Comparison of linear algebra libraries

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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[edit]

General information[edit]

Creator Language First public release Latest stable version Source code availability License Notes
ALGLIB Sergey Bochkanov C++, C#, FreePascal, VBA 2006 2.6.0 / 06.2010 Free GPL General purpose numerical analysis library. Uses automatic code generation to support several programming languages.
ATLAS R. Clint Whaley et al. C 2001 3.8.3 / 02.2009 Free BSD Automatically tuned implementation of BLAS. Also includes LU and Cholesky decompositions.
DMelt S.Chekanov et al. Java 2005 2015 GPL BSD A general purpose. Includes JBLAS and JLAPACK
GNU Scientific Library GNU Project C, C++ 1996 1.16 / 07.2013 Free 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 Non-free Proprietary General purpose numerical analysis library.
LAPACK Fortran 1992 3.4.0 / 11.2011 Free 3-clause BSD Numerical linear algebra library with long history
MKL Intel C++, Fortran 2003 10.3 update 8 / 2011 Non-free Proprietary Numerical analysis library optimized for Intel CPUs
NAG Numerical Library The Numerical Algorithms Group C, Fortran 1971 many components Non-free Proprietary General purpose numerical analysis library.
NMath CenterSpace Software C# 2003 4.0 / November 2009 Non-free Proprietary Math and statistical libraries for the .NET Framework
SciPy Enthought Python 2001 0.8.0 / 2010 Free BSD Based on Python
Eigen Benoît Jacob C++ 2008 3.2.8 / 2016 Free MPL2 Eigen is a C++ template library for linear algebra: matrices, vectors, numerical solvers, and related algorithms.
Armadillo NICTA C++ 2009 4.650 / 2015 Free MPL2 C++ template library for linear algebra; includes various decompositions and factorisations; syntax (API) is similar to MATLAB.
Blaze Klaus Iglberger C++ 2012 Free BSD Blaze is an open-source, high-performance C++ math library for dense and sparse arithmetic. Benchmarks shown here.
librsb Michele Martone C, Fortran, M4 2011 1.2 / September 2016 Free 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.

Matrix types and operations[edit]

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:[1]

  • TF - triangular factorizations (LU, Cholesky)
  • OF - orthogonal factorizations (QR, QL, generalized factorizations)
  • EVD - eigenproblems
  • SVD - singular value decomposition
  • GEVD - generalized EVD
  • GSVD - generalized SVD
Real Complex SPD HPD SY HE BND TF OF EVD SVD GEVD GSVD
ALGLIB Yes Yes Yes Yes No No No Yes Yes Yes Yes Yes No
ATLAS Yes Yes Yes Yes No No No Yes No No No No No
GNU Scientific Library Yes Yes Yes Yes No No No Yes Yes Yes Yes Yes No
ILNumerics.Net Yes Yes Yes Yes No No No Yes Yes Yes Yes No No
IMSL Numerical Libraries Yes Yes Yes Yes No No Yes Yes No Yes Yes Yes No
LAPACK Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
MKL Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
NAG Numerical Library Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
NMath Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No No
SciPy (Python packages) Yes Yes Yes Yes No No No Yes Yes Yes Yes No No
Eigen Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No
Armadillo Yes Yes Yes Yes Yes Yes No Yes Yes Yes Yes Yes No