Eigen_ppt

11000 10000 9000 8000 7000 MFLOPS 6000 5000 4000 3000 2000 1000 0 ’eigen3’ ’eigen2’ ’GOTO2’ ’INTEL_MKL’ ’gmm’ ’ublas’ ’ATLAS’
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Fast, Easy Linear Algebra in C++ with Eigen
Benjamin S. Skrainka
University of Chicago The Harris School of Public Policy skrainka@
May 16, 2012
Plan for this Talk
Getting Started Eigen’s Containers: Matrix<T> and Array<T> Advanced Operations Mersenne Twister
Benefits of Eigen
Eigen makes dense linear algebra easy in C++:
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Includes: abs() min() max() square() pow() exp() log() sqrt()
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Must convert Matrix<T> to Array<T> using array() member function in order to perform coefficient-wise operations Performed coefficient-wise, i.e. like MATLAB ◆ where ✓ exp (a12 ) exp (a12 ) m.array().exp() is exp (a21 ) exp (a22 )
Overview of Basic Linear Solving
Eigen also contains many linear solvers: Decomposition PartialPivLU FullPivLU HouseholderQR ColPivHouseholderQR FullPivHouseholderQR LLT (Cholesky) LDLT (Robust Cholesky) Speed ++ ++ + +++ +++ Accuracy + +++ + ++ +++ + ++
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Figure is taken from Eigen documentation.
Eigen Benchmark
triangular solver - vector (X = inv(L) X)
8000 ’eigen3’ ’INTEL_MKL’ ’eigen2’ ’GOTO2’ ’ATLAS’ ’gmm’ ’ublas’
To install,
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Help
There are many resources for help:
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Online documentation Online Getting Started Tutorial Online Quick Reference
A First Application
For production code, compile with -DEIGEN_NO_DEBUG:
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-pedantic forces strict conformance to ANSI/ISO C++ standards But, Eigen requires long long which is not yet officially supported. . . Compile with -DEIGEN_NO_DEBUG Huge speetalk’s objectives:
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State benefits of using Eigen from linear algebra List key components of Eigen Use Eigen to perform typical linear algebra operations Generate high quality pseudo-random numbers with Mersenne Twister
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Entire library consists of header files No need to compile or build any binary libraries Just download and copy it to where you want it Download latest stable release from /eigen/eigen/get/3.0.5.tar.gz Unpack: $ tar xzvf eigen-eigen-6e7488e20373.tar.gz $ mv eigen-eigen-6e7488e20373 eigen-3.0.5
There are also SVD and eigenvalue decompositions
Array<T> vs. Matrix<T>
Select Array<T> or Matrix<T> depending on desired behavior:
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Matrix<T>:
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Designed for linear algebra Supports matrix arithmetic Has some coefficient-wise member functions Convert to an Array<T> with Matrix<T>::array() General purpose array Coefficient-wise arithmetic Can perform coefficient-wise operations, such as add a number to all elements Convert to Matrix<T> with Array<T>::matrix()
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Figure is taken from Eigen documentation.
Overview of Eigen Libraries
Eigen provides several templated Matrix and Array types:
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1e+06
Figure is taken from Eigen documentation.
Eigen Benchmark
matrix vector product
12000 ’eigen3’ ’INTEL_MKL’ ’eigen2’ ’ATLAS’ ’GOTO2’ ’gmm’ ’ublas’
Building an Application with Eigen
To build an application with Eigen, use a supported C++ compiler such as GNU or MSVC++:
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Specify path to Eigen header files with -I/path/to/Eigen Do not compile with -pedantic:
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All basic features and many more advanced ones as well Template-based ) works with all arithmetic types Syntax is almost as easy to use as MATLAB’s
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For production code: $ g++ -Wall -Wextra -O2 -m64 \ -DEIGEN_NO_DEBUG \ -I/home/skrainka/public/sw/include \ eigenExample.cpp -o eigenExample
Practical Tips on Use
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Disable debugging checks in product code:
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Example Compilation
Here is an example compilation
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For debugging (development): $ g++ -Wall -Wextra -O0 -g -m64 \ -I/home/skrainka/public/sw/include \ eigenExample.cpp -o eigenExample
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Array<T>:
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Getting Started
First Steps
Let’s start by discussing:
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Installation Configuration Getting Help