List of numerical libraries

This is a list of notable numerical libraries, which are libraries used in software development for performing numerical calculations. It is not a complete listing but is instead a list of numerical libraries with articles on Wikipedia, with few exceptions.

The choice of a typical library depends on a diverse range of requirements such as: desired features (e.g.: large dimensional linear algebra, parallel computation, partial differential equations), commercial/opensource nature, readability of API, portability or platform/compiler dependence (for e.g.: Linux, Windows, Visual C++, GCC), performance in speed, ease-of-use, continued support from developers, standard compliance, specialized optimization in code for specific application scenarios or even the size of the code-base to be installed.

As we find comprehensive surveys rarely available, there is almost always (at least initially) a difficult choice among a number of possible libraries. Often it tends to be at the discretion of the user based on his own taste and comforts, only due to the lack of proper information.

Multi-language
  • ALGLIB is an open source numerical analysis library which may be used from C++, C#, FreePascal, Delphi, VBA.
  • ArrayFire is a high performance open source software library for parallel computing with an easy-to-use API.
  • IMSL Numerical Libraries are libraries of numerical analysis functionality implemented in standard programming languages like C, Java, C# .NET, Fortran, and Python.
  • The NAG Library 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).
  • GNU Octave 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.
  • librsb is an open source library for high performance sparse matrix computations providing multi-threaded primitives to build iterative solvers (implements also the Sparse BLAS standard). It can be used from C, C++, Fortran, and a dedicated GNU Octave package.

C

C++
  • Adept is a combined automatic differentiation and array library.
  • Advanced Simulation Library is free and open source hardware accelerated multiphysics simulation software with an OpenCL-based internal computational engine.
  • ALGLIB is an open source / commercial numerical analysis library with C++ version
  • Armadillo is a C++ linear algebra library (matrix and vector maths), aiming towards a good balance between speed and ease of use.[1] It employs template classes, and has optional links to BLAS and LAPACK. The syntax (API) is similar to MATLAB.
  • Blaze is an open-source, high-performance C++ math library for dense and sparse arithmetic.
  • Blitz++ is a high-performance vector mathematics library written in C++.
  • Boost.uBLAS C++ libraries for numerical computation
  • deal.II is a library supporting all the finite element solution of partial differential equations.
  • Dlib is a modern C++ library with easy to use linear algebra and optimization tools which benefit from optimized BLAS and LAPACK libraries.
  • Eigen is a vector mathematics library with performance comparable with Intel's Math Kernel Library
  • Hermes Project: C++/Python library for rapid prototyping of space- and space-time adaptive hp-FEM solvers.
  • IML++ is a C++ library for solving linear systems of equations, capable of dealing with dense, sparse, and distributed matrices.
  • IT++ is a C++ library for linear algebra (matrices and vectors), signal processing and communications. Functionality similar to MATLAB and Octave.
  • LAPACK++, a C++ wrapper library for LAPACK and BLAS
  • MFEM is a free, lightweight, scalable C++ library for finite element methods.
  • Intel MKL, 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.
  • mlpack 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
  • MTL4 is a generic C++ template library providing sparse and dense BLAS functionality. MTL4 establishes an intuitive interface (similar to MATLAB) and broad applicability thanks to Generic programming.
  • The NAG Library has C++ API
  • NTL is a C++ library for number theory.
  • Trilinos 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 packages.

Delphi
  • Analytics & Physics: commercial Delphi libraries for symbolic and numerical calculations (including symbolic derivatives) and working with physical values and units of measurement.
  • ALGLIB - an open source numerical analysis library.

.NET Framework languages C#, F#, VB.NET and PowerShell
  • Accord.NET 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.
  • AForge.NET 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.
  • ALGLIB is an open source numerical analysis library with C# version. Dual licensed: GPLv2+, commercial license.
  • ILNumerics.Net 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.
  • IMSL Numerical Libraries have C# version (commercially licensed). IMSL .Net have announced end of life at the end of 2020.
  • Math.NET Numerics aims to provide methods and algorithms for numerical computations in science, engineering and every day use. Covered topics include special functions, linear algebra, probability models, random numbers, interpolation, integral transforms and more. Free software under MIT/X11 license.
  • Measurement Studio 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.
  • ML.NET is a free software machine learning library for the C# programming language.[2][3]
  • The NAG Library has C# API. Commercially licensed.
  • NMath by CenterSpace Software: Commercial numerical component libraries for the .NET platform, including signal processing (FFT) classes, a linear algebra (LAPACK & BLAS) framework, and a statistics package.

Fortran

Java
  • ND4J is an open-source library that supports n-dimensional (ND) arrays, similar to NumPy. It runs on distributed GPUs or CPUs cross-platform, and leverages Spark for parallel computation. It supports the deep learning library Deeplearning4j.
  • Apache Commons, is an open-source for creating reusable Java components. It has numerical packages for linear algebra and non-linear optimization.
  • Colt provides a set of Open Source Libraries for High Performance Scientific and Technical Computing.
  • Efficient Java Matrix Library (EJML) is an open-source linear algebra library for manipulating dense matrices.
  • JAMA, a numerical linear algebra toolkit for the Java programming language. No active development has taken place since 2005, but it still one of the more popular linear algebra packages in Java.
  • Jblas: Linear Algebra for Java, a linear algebra library which is an easy to use wrapper around BLAS and LAPACK.
  • jDSP, a library of digital signal processing tools written in Java aimed at providing functionalities as available in scipy-signal package for Python.
  • Parallel Colt is an open source library for scientific computing. A parallel extension of Colt.
  • Matrix Toolkit Java is a linear algebra library based on BLAS and LAPACK.
  • ojAlgo is an open source Java library for mathematics, linear algebra and optimisation.
  • exp4j is a small Java library for evaluation of mathematical expressions.

Scala
  • ND4S is a scientific computing library for Scala that includes support for n-dimensional arrays on the JVM.

Perl
  • Perl Data Language gives standard Perl the ability to compactly store and speedily manipulate the large N-dimensional data arrays.

Python
  • NumPy (former numeric), 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 SciPy. De facto standard for matrix/tensor operations in Python.
  • Pandas a library for data manipulation and analysis.
  • SageMath is a large mathematical software application which integrates the work of nearly 100 free software projects and supports linear algebra, combinatorics, numerical mathematics, calculus, and more.[10]
  • SciPy,[11][12][13] a large BSD-licensed library of scientific tools. De facto standard for scientific computations in Python.
  • ScientificPython, a library with a different set of scientific tools
  • SymPy, 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.

Others

See also

References
  1. Sanderson, C., & Curtin, R. (2016). Armadillo: a template-based C++ library for linear algebra. Journal of Open Source Software, 1(2), 26.
  2. David Ramel (2018-05-08). "Open Source, Cross-Platform ML.NET Simplifies Machine Learning -- Visual Studio Magazine". Visual Studio Magazine. Retrieved 2018-05-10.
  3. Kareem Anderson (2017-05-09). "Microsoft debuts ML.NET cross-platform machine learning framework". On MSFT. Retrieved 2018-05-10.
  4. 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.
  5. Anderson, E., Bai, Z., Bischof, C., Blackford, S., Dongarra, J., Du Croz, J., ... & Sorensen, D. (1999). LAPACK Users' guide (Vol. 9). SIAM.
  6. 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.
  7. Dongarra, J. J., Moler, C. B., Bunch, J. R., & Stewart, G. W. (1979). LINPACK users' guide. Society for Industrial and Applied Mathematics.
  8. 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.
  9. Dongarra, J. J. (1987, June). The LINPACK benchmark: An explanation. In International Conference on Supercomputing (pp. 456-474). Springer, Berlin, Heidelberg.
  10. Zimmermann, P., Casamayou, A., Cohen, N., Connan, G., Dumont, T., Fousse, L., ... & Bray, E. (2018). Computational Mathematics with SageMath. SIAM.
  11. Jones, E., Oliphant, T., & Peterson, P. (2001). SciPy: Open source scientific tools for Python.
  12. Bressert, E. (2012). SciPy and NumPy: an overview for developers. " O'Reilly Media, Inc.".
  13. Blanco-Silva, F. J. (2013). Learning SciPy for numerical and scientific computing. Packt Publishing Ltd.
  14. S.M. Rump: INTLAB – INTerval LABoratory. In Tibor Csendes, editor, Developments in Reliable Computing, pages 77–104. Kluwer Academic Publishers, Dordrecht, 1999.
  15. Moore, R. E., Kearfott, R. B., & Cloud, M. J. (2009). Introduction to Interval Analysis. Society for Industrial and Applied Mathematics.
  16. Rump, S. M. (2010). Verification methods: Rigorous results using floating-point arithmetic. Acta Numerica, 19, 287–449.
  17. Hargreaves, G. I. (2002). Interval analysis in MATLAB. Numerical Algorithms, (2009.1).
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