The following tables provide a comparison of linear algebra software libraries, either specialized or general purpose libraries with significant linear algebra coverage.
Dense linear algebra
General information Creator Language First public release Latest stable version Source code availability License Notes ALGLIBBochkanov, S., & Bystritsky, V. (2011). ALGLIB-a cross-platform numerical analysis and data processing library. ALGLIB Project. ALGLIB Project C++, C#, Python, FreePascal 2006 4.00.0 / 05.2023 GPL/commercial General purpose numerical analysis library with C++, C#, Python, FreePascal interfaces. ArmadilloSanderson, C., & Curtin, R. (2016). Armadillo: a template-based C++ library for linear algebra. Journal of Open Source Software, 1(2), 26.Sanderson, C. (2010). Armadillo: An open source C++ linear algebra library for fast prototyping and computationally intensive experiments (p. 84). Technical report, NICTA. NICTA C++ 2009 12.6.6 / 10.2023 Apache License 2.0 C++ template library for linear algebra; includes various decompositions and factorisations; syntax (API) is similar to MATLAB. ATLAS R. Clint Whaley et al. C 2001 3.10.3 / 07.2016 BSD Automatically tuned implementation of BLAS. Also includes LU and Cholesky decompositions. Blaze K. Iglberger et al. C++ 2012 3.8 / 08.2020 BSD Blaze is an open-source, high-performance C++ math library for dense and sparse arithmetic. Blitz++ Todd Veldhuizen C++ ? 1.0.2 / 10.2019 GPL Blitz++ is a C++ template class library that provides high-performance multidimensional array containers for scientific computing. Boost uBLAS J. Walter, M. Koch C++ 2000 1.84.0 / 12.2023 Boost Software License uBLAS is a C++ template class library that provides BLAS level 1, 2, 3 functionality for dense, packed and sparse matrices. Dlib Davis E. King C++ 2006 19.24.2 / 05.2023 Boost C++ template library; binds to optimized BLAS such as the Intel MKL; Includes matrix decompositions, non-linear solvers, and machine learning tooling Eigen Benoît Jacob C++ 2008 3.4.0 / 08.2021 MPL2 Eigen is a C++ template library for linear algebra: matrices, vectors, numerical solvers, and related algorithms. Fastor R. Poya, A. J. Gil and R. Ortigosa C++ 2016 0.6.4 / 06.2023 MIT License Fastor is a high performance tensor (fixed multi-dimensional array) library for modern C++. GNU Scientific LibraryGough, B. (2009). GNU scientific library reference manual. Network Theory Ltd. GNU Project C, C++ 1996 2.7.1 / 11.2021 GPL General purpose numerical analysis library. Includes some support for linear algebra. IMSL Numerical Libraries Rogue Wave Software C, Java, C#, Fortran, Python 1970 many components Proprietary General purpose numerical analysis library. LAPACKAnderson, E., Bai, Z., Bischof, C., Blackford, S., Dongarra, J., Du Croz, J., ... & Sorensen, D. (1999). LAPACK Users' guide. SIAM.Anderson, E., Bai, Z., Dongarra, J., Greenbaum, A., McKenney, A., Du Croz, J., ... & Sorensen, D. (1990, November). LAPACK: A portable linear algebra library for high-performance computers. In Proceedings of the 1990 ACM/IEEE conference on Supercomputing (pp. 2–11). IEEE Computer Society Press. Fortran 1992 3.12.0 / 11.2023 3-clause BSD Numerical linear algebra library with long history librsb Michele Martone C, Fortran, M4 2011 1.2.0 / 09.2016 GPL High-performance multi-threaded primitives for large sparse matrices. Support operations for iterative solvers: multiplication, triangular solve, scaling, matrix I/O, matrix rendering. Many variants: e.g.: symmetric, hermitian, complex, quadruple precision. oneMKL Intel C, C++, Fortran 2003 2023.1 / 03.2023 Intel Simplified Software License Numerical analysis library optimized for Intel CPUs and GPUs. C++ SYCL based reference API implementation available in source for free. Math.NET Numerics C. Rüegg, M. Cuda, et al. C# 2009 5.0.0 / 04.2022 MIT License C# numerical analysis library with linear algebra support Matrix Template Library Jeremy Siek, Peter Gottschling, Andrew Lumsdaine, et al. C++ 1998 4.0 / 2018 Boost Software License High-performance C++ linear algebra library based on Generic programming NAG Numerical Library The Numerical Algorithms Group C, Fortran 1971 many components Proprietary General purpose numerical analysis library. NMath CenterSpace Software C# 2003 7.1 / 12.2019 Proprietary Math and statistical libraries for the .NET Framework SciPyJones, 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. Enthought Python 2001 1.11.1 / 6.2023 BSD Based on Python Xtensor S. Corlay, W. Vollprecht, J. Mabille et al. C++ 2016 0.21.10 / 11.2020 3-clause BSD Xtensor is a C++ library meant for numerical analysis with multi-dimensional array expressions, broadcasting and lazy computing.
Matrix types and operations Matrix types (special types like bidiagonal/tridiagonal are not listed): Real – general (nonsymmetric) real Complex – general (nonsymmetric) complex SPD – symmetric positive definite (real) HPD – Hermitian positive definite (complex) SY – symmetric (real) HE – Hermitian (complex) BND – band
Operations: TF – triangular factorizations (LU, Cholesky) OF – orthogonal factorizations (QR, QL, generalized factorizations) EVP – eigenvalue problems SVD – singular value decomposition GEVP – generalized EVP GSVD – generalized SVD
Real Complex SPD HPD SY HE BND TF OF EVP SVD GEVP GSVD ALGLIB ATLAS Dlib GNU Scientific Library ILNumerics.Net IMSL Numerical Libraries LAPACK oneMKL NAG Numerical Library NMath SciPy (Python packages) Eigen Armadillo
References
External links