LinearOperator - a generic, high-level expression syntax for linear algebra

This repository contains all benchmarks and source codes to reproduce the results of the article

LinearOperator - a generic, high-level expression syntax for linear algebra

2016, Matthias Maier, Mauro Bardelloni, Luca Heltai

In particular, it requires the deal.II library (version greater or equal than 8.3) and the eigen and blaze libraries.

Submodules for both eigen and blaze are provided, for your convenience. If you install from github, you should make sure you download all submodules:

git clone --recursive https://github.com/mathLab/LinearOperator.git

or, if you already have a clone of the LinearOperator repository, you can get the submodules by the following command (inside your local LinearOperator repository)

git submodule update --init --recursive

Installation

Assuming you installed correctly the deal.II library (www.dealii.org) under the path /path/to/dealii, then issuing the following commands should create all executables for the benchmarks presented in the paper:

mkdir build
cd build
cmake -DDEAL_II_DIR=/path/to/dealii .. # Alternatively, set DEAL_II_DIR env variable
make 

this will create a few executables in the build directory.

If you want to reproduce the results of the articles, we provide the following script

./script/matrix.sh

which will create a directory build_matrix_test, configure, build and run all tests, outputting the results into the directory ./build_matrix_test/output_dir

benchmarks:

Each benchmark is included in the directory ./apps, and makes a comparison between some simple operations involving either dense matrices or sparse matrices implemented in dealii, eigen, or blaze, and two variants involving LinearOperator and PackagedOperation objects. The first variant involves the creation of temporary PackagedOperation objects in each loop, while the second makes one construction outside the loop, and only uses the objects that have been previously constructed.

Each benchmark requires two arguments at commandline: a matrix size (for the dense matrix case) or a refinement level (for the sparse matrix cases) and a number of repetitions for the test. For example

./full_matrix_01 100 1000

performs the test full_matrix_01 on 100x100 matrices for 1000 repetitions, while

./sparse_matrix_01 3 100

performs the test sparse_matrix_01 on a grid of 3 by 3 cells, assemblying the stiffness matrix of a Poisson problem, and performs the test 100 times.

The following tests are provided:

• {full,sparse}_matrix_01.cc: compute M*v

• {full,sparse}_matrix_02.cc: compute M*M*M*v

• {full,sparse}_matrix_03.cc: compute (3*Id+M)*M*v

• {full,sparse}_matrix_04.cc: compute M*(x+y+z)

• step_32.cc: compute a preconditioner for Stokes system, using a low level deal.II implementation, or using a LinearOperator variant.