPACK, ScaLAPACK, sparse solvers, fast Fourier transforms, and vector math.</li> <li><a href="/facts/Integrated_Performance_Primitives/q9TJI4E0">Intel IPP</a> is a multi-threaded software library of functions for multimedia and data processing applications.</li> <li><a href="/facts/OpenBLAS/5mDADpsA">OpenBLAS</a> is an open source implementation of the BLAS API with many hand-crafted optimizations for specific processor types. It performs similar to Intel MKL on Intel processors and higher on various others.</li> <li><a href="/facts/Portable%2c_Extensible_Toolkit_for_Scientific_Computation/kpgPvndI">Portable, Extensible Toolkit for Scientific Computation</a> (PETSc), is a suite of <a href="/facts/Data_structures/yNsNvL1I">data structures</a> and <a href="/facts/Source_code/o9J6Jv23">routines</a> for the <a href="/facts/Scalability/jh7JomPa">scalable</a> (<a href="/facts/Parallel_computing/nQzcpzQt">parallel</a>) solution of <a href="/facts/Scientific_computing/PnVD19hw">scientific applications</a> modeled by <a href="/facts/Partial_differential_equations/DyPsBlv7">partial differential equations</a>.</li> <li><a href="/facts/SLEPc/e1nYxd5T">SLEPc</a> Scalable Library for Eigenvalue Problem Computations is a <a href="/facts/PETSc/kpgPvndI">PETSc</a>-based <a href="/facts/Open_source/7X9rCdz4">open-source</a> <a href="/facts/Library_(computing)/xRzL3P7q">library</a> for the <a href="/facts/Scalability/jh7JomPa">scalable</a> (<a href="/facts/Parallel_computing/nQzcpzQt">parallel</a>) solution of eigenvalue problems.</li> <li><a href="/facts/UMFPACK/p1RWGvTk">UMFPACK</a> is a library for solving sparse linear systems, written in Ansi C. It is the backend for sparse matrices in <a href="/facts/MATLAB/qPjLISCk">MATLAB</a> and <a href="/facts/SciPy/bNcMQGc0">SciPy</a>.</li></ul> <h2 id="c"><a href="/facts/C%252B%252B/Et0F2qn9">C++</a></h2> <ul><li><a href="/facts/Adept_(C%252B%252B_library)/MAXdfUeH">Adept</a> is a combined <a href="/facts/Automatic_differentiation/dQcdhBAM">automatic differentiation</a> and <a href="/facts/Array_programming/gFx1SxIY">array</a> library.</li> <li><a href="/facts/Advanced_Simulation_Library/89AzuD0o">Advanced Simulation Library</a> is free and open source hardware accelerated multiphysics simulation software with an <a href="/facts/OpenCL/ns8y6np7">OpenCL</a>-based internal computational engine.</li> <li><a href="/facts/ALGLIB/fSduLPd2">ALGLIB</a> is an open source / commercial numerical analysis library with C++ version</li> <li><a href="/facts/Armadillo_(C%252B%252B_library)/ANyYTA2o">Armadillo</a> is a C++ linear algebra library (matrix and vector maths), aiming towards a good balance between speed and ease of use.<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a> It employs template classes, and has optional links to BLAS and LAPACK. The syntax (<a href="/facts/Application_Programming_Interface/GMlN4vUr">API</a>) is similar to <a href="/facts/MATLAB/qPjLISCk">MATLAB</a>.</li> <li><a href="/facts/Blitz%252B%252B/EzHqnDzu">Blitz++</a> is a high-performance vector mathematics library written in C++.</li> <li><a href="/facts/Boost_(C%252B%252B_libraries)/vGLGG51A">Boost.uBLAS</a> C++ libraries for numerical computation</li> <li><a href="/facts/Deal.II/RBBkBX0S">deal.II</a> is a library supporting all the finite element solution of partial differential equations.</li> <li><a href="/facts/Dlib/IAcDlHz1">Dlib</a> is a modern C++ library with easy to use linear algebra and optimization tools which benefit from optimized BLAS and LAPACK libraries.</li> <li><a href="/facts/Eigen_(C%252B%252B_library)/js8e67k3">Eigen</a> is a vector mathematics library with performance comparable with Intel's <a href="/facts/Math_Kernel_Library/nwPPAUpe">Math Kernel Library</a></li> <li><a href="/facts/Hermes_Project/675jSKJc">Hermes Project</a>: C++/Python library for rapid prototyping of space- and space-time adaptive hp-FEM solvers.</li> <li><a href="/facts/IML%252B%252B/JADYpPEz">IML++</a> is a C++ library for solving linear systems of equations, capable of dealing with dense, sparse, and distributed matrices.</li> <li><a href="/facts/IT%252B%252B/B4gdSCkR">IT++</a> is a C++ library for linear algebra (matrices and vectors), signal processing and communications. Functionality similar to MATLAB and Octave.</li> <li><a href="/facts/LAPACK%252B%252B/6sMk7odj">LAPACK++</a>, a C++ wrapper library for <a href="/facts/LAPACK/sMGe0RhF">LAPACK</a> and <a href="/facts/BLAS/T8Jq1Jpq">BLAS</a></li> <li><a href="/facts/MFEM/XzClp9aa">MFEM</a> is a free, lightweight, scalable C++ library for <a href="/facts/Finite_element_method/eUcfP1vn">finite element methods</a>.</li> <li><a href="/facts/Intel_MKL/nwPPAUpe">Intel MKL</a>, Intel Math Kernel Library (in C and C++), a library of optimized math routines for science, engineering, and financial applications, written in C/C++ and Fortran. Core math functions include BLAS, LAPACK, ScaLAPACK, sparse solvers, fast Fourier transforms, and vector math.</li> <li><a href="/facts/Mlpack/qvVhMxLL">mlpack</a> is an open-source library for machine learning, exploiting C++ language features to provide maximum performance and flexibility while providing a simple and consistent API</li> <li><a href="/facts/Matrix_Template_Library/zc5bSbqF">MTL4</a> is a generic <a href="/facts/C%252B%252B/Et0F2qn9">C++</a> template library providing sparse and dense BLAS functionality. MTL4 establishes an intuitive interface (similar to <a href="/facts/MATLAB/qPjLISCk">MATLAB</a>) and broad applicability thanks to <a href="/facts/Generic_programming/kqtqJk7p">Generic programming</a>.</li> <li>The <a href="/facts/NAG_Numerical_Library/PKd05xdo">NAG Library</a> has C++ API</li> <li><a href="/facts/Number_Theory_Library/DdzyoUnt">NTL</a> is a C++ library for number theory.</li> <li><a href="/facts/OpenFOAM/juBSzlRz">OpenFOAM</a> is an open-source C++ library for solving partial differential equations in computational fluid dynamics (CFD).</li> <li><a href="/facts/SU2_code/IGaothCJ">SU2 code</a> is an open-source library for solving partial differential equations with the finite volume or finite element method.</li> <li><a href="/facts/Trilinos/sREgsmJe">Trilinos</a> is an effort to develop algorithms and enabling technologies for the solution of large-scale, complex multi-physics engineering and scientific problems. It is a collection of <i>packages</i>.</li> <li><a href="/facts/Template_Numerical_Toolkit/AJ0djgzI">Template Numerical Toolkit</a> (TNT) linear algebra software in the public domain and entirely in the form of headers, from NIST. TNT was originally presented as a successor to Lapack++, Sparselib++, and IML++.<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a></li></ul> <h2 id="delphi"><a href="/facts/Delphi_(programming_language)/sUFUXQ8r">Delphi</a></h2> <ul><li><a href="/facts/ALGLIB/fSduLPd2">ALGLIB</a> - an open source numerical analysis library.</li></ul> <h2 id="net-framework-languages-c-f-vbnetand-powershell">.NET Framework languages <a href="/facts/C_Sharp_(programming_language)/UC2gxeyb">C#</a>, <a href="/facts/F_Sharp_(programming_language)/jdXHnYz5">F#</a>, <a href="/facts/Visual_Basic_.NET/09mPEo4q">VB.NET</a> and <a href="/facts/Windows_PowerShell/G1d10lwn">PowerShell</a></h2> <ul><li><a href="/facts/Accord.NET/qpuljvtx">Accord.NET</a> is a collection of libraries for scientific computing, including numerical linear algebra, optimization, statistics, artificial neural networks, machine learning, signal processing and computer vision. LGPLv3, partly GPLv3.</li> <li><a href="/facts/AForge.NET/V0NuKTfz">AForge.NET</a> is a computer vision and artificial intelligence library. It implements a number of genetic, fuzzy logic and machine learning algorithms with several architectures of artificial neural networks with corresponding training algorithms. LGPLv3 and partly GPLv3.</li> <li><a href="/facts/ALGLIB/fSduLPd2">ALGLIB</a> is an open source numerical analysis library with C# version. Dual licensed: GPLv2+, commercial license.</li> <li><a href="/facts/ILNumerics.Net/G91bSaIr">ILNumerics.Net</a> Commercial high performance, typesafe numerical array classes and functions for general math, FFT and linear algebra, aims .NET/mono, 32&64 bit, script-like syntax in C#, 2D & 3D plot controls, efficient memory management.</li> <li><a href="/facts/IMSL_Numerical_Libraries/H6pg7hgj">IMSL Numerical Libraries</a> have C# version (commercially licensed). IMSL .Net have announced end of life at the end of 2020.</li> <li><a href="/facts/Math.NET_Numerics/1n4Ixm0u">Math.NET Numerics</a> aims to provide methods and algorithms for numerical computations in science, engineering and everyday use. Covered topics include special functions, linear algebra, probability models, random numbers, interpolation, integral transforms and more. Free software under MIT/X11 license.</li> <li><a href="/facts/Measurement_Studio/LxXgHab0">Measurement Studio</a> is a commercial integrated suite UI controls and class libraries for use in developing test and measurement applications. The analysis class libraries provide various digital signal processing, signal filtering, signal generation, peak detection, and other general mathematical functionality.</li> <li><a href="/facts/ML.NET/VT9L7fwH">ML.NET</a> is a <a href="/facts/Free_software/IaoVtJXn">free software</a> <a href="/facts/Machine_learning/e0w0XJTu">machine learning</a> <a href="/facts/Library_(computing)/xRzL3P7q">library</a> for the <a href="/facts/C_Sharp_(programming_language)/UC2gxeyb">C#</a> programming language.<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a><a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a></li> <li>The <a href="/facts/NAG_Numerical_Library/PKd05xdo">NAG Library</a> has C# API. Commercially licensed.</li> <li><a href="/facts/NMath/4MrPp3jr">NMath</a> by <a href="/facts/CenterSpace_Software/oDuXKTHy">CenterSpace Software</a>: Commercial numerical component libraries for the .NET platform, including signal processing (FFT) classes, a linear algebra (LAPACK & BLAS) framework, and a statistics package.</li></ul> <h2 id="fortran"><a href="/facts/Fortran/m1KqjcMU">Fortran</a></h2> <ul><li><a href="/facts/BLAS/T8Jq1Jpq">BLAS</a> (Basic Linear Algebra Subprograms) is a de facto <a href="/facts/Application_programming_interface/GMlN4vUr">application programming interface</a> standard for publishing libraries to perform basic <a href="/facts/Linear_algebra/8VaB4VWk">linear algebra</a> operations such as <a href="/facts/Vector_space/M1pxMLx2">vector</a> and <a href="/facts/Matrix_multiplication/lYDB6Ro2">matrix multiplication</a>.</li> <li><a href="/facts/CERN_Program_Library/T9bCUSbB">CERNLIB</a> is a collection of <a href="/facts/FORTRAN_77/m1KqjcMU">FORTRAN 77</a> libraries and modules.</li> <li><a href="/facts/EISPACK/qASUMUFW">EISPACK</a> is a <a href="/facts/Software_library/xRzL3P7q">software library</a> for <a href="/facts/Numerical_computation/QT9cYa9z">numerical computation</a> of <a href="/facts/Eigenvalues/8TjEoT8u">eigenvalues</a> and <a href="/facts/Eigenvectors/8TjEoT8u">eigenvectors</a> of matrices,<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a> written in <a href="/facts/FORTRAN/m1KqjcMU">FORTRAN</a>. It contains subroutines for calculating the eigenvalues of nine classes of <a href="/facts/Matrix_(Mathematics)/qa8FI4ko">matrices</a>: complex general, complex <a href="/facts/Hermitian/UbfypD8h">Hermitian</a>, real general, real symmetric, real symmetric <a href="/facts/Band_matrix/Iz803N35">banded</a>, real symmetric tridiagonal, special real tridiagonal, generalized real, and generalized real symmetric matices.</li> <li><a href="/facts/IMSL_Numerical_Libraries/H6pg7hgj">IMSL Numerical Libraries</a> are cross-platform libraries containing a comprehensive set of mathematical and statistical functions that can be embedded in a users application.</li> <li><a href="/facts/Harwell_Subroutine_Library/PIbfr4zw">Harwell Subroutine Library</a> is a collection of <a href="/facts/Fortran_77/m1KqjcMU">Fortran 77</a> and 95 codes that address core problems in numerical analysis.</li> <li><a href="/facts/LAPACK/sMGe0RhF">LAPACK</a>,<a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a><a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a> the Linear Algebra PACKage, is a <a href="/facts/Software_library/xRzL3P7q">software library</a> for <a href="/facts/Numerical_computation/QT9cYa9z">numerical computing</a> originally written in <a href="/facts/Fortran/m1KqjcMU">FORTRAN 77</a> and now written in <a href="/facts/Fortran/m1KqjcMU">Fortran 90</a>.</li> <li><a href="/facts/LINPACK/2VtBJ2va">LINPACK</a> is a software <a href="/facts/Library_(computer_science)/xRzL3P7q">library</a> for performing numerical <a href="/facts/Linear_algebra/8VaB4VWk">linear algebra</a> on digital computers.<a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a><a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a><a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a> It was written in <a href="/facts/Fortran/m1KqjcMU">Fortran</a> by <a href="/facts/Jack_Dongarra/xBWGdDT9">Jack Dongarra</a>, Jim Bunch, <a href="/facts/Cleve_Moler/o0wxumjp">Cleve Moler</a>, and Pete Stewart, and was intended for use on <a href="/facts/Supercomputer/HT9NwGAN">supercomputers</a> in the 1970s and early 1980s. It has been largely superseded by <a href="/facts/LAPACK/sMGe0RhF">LAPACK</a>, which will run more efficiently on modern architectures.</li> <li><a href="/facts/Lis_(linear_algebra_library)/LxWHXaJQ">Lis</a> is a scalable parallel library for solving systems of linear equations and eigenvalue problems using iterative methods.</li> <li><a href="/facts/MINPACK/8so70MtG">MINPACK</a> is a library of <a href="/facts/FORTRAN/m1KqjcMU">FORTRAN</a> subroutines for the solving of systems of nonlinear equations, or the <a href="/facts/Least_squares/50jIwbxC">least squares</a> minimization of the residual of a set of <a href="/facts/System_of_linear_equations/fk9CFdgp">linear</a> or nonlinear equations.</li> <li>The <a href="/facts/NAG_Numerical_Library/PKd05xdo">NAG Fortran Library</a> is a collection of mathematical and statistical routines for Fortran.</li> <li><a href="/facts/Naval_Observatory_Vector_Astrometry_Subroutines/sGVmsF4W">NOVAS</a> is a software library for astrometry-related numerical computations. Both <a href="/facts/Fortran/m1KqjcMU">Fortran</a> and <a href="/facts/C_(programming_language)/Ky2No763">C</a> versions are available.</li> <li><a href="/facts/Netlib/4QQJ2DKk">Netlib</a> is a repository of scientific computing software which contains a large number of separate programs and libraries including <a href="/facts/BLAS/T8Jq1Jpq">BLAS</a>, <a href="/facts/EISPACK/qASUMUFW">EISPACK</a>, <a href="/facts/LAPACK/sMGe0RhF">LAPACK</a> and others.</li> <li><a href="/facts/Physics_Analysis_Workstation/ApHa8KMC">PAW</a> is a free <a href="/facts/Data_analysis/CNtARxLW">data analysis</a> package developed at <a href="/facts/CERN/y1gwRchm">CERN</a>.</li> <li><a href="/facts/Portable%2c_Extensible_Toolkit_for_Scientific_Computation/kpgPvndI">Portable, Extensible Toolkit for Scientific Computation</a> (PETSc), is a suite of <a href="/facts/Data_structures/yNsNvL1I">data structures</a> and <a href="/facts/Source_code/o9J6Jv23">routines</a> for the <a href="/facts/Scalability/jh7JomPa">scalable</a> (<a href="/facts/Parallel_computing/nQzcpzQt">parallel</a>) solution of <a href="/facts/Scientific_computing/PnVD19hw">scientific applications</a> modeled by <a href="/facts/Partial_differential_equations/DyPsBlv7">partial differential equations</a>.</li> <li><a href="/facts/QUADPACK/yqYHHRV4">QUADPACK</a> is a <a href="/facts/FORTRAN_77/m1KqjcMU">FORTRAN 77</a> library for <a href="/facts/Numerical_integration/MwJnvcDV">numerical integration</a> of one-dimensional functions</li> <li><a href="/facts/SLATEC/cG1YDbXc">SLATEC</a> is a <a href="/facts/FORTRAN_77/m1KqjcMU">FORTRAN 77</a> library of over 1400 general purpose mathematical and statistical routines.</li> <li><a href="/facts/SOFA_(Astronomy)/ve8wCnrz">SOFA</a> is a collection of subroutines that implement official <a href="/facts/International_Astronomical_Union/GMFPImXo">IAU</a> <a href="/facts/Algorithms/fnl5NmRt">algorithms</a> for <a href="/facts/Astronomy/0ArJVM1p">astronomical</a> computations. Both <a href="/facts/Fortran/m1KqjcMU">Fortran</a> and <a href="/facts/C_(programming_language)/Ky2No763">C</a> versions are available.</li> <li><a href="/facts/ARPACK/KpvjAu67">ARPACK</a> is a collection of Fortran77 subroutines designed to solve large scale eigenvalue problems.</li> <li><a href="/facts/BLIS_(software)/V6volqq5">BLIS</a> is an open-source framework for implementing a superset of BLAS functionality for specific processor types that was awarded the <a href="/facts/J._H._Wilkinson_Prize_for_Numerical_Software/5pQ82QP5">J. H. Wilkinson Prize for Numerical Software</a>.</li></ul> <h2 id="java"><a href="/facts/Java_(programming_language)/9ScgFyAL">Java</a></h2> <ul><li><a href="/facts/Apache_Commons/wTW3nDuz">Apache Commons</a>, is an <a href="/facts/Open_source/7X9rCdz4">open-source</a> for creating reusable Java components. It has numerical packages for linear algebra and non-linear optimization.</li> <li><a href="/facts/Colt_(libraries)/EDESm0bX">Colt</a> provides a set of Open Source Libraries for High Performance Scientific and Technical Computing.</li> <li><a href="/facts/Efficient_Java_Matrix_Library/NWRRnhPu">Efficient Java Matrix Library (EJML)</a> is an open-source linear algebra library for manipulating dense matrices.</li> <li><a href="/facts/JAMA_(numerical_linear_algebra_library)/8WNwtINt">JAMA</a>, a numerical <a href="/facts/Linear_algebra/8VaB4VWk">linear algebra</a> toolkit for the <a href="/facts/Java_programming_language/9ScgFyAL">Java programming language</a>. No active development has taken place since 2005, but it still one of the more popular linear algebra packages in Java.</li> <li><a href="/facts/Jblas%3a_Linear_Algebra_for_Java/kkGz7vo6">Jblas: Linear Algebra for Java</a>, a linear algebra library which is an easy to use wrapper around <a href="/facts/BLAS/T8Jq1Jpq">BLAS</a> and <a href="/facts/LAPACK/sMGe0RhF">LAPACK</a>.</li> <li><a href="/facts/Parallel_Colt/XkEXvF85">Parallel Colt</a> is an open source library for scientific computing. A parallel extension of <a href="/facts/Colt_(libraries)/EDESm0bX">Colt</a>.</li> <li><a href="/facts/Matrix_Toolkit_Java/cUpyB9jE">Matrix Toolkit Java</a> is a linear algebra library based on <a href="/facts/BLAS/T8Jq1Jpq">BLAS</a> and <a href="/facts/LAPACK/sMGe0RhF">LAPACK</a>.</li> <li><a href="/facts/OjAlgo/ytRqsY5f">ojAlgo</a> is an open source Java library for mathematics, linear algebra and optimisation.</li> <li><a href="/facts/Exp4j/rV2eGHxd">exp4j</a> is a small <a href="/facts/Java_(programming_language)/9ScgFyAL">Java</a> library for evaluation of mathematical expressions.</li> <li><a href="/facts/SuanShu_numerical_library/mV3rmW6q">SuanShu</a> is an open-source Java math library. It supports numerical analysis, statistics and optimization.</li> <li><a href="https://github.com/kspalaiologos/Maja">Maja</a> is an open-source Java library focusing primarily on correct implementations of various <a href="/facts/Special_functions/JETSeucA">special functions</a>.</li></ul> <h2 id="ocaml"><a href="/facts/OCaml/ThBGLND8">OCaml</a></h2> <ul><li><a href="/facts/OCaml/ThBGLND8">OCaml</a> programming language has support for array programming in the standard library, also with an specific module named bigarrays for multi-dimensional, numerical arrays, with both C and Fortran layout options. A comprehensive support of numerical computations is provided by the library <a href="/facts/Owl_Scientific_Computing/v8tTDzbs">Owl Scientific Computing</a> which provides methods for statistics, linear algebra (using OpenBLAS), differential equations, algorithmic differentiation, Fourier fast transform, or deep neural networks.<a class="footnote-ref" id="fnref:11" href="#fn:11"><sup>11</sup></a> Other numerical libraries in OCaml are <a href="https://mmottl.github.io/lacaml/">Lacaml</a> that interfaces BLAS and LAPACK Fortran/C libraries, <a href="https://github.com/Chris00/L-BFGS-ocaml">L-BFGS-ocaml</a> (OCaml bindings for L-BFGS). For visualization there are libraries for plotting using <a href="/facts/PLplot/ldTExbD1">PLplot</a>, <a href="/facts/Gnuplot/fWoweJQJ">gnuplot</a> or <a href="/facts/Matplotlib/JQSu8CBj">matplotlib</a>.</li></ul> <h2 id="perl"><a href="/facts/Perl/fx31kjlT">Perl</a></h2> <ul><li><a href="/facts/Perl_Data_Language/wzAaHo98">Perl Data Language</a> gives standard Perl the ability to compactly store and speedily manipulate the large <i>N</i>-dimensional data arrays.<a class="footnote-ref" id="fnref:12" href="#fn:12"><sup>12</sup></a> It can perform complex and matrix maths, and has interfaces for the <a href="/facts/GNU_Scientific_Library/WKX9L554">GNU Scientific Library</a>, <a href="/facts/LINPACK/2VtBJ2va">LINPACK</a>, <a href="/facts/PROJ/gcvPmjpU">PROJ</a>, and plotting with <a href="/facts/PGPLOT/qpIEAz4d">PGPLOT</a>. There are libraries on <a href="/facts/CPAN/MB7Iv662">CPAN</a> adding support for the linear algebra library <a href="/facts/LAPACK/sMGe0RhF">LAPACK</a>,<a class="footnote-ref" id="fnref:13" href="#fn:13"><sup>13</sup></a> the Fourier transform library <a href="/facts/Fastest_Fourier_Transform_in_the_West/Q7STPyIk">FFTW</a>,<a class="footnote-ref" id="fnref:14" href="#fn:14"><sup>14</sup></a> and plotting with <a href="/facts/Gnuplot/fWoweJQJ">gnuplot</a>,<a class="footnote-ref" id="fnref:15" href="#fn:15"><sup>15</sup></a> and <a href="/facts/PLplot/ldTExbD1">PLplot</a>.<a class="footnote-ref" id="fnref:16" href="#fn:16"><sup>16</sup></a></li></ul> <h2 id="python"><a href="/facts/Python_(programming_language)/YbuGqofa">Python</a></h2> <ul><li><a href="/facts/NumPy/T6FnhWWD">NumPy</a>, a BSD-licensed library that adds support for the manipulation of large, multi-dimensional arrays and matrices; it also includes a large collection of high-level mathematical functions. NumPy serves as the backbone for a number of other numerical libraries, notably <a href="/facts/SciPy/bNcMQGc0">SciPy</a>. De facto standard for matrix/tensor operations in Python.</li> <li><a href="/facts/Pandas_(software)/VKkTK8RL">Pandas</a>, a library for data manipulation and analysis.</li> <li><a href="/facts/SageMath/5mzh5TlB">SageMath</a> is a large mathematical software application which integrates the work of nearly 100 <a href="/facts/Free_software/IaoVtJXn">free software</a> projects and supports linear algebra, combinatorics, numerical mathematics, calculus, and more.<a class="footnote-ref" id="fnref:17" href="#fn:17"><sup>17</sup></a></li> <li><a href="/facts/SciPy/bNcMQGc0">SciPy</a>,<a class="footnote-ref" id="fnref:18" href="#fn:18"><sup>18</sup></a><a class="footnote-ref" id="fnref:19" href="#fn:19"><sup>19</sup></a><a class="footnote-ref" id="fnref:20" href="#fn:20"><sup>20</sup></a> a large BSD-licensed library of scientific tools. De facto standard for scientific computations in Python.</li> <li><a href="/facts/ScientificPython/0XJBIufP">ScientificPython</a>, a library with a different set of scientific tools</li> <li><a href="/facts/SymPy/vWSsBCG0">SymPy</a>, a library based on New BSD license for symbolic computation. Features of Sympy range from basic symbolic arithmetic to calculus, algebra, discrete mathematics and quantum physics.</li></ul> <h2 id="others">Others</h2> <ul><li><a href="/facts/XNUMBERS/HrdBhQpv">XNUMBERS</a> – multi-precision floating-Point computing and numerical methods for <a href="/facts/Microsoft_Excel/Ezal6G75">Microsoft Excel</a>.</li> <li><a href="/facts/INTLAB/cI4TAqYV">INTLAB</a> – <a href="/facts/Interval_arithmetic/1ylnKraf">interval arithmetic</a> library for <a href="/facts/MATLAB/qPjLISCk">MATLAB</a>.<a class="footnote-ref" id="fnref:21" href="#fn:21"><sup>21</sup></a><a class="footnote-ref" id="fnref:22" href="#fn:22"><sup>22</sup></a><a class="footnote-ref" id="fnref:23" href="#fn:23"><sup>23</sup></a><a class="footnote-ref" id="fnref:24" href="#fn:24"><sup>24</sup></a></li></ul> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/List_of_computer_algebra_systems/e5m8nyK2">List of computer algebra systems</a></li> <li><a href="/facts/Comparison_of_numerical-analysis_software/VDvWr7LR">Comparison of numerical-analysis software</a></li> <li><a href="/facts/List_of_information_graphics_software/HyDmFJ01">List of information graphics software</a></li> <li><a href="/facts/List_of_programming_languages_by_type/XuWNoawk">List of numerical analysis programming languages</a></li> <li><a href="/facts/List_of_numerical-analysis_software/yKFzDBDK">List of numerical-analysis software</a></li> <li><a href="/facts/List_of_open_source_code_libraries/Ig3Wv2tJ">List of open source code libraries</a></li> <li><a href="/facts/List_of_optimization_software/DWHyr6mj">List of optimization software</a></li> <li><a href="/facts/List_of_statistical_software/QFqfrzWo">List of statistical software</a></li></ul> <h2 id="external-links">External links</h2> <ul><li><a href="http://mathforum.org/library/topics/num_analysis/">The Math Forum - Math Libraries</a>, an extensive list of mathematical libraries with short descriptions</li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Sanderson, C., & Curtin, R. (2016). Armadillo: a template-based C++ library for linear algebra. Journal of Open Source Software, 1(2), 26. <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Pozo, Roldan (1997). "Template Numerical Toolkit for Linear Algebra: High Performance Programming With C++ and the Standard Template Library". The International Journal of Supercomputer Applications and High Performance Computing. 11 (3). Association for Computing Machinery: 251–263. doi:10.1177/109434209701100307. Retrieved 15 October 2024. <a href="https://dl.acm.org/doi/abs/10.1177/109434209701100307" target="_blank">https://dl.acm.org/doi/abs/10.1177/109434209701100307</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>David Ramel (2018-05-08). "Open Source, Cross-Platform ML.NET Simplifies Machine Learning -- Visual Studio Magazine". Visual Studio Magazine. Retrieved 2018-05-10. <a href="https://visualstudiomagazine.com/articles/2018/05/08/ml-net-framework.aspx" target="_blank">https://visualstudiomagazine.com/articles/2018/05/08/ml-net-framework.aspx</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Kareem Anderson (2017-05-09). "Microsoft debuts ML.NET cross-platform machine learning framework". On MSFT. Retrieved 2018-05-10. <a href="https://www.onmsft.com/news/microsoft-debuts-ml-net-cross-platform-machine-learning-framework" target="_blank">https://www.onmsft.com/news/microsoft-debuts-ml-net-cross-platform-machine-learning-framework</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>Smith, B. T., Boyle, J. M., Garbow, B. S., Ikebe, Y., Klema, V. C., & Moler, C. B. (2013). Matrix eigensystem routines-EISPACK guide (Vol. 6). Springer. <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>Anderson, E., Bai, Z., Bischof, C., Blackford, S., Dongarra, J., Du Croz, J., ... & Sorensen, D. (1999). LAPACK Users' guide (Vol. 9). SIAM. <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>Demmel, J. (1989, December). LAPACK: A portable linear algebra library for supercomputers. In IEEE Control Systems Society Workshop on Computer-Aided Control System Design (pp. 1-7). IEEE. <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>Dongarra, J. J., Moler, C. B., Bunch, J. R., & Stewart, G. W. (1979). LINPACK users' guide. Society for Industrial and Applied Mathematics. <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>Dongarra, J. J., Luszczek, P., & Petitet, A. (2003). The LINPACK benchmark: past, present and future. Concurrency and Computation: practice and experience, 15(9), 803-820. <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li> <li id="fn:10"><p>Dongarra, J. J. (1987, June). The LINPACK benchmark: An explanation. In International Conference on Supercomputing (pp. 456-474). Springer, Berlin, Heidelberg. <a href="#fnref:10" class="footnote-back-ref">↩</a></p></li> <li id="fn:11"><p>"Owl Online Tutorial". Owl Online Tutorial. Retrieved 2025-02-09. <a href="https://ocaml.xyz/tutorial/" target="_blank">https://ocaml.xyz/tutorial/</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></p></li> <li id="fn:12"><p>"Perl Data Language - metacpan.org". July 26, 2021. <a href="https://metacpan.org/release/PDL" target="_blank">https://metacpan.org/release/PDL</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></p></li> <li id="fn:13"><p>"PDL::LinearAlgebra - Linear Algebra utils for PDL - metacpan.org". July 26, 2021. <a href="https://metacpan.org/dist/PDL-LinearAlgebra" target="_blank">https://metacpan.org/dist/PDL-LinearAlgebra</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></p></li> <li id="fn:14"><p>"PDL::FFTW3 - PDL interface to the Fastest Fourier Transform in the West - metacpan.org". July 26, 2021. <a href="https://metacpan.org/dist/PDL-FFTW3" target="_blank">https://metacpan.org/dist/PDL-FFTW3</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></p></li> <li id="fn:15"><p>"PDL::Graphics::Gnuplot - Gnuplot-based plotting for PDL - metacpan.org". July 26, 2021. <a href="https://metacpan.org/dist/PDL-Graphics-Gnuplot" target="_blank">https://metacpan.org/dist/PDL-Graphics-Gnuplot</a> <a href="#fnref:15" class="footnote-back-ref">↩</a></p></li> <li id="fn:16"><p>"PDL::Graphics::PLplot - Object-oriented interface from perl/PDL to the PLPLOT plotting library - metacpan.org". July 26, 2021. <a href="https://metacpan.org/dist/PDL-Graphics-PLplot" target="_blank">https://metacpan.org/dist/PDL-Graphics-PLplot</a> <a href="#fnref:16" class="footnote-back-ref">↩</a></p></li> <li id="fn:17"><p>Zimmermann, P., Casamayou, A., Cohen, N., Connan, G., Dumont, T., Fousse, L., ... & Bray, E. (2018). Computational Mathematics with SageMath. SIAM. <a href="#fnref:17" class="footnote-back-ref">↩</a></p></li> <li id="fn:18"><p>Jones, E., Oliphant, T., & Peterson, P. (2001). SciPy: Open source scientific tools for Python. <a href="#fnref:18" class="footnote-back-ref">↩</a></p></li> <li id="fn:19"><p>Bressert, E. (2012). SciPy and NumPy: an overview for developers. " O'Reilly Media, Inc.". <a href="#fnref:19" class="footnote-back-ref">↩</a></p></li> <li id="fn:20"><p>Blanco-Silva, F. J. (2013). Learning SciPy for numerical and scientific computing. Packt Publishing Ltd. <a href="#fnref:20" class="footnote-back-ref">↩</a></p></li> <li id="fn:21"><p>S.M. 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