Armadillo C++ linear algebra library Umair Muslim 341318 Overview - PowerPoint PPT Presentation

Armadillo C++ linear algebra library Umair Muslim 341318

Overview  Introduction  Libraries comparison  Features  History  API  Structural Representation  Functionality overview  Evaluation  Conclusion 2 Armadillo by Umair Muslim

Introduction  A linear algebra library (matrix math’s ) with high quality syntax  Well balanced between speed and syntax simplicity.  Similar syntax as Matlab  Why not Matlab?  Proprietary program  Weak dynamically typed  Cross platform inconsistency 3 Armadillo by Umair Muslim

Comparison with other Libraries  Newmat  Unclear license  Reimplementation instead of reuse of LAPACK  Lack high-performance  uBLAS (Boost C++ lib)  Less availability of basic functionality (e.g. Matrix inversion)  IT++ (ITPP)  Use restrictive GNU General Public License (GPL) • Any library under it becomes infected with GPL • Software must come with source code 4 Armadillo by Umair Muslim

Features  Simple syntax: Matlab or Octave.  Numerical type support.  Based on LAPACK library.  Fast matrix manipulation using template meta- programing.  Matrix save and load in file as Matlab  Interfacing with other libraries: via STL-iterators  Open source development  Cross-platform usability 5 Armadillo by Umair Muslim

History  Version 1.x  Added some basic functions: .min(), .max(), .floor(), save/load  Version 2.x  Support for C++11  Exception handling: solve(), svd(), pinv(), syl() etc, std::runtime_error  Version 3.x  Added Constants: datum class.  Template meta-programming, matrix addition etc.  Version 5.x  Auto handling of 64 bit Integers  Version 6.x  Improved functionality while using Intel MKL, ATLAS & OpenBLAS, like norm(), accu() etc. 6 Armadillo by Umair Muslim

Structural Representation BaseCube Base Base Object field Cube Mat Object classes Mat Binary Mat Unary Cube Binary Cube Unary Four Families Op Op Op Op 7 Armadillo by Umair Muslim

Functionality overview  Base datatypes  Mat< type > : mat  Col <type> : colvec, vec  Row <type> : rowvec  Cube <type> : cube  Field <type> : field  Operators: + - * / % == != <= >= < >  Functions: .transform(), .fill(), .diag(), .is_empty(), .print(), .save()/.load() . . . etc.  Generators: zeros, eye, ones, rand, randi, randu, . . . etc. 8 Armadillo by Umair Muslim

Functionality overview  Optimizations:  SIMD vectorization • SSE2 • Elementary expressions (matrix addition, multiplication by scaler etc.) • Using GCC 4.7+ with -03. • SSE3, SSE4 or AVX, -march=native  Lazy evaluation • Template meta-programming • Evaluating mathematical expressions • trans ( X ) => Op< Mat, op_trans > • trans ( square ( X ) ) => Op< eOp< Mat, eop_square >, op_trans > 9

Example 1 - PageRank 10

Evaluation  Speedup factor of Armadillo relative to other software  A, B, C, D and Q are NxN matrices, where N=500.  g++ example.cpp – o example – O2 – fwhole-program – l lib Operation Formula Matlab Newmat IT++ Add & scalar mult. Q=0.1*A + 0.2*B + 0.3*C; 2.9 5.6 4.5 Traspose, matrix Q = Q + 0.1*A’ * 0.2 * B; 1.0 3.2 1.1 mult Submatrix copy A( 2:N, 2:N ) = B( 1:N-1, 1:N-1 ); 3.6 7.8 8.5 Direct element for c = 1:N 14.7 5.1 2.0 access for r = 1:N Q(r,c) = A(N+1-r, c)+B(r, N+1-c) + C(N+1-r, N+1-c); end End 11

Conclusion  Problems with Matlab and other linear algebra libraries.  Provides balance between speed and syntax simplicity.  Template meta-programming.  Perform faster than Matlab, IT++ and Newmat libraries. 12

Question please. THANK YOU. 13

Armadillo Optimization 120 111.55206 99.01259 100 80 60 40 20 7.72342 1.15342 0.55742 0.22967 0.00904 0.00248 0 Sum & Mult Trans & Mult SubMat copy Elem Access 14

Armadillo Evaluation Imp 15

IT++ Evaluation Imp 16

Newmat Evaluation Imp 17

File loading Implementaion  Newmat IT++ 18