Eigen is a C++ template library for linear algebra: matrices, vectors, numerical solvers, and related algorithms.
Eigen 3.3.9 released! (04.12.2020)
Eigen 3.3.9 has been released on December 4, 2020.
This is a maintenance release fixing minor bugs and compilation issues. For more details have a look at the changelog.The sources are available at https://gitlab.com/libeigen/eigen/-/releases/3.3.9.
Eigen on Discord (16.11.2020)
Join our Discord server to discuss Eigen-related topics with other users and developers.
Eigen 3.3.8 released! (05.10.2020)
Eigen 3.3.8 has been released on October 5, 2020.
This is a maintenance release fixing minor bugs and compilation issues. For more details have a look at the changelog.The sources are available at https://gitlab.com/libeigen/eigen/-/releases/3.3.8.
Eigen is now on GitLab.com (30.07.2020)
Since the end of 2019, Eigen's repository and bugtracker are now both hosted on GitLab.com, meaning that Eigen is now using git for source code management. The old mercurial repository is still readable on bitbucket.org, but it is not synchronized with the git repository, meaning that it should be used for archive purposes only. The same remark applies for the old bugzilla instance.
Following the decision of Bitbucket.org to delete all mercurial repositories next spring, we decided to migrate to a git repository hosted on gitlab.com. We also decided to take this opportunity to migrate our self hosted bugzilla instance to gitlab.com. Both migrations are scheduled on the 4th of December, starting at 8:00 UTC, and the new project:
Details on the migration process:
To check out the Eigen repository using Mercurial, also known as "hg", do:
hg clone https://bitbucket.org/eigen/eigen/
Looking for the outdated Eigen2 version? Check it here.
- Eigen is versatile.
- It supports all matrix sizes, from small fixed-size matrices to arbitrarily large dense matrices, and even sparse matrices.
- It supports all standard numeric types, including std::complex, integers, and is easily extensible to custom numeric types.
- It supports various matrix decompositions and geometry features.
- Its ecosystem of unsupported modules provides many specialized features such as non-linear optimization, matrix functions, a polynomial solver, FFT, and much more.
- Eigen is fast.
- Expression templates allow to intelligently remove temporaries and enable lazy evaluation, when that is appropriate.
- Explicit vectorization is performed for SSE 2/3/4, ARM NEON, and AltiVec instruction sets, with graceful fallback to non-vectorized code.
- Fixed-size matrices are fully optimized: dynamic memory allocation is avoided, and the loops are unrolled when that makes sense.
- For large matrices, special attention is paid to cache-friendliness.
- Eigen is reliable.
- Eigen is elegant.
- The API is extremely clean and expressive while feeling natural to C++ programmers, thanks to expression templates.
- Implementing an algorithm on top of Eigen feels like just copying pseudocode.
- Eigen has good compiler support as we run our test suite against many compilers to guarantee reliability and work around any compiler bugs. Eigen also is standard C++98 and maintains very reasonable compilation times.
- Eigen 3 documentation: this includes a getting started guide, a long tutorial, a quick reference, and page about porting from Eigen 2 to Eigen 3.
Eigen doesn't have any dependencies other than the C++ standard library.
We use the CMake build system, but only to build the documentation and unit-tests, and to automate installation. If you just want to use Eigen, you can use the header files right away. There is no binary library to link to, and no configured header file. Eigen is a pure template library defined in the headers.
Earlier versions were licensed under the LGPL3+.
Note that currently, a few features rely on third-party code licensed under the LGPL: SimplicialCholesky, AMD ordering, and constrained_cg. Such features can be explicitly disabled by compiling with the EIGEN_MPL2_ONLY preprocessor symbol defined. Furthermore, Eigen provides interface classes for various third-party libraries (usually recognizable by the <Eigen/*Support> header name). Of course you have to mind the license of the so-included library when using them.
Virtually any software may use Eigen. For example, closed-source software may use Eigen without having to disclose its own source code. Many proprietary and closed-source software projects are using Eigen right now, as well as many BSD-licensed projects.
Eigen is standard C++98 and so should theoretically be compatible with any compliant compiler. Whenever we use some non-standard feature, that is optional and can be disabled.
Eigen is being successfully used with the following compilers:
- GCC, version 4.1 and newer. Very good performance with GCC 4.2 and newer.
- MSVC (Visual Studio), 2008 and newer (the old 2.x versions of Eigen support MSVC 2005, but without vectorization).
- Intel C++ compiler. Very good performance.
- LLVM/CLang++ (2.8 and newer).
- MinGW, recent versions. Very good performance when using GCC 4.
- QNX's QCC compiler.
Need help using Eigen? Try this:
- The Users Forum is your best resource.
- You can always try our IRC channel.
- Want to discuss something with the developers? Use our mailing list.
- To subscribe, send a mail with subject subscribe to firstname.lastname@example.org
- To unsubscribe, send a mail with subject unsubscribe to email@example.com
The Eigen mailing list can be used for discussing general Eigen development topics. End-user questions are often better asked on the Users Forum. Development of specific features is best tracked and discussed on our Bugzilla. See this page.
Important: You must subscribe before you may post. Sorry, this is our only way to prevent spam.
Important: After you sent your subscription request, you will receive a confirmation e-mail. Check your spam folder, as these confirmation e-mails are often filtered as spam!
There is also a private mailing list which should only be used if you want to write privately to a few core developers (it is read by Benoît, Gaël and Jitse). The address is eigen-core-team at the same lists server as for the Eigen mailing list. You do not need to subscribe (actually, subscription is closed). For all Eigen development discussion, use the public mailing list or Bugzilla instead.
Everybody's welcome to discuss Eigen-related topics or just chat. Some quick Eigen development chat happens over IRC, but the main place for Eigen development discussion remains the Eigen mailing list. Some user support also happens over IRC, but the main place for Eigen user support is the Users Forum.
Contributing to Eigen
Eigen is written and maintained by volunteers. You can contribute in many ways to help: give support to new users, write and improve documentation, helping with bugs and other issues in bugzilla, discussing the design and the API, running tests and writing code. See our page on Contributing to Eigen for pointers to get you started.
Projects using Eigen
Feel free to add yourself! If you don't have access to the wiki or if you are not sure about the relevance of your project, ask at the #Mailing list.
Extensions, numerical computation and bindings
- Google's Ceres solver is a portable C++ library that allows for modeling and solving large complicated nonlinear least squares problems.
- The Manifold ToolKit MTK provides easy mechanisms to enable arbitrary algorithms to operate on manifolds. It also provides a Sparse Least Squares Solver (SLoM) and an Unscented Kalman Filter (UKFoM).
- GTSAM is a library implementing smoothing and mapping (SAM) in robotics and vision, using factor graphs and Bayes networks.
- g2o is an open-source C++ framework for optimizing graph-based nonlinear least-square problems.
- minieigen is small boost::python wrapper for Eigen's core classes (dense fixed and dynamic-sized vectors, matrices, aligned boxes, quaternions; with integer, floating and complex scalars) including operators and subset of Eigen's API methods.
- redsvd is a RandomizED Singular Value Decomposition library for sparse or very large dense matrices.
- The RcppEigen package provides bindings and more for R.
- trustOptim is a trust-region based non linear solver supporting sparse Hessians (C++ implementation with R binding).
- sparray: a python binding of the Sparse module - alpha stage.
- Shogun: a large scale machine learning toolbox.
- Stan: a statistical package based on Eigen that includes a reverse-mode automatic differentiation implementation.
- jeigen, a Java wrapper for Eigen.
- Eigen4AutoIt, a wrapper for the AutoIt scripting language.
- Ceemple is a scientific programming environment allowing to rapidly prototype applications C++ as in MatLab or Python.
- EigenLab is a header only library to parse and evaluate expressions working on Eigen matrices.
- SpaFEDte a C++ library for discontinuous Galerkin discretizations on general meshes.
- biicode a C and C++ dependency manager that #includes the most popular and useful C/C++ libs and frameworks.
- The ATLAS experiment at the LHC (Large Hadron Collider) at CERN is using Eigen, as reported in this article, noting "Eigen was chosen since it offered the largest performance improvements for ATLAS use cases of the options investigated."
- The Large Survey Synoptic Telescope (website; trac) is a project to build a 3.2Mpixel camera on an 8.4m telescope and survey the entire visible sky every three days.
- Gnu Data Language, a GPL interpretor of IDL syntax codes.
- The Space Trajectory Analysis project at the European Space Agency. They even have an announcement on using Eigen.
- Avogadro, an opensource advanced molecular editor.
- The 3D astronomical visualization application Celestia is now using Eigen for all orbital and geometric calculation.
- Yade, platform for dynamic particle models, uses Eigen for geometric computations (switched from the WildMagic package)
- SLangTNG, an application suite for numerical analysis, linear algebra, advanced statistics, FEM, structural dynamics, data visualization, etc.
- Clip, an opensource program for the orientation of Laue exposures.
- Multiprecision Computing Toolbox for MATLAB uses Eigen as core library for matrix computations.
- Pteros, a C++ library for molecular modeling.
- Cufflinks, a tool for transcript assembly, differential expression, and differential regulation for RNA-Sequences.
- Vortexje: a GPL library for simulation implementing the source-doublet panel method.
- Woo(dem), particle dynamics software (DEM, FEM); Eigen wrapped using minieigen in Python.
Robotics and engineering
- The Yujin Robot company uses Eigen for the navigation and arm control of their next gen robots. (switched from blitz, ublas and tvmet)
- The Robotic Operating System (ROS) developed by Willow Garage.
- openAHRS Open Source IMU / AHRS
- The Darmstadt Dribblers autonomous Humanoid Robot Soccer Team and Darmstadt Rescue Robot Team use Eigen for navigation and world modeling.
- The Mobile Robot Programming Toolkit (MRPT), a set of libraries for SLAM, localization and computer vision, moved to Eigen (blog announcement) (switched from home made math classes).
- RBDL: a C++ library for rigid body dynamics.
- RL a self-contained C++ library for robot kinematics, motion planning and control.
- BTK is a Biomechanical ToolKit, licensed under BSD whose primary goal is to propose a set of tools for the analysis of the human body motion which is independent of any acquisition system. It proposes bindings for Matlab/Octave and Python, and a GUI software called Mokka to visualize/analyze 3D/2D motion capture data.
- libpointmatcher is a "Iterative Closest Point" library for 3D mapping in robotics.
- RobOptim is a modern, Open-Source, C++ library for numerical optimization applied to robotics.
- Computational Geometry Algorithms Library (CGAL), a collaborative effort to develop a robust, easy to use, and efficient C++ software library of geometric data structures and algorithms.
- Point Cloud Library (PCL), a large scale, BSD licensed, open project for point cloud processing. Uses Eigen as their math backend.
- VcgLib, an opensource C++ template library for the manipulation and processing of triangle and tetrahedral meshes. (switched from home made math classes)
- MeshLab, an opensource software for the processing and editing of unstructured 3D triangular meshes and point cloud. (switched from vcglib's math classes)
- Expe, an experimental framework for the rapid prototyping of graphics applications. No release yet, but it uses 90% of Eigen's features. (switched from home made math classes).
- libmv, an opensource structure from motion library. (switched from FLENS)
- openMVG, a simple library for multiple view geometry.
- metronome , a simple metric storage/graphing engine using Eigen for SVD least squares interpolation & data consolidation
- piccante, a C++ imaging library designed for High Dynamic Range (HDR) processing.
- libigl is a simple C++ geometry processing library with wide functionality.
- ApproxMVBB is a small library to compute fast approximate oriented bounding boxes of 3D point clouds.
- Google uses Eigen for machine learning, computer vision, and optimization.
- In particular, see the mention of Ceres above.
- Layar, an augmented reality appplication for IPhone and Android.
- Red Sword Studios, maker of the iPhone games Gradient, Fortress Luna, Stimulus, and Lustre, uses Eigen extensively. Why roll your own matrix/vector/transformation code when there's Eigen?
- iPerfectPutt, an iPhone game, uses Eigen for 3D geometry calculations.
- WhirlyGlobe-Maply an open source geospatial display toolkit for iOS and Android. It implements both a 3D interactive globe and a 2D (slippy) map
KDE (our origins!)
- Step, an educational physics simulator.
- Koffice2 (KDE's office suite), in particular Krita, the painting and image editing module. Eigen is also used a bit by KSpread, the spreadsheet module, for matrix functions such as MINVERSE, MMULT, MDETERM.
- Kalzium uses Eigen indirectly through the aforementioned Avogadro library.
- the Mandelbrot wallpaper plugin, some screensavers, kgllib, solidkreator, etc.
If you are aware of some interesting projects using Eigen, please send us a message or directly edit this wiki page !
The Eigen project was started by Benoît Jacob (founder) and Gaël Guennebaud (guru). Many other people have since contributed their talents to help make Eigen successful. Here's an alphabetical list: (note to contributors: do add yourself!)
|Philip Avery||Fix bug and add functionality to AutoDiff module|
|Abraham Bachrach||Added functions for cwise min/max with a scalar|
|Sebastien Barthelemy||Fix EIGEN_INITIALIZE_MATRICES_BY_NAN|
|Carlos Becker||Wrote some of the pages of the tutorial|
|David Benjamin||Artwork: the owls|
|Cyrille Berger||Fix error in logic of installation script|
|Armin Berres||Lots of fixes (compilation warnings and errors)|
|Jose Luis Blanco||Build fixes for MSVC and AMD64, correction in docs|
|Mark Borgerding||FFT module|
|Romain Bossart||Updates to Sparse solvers|
|Kolja Brix||Added docs to Householder module, fixes for ARPACK wrapper, KroneckerProduct and GMRES|
|Gauthier Brun||Making a start with a divide-and-conquer SVD implementation|
|Philipp Büttgenbach||Bug fix when differentiating a one-dimensional spline|
|Thomas Capricelli||Migration to mercurial, Non-linear optimization and numerical differentiation, cron-job to update the online dox|
|Nicolas Carre||Making a start with a divide-and-conquer SVD implementation|
|Jean Ceccato||Making a start with a divide-and-conquer SVD implementation|
|Vladimir Chalupecky||CMake fix|
|Benjamin Chrétien||Bug fix for PolynomialSolver (linear polynomials), various typos|
|Andrew Coles||Fixes (including a compilation error)|
|Jeff "complexzeros"||Spline interpolation with derivatives|
|Marton Danoczy||MSVC compilation fix, support for ARM NEON with Clang 3.0 and LLVM-GCC|
|Jeff Dean||Fix in vectorized square root for small arguments|
|Georg Drenkhahn||CMake and STL fixes|
|Christian Ehrlicher||MSVC compilation fix|
|Martinho Fernandes||Make our aligned allocator support C++11|
|Daniel Gomez Ferro||Improvements in Sparse and in matrix product|
|Rohit Garg||Vectorized quaternion and cross products, improved integer product|
|Mathieu Gautier||QuaternionMap and related improvements|
|Anton Gladky||Visual Studio 2008 and GCC 4.6 compilation fixes|
|Stuart Glaser||Prevent allocations in LU decomposition|
|Marc Glisse||C++11 compilation issues (suffices for literals)|
|Frederic Gosselin||Improve filter for hidden files in CMake|
|Gaël Guennebaud||Core developer|
|Philippe Hamelin||Allow CMake project to be included in another project|
|Marcus D. Hanwell||CMake improvements. Marcus is a developer at Kitware!|
|David Harmon||Arpack support module|
|Chen-Pang He||Many improvements to MatrixFunctions and KroneckerProduct modules|
|Hauke Heibel||Extended matrix functions, STL compatibility, Splines, CMake improvements, and more ...|
|Christoph Hertzberg||Quaternions, shifts for Cholmod, bug fixes, lots of user support on forums and IRC|
|Pavel Holoborodko||Multi-precision support with MPFR C++, bug fixes for non-standard scalar types|
|Tim Holy||Improvements to tutorial, LDLT update and downdate|
|Intel||Back-end to Intel Math Kernel Library (MKL)|
|Trevor Irons||Square root for complex numbers, fix compile errors and mistake in docs|
|Benoît Jacob||Core developer|
|Bram de Jong||Improvement to benchmark suite|
|Kibeom Kim||Implement *= /= * / operations for VectorwiseOp|
|Moritz Klammler||Avoid memory leak when constructor of user-defined type throws exception|
|Claas Köhler||Improvements to Fortran and FFTW in CMake|
|Alexey Korepanov||Add RealQZ class|
|Igor Krivenko||Properly cast constants when using non-standard scalars|
|Marijn Kruisselbrink||CMake fixes|
|Abhijit Kundu||Fix compilation errors in OpenGL demos|
|Moritz Lenz||Allow solving transposed problem with SuperLU|
|Bo Li||Fix bugs in Spline constructor|
|Sebastian Lipponer||MSVC compilation support|
|Daniel Lowenberg||Add SparseView class|
|David J. Luitz||Bug fix for sparse * dense matrix product|
|Naumov Maks||Bug fix in polynomial solver test|
|Angelos Mantzaflaris||Fix to allow IncompleteLUT to be used with MPFR|
|D J Marcin||Fix operator& precedence bug|
|Konstantinos A. Margaritis||AltiVec and ARM NEON vectorization|
|Roger Martin||Component-wise arc tangent function|
|Ricard Marxer||Reverse, redux improvements, the count() method, some dox|
|Vincenzo Di Massa||CMake fix|
|Christian Mayer||Early code review and input in technical/design discussions|
|Frank Meier-Dörnberg||MSVC compatibility fixes|
|Keir Mierle||LDLT decomposition and other improvements, help with MPL relicensing|
|Laurent Montel||CMake improvements. Laurent is (with Alexander) one of the CMake gurus at KDE!|
|Eamon Nerbonne||Compilation fixes for win32|
|Alexander Neundorf||CMake improvements. Alexander is (with Laurent) one of the CMake gurus at KDE!|
|Jason Newton||Componentwise tangent functions|
|Jitse Niesen||Matrix functions, large improvements in the Eigenvalues module and in the docs, and more ...|
|Desire Nuentsa||Many improvements to Sparse module: SparseLU, SparseQR, ILUT, PaStiXSupport, …|
|Jan Oberländer||Compatibility with termios.h|
|Jos van den Oever||Compilation fix|
|Michael Olbrich||Early patches, including the initial loop meta-unroller|
|Simon Pilgrim||Optimizations for NEON|
|Bjorn Piltz||Visual C compilation fix|
|Benjamin Piwowarski||Add conservativeResize() for sparse matrices|
|Zach Ploskey||Copy-editing of tutorial|
|Giacomo Po||MINRES iterative solver|
|Sergey Popov||Fix bug in SelfAdjointEigenSolver|
|Manoj Rajagopalan||Introduce middleRows() / middleCols(), bug fix for nonstandard numeric types|
|Stjepan Rajko||MSVC compatibility fix|
|Jure Repinc||CMake fixes|
|Kenneth Frank Riddile||Lots of Windows/MSVC compatibility fixes, handling of alignment issues|
|Richard Roberts||Bug fix in selection of MKL Householder QR|
|Adolfo Rodriguez||Prevent allocations in matrix decompositions|
|Peter Román||Support for SuperLU's ILU factorization|
|Oliver Ruepp||Bug fix in sparse matrix product with row-major matrices|
|Radu Bogdan Rusu||Fix compilation warning|
|Guillaume Saupin||Skyline matrices|
|Olivier Saut||Typo in documentation|
|Benjamin Schindler||gdb pretty printers|
|Michael Schmidt||Fix in assembly when identifying CPU, Compilation fix connected to min/max|
|Dennis Schridde||New typedefs like AlignedBox3f|
|Jakob Schwendner||Test for unaligned quaternions, Benchmark for Geometry module|
|Christian Seiler||The Tensor module|
|Martin Senst||Bug fix for empty matrices|
|Sameer Sheorey||Fix gdb pretty printer for variable-size matrices|
|Andy Somerville||Functions to get intersection between two ParametrizedLines|
|Alex Stapleton||Help with tough C++ questions|
|Benoit Steiner||Faster matrix multiplication, Tensor module, CUDA|
|Sven Strothoff||Add intersects() method to AlignedBox|
|Leszek Swirski||Fix oversight in installation scripts|
|Adam Szalkowski||Bug fix in MatrixBase::makeHouseholder()|
|Silvio Traversaro||Fix for FindEigen3.cmake|
|Piotr Trojanek||QCC compilation fixes|
|Anthony Truchet||Bugfix in QTransform and QMatrix support|
|Adolfo Rodriguez Tsourouksdissian||Version of JacobiSVD that pre-allocates its resources|
|James Richard Tyrer||CMake fix|
|Rhys Ulerich||Pkg-config support, improved GDB pretty-printer|
|Henry de Valence||Typo in documentation|
|Ingmar Vanhassel||CMake fix|
|Michiel Van Dyck||Multi-threading documentation bug fix|
|Scott Wheeler||Documentation improvements|
|Freddie Witherden||CMake fixes, allow LevenbergMarquardt to work with non-standard types|
|Urs Wolfer||Fixed a serious warning|
|Manuel Yguel||Bug fixes, work on inverse-with-check, the Polynomial module|
|Pierre Zoppitelli||Making a start with a divide-and-conquer SVD implementation|
Eigen is also using code that we copied from other sources. They are acknowledged in our sources and in the Mercurial history, but let's also mention them here:
|Intel Corporation||SSE code for 4x4 matrix inversion taken from here.|
|Tim Davis||AMD reordering simplicial sparse Cholesky factorization adapted from SuiteSparse|
|Julien Pommier||SSE implementation of exp,log,cos,sin math functions from GMM++|
|Yousef Saad||IncompleteLUT preconditioner coming from ITSOL|
|Minpack authors||Algorithms for non linear optimization.|
Special thanks to Tuxfamily for the wonderful quality of their services, and the GCC Compile Farm Project that gives us access to many various systems including ARM NEON.
If you are looking for a BibTeX entry to use to cite Eigen in academic papers, see the BibTeX page.