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Eigen 矩陣運算庫在實際項目中的使用情況如何？

01-08

心血來潮，試了試純模板技術寫的 Eigen 並作了簡單的性能測試，三個 1000 階的方陣連乘運算 Eigen 比 MATLAB 快了一倍，比 OpenCV 快了 2 倍，但是這個庫在實際項目中的穩定性和速度如何我還不大清楚，故有此問。

另外，目前流行的 C++ 數值計算庫很多都使用了 expression template 技術來抑制臨時對象的生成，極大提高了運算性能，但對於同樣使用這個技術的不同的庫，速度卻相差很大，例如 Armadillo，雖然它的底層採用了 BLAS 和 LAPACK，但在上述運算中比 Eigen 慢了整整 4 倍。產生這種現象的原因是什麼？

總體來說還是Armadillo快些，需要自己設置一下，方法的網上有教程。

下面是Eigen的項目：

Projects using Eigen

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).
  • 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.

Science

  • 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 (blogannouncement) (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.

Computer Graphics

  • 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.

Google

  • Google uses Eigen for machine learning, computer vision, and optimization.
  • In particular, see the mention of Ceres above.

Mobile apps

  • 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.

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.

Others

  • WhirlyGlobe a 3D globe component.

同志，你確定純用Eigen比MATLAB會快？我想知道你是怎麼設置的？

我用Eigen+Intel MKL在Release x64模式下也只是跟MATLAB運算速度差不多而已

Visual Studio下實現Eigen+Intel MKL的矩陣乘法

顯然openblas比matlab的mkl快。要速度的話，GPU加速吧，至少快5倍。

Benchmark - Eigen

圖中可以看到Eigen和主流的MKL不相上下，實際使用中也有類似的體驗。值得注意的是Eigen的稀疏矩陣處理非常優秀，Armadillo之流無法與之相比。

查看Libmesh才發現，其中也用到了Eigen，在Eigen頁面里沒有提到。

LZ提到比Armadillo快了4倍，我覺得是可能的，Armadillo只是個和matlab長得像的殼子，具體計算還是調用Blas庫來進行運算的，在優化層次上比不上Eigen

我依稀記得OpenCV底層支持Eigen，OpenCV在機器視覺領域是王者之一，Eigen的影響力可見一斑。我在自己的項目大量使用Eigen來做數值計算，我覺得Eigen就是方便好用，速度瓶頸主要在演算法而不是底層庫。

如果代碼基本一樣，eigen比arm快，看看底層是具體用的哪個庫做運算，還有編譯選項也很重要，template在-o2和-o0上會完全是兩個速度

Armadillo+Openblas的組合更快，而且Armadillo的函數更接近Matlab

有沒有遇到過這種情況，在用eigen庫的時候用比較大的維數矩陣運算的時候

，會出現這樣的錯誤

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