Fixed README.

Author: luca-heltai

README.md

@@ -1,67 +1,73 @@
-# Benchmark
+# LinearOperator - a generic, high-level expression syntax for linear algebra
 
-## files:
+This repository contains all benchmarks and source codes to reproduce the 
+results of the article
 
-  - **./bench_scripts/run.sh** : generate all benchmark
+*LinearOperator - a generic, high-level expression syntax for linear algebra*
 
-## benchmarks:
+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.
 
-### eigen.cc
+Submodules for both eigen and blaze are provided, for your convenience. If you install
+from github, you should make sure you download all submodules:
 
-Compare a simple and a smart implementation of a code based on Eigen with a
-code based on LinearOperator Class.
+    git clone --recursive https://github.com/mathLab/LinearOperator.git
 
-The benchmark consists in the evaluation of **A^3** where **A** is a
-matrix.
+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)
 
-### full_matrix_01.cc
+    git submodule update --init --recursive
 
-Define a full matrix and compare a raw implementation of matrix-vector
-multiplication with the one based on LinearOperator Class.
+## Installation
 
-### full_matrix_02.cc
+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: 
 
-Define a full matrix **A** and compare a raw implementation of **(3Id +
-A)A** with the one based on LinearOperator Class.
+    mkdir build
+    cd build
+    cmake -DDEAL_II_DIR=/path/to/dealii .. # Alternatively, set DEAL_II_DIR env variable
+    make 
 
-### sparse_matrix_01.cc
+this will create a few executables in the `build` directory.
 
-Define a sparse matrix and compare a raw implementation of matrix-vector
-multiplication with the one based on LinearOperator Class.
+If you want to reproduce the results of the articles, we provide the following script
+    
+    ./script/matrix.sh
 
-### sparse_matrix_02.cc
+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`
 
-Define a sparse matrix **A** and compare a raw implementation of $(3Id +
-A)A$ with the one based on LinearOperator Class.
+## benchmarks:
 
-### triple_add_01.cc
+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. 
 
-Compare a raw implementation of $A(x+y+z)$ with the one based on
-LinearOperator Class.
+The following tests are provided:
 
-This code uses **vmult_add** in the raw section.
+### `{full,sparse}_matrix_01.cc`
 
-### triple_add_02.cc
+Compute `M*v`
 
-Compare a raw implementation of $A(x+y+z)$ with the one based on
-LinearOperator Class.
+### `{full,sparse}_matrix_02.cc`
 
-This code uses **+=** in the raw section.
+Compute `M*M*M*v`
 
-### Stokes
+### `{full,sparse}_matrix_03.cc`
 
-Benchmark for the LinearOperator class. This code assemble a preconditioner
-for Stokes using two different approaches:
- - Assembling the matrix and performing
-every operation in the usual way
- - Assembling the matrix, defining the
-associated LinearOperators, and then performing all the operations using an
-high-level syntax (LinearOperator).
+Compute `(3*Id+M)*M*v`
 
-### step-6
+### `{full,sparse}_matrix_04.cc`
 
-Benchmark for constraints linear operator.
+Compute `M*(x+y+z)`
 
-### step-40
+### step_32.cc
 
-Parallel version of the previous benchmark.
+Compute a preconditioner for Stokes system, using a low level `deal.II` implementation, 
+or using a `LinearOperator` variant.