From 18cb85fd3967a4c46c9582e8515cef9af3448269 Mon Sep 17 00:00:00 2001 From: couturie Date: Mon, 25 Feb 2013 11:23:12 +0100 Subject: [PATCH 1/1] ch13 --- BookGPU/BookGPU.tex | 1 + BookGPU/Chapters/chapter13/biblio13.bib | 155 + BookGPU/Chapters/chapter13/bibunits.sty | 314 + BookGPU/Chapters/chapter13/ch12.tex~ | 1080 + BookGPU/Chapters/chapter13/ch13.aux | 118 + BookGPU/Chapters/chapter13/ch13.tex | 710 + BookGPU/Chapters/chapter13/ch13.tex~ | 710 + BookGPU/Chapters/chapter13/ex1.cu | 30 + BookGPU/Chapters/chapter13/ex2.cu | 48 + BookGPU/Chapters/chapter13/ex3.cu | 8 + BookGPU/Chapters/chapter13/ex4.cu | 54 + BookGPU/Chapters/chapter13/figures/bib.bib | 358 + .../Chapters/chapter13/figures/cluster.eps | 710 + .../Chapters/chapter13/figures/cluster.pdf | Bin 0 -> 13688 bytes BookGPU/Chapters/chapter13/figures/matrix.eps | 11181 ++ BookGPU/Chapters/chapter13/figures/matrix.pdf | Bin 0 -> 21178 bytes .../Chapters/chapter13/figures/points3D.eps | 117734 +++++++++++++++ .../Chapters/chapter13/figures/points3D.pdf | Bin 0 -> 23825 bytes .../chapter13/figures/rouge-noir-y.eps | 6912 + .../chapter13/figures/rouge-noir-y.pdf | Bin 0 -> 31665 bytes .../Chapters/chapter13/figures/rouge-noir.eps | 6822 + .../Chapters/chapter13/figures/rouge-noir.pdf | Bin 0 -> 31615 bytes BookGPU/Chapters/chapter13/figures/scale.eps | 808 + BookGPU/Chapters/chapter13/figures/scale.pdf | Bin 0 -> 7463 bytes .../Chapters/chapter13/figures/splitCPU.eps | 347 + .../Chapters/chapter13/figures/splitCPU.pdf | Bin 0 -> 9786 bytes .../Chapters/chapter13/figures/splitGPU.eps | 366 + .../Chapters/chapter13/figures/splitGPU.pdf | Bin 0 -> 9410 bytes BookGPU/Chapters/chapter16/ch16.aux | 134 +- BookGPU/Chapters/chapter18/ch18.aux | 64 +- BookGPU/Makefile | 5 +- 31 files changed, 148568 insertions(+), 101 deletions(-) create mode 100644 BookGPU/Chapters/chapter13/biblio13.bib create mode 100644 BookGPU/Chapters/chapter13/bibunits.sty create mode 100755 BookGPU/Chapters/chapter13/ch12.tex~ create mode 100644 BookGPU/Chapters/chapter13/ch13.aux create mode 100755 BookGPU/Chapters/chapter13/ch13.tex create mode 100755 BookGPU/Chapters/chapter13/ch13.tex~ create mode 100644 BookGPU/Chapters/chapter13/ex1.cu create mode 100644 BookGPU/Chapters/chapter13/ex2.cu create mode 100644 BookGPU/Chapters/chapter13/ex3.cu create mode 100644 BookGPU/Chapters/chapter13/ex4.cu create mode 100644 BookGPU/Chapters/chapter13/figures/bib.bib create mode 100644 BookGPU/Chapters/chapter13/figures/cluster.eps create mode 100644 BookGPU/Chapters/chapter13/figures/cluster.pdf create mode 100755 BookGPU/Chapters/chapter13/figures/matrix.eps create mode 100644 BookGPU/Chapters/chapter13/figures/matrix.pdf create mode 100644 BookGPU/Chapters/chapter13/figures/points3D.eps create mode 100644 BookGPU/Chapters/chapter13/figures/points3D.pdf create mode 100644 BookGPU/Chapters/chapter13/figures/rouge-noir-y.eps create mode 100644 BookGPU/Chapters/chapter13/figures/rouge-noir-y.pdf create mode 100644 BookGPU/Chapters/chapter13/figures/rouge-noir.eps create mode 100644 BookGPU/Chapters/chapter13/figures/rouge-noir.pdf create mode 100644 BookGPU/Chapters/chapter13/figures/scale.eps create mode 100644 BookGPU/Chapters/chapter13/figures/scale.pdf create mode 100644 BookGPU/Chapters/chapter13/figures/splitCPU.eps create mode 100644 BookGPU/Chapters/chapter13/figures/splitCPU.pdf create mode 100644 BookGPU/Chapters/chapter13/figures/splitGPU.eps create mode 100644 BookGPU/Chapters/chapter13/figures/splitGPU.pdf diff --git a/BookGPU/BookGPU.tex b/BookGPU/BookGPU.tex index 76dc8f6..f4f8323 100755 --- a/BookGPU/BookGPU.tex +++ b/BookGPU/BookGPU.tex @@ -148,6 +148,7 @@ \include{Chapters/chapter9/ch9} \include{Chapters/chapter11/ch11} \include{Chapters/chapter12/ch12} +\include{Chapters/chapter13/ch13} \include{Chapters/chapter14/ch14} \include{Chapters/chapter15/ch15} \include{Chapters/chapter16/ch16} diff --git a/BookGPU/Chapters/chapter13/biblio13.bib b/BookGPU/Chapters/chapter13/biblio13.bib new file mode 100644 index 0000000..b5ca7f0 --- /dev/null +++ b/BookGPU/Chapters/chapter13/biblio13.bib @@ -0,0 +1,155 @@ +@article{ref1, +title = {Asynchronous grid computation for {A}merican options derivatives}, +author = {Chau, Ming and Couturier, Rapha\"el and Bahi, Jacques M. and Spiteri, Pierre}, +journal = {Advances in Engineering Software}, +volume = {}, +number = {0}, +pages = {}, +note = {}, +year = {2012}, +} + +@article{ref2, +title = {Matrix iterative analysis}, +author = {Varga, Richard S.}, +journal = {Prentice Hall}, +volume = {}, +number = {}, +pages = {}, +note = {}, +year = {}, +} + +@article{ref3, + author = {Baudet, G\'erard M.}, + title = {Asynchronous iterative methods for multiprocessors}, + journal = {Journal Assoc. Comput. Mach.}, + volume = {25}, + number = {}, + pages = {226--244}, + year = {1978}, +} + +@article{ref4, + author = {Bertsekas, Dimitri P. and Tsitsiklis, John N.}, + title = {Parallel and distributed computation, numerical methods}, + journal = {Prentice Hall Englewood Cliffs N. J. (1989)}, + volume = {}, + number = {}, + pages = {}, + year = {1989}, +} + +@article{ref5, + author = {Bahi, Jacques M. and Contassot-Vivier, Sylvain and Couturier, Rapha\"el}, + title = {Parallel iterative algorithms: from sequential to grid computing}, + journal = {Chapman \& Hall/CRC, Numerical Analysis \& Scientific Computating 1 (2007)}, + volume = {}, + number = {}, + pages = {}, + year = {2007}, +} + +@article{ref6, + author = {Miellou, Jean-Claude and Spiteri, Pierre}, + title = {Two criteria for the convergence of asynchronous iterations}, + journal = {in Computers and computing, P. Chenin et al. ed., Wiley Masson}, + volume = {}, + number = {}, + pages = {91--95}, + year = {1985}, +} + +@article{ref7, + author = {Miellou, Jean-Claude}, + title = {Algorithmes de relaxation chaotique \`a retards}, + journal = {RAIRO Analyse num\'erique}, + volume = {R1}, + number = {}, + pages = {55--82}, + year = {1975}, +} + +@article{ref8, +title = {{CUDA} Toolkit 4.2 {CUBLAS} Library}, +author = {NVIDIA Corporation}, +journal = {}, +volume = {}, +number = {}, +pages = {}, +note = {\url{http://developer.download.nvidia.com/compute/DevZone/docs/html/CUDALibraries/doc/CUBLAS_Library.pdf}}, +year = {2012}, +} + +@article{ref9, + author = {Micikevicius, Paulius}, + title = {{3D} finite difference computation on {GPUs} using {CUDA}}, + journal = {Proceedings of 2nd Workshop on General Purpose Processing on Graphics Processing Units}, + volume = {}, + number = {}, + pages = {79--84}, + year = {2009}, +} + +@article{ref10, + author = {Leist, Aron and Playne, Daniel P. and Hawick, Ken A.}, + title = {Exploiting graphical processing units for data-parallel scientific applications}, + journal = {Concurrency and Computation: Practice and Experience}, + volume = {21}, + number = {18}, + pages = {2400--2437}, + year = {2009}, +} + +@article{ref11, + author = {Chau, Ming and Couturier, Rapha\"el and Bahi, Jacques M. and Spiteri, Pierre}, + title = {Parallel solution of the obstacle problem in grid environments}, + journal = {International Journal of High Performance Computing Applications}, + volume = {25}, + number = {4}, + pages = {488--495}, + year = {2011}, +} + +@article{ref12, + author = {Nvidia}, + title = {{NVIDIA} {CUDA} {C} {P}rogramming {G}uide}, + journal = {Version 4.2 (2012)}, + volume = {}, + number = {}, + pages = {}, + year = {2012}, +} + +@article{ref13, + author = {Evans, David J.}, + title = {Parallel {S}.{O}.{R}. iterative methods}, + journal = {Parallel Computing}, + volume = {1}, + number = {1}, + pages = {3--18}, + year = {1984}, +} + +@article{ref14, + author = {Iwashita, Takeshi and Shimasaki, Masaaki}, + title = {Block red-black ordering method for parallel processing of {ICCG} solver}, + journal = {High Performance Computing}, + volume = {2327}, + number = {}, + pages = {}, + year = {2006}, +} + +@article{ref15, +title = {Iterative methods for sparse linear systems}, +author = {Saad, Yousef}, +journal = {Society for Industrial and Applied Mathematics, 2nd edition}, +volume = {}, +number = {}, +pages = {}, +year = {2003}, +} + + + diff --git a/BookGPU/Chapters/chapter13/bibunits.sty b/BookGPU/Chapters/chapter13/bibunits.sty new file mode 100644 index 0000000..e5e7bb9 --- /dev/null +++ b/BookGPU/Chapters/chapter13/bibunits.sty @@ -0,0 +1,314 @@ +%% +%% This is file `bibunits.sty', +%% generated with the docstrip utility. +%% +%% The original source files were: +%% +%% bibunits.dtx (with options: `package') +%% +%% IMPORTANT NOTICE: +%% +%% For the copyright see the source file. +%% +%% Any modified versions of this file must be renamed +%% with new filenames distinct from bibunits.sty. +%% +%% For distribution of the original source see the terms +%% for copying and modification in the file bibunits.dtx. +%% +%% This generated file may be distributed as long as the +%% original source files, as listed above, are part of the +%% same distribution. (The sources need not necessarily be +%% in the same archive or directory.) +%% Package `bibunits' to use with LaTeX2e. +%% Copyright (C) 1999, 2000 by Thorsten Hansen. All rights reserved. +%% +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{bibunits} + [2000/10/10 v2.2 Multiple bibliographies in one document.] +\newif\iflabelstoglobalaux \labelstoglobalauxfalse +\DeclareOption{labelstoglobalaux}{\labelstoglobalauxtrue} +\newif\ifglobalcitecopy +\globalcitecopyfalse +\DeclareOption{globalcitecopy}{\globalcitecopytrue} +\ProcessOptions +\newwrite\@bibunitaux +\newcount\@bibunitauxcnt \@bibunitauxcnt=0 +\def\@bibunitname{bu\the\@bibunitauxcnt} +\newif\if@starredversion +\let\std@cite\cite +\DeclareRobustCommand\bu@cite{% + \@ifstar + {\@starredversiontrue\std@cite}% + {\@starredversionfalse\std@cite}% +} +\AtBeginDocument{% + \@ifpackageloaded{natbib}% + {% + \NAT@set@cites \let\std@@citex\@citex + \def\bu@@citex[#1][#2]#3{% + \@startbibunitorrelax + \leavevmode + \begingroup\let\@auxout\@bibunitaux\std@@citex[#1][#2]{#3}\endgroup + \ifglobalcitecopy + \std@nocite{#3}% + \fi + }% + }% + {% + \@ifpackageloaded{overcite}% + {% + \let\std@@citew\@citew + \def\bu@@citew#1{% + \@startbibunitorrelax + \leavevmode + {\let\@auxout\@bibunitaux \std@@citew{#1}}% + \ifglobalcitecopy + \@nocite{#1}% + \else + \if@starredversion + \@nocite{#1}% + \fi + \fi + } + \let\std@@citex\@citex + \def\bu@@citex[#1]#2{% + \@startbibunitorrelax + \leavevmode + {\let\@auxout\@bibunitaux \std@@citex[#1]{#2}}% + \ifglobalcitecopy + \@nocite{#2}% + \else + \if@starredversion + \@nocite{#2}% + \fi + \fi + } + }% + {% + \@ifpackageloaded{jurabib}% + {% + \let\std@@citex\@citex + \def\bu@@citex[#1][#2]#3{% + \@startbibunitorrelax + \leavevmode + {\let\@auxout\@bibunitaux \std@@citex[#1][#2]{#3}}% + \ifglobalcitecopy + \std@nocite{#3}% + \else + \if@starredversion + \std@nocite{#3}% + \fi + \fi + }% + }% + {% + \let\std@@citex\@citex + \def\bu@@citex[#1]#2{% + \@startbibunitorrelax + \leavevmode + {\let\@auxout\@bibunitaux \std@@citex[#1]{#2}}% + \ifglobalcitecopy + \std@nocite{#2}% + \else + \if@starredversion + \std@nocite{#2}% + \fi + \fi + }% + }% + }% + }% +}% +\let\std@nocite\nocite +\def\bu@nocite{% + \@ifstar + {\@starredversiontrue\@bu@nocite}% + {\@starredversionfalse\@bu@nocite}% +} +\def\@bu@nocite#1{% + \@startbibunitorrelax + {\let\@auxout\@bibunitaux \std@nocite{#1}}% + \ifglobalcitecopy + \std@nocite{#1}% + \else + \if@starredversion + \std@nocite{#1}% + \fi + \fi +} +\def\bu@bibdata{} +\AtBeginDocument{% + \iflabelstoglobalaux + \else + \let\orig@bibliography\bibliography + \def\bibliography#1{% + \if@filesw + \immediate\openout\@bibunitaux bu.aux + \immediate\write\@mainaux{\string\@input{bu.aux}}% + \fi + \orig@bibliography{#1}% + \if@filesw + \immediate\closeout\@bibunitaux + \fi + }% + \fi + \let\std@bibliography\bibliography +} +\def\bu@bibliography{% + \@ifstar + {\@starredversiontrue\@bu@bibliography}% + {\@starredversionfalse\@bu@bibliography}% +} +\def\@bu@bibliography#1{% + \if@filesw + \immediate\write\@auxout{\string\gdef\string\bu@bibdata{#1}}% + \fi + \gdef\bu@bibdata{#1}% + \if@starredversion + \else + \std@bibliography{#1}% + \fi +} +\def\bu@bibstyle{} +\let\std@bibliographystyle\bibliographystyle +\def\bu@bibliographystyle{% + \@ifstar + {\@starredversiontrue\@bu@bibliographystyle}% + {\@starredversionfalse\@bu@bibliographystyle}% +} +\def\@bu@bibliographystyle#1{% + \if@filesw + \immediate\write\@auxout{\string\gdef\string\bu@bibstyle{#1}}% + \fi + \gdef\bu@bibstyle{#1}% + \if@starredversion + \else + \std@bibliographystyle{#1}% + \fi +} +\def\bibunit{% + \global\let\cite\bu@cite + \global\let\@citex\bu@@citex + \global\let\@citew\bu@@citew + \global\let\nocite\bu@nocite + \global\let\@startbibunitorrelax\@startbibunit + \global\let\@finishbibunit\relax + \@ifnextchar[{\@bibunitx}{\@bibunitx[\bu@bibstyle]}% +} +\def\@bibunitx[#1]{\gdef\@localbibstyle{#1}} +\def\endbibunit{% + \global\let\cite\std@cite + \global\let\@citex\std@@citex + \global\let\@citew\std@@citew + \global\let\nocite\std@nocite + \@finishbibunit + \@input{bu.aux}% +} +\def\@startbibunit{% + \global\let\@startbibunitorrelax\relax + \global\let\@finishbibunit\@finishstartedbibunit + \global\advance\@bibunitauxcnt 1 + \if@filesw + {\endlinechar-1 + \@input{\@bibunitname.aux}}% + \immediate\openout\@bibunitaux\@bibunitname.aux + \immediate\write\@bibunitaux{\string\bibstyle{\@localbibstyle}}% + \fi +} +\let\@finishbibunit\relax +\def\@finishstartedbibunit{% + \if@filesw + \immediate\closeout\@bibunitaux + \fi +} +\let\old@bibunit\@gobble +\def\@bibunit{\endbibunit\bibunit\old@bibunit} +\def\@endbibunit{} +\def\bibliographyunit{% + \@endbibunit + \@ifnextchar[{\@bibliographyunit}{% + \global\let\old@bibunit\@gobble + \global\let\bibliography\std@bibliography + \global\let\bibliographystyle\std@bibliographystyle + \endbibunit + \gdef\@endbibunit{}}% +} +\def\@bibliographyunit[#1]{% + \global\let\bibliography\bu@bibliography + \global\let\bibliographystyle\bu@bibliographystyle + \global\let\old@bibunit#1 + \global\let#1\@bibunit + \gdef\@endbibunit{\global\let#1\old@bibunit}% +} +\def\putbib{\@ifnextchar[{\@putbib}{\@putbib[\bu@bibdata]}} +\def\@putbib[#1]{% + \@startbibunitorrelax + \if@filesw + \immediate\write\@bibunitaux{\string\bibdata{#1}}% + \fi + \@input@{\@bibunitname.bbl}% +} +\AtBeginDocument{% + \iflabelstoglobalaux + \else + \let\std@bibitem\@bibitem + \let\std@lbibitem\@lbibitem + \def\@bibitem#1{% + \let\temp@auxout\@auxout + \let\@auxout\@bibunitaux + \std@bibitem{#1}% + \let\@auxout\temp@auxout + } + \def\@lbibitem[#1]#2{% + \let\temp@auxout\@auxout + \let\@auxout\@bibunitaux + \std@lbibitem[#1]{#2}% + \let\@auxout\temp@auxout + } + \fi +} +\def\remequivalent#1\from#2{% + \let\given=#1% + \ifx#2\empty + \else + \edef#2{\expandafter\plugh#2\plugh}% + \fi +} +\def\plugh\do#1#2{% + \ifx#1\given + \else + \noexpand\do\noexpand#1% + \fi + \ifx#2\plugh + \hgulp\fi\plugh#2% +} +\def\hgulp\fi\plugh\plugh{\fi} +\remequivalent\bibcite\from\@preamblecmds +\AtBeginDocument{% + \@ifpackageloaded{natbib}% + {\renewcommand\bibcite[2]{\global\@namedef{b@#1\@extra@binfo}{#2}}}% + {\renewcommand\bibcite[2]{\global\@namedef{b@#1}{#2}}}% +} +\AtBeginDocument{% + \@ifundefined{bbl@redefine}% + {}% + {% + \bbl@redefine\@input#1{% + \@safe@activestrue\org@@input{#1}\@safe@activesfalse}% + \@ifpackageloaded{natbib}% + {% + \bbl@redefine\std@@citex[#1][#2]#3{% + \@safe@activestrue\org@std@@citex[#1][#2]{#3}\@safe@activesfalse}% + \bbl@redefine\bu@@citex[#1][#2]#3{% + \@safe@activestrue\org@bu@@citex[#1][#2]{#3}\@safe@activesfalse}% + }% + {% natbib not loaded + \bbl@redefine\std@@citex[#1]#2{% + \@safe@activestrue\org@std@@citex[#1]{#2}\@safe@activesfalse}% + }% + }% +} +\endinput +%% +%% End of file `bibunits.sty'. diff --git a/BookGPU/Chapters/chapter13/ch12.tex~ b/BookGPU/Chapters/chapter13/ch12.tex~ new file mode 100755 index 0000000..370c6c7 --- /dev/null +++ b/BookGPU/Chapters/chapter13/ch12.tex~ @@ -0,0 +1,1080 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% +%% CHAPTER 12 %% +%% %% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\chapterauthor{}{} +\chapter{Solving sparse linear systems with GMRES and CG methods on GPU clusters} + +%%--------------------------%% +%% SECTION 1 %% +%%--------------------------%% +\section{Introduction} +\label{sec:01} +The sparse linear systems are used to model many scientific and industrial problems, such as the environmental simulations or +the industrial processing of the complex or non-Newtonian fluids. Moreover, the resolution of these problems often involves the +solving of such linear systems which is considered as the most expensive process in terms of time execution and memory space. +Therefore, solving sparse linear systems must be as efficient as possible in order to deal with problems of ever increasing size. + +There are, in the jargon of numerical analysis, different methods of solving sparse linear systems that we can classify in two +classes: the direct and iterative methods. However, the iterative methods are often more suitable than their counterpart, direct +methods, for solving large sparse linear systems. Indeed, they are less memory consuming and easier to parallelize on parallel +computers than direct methods. Different computing platforms, sequential and parallel computers, are used for solving sparse +linear systems with iterative solutions. Nowadays, graphics processing units (GPUs) have become attractive for solving these +linear systems, due to their computing power and their ability to compute faster than traditional CPUs. + +In Section~\ref{sec:02}, we describe the general principle of two well-known iterative methods: the conjugate gradient method and +the generalized minimal residual method. In Section~\ref{sec:03}, we give the main key points of the parallel implementation of both +methods on a cluster of GPUs. Then, in Section~\ref{sec:04}, we present the experimental results obtained on a CPU cluster and on +a GPU cluster, for solving sparse linear systems associated to matrices of different structures. Finally, in Section~\ref{sec:05}, +we apply the hypergraph partitioning technique to reduce the total communication volume between the computing nodes and, thus, to +improve the execution times of the parallel algorithms of both iterative methods. + + +%%--------------------------%% +%% SECTION 2 %% +%%--------------------------%% +\section{Krylov iterative methods} +\label{sec:02} +Let us consider the following system of $n$ linear equations in $\mathbb{R}$: +\begin{equation} +Ax=b, +\label{eq:01} +\end{equation} +where $A\in\mathbb{R}^{n\times n}$ is a sparse nonsingular square matrix, $x\in\mathbb{R}^{n}$ is the solution vector, +$b\in\mathbb{R}^{n}$ is the right-hand side and $n\in\mathbb{N}$ is a large integer number. + +The iterative methods for solving the large sparse linear system~(\ref{eq:01}) proceed by successive iterations of a same +block of elementary operations, during which an infinite number of approximate solutions $\{x_k\}_{k\geq 0}$ are computed. +Indeed, from an initial guess $x_0$, an iterative method determines at each iteration $k>0$ an approximate solution $x_k$ +which, gradually, converges to the exact solution $x^{*}$ as follows: +\begin{equation} +x^{*}=\lim\limits_{k\to\infty}x_{k}=A^{-1}b. +\label{eq:02} +\end{equation} +The number of iterations necessary to reach the exact solution $x^{*}$ is not known beforehand and can be infinite. In +practice, an iterative method often finds an approximate solution $\tilde{x}$ after a fixed number of iterations and/or +when a given convergence criterion is satisfied as follows: +\begin{equation} +\|b-A\tilde{x}\| < \varepsilon, +\label{eq:03} +\end{equation} +where $\varepsilon<1$ is the required convergence tolerance threshold. + +Some of the most iterative methods that have proven their efficiency for solving large sparse linear systems are those +called \textit{Krylov sub-space methods}~\cite{ref1}. In the present chapter, we describe two Krylov methods which are +widely used: the conjugate gradient method (CG) and the generalized minimal residual method (GMRES). In practice, the +Krylov sub-space methods are usually used with preconditioners that allow to improve their convergence. So, in what +follows, the CG and GMRES methods are used for solving the left-preconditioned sparse linear system: +\begin{equation} +M^{-1}Ax=M^{-1}b, +\label{eq:11} +\end{equation} +where $M$ is the preconditioning matrix. + +%%****************%% +%%****************%% +\subsection{CG method} +\label{sec:02.01} +The conjugate gradient method is initially developed by Hestenes and Stiefel in 1952~\cite{ref2}. It is one of the well +known iterative method for solving large sparse linear systems. In addition, it can be adapted for solving nonlinear +equations and optimization problems. However, it can only be applied to problems with positive definite symmetric matrices. + +The main idea of the CG method is the computation of a sequence of approximate solutions $\{x_k\}_{k\geq 0}$ in a Krylov +sub-space of order $k$ as follows: +\begin{equation} +x_k \in x_0 + \mathcal{K}_k(A,r_0), +\label{eq:04} +\end{equation} +such that the Galerkin condition must be satisfied: +\begin{equation} +r_k \bot \mathcal{K}_k(A,r_0), +\label{eq:05} +\end{equation} +where $x_0$ is the initial guess, $r_k=b-Ax_k$ is the residual of the computed solution $x_k$ and $\mathcal{K}_k$ the Krylov +sub-space of order $k$: \[\mathcal{K}_k(A,r_0) \equiv\text{span}\{r_0, Ar_0, A^2r_0,\ldots, A^{k-1}r_0\}.\] +In fact, CG is based on the construction of a sequence $\{p_k\}_{k\in\mathbb{N}}$ of direction vectors in $\mathcal{K}_k$ +which are pairwise $A$-conjugate ($A$-orthogonal): +\begin{equation} +\begin{array}{ll} +p_i^T A p_j = 0, & i\neq j. +\end{array} +\label{eq:06} +\end{equation} +At each iteration $k$, an approximate solution $x_k$ is computed by recurrence as follows: +\begin{equation} +\begin{array}{ll} +x_k = x_{k-1} + \alpha_k p_k, & \alpha_k\in\mathbb{R}. +\end{array} +\label{eq:07} +\end{equation} +Consequently, the residuals $r_k$ are computed in the same way: +\begin{equation} +r_k = r_{k-1} - \alpha_k A p_k. +\label{eq:08} +\end{equation} +In the case where all residuals are nonzero, the direction vectors $p_k$ can be determined so that the following recurrence +holds: +\begin{equation} +\begin{array}{lll} +p_0=r_0, & p_k=r_k+\beta_k p_{k-1}, & \beta_k\in\mathbb{R}. +\end{array} +\label{eq:09} +\end{equation} +Moreover, the scalars $\{\alpha_k\}_{k>0}$ are chosen so as to minimize the $A$-norm error $\|x^{*}-x_k\|_A$ over the Krylov +sub-space $\mathcal{K}_{k}$ and the scalars $\{\beta_k\}_{k>0}$ are chosen so as to ensure that the direction vectors are +pairwise $A$-conjugate. So, the assumption that matrix $A$ is symmetric and the recurrences~(\ref{eq:08}) and~(\ref{eq:09}) +allow to deduce that: +\begin{equation} +\begin{array}{ll} +\alpha_{k}=\frac{r^{T}_{k-1}r_{k-1}}{p_{k}^{T}Ap_{k}}, & \beta_{k}=\frac{r_{k}^{T}r_{k}}{r_{k-1}^{T}r_{k-1}}. +\end{array} +\label{eq:10} +\end{equation} + +Algorithm~\ref{alg:01} shows the main key points of the preconditioned CG method. It allows to solve the left-preconditioned +sparse linear system~(\ref{eq:11}). In this algorithm, $\varepsilon$ is the convergence tolerance threshold, $maxiter$ is the maximum +number of iterations and $(\cdot,\cdot)$ defines the dot product between two vectors in $\mathbb{R}^{n}$. At every iteration, a direction +vector $p_k$ is determined, so that it is orthogonal to the preconditioned residual $z_k$ and to the direction vectors $\{p_i\}_{i0}$ in a Krylov sub-space $\mathcal{K}_k$ as follows: +\begin{equation} +\begin{array}{ll} +x_k \in x_0 + \mathcal{K}_k(A, v_1),& v_1=\frac{r_0}{\|r_0\|_2}, +\end{array} +\label{eq:12} +\end{equation} +so that the Petrov-Galerkin condition is satisfied: +\begin{equation} +\begin{array}{ll} +r_k \bot A \mathcal{K}_k(A, v_1). +\end{array} +\label{eq:13} +\end{equation} +GMRES uses the Arnoldi process~\cite{ref5} to construct an orthonormal basis $V_k$ for the Krylov sub-space $\mathcal{K}_k$ +and an upper Hessenberg matrix $\bar{H}_k$ of order $(k+1)\times k$: +\begin{equation} +\begin{array}{ll} +V_k = \{v_1, v_2,\ldots,v_k\}, & \forall k>1, v_k=A^{k-1}v_1, +\end{array} +\label{eq:14} +\end{equation} +and +\begin{equation} +V_k A = V_{k+1} \bar{H}_k. +\label{eq:15} +\end{equation} + +Then, at each iteration $k$, an approximate solution $x_k$ is computed in the Krylov sub-space $\mathcal{K}_k$ spanned by $V_k$ +as follows: +\begin{equation} +\begin{array}{ll} +x_k = x_0 + V_k y, & y\in\mathbb{R}^{k}. +\end{array} +\label{eq:16} +\end{equation} +From both formulas~(\ref{eq:15}) and~(\ref{eq:16}) and $r_k=b-Ax_k$, we can deduce that: +\begin{equation} +\begin{array}{lll} + r_{k} & = & b - A (x_{0} + V_{k}y) \\ + & = & r_{0} - AV_{k}y \\ + & = & \beta v_{1} - V_{k+1}\bar{H}_{k}y \\ + & = & V_{k+1}(\beta e_{1} - \bar{H}_{k}y), +\end{array} +\label{eq:17} +\end{equation} +such that $\beta=\|r_0\|_2$ and $e_1=(1,0,\cdots,0)$ is the first vector of the canonical basis of $\mathbb{R}^k$. So, +the vector $y$ is chosen in $\mathbb{R}^k$ so as to minimize at best the Euclidean norm of the residual $r_k$. Consequently, +a linear least-squares problem of size $k$ is solved: +\begin{equation} +\underset{y\in\mathbb{R}^{k}}{min}\|r_{k}\|_{2}=\underset{y\in\mathbb{R}^{k}}{min}\|\beta e_{1}-\bar{H}_{k}y\|_{2}. +\label{eq:18} +\end{equation} +The QR factorization of matrix $\bar{H}_k$ is used to compute the solution of this problem by using Givens rotations~\cite{ref1,ref3}, +such that: +\begin{equation} +\begin{array}{lll} +\bar{H}_{k}=Q_{k}R_{k}, & Q_{k}\in\mathbb{R}^{(k+1)\times (k+1)}, & R_{k}\in\mathbb{R}^{(k+1)\times k}, +\end{array} +\label{eq:19} +\end{equation} +where $Q_kQ_k^T=I_k$ and $R_k$ is an upper triangular matrix. + +The GMRES method computes an approximate solution with a sufficient precision after, at most, $n$ iterations ($n$ is the size of the +sparse linear system to be solved). However, the GMRES algorithm must construct and store in the memory an orthonormal basis $V_k$ whose +size is proportional to the number of iterations required to achieve the convergence. Then, to avoid a huge memory storage, the GMRES +method must be restarted at each $m$ iterations, such that $m$ is very small ($m\ll n$), and with $x_m$ as the initial guess to the +next iteration. This allows to limit the size of the basis $V$ to $m$ orthogonal vectors. + +Algorithm~\ref{alg:02} shows the main key points of the GMRES method with restarts. It solves the left-preconditioned sparse linear +system~(\ref{eq:11}), such that $M$ is the preconditioning matrix. At each iteration $k$, GMRES uses the Arnoldi process (defined +from line~$7$ to line~$17$) to construct a basis $V_m$ of $m$ orthogonal vectors and an upper Hessenberg matrix $\bar{H}_m$ of size +$(m+1)\times m$. Then, it solves the linear least-squares problem of size $m$ to find the vector $y\in\mathbb{R}^{m}$ which minimizes +at best the residual norm (line~$18$). Finally, it computes an approximate solution $x_m$ in the Krylov sub-space spanned by $V_m$ +(line~$19$). The GMRES algorithm is stopped when the residual norm is sufficiently small ($\|r_m\|_2<\varepsilon$) and/or the maximum +number of iterations ($maxiter$) is reached. + +\begin{algorithm} + \SetLine + \linesnumbered + Choose an initial guess $x_0$\; + $convergence$ = false\; + $k = 1$\; + $r_{0} = M^{-1}(b-Ax_{0})$\; + $\beta = \|r_{0}\|_{2}$\; + \While{$\neg convergence$}{ + $v_{1} = r_{0}/\beta$\; + \For{$j=1$ \KwTo $m$}{ + $w_{j} = M^{-1}Av_{j}$\; + \For{$i=1$ \KwTo $j$}{ + $h_{i,j} = (w_{j},v_{i})$\; + $w_{j} = w_{j}-h_{i,j}v_{i}$\; + } + $h_{j+1,j} = \|w_{j}\|_{2}$\; + $v_{j+1} = w_{j}/h_{j+1,j}$\; + } + Set $V_{m}=\{v_{j}\}_{1\leq j \leq m}$ and $\bar{H}_{m}=(h_{i,j})$ a $(m+1)\times m$ upper Hessenberg matrix\; + Solve a least-squares problem of size $m$: $min_{y\in\mathrm{I\!R}^{m}}\|\beta e_{1}-\bar{H}_{m}y\|_{2}$\; + $x_{m} = x_{0}+V_{m}y_{m}$\; + $r_{m} = M^{-1}(b-Ax_{m})$\; + $\beta = \|r_{m}\|_{2}$\; + \eIf{ $(\beta<\varepsilon)$ {\bf or} $(k\geq maxiter)$}{ + $convergence$ = true\; + }{ + $x_{0} = x_{m}$\; + $r_{0} = r_{m}$\; + $k = k + 1$\; + } + } +\caption{Left-preconditioned GMRES method with restarts} +\label{alg:02} +\end{algorithm} + + +%%--------------------------%% +%% SECTION 3 %% +%%--------------------------%% +\section{Parallel implementation on a GPU cluster} +\label{sec:03} +In this section, we present the parallel algorithms of both iterative CG and GMRES methods for GPU clusters. +The implementation is performed on a GPU cluster composed of different computing nodes, such that each node +is a CPU core managed by a MPI process and equipped with a GPU card. The parallelization of these algorithms +is carried out by using the MPI communication routines between the GPU computing nodes and the CUDA programming +environment inside each node. In what follows, the algorithms of the iterative methods are called iterative +solvers. + +%%****************%% +%%****************%% +\subsection{Data partitioning} +\label{sec:03.01} +The parallel solving of the large sparse linear system~(\ref{eq:11}) requires a data partitioning between the computing +nodes of the GPU cluster. Let $p$ denotes the number of the computing nodes on the GPU cluster. The partitioning operation +consists in the decomposition of the vectors and matrices, involved in the iterative solver, in $p$ portions. Indeed, this +operation allows to assign to each computing node $i$: +\begin{itemize*} +\item a portion of size $\frac{n}{p}$ elements of each vector, +\item a sparse rectangular sub-matrix $A_i$ of size $(n,\frac{n}{p})$ and, +\item a square preconditioning sub-matrix $M_i$ of size $(\frac{n}{p},\frac{n}{p})$, +\end{itemize*} +where $n$ is the size of the sparse linear system to be solved. In the first instance, we perform a naive row-wise partitioning +(decomposition row-by-row) on the data of the sparse linear systems to be solved. Figure~\ref{fig:01} shows an example of a row-wise +data partitioning between four computing nodes of a sparse linear system (sparse matrix $A$, solution vector $x$ and right-hand +side $b$) of size $16$ unknown values. + +\begin{figure} +\centerline{\includegraphics[scale=0.35]{Chapters/chapter12/figures/partition}} +\caption{A data partitioning of the sparse matrix $A$, the solution vector $x$ and the right-hand side $b$ into four portions.} +\label{fig:01} +\end{figure} + +%%****************%% +%%****************%% +\subsection{GPU computing} +\label{sec:03.02} +After the partitioning operation, all the data involved from this operation must be transferred from the CPU memories to the GPU +memories, in order to be processed by GPUs. We use two functions of the CUBLAS library (CUDA Basic Linear Algebra Subroutines), +developed by Nvidia~\cite{ref6}: \verb+cublasAlloc()+ for the memory allocations on GPUs and \verb+cublasSetVector()+ for the +memory copies from the CPUs to the GPUs. + +An efficient implementation of CG and GMRES solvers on a GPU cluster requires to determine all parts of their codes that can be +executed in parallel and, thus, take advantage of the GPU acceleration. As many Krylov sub-space methods, the CG and GMRES methods +are mainly based on arithmetic operations dealing with vectors or matrices: sparse matrix-vector multiplications, scalar-vector +multiplications, dot products, Euclidean norms, AXPY operations ($y\leftarrow ax+y$ where $x$ and $y$ are vectors and $a$ is a +scalar) and so on. These vector operations are often easy to parallelize and they are more efficient on parallel computers when +they work on large vectors. Therefore, all the vector operations used in CG and GMRES solvers must be executed by the GPUs as kernels. + +We use the kernels of the CUBLAS library to compute some vector operations of CG and GMRES solvers. The following kernels of CUBLAS +(dealing with double floating point) are used: \verb+cublasDdot()+ for the dot products, \verb+cublasDnrm2()+ for the Euclidean +norms and \verb+cublasDaxpy()+ for the AXPY operations. For the rest of the data-parallel operations, we code their kernels in CUDA. +In the CG solver, we develop a kernel for the XPAY operation ($y\leftarrow x+ay$) used at line~$12$ in Algorithm~\ref{alg:01}. In the +GMRES solver, we program a kernel for the scalar-vector multiplication (lines~$7$ and~$15$ in Algorithm~\ref{alg:02}), a kernel for +solving the least-squares problem and a kernel for the elements updates of the solution vector $x$. + +The least-squares problem in the GMRES method is solved by performing a QR factorization on the Hessenberg matrix $\bar{H}_m$ with +plane rotations and, then, solving the triangular system by backward substitutions to compute $y$. Consequently, solving the least-squares +problem on the GPU is not interesting. Indeed, the triangular solves are not easy to parallelize and inefficient on GPUs. However, +the least-squares problem to solve in the GMRES method with restarts has, generally, a very small size $m$. Therefore, we develop +an inexpensive kernel which must be executed in sequential by a single CUDA thread. + +The most important operation in CG and GMRES methods is the sparse matrix-vector multiplication (SpMV), because it is often an +expensive operation in terms of execution time and memory space. Moreover, it requires to take care of the storage format of the +sparse matrix in the memory. Indeed, the naive storage, row-by-row or column-by-column, of a sparse matrix can cause a significant +waste of memory space and execution time. In addition, the sparsity nature of the matrix often leads to irregular memory accesses +to read the matrix nonzero values. So, the computation of the SpMV multiplication on GPUs can involve non coalesced accesses to +the global memory, which slows down even more its performances. One of the most efficient compressed storage formats of sparse +matrices on GPUs is HYB format~\cite{ref7}. It is a combination of ELLpack (ELL) and Coordinate (COO) formats. Indeed, it stores +a typical number of nonzero values per row in ELL format and remaining entries of exceptional rows in COO format. It combines +the efficiency of ELL due to the regularity of its memory accesses and the flexibility of COO which is insensitive to the matrix +structure. Consequently, we use the HYB kernel~\cite{ref8} developed by Nvidia to implement the SpMV multiplication of CG and +GMRES methods on GPUs. Moreover, to avoid the non coalesced accesses to the high-latency global memory, we fill the elements of +the iterate vector $x$ in the cached texture memory. + +%%****************%% +%%****************%% +\subsection{Data communications} +\label{sec:03.03} +All the computing nodes of the GPU cluster execute in parallel the same iterative solver (Algorithm~\ref{alg:01} or Algorithm~\ref{alg:02}) +adapted to GPUs, but on their own portions of the sparse linear system: $M^{-1}_iA_ix_i=M^{-1}_ib_i$, $0\leq i0,\\ +(\frac{\partial u}{\partial t}+b^t.\nabla u-\eta.\Delta u+c.u-f)(u-\phi)=0\mbox{,~a.e.w. in~}\lbrack 0,T\rbrack\times\Omega,\\ +u(0,x,y,z)=u_0(x,y,z),\\ +\mbox{B.C. on~}u(t,x,y,z)\mbox{~defined on~}\partial\Omega, +\end{array} +\right. +\label{eq:01} +\end{equation} +where $u_0$ is the initial condition, $c\geq 0$, $b$ and $\eta$ are physical parameters, $T$ is the final time, $u=u(t,x,y,z)$ +is an element of the solution vector $U$ to compute, $f$ is the right-hand right that could represent, for example, the external +forces, B.C. describes the boundary conditions on the boundary $\partial\Omega$ of the domain $\Omega$, $\phi$ models a constraint +imposed to $u$, $\Delta$ is the Laplacian operator, $\nabla$ is the gradient operator, a.e.w. means almost every where and ``.'' +defines the products between two scalars, a scalar and a vector or a matrix and a vector. In practice the boundary condition, +generally considered, is the Dirichlet condition (where $u$ is fixed on $\partial\Omega$) or the Neumann condition (where the +normal derivative of $u$ is fixed on $\partial\Omega$). + +The time dependent equation~(\ref{eq:01}) is numerically solved by considering an implicit or a semi-implicit time marching, +where at each time step $k$ a stationary nonlinear problem is solved: +\begin{equation} +\left\{ +\begin{array}{l} +b^t.\nabla u-\eta.\Delta u+(c+\delta).u-g\geq 0\mbox{,~}u\geq\phi\mbox{,~a.e.w. in~}\lbrack 0,T\rbrack\times\Omega\mbox{,~}\eta>0, \\ +(b^t.\nabla u-\eta.\Delta u+(c+\delta).u- g)(u-\phi)=0\mbox{,~a.e.w. in~}\lbrack 0,T\rbrack\times\Omega, \\ +\mbox{B.C. on~}u(t,x,y,z)\mbox{~defined on~}\partial\Omega, +\end{array} +\right. +\label{eq:02} +\end{equation} +where $\delta=\frac{1}{k}$ is the inverse of the time step $k$, $g=f+\delta u^{prev}$ and $u^{prev}$ is the solution computed at the +previous time step. + + +%%******************* +%%******************* +\subsection{Discretization} +\label{sec:02.02} +First, we note that the spatial discretization of the previous stationary problem~(\ref{eq:02}) does not provide a symmetric matrix, +because the convection-diffusion operator is not self-adjoint. Moreover, the fact that the operator is self-adjoint or not plays an +important role in the choice of the appropriate algorithm for solving nonlinear systems derived from the discretization of the obstacle +problem. Nevertheless, since the convection coefficients arising in the operator~(\ref{eq:02}) are constant, we can formulate the same +problem by an self-adjoint operator by performing a classical change of variables. Then, we can replace the stationary convection-diffusion +problem: +\begin{equation} +b^{t}.\nabla v-\eta.\Delta v+(c+\delta).v=g\mbox{,~a.e.w. in~}\lbrack 0,T\rbrack\times\Omega\mbox{,~}c\geq 0\mbox{,~}\delta\geq~0, +\label{eq:03} +\end{equation} +by the following stationary diffusion operator: +\begin{equation} +-\eta.\Delta u+(\frac{\|b\|^{2}_{2}}{4\eta}+c+\delta).u=e^{-a}g=f, +\label{eq:04} +\end{equation} +where $b=\{b_{1},b_{2},b_{3}\}$, $\|b\|_{2}$ denotes the Euclidean norm of $b$ and $v=e^{-a}.u$ represents the general change of variables +such that $a=\frac{b^{t}(x,y,z)}{2\eta}$. Consequently, the numerical resolution of the diffusion problem (the self-adjoint operator~(\ref{eq:04})) +is done by optimization algorithms, in contrast, that of the convection-diffusion problem (non self-adjoint operator~(\ref{eq:03})) is +done by relaxation algorithms. In the case of our studied algorithm, the convergence is ensured by M-matrix property then, the performance +is linked to the magnitude of the spectral radius of the iteration matrix, which is independent of the condition number. + +Next, the three-dimensional domain $\Omega\subset\mathbb{R}^{3}$ is set to $\Omega=\lbrack 0,1\rbrack^{3}$ and discretized with an uniform +Cartesian mesh constituted by $M=m^3$ discretization points, where $m$ related to the spatial discretization step by $h=\frac{1}{m+1}$. This +is carried out by using a classical order 2 finite difference approximation of the Laplacian. So, the complete discretization of both stationary +boundary value problems~(\ref{eq:03}) and~(\ref{eq:04}) leads to the solution of a large discrete complementary problem of the following +form, when both Dirichlet or Neumann boundary conditions are used: +\begin{equation} +\left\{ +\begin{array}{l} +\mbox{Find~}U^{*}\in\mathbb{R}^{M}\mbox{~such~that} \\ +(A+\delta I)U^{*}-G\geq 0\mbox{,~}U^{*}\geq\bar{\Phi},\\ +((A+\delta I)U^{*}-G)^{T}(U^{*}-\bar{\Phi})=0,\\ +\end{array} +\right. +\label{eq:05} +\end{equation} +where $A$ is a matrix obtained after the spatial discretization by a finite difference method, $G$ is derived from the Euler first order implicit time +marching scheme and from the discretized right-hand side of the obstacle problem, $\delta$ is the inverse of the time step $k$ and $I$ is the identity +matrix. The matrix $A$ is symmetric when the self-adjoint operator is considered and nonsymmetric otherwise. + +According to the chosen discretization scheme of the Laplacian, $A$ is an M-matrix (irreducibly diagonal dominant, see~\cite{ref2}) and, consequently, +the matrix $(A+\delta I)$ is also an M-matrix. This property is important to the convergence of iterative methods. + + +%%--------------------------%% +%% SECTION 3 %% +%%--------------------------%% +\section{Parallel iterative method} +\label{sec:03} +Owing to the large size of the previous discrete complementary problem~(\ref{eq:05}), we will solve it by parallel synchronous or asynchronous iterative +algorithms (see~\cite{ref3,ref4,ref5}). In this chapter, we aim at harnessing the computing power of GPU clusters for solving these large nonlinear systems. +Then, we choose to use the projected Richardson iterative method for solving the diffusion problem~(\ref{eq:04}). Indeed, this method is based on the iterations +of the Jacobi method which are easy to parallelize on parallel computers and easy to adapt to GPU architectures. Then, according to the boundary value problem +formulation with a self-adjoint operator~(\ref{eq:04}), we can consider here the equivalent optimization problem and the fixed point mapping associated to +its solution. + +Assume that $E=\mathbb{R}^{M}$ is a Hilbert space, in which $\scalprod{.}{.}$ is the scalar product and $\|.\|$ its associated norm. So, the general fixed +point problem to be solved is defined as follows: +\begin{equation} +\left\{ +\begin{array}{l} +\mbox{Find~} U^{*} \in E \mbox{~such that} \\ +U^{*} = F(U^{*}), \\ +\end{array} +\right. +\label{eq:06} +\end{equation} +where $U\mapsto F(U)$ is an application from $E$ to $E$. + +Let $K$ be a closed convex set defined by: +\begin{equation} +K = \{U | U \geq \Phi \mbox{~everywhere in~} E\}, +\label{eq:07} +\end{equation} +where $\Phi$ is the discrete obstacle function. In fact, the obstacle problem~(\ref{eq:05}) is formulated as the following constrained optimization problem: +\begin{equation} +\left\{ +\begin{array}{l} +\mbox{Find~} U^{*} \in K \mbox{~such that} \\ +\forall V \in K, J(U^{*}) \leq J(V), \\ +\end{array} +\right. +\label{eq:08} +\end{equation} +where the cost function is given by: +\begin{equation} +J(U) = \frac{1}{2}\scalprod{\mathcal{A}.U}{U} - \scalprod{G}{U}, +\label{eq:09} +\end{equation} +in which $\scalprod{.}{.}$ denotes the scalar product in $E$, $\mathcal{A}=A+\delta I$ is a symmetric positive definite, $A$ is the discretization matrix +associated with the self-adjoint operator~(\ref{eq:04}) after change of variables. + +For any $U\in E$, let $P_K(U)$ be the projection of $U$ on $K$. For any $\gamma\in\mathbb{R}$, $\gamma>0$, the fixed point mapping $F_{\gamma}$ of the projected +Richardson method is defined as follows: +\begin{equation} +U^{*} = F_{\gamma}(U^{*}) = P_K(U^{*} - \gamma(\mathcal{A}.U^{*} - G)). +\label{eq:10} +\end{equation} +In order to reduce the computation time, the large optimization problem is solved in a numerical way by using a parallel asynchronous algorithm of the projected +Richardson method on the convex set $K$. Particularly, we will consider an asynchronous parallel adaptation of the projected Richardson method~\cite{ref6}. + +Let $\alpha\in\mathbb{N}$ be a positive integer. We consider that the space $E=\displaystyle\prod_{i=1}^{\alpha} E_i$ is a product of $\alpha$ subspaces $E_i$ +where $i\in\{1,\ldots,\alpha\}$. Note that $E_i=\mathbb{R}^{m_i}$, where $\displaystyle\sum_{i=1}^{\alpha} m_{i}=M$, is also a Hilbert space in which $\scalprod{.}{.}_i$ +denotes the scalar product and $|.|_i$ the associated norm, for all $i\in\{1,\ldots,\alpha\}$. Then, for all $u,v\in E$, $\scalprod{u}{v}=\displaystyle\sum_{i=1}^{\alpha}\scalprod{u_i}{v_i}_i$ +is the scalar product on $E$. + +Let $U\in E$, we consider the following decomposition of $U$ and the corresponding decomposition of $F_\gamma$ into $\alpha$ blocks: +\begin{equation} +\begin{array}{rcl} +U & = & (U_1,\ldots,U_{\alpha}), \\ +F_{\gamma}(U) & = & (F_{1,\gamma}(U),\ldots,F_{\alpha,\gamma}(U)). \\ +\end{array} +\label{eq:11} +\end{equation} +Assume that the convex set $K=\displaystyle\prod_{i=1}^{\alpha}K_{i}$, such that $\forall i\in\{1,\ldots,\alpha\},K_i\subset E_i$ and $K_i$ is a closed convex set. +Let also $G=(G_1,\ldots,G_{\alpha})\in E$ and, for any $U\in E$, $P_K(U)=(P_{K_1}(U_1),\ldots,P_{K_{\alpha}}(U_{\alpha}))$ is the projection of $U$ on $K$ where $\forall i\in\{1,\ldots,\alpha\},P_{K_i}$ +is the projector from $E_i$ onto $K_i$. So, the fixed point mapping of the projected Richardson method~(\ref{eq:10}) can be written in the following way: +\begin{equation} +\forall U\in E\mbox{,~}\forall i\in\{1,\ldots,\alpha\}\mbox{,~}F_{i,\gamma}(U) = P_{K_i}(U_i - \gamma(\mathcal{A}_i.U - G_i)). +\label{eq:12} +\end{equation} +Note that $\displaystyle\mathcal{A}_i.U= \sum_{j=1}^{\alpha}\mathcal{A}_{i,j}.U_j$, where $\mathcal{A}_{i,j}$ denote block matrices of $\mathcal{A}$. + +The parallel asynchronous iterations of the projected Richardson method for solving the obstacle problem~(\ref{eq:08}) are defined as follows: let $U^0\in E,U^0=(U^0_1,\ldots,U^0_\alpha)$ be +the initial solution, then for all $p\in\mathbb{N}$, the iterate $U^{p+1}=(U^{p+1}_1,\ldots,U^{p+1}_{\alpha})$ is recursively defined by: +\begin{equation} +U_i^{p+1} = +\left\{ +\begin{array}{l} +F_{i,\gamma}(U_1^{\rho_1(p)}, \ldots, U_{\alpha}^{\rho_{\alpha}(p)}) \mbox{~if~} i\in s(p), \\ +U_i^p \mbox{~otherwise}, \\ +\end{array} +\right. +\label{eq:13} +\end{equation} +where +\begin{equation} +\left\{ +\begin{array}{l} +\forall p\in\mathbb{N}, s(p)\subset\{1,\ldots,\alpha\}\mbox{~and~} s(p)\ne\emptyset, \\ +\forall i\in\{1,\ldots,\alpha\},\{p \ | \ i \in s(p)\}\mbox{~is denombrable}, +\end{array} +\right. +\label{eq:14} +\end{equation} +and $\forall j\in\{1,\ldots,\alpha\}$, +\begin{equation} +\left\{ +\begin{array}{l} +\forall p\in\mathbb{N}, \rho_j(p)\in\mathbb{N}, 0\leq\rho_j(p)\leq p\mbox{~and~}\rho_j(p)=p\mbox{~if~} j\in s(p),\\ +\displaystyle\lim_{p\to\infty}\rho_j(p) = +\infty.\\ +\end{array} +\right. +\label{eq:15} +\end{equation} + +The previous asynchronous scheme of the projected Richardson method models computations that are carried out in parallel +without order nor synchronization (according to the behavior of the parallel iterative method) and describes a subdomain +method without overlapping. It is a general model that takes into account all possible situations of parallel computations +and non-blocking message passing. So, the synchronous iterative scheme is defined by: +\begin{equation} +\forall j\in\{1,\ldots,\alpha\} \mbox{,~} \forall p\in\mathbb{N} \mbox{,~} \rho_j(p)=p. +\label{eq:16} +\end{equation} +The values of $s(p)$ and $\rho_j(p)$ are defined dynamically and not explicitly by the parallel asynchronous or synchronous +execution of the algorithm. Particularly, it enables one to consider distributed computations whereby processors compute at +their own pace according to their intrinsic characteristics and computational load. The parallelism between the processors is +well described by the set $s(p)$ which contains at each step $p$ the index of the components relaxed by each processor on a +parallel way while the use of delayed components in~(\ref{eq:13}) permits one to model nondeterministic behavior and does not +imply inefficiency of the considered distributed scheme of computation. Note that, according to~\cite{ref7}, theoretically, +each component of the vector must be relaxed an infinity of time. The choice of the relaxed components to be used in the +computational process may be guided by any criterion and, in particular, a natural criterion is to pick-up the most recently +available values of the components computed by the processors. Furthermore, the asynchronous iterations are implemented by +means of non-blocking MPI communication subroutines (asynchronous communications). + +The important property ensuring the convergence of the parallel projected Richardson method, both synchronous and asynchronous +algorithms, is the fact that $\mathcal{A}$ is an M-matrix. Moreover, the convergence proceeds from a result of~\cite{ref6}. +Indeed, there exists a value $\gamma_0>0$, such that $\forall\gamma\in ]0,\gamma_0[$, the parallel iterations~(\ref{eq:13}), +(\ref{eq:14}) and~(\ref{eq:15}), associated to the fixed point mapping $F_\gamma$~(\ref{eq:12}), converge to the unique solution +$U^{*}$ of the discretized problem. + + +%%--------------------------%% +%% SECTION 4 %% +%%--------------------------%% +\section{Parallel implementation on a GPU cluster} +\label{sec:04} +In this section, we give the main key points of the parallel implementation of the projected Richardson method, both synchronous +and asynchronous versions, on a GPU cluster, for solving the nonlinear systems derived from the discretization of large obstacle +problems. More precisely, each nonlinear system is solved iteratively using the whole cluster. We use a heteregeneous CUDA/MPI +programming. Indeed, the communication of data, at each iteration between the GPU computing nodes, can be either synchronous +or asynchronous using the MPI communication subroutines, whereas inside each GPU node, a CUDA parallelization is performed. + +\begin{figure}[!h] +\centerline{\includegraphics[scale=0.30]{Chapters/chapter13/figures/splitCPU}} +\caption{Data partitioning of a problem to be solved among $S=3\times 4$ computing nodes.} +\label{fig:01} +\end{figure} + +Let $S$ denote the number of computing nodes on the GPU cluster, where a computing node is composed of CPU core holding one MPI +process and a GPU card. So, before starting computations, the obstacle problem of size $(NX\times NY\times NZ)$ is split into $S$ +parallelepipedic sub-problems, each for a node (MPI process, GPU), as is shown in Figure~\ref{fig:01}. Indeed, the $NY$ and $NZ$ +dimensions (according to the $y$ and $z$ axises) of the three-dimensional problem are, respectively, split into $Sy$ and $Sz$ parts, +such that $S=Sy\times Sz$. In this case, each computing node has at most four neighboring nodes. This kind of the data partitioning +reduces the data exchanges at subdomain boundaries compared to a naive $z$-axis-wise partitioning. + +\begin{algorithm}[!t] +%\SetLine +%\linesnumbered +Initialization of the parameters of the sub-problem\; +Allocate and fill the data in the global memory GPU\; +\For{$i=1$ {\bf to} $NbSteps$}{ + $G = \frac{1}{k}.U^0 + F$\; + Solve($A$, $U^0$, $G$, $U$, $\varepsilon$, $MaxRelax$)\; + $U^0 = U$\; +} +Copy the solution $U$ back from GPU memory\; +\caption{Parallel solving of the obstacle problem on a GPU cluster} +\label{alg:01} +\end{algorithm} + +All the computing nodes of the GPU cluster execute in parallel the same Algorithm~\ref{alg:01} but on different three-dimensional +sub-problems of size $(NX\times ny\times nz)$. This algorithm gives the main key points for solving an obstacle problem defined in +a three-dimensional domain, where $A$ is the discretization matrix, $G$ is the right-hand side and $U$ is the solution vector. After +the initialization step, all the data generated from the partitioning operation are copied from the CPU memories to the GPU global +memories, to be processed on the GPUs. Next, the algorithm uses $NbSteps$ time steps to solve the global obstacle problem. In fact, +it uses a parallel algorithm adapted to GPUs of the projected Richardson iterative method for solving the nonlinear systems of the +obstacle problem. This function is defined by {\it Solve()} in Algorithm~\ref{alg:01}. At every time step, the initial guess $U^0$ +for the iterative algorithm is set to the solution found at the previous time step. Moreover, the right-hand side $G$ is computed +as follows: \[G = \frac{1}{k}.U^{prev} + F\] where $k$ is the time step, $U^{prev}$ is the solution computed in the previous time +step and each element $f(x, y, z)$ of the vector $F$ is computed as follows: +\begin{equation} +f(x,y,z)=\cos(2\pi x)\cdot\cos(4\pi y)\cdot\cos(6\pi z). +\label{eq:18} +\end{equation} +Finally, the solution $U$ of the obstacle problem is copied back from the GPU global memories to the CPU memories. We use the +communication subroutines of the CUBLAS library~\cite{ref8} (CUDA Basic Linear Algebra Subroutines) for the memory allocations in +the GPU (\verb+cublasAlloc()+) and the data transfers between the CPU and its GPU: \verb+cublasSetVector()+ and \verb+cublasGetVector()+. + +\begin{algorithm}[!t] +% \SetLine +% \linesnumbered + $p = 0$\; + $conv = false$\; + $U = U^{0}$\; + \Repeat{$(conv=true)$}{ + Determine\_Bordering\_Vector\_Elements($U$)\; + Compute\_New\_Vector\_Elements($A$, $G$, $U$)\; + $tmp = U^{0} - U$\; + $error = \|tmp\|_{2}$\; + $U^{0} = U$\; + $p = p + 1$\; + $conv$ = Convergence($error$, $p$, $\varepsilon$, $MaxRelax$)\; + } +\caption{Parallel iterative solving of the nonlinear systems on a GPU cluster ($Solve()$ function)} +\label{alg:02} +\end{algorithm} + +As many other iterative methods, the algorithm of the projected Richardson method is based on algebraic functions operating on vectors +and/or matrices, which are more efficient on parallel computers when they work on large vectors. Its parallel implementation on the GPU +cluster is carried out so that the GPUs execute the vector operations as kernels and the CPUs execute the serial codes, supervise the +kernel executions and the data exchanges with the neighboring nodes and supply the GPUs with data. Algorithm~\ref{alg:02} shows the +main key points of the parallel iterative algorithm (function $Solve()$ in Algorithm~\ref{alg:01}). All the vector operations inside +the main loop ({\bf repeat} ... {\bf until}) are executed by the GPU. We use the following functions of the CUBLAS library: +\begin{itemize} +\item \verb+cublasDaxpy()+ to compute the difference between the solution vectors $U^{p}$ and $U^{p+1}$ computed in two successive relaxations +$p$ and $p+1$ (line~$7$ in Algorithm~\ref{alg:02}), +\item \verb+cublasDnrm2()+ to perform the Euclidean norm (line~$8$) and, +\item \verb+cublasDcpy()+ for the data copy of a vector to another one in the GPU memory (lines~$3$ and~$9$). +\end{itemize} + +The dimensions of the grid and blocks of threads that execute a given kernel depend on the resources of the GPU multiprocessor and the +resource requirements of the kernel. So, if $block$ defines the size of a thread block, which must not exceed the maximum size of a thread +block, then the number of thread blocks in the grid, denoted by $grid$, can be computed according to the size of the local sub-problem +as follows: \[grid = \frac{(NX\times ny\times nz)+block-1}{block}.\] However, when solving very large problems, the size of the thread +grid can exceed the maximum number of thread blocks that can be executed on the GPUs (up-to $65.535$ thread blocks) and, thus, the kernel +will fail to launch. Therefore, for each kernel, we decompose the three-dimensional sub-problem into $nz$ two-dimensional slices of size +($NX\times ny$), as is shown in Figure~\ref{fig:02}. All slices of the same kernel are executed using {\bf for} loop by $NX\times ny$ parallel +threads organized in a two-dimensional grid of two-dimensional thread blocks, as is shown in Listing~\ref{list:01}. Each thread is in charge +of $nz$ discretization points (one from each slice), accessed in the GPU memory with a constant stride $(NX\times ny)$. + +\begin{figure} +\centerline{\includegraphics[scale=0.30]{Chapters/chapter13/figures/splitGPU}} +\caption{Decomposition of a sub-problem in a GPU into $nz$ slices.} +\label{fig:02} +\end{figure} + +\begin{center} +\lstinputlisting[label=list:01,caption=Skeleton codes of a GPU kernel and a CPU function]{Chapters/chapter13/ex1.cu} +\end{center} +The function $Determine\_Bordering\_Vector\_Elements()$ (line~$5$ in Algorithm~\ref{alg:02}) determines the values of the vector +elements shared at the boundaries with neighboring computing nodes. Its main operations are defined as follows: +\begin{enumerate} +\item define the values associated to the bordering points needed by the neighbors, +\item copy the values associated to the bordering points from the GPU to the CPU, +\item exchange the values associated to the bordering points between the neighboring CPUs, +\item copy the received values associated to the bordering points from the CPU to the GPU, +\end{enumerate} +The first operation of this function is implemented as kernels to be performed by the GPU: +\begin{itemize} +\item a kernel executed by $NX\times nz$ threads to define the values associated to the bordering vector elements along $y$-axis and, +\item a kernel executed by $NX\times ny$ threads to define the values associated to the bordering vector elements along $z$-axis. +\end{itemize} +As mentioned before, we develop the \emph{synchronous} and \emph{asynchronous} algorithms of the projected Richardson method. Obviously, +in this scope, the synchronous or asynchronous communications refer to the communications between the CPU cores (MPI processes) on the +GPU cluster, in order to exchange the vector elements associated to subdomain boundaries. For the memory copies between a CPU core and +its GPU, we use the synchronous communication routines of the CUBLAS library: \verb+cublasSetVector()+ and \verb+cublasGetVector()+ +in the synchronous algorithm and the asynchronous ones: \verb+cublasSetVectorAsync()+ and \verb+cublasGetVectorAsync()+ in the +asynchronous algorithm. Moreover, we use the communication routines of the MPI library to carry out the data exchanges between the neighboring +nodes. We use the following communication routines: \verb+MPI_Isend()+ and \verb+MPI_Irecv()+ to perform non-blocking sends and receptions, +respectively. For the synchronous algorithm, we use the MPI routine \verb+MPI_Waitall()+ which puts the MPI process of a computing node +in blocking status until all data exchanges with neighboring nodes (sends and receptions) are completed. In contrast, for the asynchronous +algorithms, we use the MPI routine \verb+MPI_Test()+ which tests the completion of a data exchange (send or reception) without putting the +MPI process in blocking status. + +The function $Compute\_New\_Vector\_Elements()$ (line~$6$ in Algorithm~\ref{alg:02}) computes, at each iteration, the new elements +of the iterate vector $U$. Its general code is presented in Listing~\ref{list:01} (CPU function). The iterations of the projected +Richardson method, based on those of the Jacobi method, are defined as follows: +\begin{equation} +\begin{array}{ll} +u^{p+1}(x,y,z) =& \frac{1}{Center}(g(x,y,z) - (Center\cdot u^{p}(x,y,z) + \\ +& West\cdot u^{p}(x-h,y,z) + East\cdot u^{p}(x+h,y,z) + \\ +& South\cdot u^{p}(x,y-h,z) + North\cdot u^{p}(x,y+h,z) + \\ +& Rear\cdot u^{p}(x,y,z-h) + Front\cdot u^{p}(x,y,z+h))), +\end{array} +\label{eq:17} +\end{equation} +where $u^{p}(x,y,z)$ is an element of the iterate vector $U$ computed at the iteration $p$ and $g(x,y,z)$ is a vector element of the +right-hand side $G$. The scalars $Center$, $West$, $East$, $South$, $North$, $Rear$ and $Front$ define constant coefficients of the +block matrix $A$. Figure~\ref{fig:03} shows the positions of these coefficients in a three-dimensional domain. + +\begin{figure} +\centerline{\includegraphics[scale=0.35]{Chapters/chapter13/figures/matrix}} +\caption{Matrix constant coefficients in a three-dimensional domain.} +\label{fig:03} +\end{figure} + +The kernel implementations of the projected Richardson method on GPUs uses a perfect fine-grain multithreading parallelism. Since the +projected Richardson algorithm is implemented as a fixed point method, each kernel is executed by a large number of GPU threads such +that each thread is in charge of the computation of one element of the iterate vector $U$. Moreover, this method uses the vector elements +updates of the Jacobi method, which means that each thread $i$ computes the new value of its element $u_{i}^{p+1}$ independently of the +new values $u_{j}^{p+1}$, where $j\neq i$, of those computed in parallel by other threads at the same iteration $p+1$. Listing~\ref{list:02} +shows the GPU implementations of the main kernels of the projected Richardson method, which are: the matrix-vector multiplication +(\verb+MV_Multiplication()+) and the vector elements updates (\verb+Vector_Updates()+). The codes of these kernels are based on +that presented in Listing~\ref{list:01}. + +\lstinputlisting[label=list:02,caption=GPU kernels of the projected Richardson method]{Chapters/chapter13/ex2.cu} + +\begin{figure} +\centerline{\includegraphics[scale=0.3]{Chapters/chapter13/figures/points3D}} +\caption{Computation of a vector element with the projected Richardson method.} +\label{fig:04} +\end{figure} + +Each kernel is executed by $NX\times ny$ GPU threads so that $nz$ slices of $(NX\times ny)$ vector elements are computed in +a {\bf for} loop. In this case, each thread is in charge of one vector element from each slice (in total $nz$ vector elements +along $z$-axis). We can notice from the formula~(\ref{eq:17}) that the computation of a vector element $u^{p+1}(x,y,z)$, by +a thread at iteration $p+1$, requires seven vector elements computed at the previous iteration $p$: two vector elements in +each dimension plus the vector element at the intersection of the three axises $x$, $y$ and $z$ (see Figure~\ref{fig:04}). +So, to reduce the memory accesses to the high-latency global memory, the vector elements of the current slice can be stored +in the low-latency shared memories of thread blocks, as is described in~\cite{ref9}. Nevertheless, the fact that the computation +of a vector element requires only two elements in each dimension does not allow to maximize the data reuse from the shared memories. +The computation of a slice involves in total $(bx+2)\times(by+2)$ accesses to the global memory per thread block, to fill the +required vector elements in the shared memory where $bx$ and $by$ are the dimensions of a thread block. Then, in order to optimize +the memory accesses on GPUs, the elements of the iterate vector $U$ are filled in the cache texture memory (see~\cite{ref10}). +In new GPU generations as Fermi or Kepler, the global memory accesses are always cached in L1 and L2 caches. For example, for +a given kernel, we can favour the use of the L1 cache to that of the shared memory by using the function \verb+cudaFuncSetCacheConfig(Kernel,cudaFuncCachePreferL1)+. +So, the initial access to the global memory loads the vector elements required by the threads of a block into the cache memory +(texture or L1/L2 caches). Then, all the following memory accesses read from this cache memory. In Listing~\ref{list:02}, the +function \verb+fetch_double(v,i)+ is used to read from the texture memory the $i^{th}$ element of the double-precision vector +\verb+v+ (see Listing~\ref{list:03}). Moreover, the seven constant coefficients of matrix $A$ can be stored in the constant memory +but, since they are reused $nz$ times by each thread, it is more interesting to fill them on the low-latency registers of each thread. + +\lstinputlisting[label=list:03,caption=Memory access to the cache texture memory]{Chapters/chapter13/ex3.cu} + +The function $Convergence()$ (line~$11$ in Algorithm~\ref{alg:02}) allows to detect the convergence of the parallel iterative algorithm +and is based on the tolerance threshold $\varepsilon$ and the maximum number of relaxations $MaxRelax$. We take into account the number +of relaxations since that of iterations cannot be computed in the asynchronous case. Indeed, a relaxation is the update~(\ref{eq:13}) of +a local iterate vector $U_i$ according to $F_i$. Then, counting the number of relaxations is possible in both synchronous and asynchronous +cases. On the other hand, an iteration is the update of at least all vector components with $F_i$. + +In the synchronous algorithm, the global convergence is detected when the maximal value of the absolute error, $error$, is sufficiently small +and/or the maximum number of relaxations, $MaxRelax$, is reached, as follows: +$$ +\begin{array}{l} +error=\|U^{p}-U^{p+1}\|_{2}; \\ +AllReduce(error,\hspace{0.1cm}maxerror,\hspace{0.1cm}MAX); \\ +\text{if}((maxerror<\varepsilon)\hspace{0.2cm}\text{or}\hspace{0.2cm}(p\geq MaxRelax)) \\ +conv \leftarrow true; +\end{array} +$$ +where the function $AllReduce()$ uses the MPI reduction subroutine \verb+MPI_Allreduce()+ to compute the maximal value, $maxerror$, among the +local absolute errors, $error$, of all computing nodes and $p$ (in Algorithm~\ref{alg:02}) is used as a counter of the local relaxations carried +out by a computing node. In the asynchronous algorithms, the global convergence is detected when all computing nodes locally converge. For this, +we use a token ring architecture around which a boolean token travels, in one direction, from a computing node to another. Starting from node $0$, +the boolean token is set to $true$ by node $i$ if the local convergence is reached or to $false$ otherwise and, then, it is sent to node $i+1$. +Finally, the global convergence is detected when node $0$ receives from its neighbor node $S-1$, in the ring architecture, a token set to $true$. +In this case, node $0$ sends a stop message (end of parallel solving) to all computing nodes in the cluster. + + +%%--------------------------%% +%% SECTION 5 %% +%%--------------------------%% +\section{Experimental tests on a GPU cluster} +\label{sec:05} +The GPU cluster of tests, that we used in this chapter, is an $20Gbps$ Infiniband network of six machines. Each machine is a Quad-Core Xeon +E5530 CPU running at $2.4$GHz. It provides a RAM memory of $12$GB with a memory bandwidth of $25.6$GB/s and it is equipped with two Nvidia +Tesla C1060 GPUs. A Tesla GPU contains in total $240$ cores running at $1.3$GHz. It provides $4$GB of global memory with a memory bandwidth +of $102$GB/s, accessible by all its cores and also by the CPU through the PCI-Express 16x Gen 2.0 interface with a throughput of $8$GB/s. +Hence, the memory copy operations between the GPU and the CPU are about $12$ times slower than those of the Tesla GPU memory. We have performed +our simulations on a cluster of $24$ CPU cores and on a cluster of $12$ GPUs. Figure~\ref{fig:05} describes the components of the GPU cluster +of tests. + +\begin{figure} +\centerline{\includegraphics[scale=0.25]{Chapters/chapter13/figures/cluster}} +\caption{GPU cluster of tests composed of 12 computing nodes (six machines, each with two GPUs.} +\label{fig:05} +\end{figure} + +Linux cluster version 2.6.39 OS is installed on CPUs. C programming language is used for coding the parallel algorithms of the methods on both +GPU cluster and CPU cluster. CUDA version 4.0~\cite{ref12} is used for programming GPUs, using CUBLAS library~\cite{ref8} to deal with vector +operations in GPUs and, finally, MPI functions of OpenMPI 1.3.3 are used to carry out the synchronous and asynchronous communications between +CPU cores. Indeed, in our experiments, a computing node is managed by a MPI process and it is composed of one CPU core and one GPU card. + +All experimental results of the parallel projected Richardson algorithms are obtained from simulations made in double precision data. The obstacle +problems to be solved are defined in constant three-dimensional domain $\Omega\subset\mathbb{R}^{3}$. The numerical values of the parameters of the +obstacle problems are: $\eta=0.2$, $c=1.1$, $f$ is computed by formula~(\ref{eq:18}) and final time $T=0.02$. Moreover, three time steps ($NbSteps=3$) +are computed with $k=0.0066$. As the discretization matrix is constant along the time steps, the convergence properties of the iterative algorithms +do not change. Thus, the performance characteristics obtained with three time steps will still be valid for more time steps. The initial function +$u(0,x,y,z)$ of the obstacle problem~(\ref{eq:01}) is set to $0$, with a constraint $u\geq\phi=0$. The relaxation parameter $\gamma$ used by the +projected Richardson method is computed automatically thanks to the diagonal entries of the discretization matrix. The formula and its proof can be +found in~\cite{ref11}, Section~2.3. The convergence tolerance threshold $\varepsilon$ is set to $1e$-$04$ and the maximum number of relaxations is +limited to $10^{6}$ relaxations. Finally, the number of threads per block is set to $256$ threads, which gives, in general, good performances for +most GPU applications. We have performed some tests for the execution configurations and we have noticed that the best configuration of the $256$ +threads per block is an organization into two dimensions of sizes $(64,4)$. + +\begin{table}[!h] +\centering +\begin{tabular}{|c|c|c|c|c|c|} +\hline +\multirow{2}{*}{\bf Pb. size} & \multicolumn{2}{c|}{\bf Synchronous} & \multicolumn{2}{c|}{\bf Asynchronous} & \multirow{2}{*}{\bf Gain\%} \\ \cline{2-5} + + & $\mathbf{T_{cpu}}$ & {\bf \#relax.} & $\mathbf{T_{cpu}}$ & {\bf \#relax.} & \\ \hline \hline + +$256^{3}$ & $575.22$ & $198,288$ & $539.25$ & $198,613$ & $6.25$ \\ \hline \hline + +$512^{3}$ & $19,250.25$ & $750,912$ & $18,237.14$ & $769,611$ & $5.26$ \\ \hline \hline + +$768^{3}$ & $206,159.44$ & $1,635,264$ & $183,582.60$ & $1,577,004$ & $10.95$ \\ \hline \hline + +$800^{3}$ & $222,108.09$ & $1,769,232$ & $188,790.04$ & $1,701,735$ & $15.00$ \\ \hline +\end{tabular} +\vspace{0.5cm} +\caption{Execution times in seconds of the parallel projected Richardson method implemented on a cluster of 24 CPU cores.} +\label{tab:01} +\end{table} + +\begin{table}[!h] +\centering +\begin{tabular}{|c|c|c|c|c|c|c|c|} +\hline +\multirow{2}{*}{\bf Pb. size} & \multicolumn{3}{c|}{\bf Synchronous} & \multicolumn{3}{c|}{\bf Asynchronous} & \multirow{2}{*}{\bf Gain\%} \\ \cline{2-7} + + & $\mathbf{T_{gpu}}$ & {\bf \#relax.} & $\mathbf{\tau}$ & $\mathbf{T_{gpu}}$ & {\bf \#relax.} & $\mathbf{\tau}$ & \\ \hline \hline + +$256^{3}$ & $29.67$ & $100,692$ & $19.39$ & $18.00$ & $94,215$ & $29.96$ & $39.33$ \\ \hline \hline + +$512^{3}$ & $521.83$ & $381,300$ & $36.89$ & $425.15$ & $347,279$ & $42.89$ & $18.53$ \\ \hline \hline + +$768^{3}$ & $4,112.68$ & $831,144$ & $50.13$ & $3,313.87$ & $750,232$ & $55.40$ & $19.42$ \\ \hline \hline + +$800^{3}$ & $3,950.87$ & $899,088$ & $56.22$ & $3,636.57$ & $834,900$ & $51.91$ & $7.95$ \\ \hline +\end{tabular} +\vspace{0.5cm} +\caption{Execution times in seconds of the parallel projected Richardson method implemented on a cluster of 12 GPUs.} +\label{tab:02} +\end{table} + +The performance measures that we took into account are the execution times and the number of relaxations performed by the parallel iterative algorithms, +both synchronous and asynchronous versions, on the GPU and CPU clusters. These algorithms are used for solving nonlinear systems derived from the discretization +of obstacle problems of sizes $256^{3}$, $512^{3}$, $768^{3}$ and $800^{3}$. In Table~\ref{tab:01} and Table~\ref{tab:02}, we show the performances +of the parallel synchronous and asynchronous algorithms of the projected Richardson method implemented, respectively, on a cluster of $24$ CPU cores +and on a cluster of $12$ GPUs. In these tables, the execution time defines the time spent by the slowest computing node and the number of relaxations +is computed as the summation of those carried out by all computing nodes. + +In the sixth column of Table~\ref{tab:01} and in the eighth column of Table~\ref{tab:02}, we give the gains in $\%$ obtained by using an +asynchronous algorithm compared to a synchronous one. We can notice that the asynchronous version on CPU and GPU clusters is slightly faster +than the synchronous one for both methods. Indeed, the cluster of tests is composed of local and homogeneous nodes communicating via low-latency +connections. So, in the case of distant and/or heterogeneous nodes (or even with geographically distant clusters) the asynchronous version +would be faster than the synchronous one. However, the gains obtained on the GPU cluster are better than those obtained on the CPU cluster. +In fact, the computation times are reduced by accelerating the computations on GPUs while the communication times still unchanged. + +The fourth and seventh columns of Table~\ref{tab:02} show the relative gains obtained by executing the parallel algorithms on the cluster +of $12$ GPUs instead on the cluster of $24$ CPU cores. We compute the relative gain $\tau$ as a ratio between the execution time $T_{cpu}$ +spent on the CPU cluster over that $T_{gpu}$ spent on the GPU cluster: \[\tau=\frac{T_{cpu}}{T_{gpu}}.\] We can see from these ratios that +solving large obstacle problems is faster on the GPU cluster than on the CPU cluster. Indeed, the GPUs are more efficient than their +counterpart CPUs to execute large data-parallel operations. In addition, the projected Richardson method is implemented as a fixed point-based +iteration and uses the Jacobi vector updates that allow a well thread-parallelization on GPUs, such that each GPU thread is in charge +of one vector component at a time without being dependent on other vector components computed by other threads. Then, this allow to exploit +at best the high performance computing of the GPUs by using all the GPU resources and avoiding the idle cores. + +Finally, the number of relaxations performed by the parallel synchronous algorithm is different in the CPU and GPU versions, because the number +of computing nodes involved in the GPU cluster and in the CPU cluster is different. In the CPU case, $24$ computing nodes ($24$ CPU cores) are +considered, whereas in the GPU case, $12$ computing nodes ($12$ GPUs) are considered. As the number of relaxations depends on the domain decomposition, +consequently it also depends on the number of computing nodes. + + +%%--------------------------%% +%% SECTION 6 %% +%%--------------------------%% +\section{Red-Black ordering technique} +\label{sec:06} +As is well-known, the Jacobi method is characterized by a slow convergence rate compared to some iterative methods (for example Gauss-Seidel method). +So, in this section, we present some solutions to reduce the execution time and the number of relaxations and, more specifically, to speed up the +convergence of the parallel projected Richardson method on the GPU cluster. We propose to use the point red-black ordering technique to accelerate +the convergence. This technique is often used to increase the parallelism of iterative methods for solving linear systems~\cite{ref13,ref14,ref15}. +We apply it to the projected Richardson method as a compromise between the Jacobi and Gauss-Seidel iterative methods. + +The general principle of the red-black technique is as follows. Let $t$ be the summation of the integer $x$-, $y$- and $z$-coordinates of a vector +element $u(x,y,z)$ on a three-dimensional domain: $t=x+y+z$. As is shown in Figure~\ref{fig:06.01}, the red-black ordering technique consists in the +parallel computing of the red vector elements having even value $t$ by using the values of the black ones then, the parallel computing of the black +vector elements having odd values $t$ by using the new values of the red ones. + +\begin{figure} +\centering + \mbox{\subfigure[Red-black ordering on x, y and z axises]{\includegraphics[width=2.3in]{Chapters/chapter13/figures/rouge-noir}\label{fig:06.01}}\quad + \subfigure[Red-black ordering on y axis]{\includegraphics[width=2.3in]{Chapters/chapter13/figures/rouge-noir-y}\label{fig:06.02}}} +\caption{Red-black ordering for computing the iterate vector elements in a three-dimensional space.} +\end{figure} + +This technique can be implemented on the GPU in two different manners: +\begin{itemize} +\item among all launched threads ($NX\times ny$ threads), only one thread out of two computes its red or black vector element at a time or, +\item all launched threads (on average half of $NX\times ny$ threads) compute the red vector elements first and, then, the black ones. +\end{itemize} +However, in both solutions, for each memory transaction, only half of the memory segment addressed by a half-warp is used. So, the computation of the +red and black vector elements leads to use twice the initial number of memory transactions. Then, we apply the point red-black ordering accordingly to +the $y$-coordinate, as is shown in Figure~\ref{fig:06.02}. In this case, the vector elements having even $y$-coordinate are computed in parallel using +the values of those having odd $y$-coordinate and then vice-versa. Moreover, in the GPU implementation of the parallel projected Richardson method (Section~\ref{sec:04}), +we have shown that a sub-problem of size $(NX\times ny\times nz)$ is decomposed into $nz$ grids of size $(NX\times ny)$. Then, each kernel is executed +in parallel by $NX\times ny$ GPU threads, so that each thread is in charge of $nz$ vector elements along $z$-axis (one vector element in each grid of +the sub-problem). So, we propose to use the new values of the vector elements computed in grid $i$ to compute those of the vector elements in grid $i+1$. +Listing~\ref{list:04} describes the kernel of the matrix-vector multiplication and the kernel of the vector elements updates of the parallel projected +Richardson method using the red-black ordering technique. + +\lstinputlisting[label=list:04,caption=GPU kernels of the projected Richardson method using the red-black technique]{Chapters/chapter13/ex4.cu} + +Finally, we exploit the concurrent executions between the host functions and the GPU kernels provided by the GPU hardware and software. In fact, the kernel +launches are asynchronous (when this environment variable is not disabled on the GPUs), such that the control is returned to the host (MPI process) before +the GPU has completed the requested task (kernel)~\cite{ref12}. Therefore, all the kernels necessary to update the local vector elements, $u(x,y,z)$ where +$00,\\ +(\frac{\partial u}{\partial t}+b^t.\nabla u-\eta.\Delta u+c.u-f)(u-\phi)=0\mbox{,~a.e.w. in~}\lbrack 0,T\rbrack\times\Omega,\\ +u(0,x,y,z)=u_0(x,y,z),\\ +\mbox{B.C. on~}u(t,x,y,z)\mbox{~defined on~}\partial\Omega, +\end{array} +\right. +\label{eq:01} +\end{equation} +where $u_0$ is the initial condition, $c\geq 0$, $b$ and $\eta$ are physical parameters, $T$ is the final time, $u=u(t,x,y,z)$ +is an element of the solution vector $U$ to compute, $f$ is the right-hand right that could represent, for example, the external +forces, B.C. describes the boundary conditions on the boundary $\partial\Omega$ of the domain $\Omega$, $\phi$ models a constraint +imposed to $u$, $\Delta$ is the Laplacian operator, $\nabla$ is the gradient operator, a.e.w. means almost every where and ``.'' +defines the products between two scalars, a scalar and a vector or a matrix and a vector. In practice the boundary condition, +generally considered, is the Dirichlet condition (where $u$ is fixed on $\partial\Omega$) or the Neumann condition (where the +normal derivative of $u$ is fixed on $\partial\Omega$). + +The time dependent equation~(\ref{eq:01}) is numerically solved by considering an implicit or a semi-implicit time marching, +where at each time step $k$ a stationary nonlinear problem is solved: +\begin{equation} +\left\{ +\begin{array}{l} +b^t.\nabla u-\eta.\Delta u+(c+\delta).u-g\geq 0\mbox{,~}u\geq\phi\mbox{,~a.e.w. in~}\lbrack 0,T\rbrack\times\Omega\mbox{,~}\eta>0, \\ +(b^t.\nabla u-\eta.\Delta u+(c+\delta).u- g)(u-\phi)=0\mbox{,~a.e.w. in~}\lbrack 0,T\rbrack\times\Omega, \\ +\mbox{B.C. on~}u(t,x,y,z)\mbox{~defined on~}\partial\Omega, +\end{array} +\right. +\label{eq:02} +\end{equation} +where $\delta=\frac{1}{k}$ is the inverse of the time step $k$, $g=f+\delta u^{prev}$ and $u^{prev}$ is the solution computed at the +previous time step. + + +%%******************* +%%******************* +\subsection{Discretization} +\label{sec:02.02} +First, we note that the spatial discretization of the previous stationary problem~(\ref{eq:02}) does not provide a symmetric matrix, +because the convection-diffusion operator is not self-adjoint. Moreover, the fact that the operator is self-adjoint or not plays an +important role in the choice of the appropriate algorithm for solving nonlinear systems derived from the discretization of the obstacle +problem. Nevertheless, since the convection coefficients arising in the operator~(\ref{eq:02}) are constant, we can formulate the same +problem by an self-adjoint operator by performing a classical change of variables. Then, we can replace the stationary convection-diffusion +problem: +\begin{equation} +b^{t}.\nabla v-\eta.\Delta v+(c+\delta).v=g\mbox{,~a.e.w. in~}\lbrack 0,T\rbrack\times\Omega\mbox{,~}c\geq 0\mbox{,~}\delta\geq~0, +\label{eq:03} +\end{equation} +by the following stationary diffusion operator: +\begin{equation} +-\eta.\Delta u+(\frac{\|b\|^{2}_{2}}{4\eta}+c+\delta).u=e^{-a}g=f, +\label{eq:04} +\end{equation} +where $b=\{b_{1},b_{2},b_{3}\}$, $\|b\|_{2}$ denotes the Euclidean norm of $b$ and $v=e^{-a}.u$ represents the general change of variables +such that $a=\frac{b^{t}(x,y,z)}{2\eta}$. Consequently, the numerical resolution of the diffusion problem (the self-adjoint operator~(\ref{eq:04})) +is done by optimization algorithms, in contrast, that of the convection-diffusion problem (non self-adjoint operator~(\ref{eq:03})) is +done by relaxation algorithms. In the case of our studied algorithm, the convergence is ensured by M-matrix property then, the performance +is linked to the magnitude of the spectral radius of the iteration matrix, which is independent of the condition number. + +Next, the three-dimensional domain $\Omega\subset\mathbb{R}^{3}$ is set to $\Omega=\lbrack 0,1\rbrack^{3}$ and discretized with an uniform +Cartesian mesh constituted by $M=m^3$ discretization points, where $m$ related to the spatial discretization step by $h=\frac{1}{m+1}$. This +is carried out by using a classical order 2 finite difference approximation of the Laplacian. So, the complete discretization of both stationary +boundary value problems~(\ref{eq:03}) and~(\ref{eq:04}) leads to the solution of a large discrete complementary problem of the following +form, when both Dirichlet or Neumann boundary conditions are used: +\begin{equation} +\left\{ +\begin{array}{l} +\mbox{Find~}U^{*}\in\mathbb{R}^{M}\mbox{~such~that} \\ +(A+\delta I)U^{*}-G\geq 0\mbox{,~}U^{*}\geq\bar{\Phi},\\ +((A+\delta I)U^{*}-G)^{T}(U^{*}-\bar{\Phi})=0,\\ +\end{array} +\right. +\label{eq:05} +\end{equation} +where $A$ is a matrix obtained after the spatial discretization by a finite difference method, $G$ is derived from the Euler first order implicit time +marching scheme and from the discretized right-hand side of the obstacle problem, $\delta$ is the inverse of the time step $k$ and $I$ is the identity +matrix. The matrix $A$ is symmetric when the self-adjoint operator is considered and nonsymmetric otherwise. + +According to the chosen discretization scheme of the Laplacian, $A$ is an M-matrix (irreducibly diagonal dominant, see~\cite{ref2}) and, consequently, +the matrix $(A+\delta I)$ is also an M-matrix. This property is important to the convergence of iterative methods. + + +%%--------------------------%% +%% SECTION 3 %% +%%--------------------------%% +\section{Parallel iterative method} +\label{sec:03} +Owing to the large size of the previous discrete complementary problem~(\ref{eq:05}), we will solve it by parallel synchronous or asynchronous iterative +algorithms (see~\cite{ref3,ref4,ref5}). In this chapter, we aim at harnessing the computing power of GPU clusters for solving these large nonlinear systems. +Then, we choose to use the projected Richardson iterative method for solving the diffusion problem~(\ref{eq:04}). Indeed, this method is based on the iterations +of the Jacobi method which are easy to parallelize on parallel computers and easy to adapt to GPU architectures. Then, according to the boundary value problem +formulation with a self-adjoint operator~(\ref{eq:04}), we can consider here the equivalent optimization problem and the fixed point mapping associated to +its solution. + +Assume that $E=\mathbb{R}^{M}$ is a Hilbert space, in which $\scalprod{.}{.}$ is the scalar product and $\|.\|$ its associated norm. So, the general fixed +point problem to be solved is defined as follows: +\begin{equation} +\left\{ +\begin{array}{l} +\mbox{Find~} U^{*} \in E \mbox{~such that} \\ +U^{*} = F(U^{*}), \\ +\end{array} +\right. +\label{eq:06} +\end{equation} +where $U\mapsto F(U)$ is an application from $E$ to $E$. + +Let $K$ be a closed convex set defined by: +\begin{equation} +K = \{U | U \geq \Phi \mbox{~everywhere in~} E\}, +\label{eq:07} +\end{equation} +where $\Phi$ is the discrete obstacle function. In fact, the obstacle problem~(\ref{eq:05}) is formulated as the following constrained optimization problem: +\begin{equation} +\left\{ +\begin{array}{l} +\mbox{Find~} U^{*} \in K \mbox{~such that} \\ +\forall V \in K, J(U^{*}) \leq J(V), \\ +\end{array} +\right. +\label{eq:08} +\end{equation} +where the cost function is given by: +\begin{equation} +J(U) = \frac{1}{2}\scalprod{\mathcal{A}.U}{U} - \scalprod{G}{U}, +\label{eq:09} +\end{equation} +in which $\scalprod{.}{.}$ denotes the scalar product in $E$, $\mathcal{A}=A+\delta I$ is a symmetric positive definite, $A$ is the discretization matrix +associated with the self-adjoint operator~(\ref{eq:04}) after change of variables. + +For any $U\in E$, let $P_K(U)$ be the projection of $U$ on $K$. For any $\gamma\in\mathbb{R}$, $\gamma>0$, the fixed point mapping $F_{\gamma}$ of the projected +Richardson method is defined as follows: +\begin{equation} +U^{*} = F_{\gamma}(U^{*}) = P_K(U^{*} - \gamma(\mathcal{A}.U^{*} - G)). +\label{eq:10} +\end{equation} +In order to reduce the computation time, the large optimization problem is solved in a numerical way by using a parallel asynchronous algorithm of the projected +Richardson method on the convex set $K$. Particularly, we will consider an asynchronous parallel adaptation of the projected Richardson method~\cite{ref6}. + +Let $\alpha\in\mathbb{N}$ be a positive integer. We consider that the space $E=\displaystyle\prod_{i=1}^{\alpha} E_i$ is a product of $\alpha$ subspaces $E_i$ +where $i\in\{1,\ldots,\alpha\}$. Note that $E_i=\mathbb{R}^{m_i}$, where $\displaystyle\sum_{i=1}^{\alpha} m_{i}=M$, is also a Hilbert space in which $\scalprod{.}{.}_i$ +denotes the scalar product and $|.|_i$ the associated norm, for all $i\in\{1,\ldots,\alpha\}$. Then, for all $u,v\in E$, $\scalprod{u}{v}=\displaystyle\sum_{i=1}^{\alpha}\scalprod{u_i}{v_i}_i$ +is the scalar product on $E$. + +Let $U\in E$, we consider the following decomposition of $U$ and the corresponding decomposition of $F_\gamma$ into $\alpha$ blocks: +\begin{equation} +\begin{array}{rcl} +U & = & (U_1,\ldots,U_{\alpha}), \\ +F_{\gamma}(U) & = & (F_{1,\gamma}(U),\ldots,F_{\alpha,\gamma}(U)). \\ +\end{array} +\label{eq:11} +\end{equation} +Assume that the convex set $K=\displaystyle\prod_{i=1}^{\alpha}K_{i}$, such that $\forall i\in\{1,\ldots,\alpha\},K_i\subset E_i$ and $K_i$ is a closed convex set. +Let also $G=(G_1,\ldots,G_{\alpha})\in E$ and, for any $U\in E$, $P_K(U)=(P_{K_1}(U_1),\ldots,P_{K_{\alpha}}(U_{\alpha}))$ is the projection of $U$ on $K$ where $\forall i\in\{1,\ldots,\alpha\},P_{K_i}$ +is the projector from $E_i$ onto $K_i$. So, the fixed point mapping of the projected Richardson method~(\ref{eq:10}) can be written in the following way: +\begin{equation} +\forall U\in E\mbox{,~}\forall i\in\{1,\ldots,\alpha\}\mbox{,~}F_{i,\gamma}(U) = P_{K_i}(U_i - \gamma(\mathcal{A}_i.U - G_i)). +\label{eq:12} +\end{equation} +Note that $\displaystyle\mathcal{A}_i.U= \sum_{j=1}^{\alpha}\mathcal{A}_{i,j}.U_j$, where $\mathcal{A}_{i,j}$ denote block matrices of $\mathcal{A}$. + +The parallel asynchronous iterations of the projected Richardson method for solving the obstacle problem~(\ref{eq:08}) are defined as follows: let $U^0\in E,U^0=(U^0_1,\ldots,U^0_\alpha)$ be +the initial solution, then for all $p\in\mathbb{N}$, the iterate $U^{p+1}=(U^{p+1}_1,\ldots,U^{p+1}_{\alpha})$ is recursively defined by: +\begin{equation} +U_i^{p+1} = +\left\{ +\begin{array}{l} +F_{i,\gamma}(U_1^{\rho_1(p)}, \ldots, U_{\alpha}^{\rho_{\alpha}(p)}) \mbox{~if~} i\in s(p), \\ +U_i^p \mbox{~otherwise}, \\ +\end{array} +\right. +\label{eq:13} +\end{equation} +where +\begin{equation} +\left\{ +\begin{array}{l} +\forall p\in\mathbb{N}, s(p)\subset\{1,\ldots,\alpha\}\mbox{~and~} s(p)\ne\emptyset, \\ +\forall i\in\{1,\ldots,\alpha\},\{p \ | \ i \in s(p)\}\mbox{~is denombrable}, +\end{array} +\right. +\label{eq:14} +\end{equation} +and $\forall j\in\{1,\ldots,\alpha\}$, +\begin{equation} +\left\{ +\begin{array}{l} +\forall p\in\mathbb{N}, \rho_j(p)\in\mathbb{N}, 0\leq\rho_j(p)\leq p\mbox{~and~}\rho_j(p)=p\mbox{~if~} j\in s(p),\\ +\displaystyle\lim_{p\to\infty}\rho_j(p) = +\infty.\\ +\end{array} +\right. +\label{eq:15} +\end{equation} + +The previous asynchronous scheme of the projected Richardson method models computations that are carried out in parallel +without order nor synchronization (according to the behavior of the parallel iterative method) and describes a subdomain +method without overlapping. It is a general model that takes into account all possible situations of parallel computations +and non-blocking message passing. So, the synchronous iterative scheme is defined by: +\begin{equation} +\forall j\in\{1,\ldots,\alpha\} \mbox{,~} \forall p\in\mathbb{N} \mbox{,~} \rho_j(p)=p. +\label{eq:16} +\end{equation} +The values of $s(p)$ and $\rho_j(p)$ are defined dynamically and not explicitly by the parallel asynchronous or synchronous +execution of the algorithm. Particularly, it enables one to consider distributed computations whereby processors compute at +their own pace according to their intrinsic characteristics and computational load. The parallelism between the processors is +well described by the set $s(p)$ which contains at each step $p$ the index of the components relaxed by each processor on a +parallel way while the use of delayed components in~(\ref{eq:13}) permits one to model nondeterministic behavior and does not +imply inefficiency of the considered distributed scheme of computation. Note that, according to~\cite{ref7}, theoretically, +each component of the vector must be relaxed an infinity of time. The choice of the relaxed components to be used in the +computational process may be guided by any criterion and, in particular, a natural criterion is to pick-up the most recently +available values of the components computed by the processors. Furthermore, the asynchronous iterations are implemented by +means of non-blocking MPI communication subroutines (asynchronous communications). + +The important property ensuring the convergence of the parallel projected Richardson method, both synchronous and asynchronous +algorithms, is the fact that $\mathcal{A}$ is an M-matrix. Moreover, the convergence proceeds from a result of~\cite{ref6}. +Indeed, there exists a value $\gamma_0>0$, such that $\forall\gamma\in ]0,\gamma_0[$, the parallel iterations~(\ref{eq:13}), +(\ref{eq:14}) and~(\ref{eq:15}), associated to the fixed point mapping $F_\gamma$~(\ref{eq:12}), converge to the unique solution +$U^{*}$ of the discretized problem. + + +%%--------------------------%% +%% SECTION 4 %% +%%--------------------------%% +\section{Parallel implementation on a GPU cluster} +\label{sec:04} +In this section, we give the main key points of the parallel implementation of the projected Richardson method, both synchronous +and asynchronous versions, on a GPU cluster, for solving the nonlinear systems derived from the discretization of large obstacle +problems. More precisely, each nonlinear system is solved iteratively using the whole cluster. We use a heteregeneous CUDA/MPI +programming. Indeed, the communication of data, at each iteration between the GPU computing nodes, can be either synchronous +or asynchronous using the MPI communication subroutines, whereas inside each GPU node, a CUDA parallelization is performed. + +\begin{figure}[!h] +\centerline{\includegraphics[scale=0.30]{Chapters/chapter13/figures/splitCPU}} +\caption{Data partitioning of a problem to be solved among $S=3\times 4$ computing nodes.} +\label{fig:01} +\end{figure} + +Let $S$ denote the number of computing nodes on the GPU cluster, where a computing node is composed of CPU core holding one MPI +process and a GPU card. So, before starting computations, the obstacle problem of size $(NX\times NY\times NZ)$ is split into $S$ +parallelepipedic sub-problems, each for a node (MPI process, GPU), as is shown in Figure~\ref{fig:01}. Indeed, the $NY$ and $NZ$ +dimensions (according to the $y$ and $z$ axises) of the three-dimensional problem are, respectively, split into $Sy$ and $Sz$ parts, +such that $S=Sy\times Sz$. In this case, each computing node has at most four neighboring nodes. This kind of the data partitioning +reduces the data exchanges at subdomain boundaries compared to a naive $z$-axis-wise partitioning. + +\begin{algorithm}[!t] +\SetLine +\linesnumbered +Initialization of the parameters of the sub-problem\; +Allocate and fill the data in the global memory GPU\; +\For{$i=1$ {\bf to} $NbSteps$}{ + $G = \frac{1}{k}.U^0 + F$\; + Solve($A$, $U^0$, $G$, $U$, $\varepsilon$, $MaxRelax$)\; + $U^0 = U$\; +} +Copy the solution $U$ back from GPU memory\; +\caption{Parallel solving of the obstacle problem on a GPU cluster} +\label{alg:01} +\end{algorithm} + +All the computing nodes of the GPU cluster execute in parallel the same Algorithm~\ref{alg:01} but on different three-dimensional +sub-problems of size $(NX\times ny\times nz)$. This algorithm gives the main key points for solving an obstacle problem defined in +a three-dimensional domain, where $A$ is the discretization matrix, $G$ is the right-hand side and $U$ is the solution vector. After +the initialization step, all the data generated from the partitioning operation are copied from the CPU memories to the GPU global +memories, to be processed on the GPUs. Next, the algorithm uses $NbSteps$ time steps to solve the global obstacle problem. In fact, +it uses a parallel algorithm adapted to GPUs of the projected Richardson iterative method for solving the nonlinear systems of the +obstacle problem. This function is defined by {\it Solve()} in Algorithm~\ref{alg:01}. At every time step, the initial guess $U^0$ +for the iterative algorithm is set to the solution found at the previous time step. Moreover, the right-hand side $G$ is computed +as follows: \[G = \frac{1}{k}.U^{prev} + F\] where $k$ is the time step, $U^{prev}$ is the solution computed in the previous time +step and each element $f(x, y, z)$ of the vector $F$ is computed as follows: +\begin{equation} +f(x,y,z)=\cos(2\pi x)\cdot\cos(4\pi y)\cdot\cos(6\pi z). +\label{eq:18} +\end{equation} +Finally, the solution $U$ of the obstacle problem is copied back from the GPU global memories to the CPU memories. We use the +communication subroutines of the CUBLAS library~\cite{ref8} (CUDA Basic Linear Algebra Subroutines) for the memory allocations in +the GPU (\verb+cublasAlloc()+) and the data transfers between the CPU and its GPU: \verb+cublasSetVector()+ and \verb+cublasGetVector()+. + +\begin{algorithm}[!t] + \SetLine + \linesnumbered + $p = 0$\; + $conv = false$\; + $U = U^{0}$\; + \Repeat{$(conv=true)$}{ + Determine\_Bordering\_Vector\_Elements($U$)\; + Compute\_New\_Vector\_Elements($A$, $G$, $U$)\; + $tmp = U^{0} - U$\; + $error = \|tmp\|_{2}$\; + $U^{0} = U$\; + $p = p + 1$\; + $conv$ = Convergence($error$, $p$, $\varepsilon$, $MaxRelax$)\; + } +\caption{Parallel iterative solving of the nonlinear systems on a GPU cluster ($Solve()$ function)} +\label{alg:02} +\end{algorithm} + +As many other iterative methods, the algorithm of the projected Richardson method is based on algebraic functions operating on vectors +and/or matrices, which are more efficient on parallel computers when they work on large vectors. Its parallel implementation on the GPU +cluster is carried out so that the GPUs execute the vector operations as kernels and the CPUs execute the serial codes, supervise the +kernel executions and the data exchanges with the neighboring nodes and supply the GPUs with data. Algorithm~\ref{alg:02} shows the +main key points of the parallel iterative algorithm (function $Solve()$ in Algorithm~\ref{alg:01}). All the vector operations inside +the main loop ({\bf repeat} ... {\bf until}) are executed by the GPU. We use the following functions of the CUBLAS library: +\begin{itemize*} +\item \verb+cublasDaxpy()+ to compute the difference between the solution vectors $U^{p}$ and $U^{p+1}$ computed in two successive relaxations +$p$ and $p+1$ (line~$7$ in Algorithm~\ref{alg:02}), +\item \verb+cublasDnrm2()+ to perform the Euclidean norm (line~$8$) and, +\item \verb+cublasDcpy()+ for the data copy of a vector to another one in the GPU memory (lines~$3$ and~$9$). +\end{itemize*} + +The dimensions of the grid and blocks of threads that execute a given kernel depend on the resources of the GPU multiprocessor and the +resource requirements of the kernel. So, if $block$ defines the size of a thread block, which must not exceed the maximum size of a thread +block, then the number of thread blocks in the grid, denoted by $grid$, can be computed according to the size of the local sub-problem +as follows: \[grid = \frac{(NX\times ny\times nz)+block-1}{block}.\] However, when solving very large problems, the size of the thread +grid can exceed the maximum number of thread blocks that can be executed on the GPUs (up-to $65.535$ thread blocks) and, thus, the kernel +will fail to launch. Therefore, for each kernel, we decompose the three-dimensional sub-problem into $nz$ two-dimensional slices of size +($NX\times ny$), as is shown in Figure~\ref{fig:02}. All slices of the same kernel are executed using {\bf for} loop by $NX\times ny$ parallel +threads organized in a two-dimensional grid of two-dimensional thread blocks, as is shown in Listing~\ref{list:01}. Each thread is in charge +of $nz$ discretization points (one from each slice), accessed in the GPU memory with a constant stride $(NX\times ny)$. + +\begin{figure} +\centerline{\includegraphics[scale=0.30]{Chapters/chapter13/figures/splitGPU}} +\caption{Decomposition of a sub-problem in a GPU into $nz$ slices.} +\label{fig:02} +\end{figure} + +\begin{center} +\lstinputlisting[label=list:01,caption=Skeleton codes of a GPU kernel and a CPU function]{Chapters/chapter13/ex1.cu} +\end{center} +The function $Determine\_Bordering\_Vector\_Elements()$ (line~$5$ in Algorithm~\ref{alg:02}) determines the values of the vector +elements shared at the boundaries with neighboring computing nodes. Its main operations are defined as follows: +\begin{enumerate*} +\item define the values associated to the bordering points needed by the neighbors, +\item copy the values associated to the bordering points from the GPU to the CPU, +\item exchange the values associated to the bordering points between the neighboring CPUs, +\item copy the received values associated to the bordering points from the CPU to the GPU, +\end{enumerate*} +The first operation of this function is implemented as kernels to be performed by the GPU: +\begin{itemize*} +\item a kernel executed by $NX\times nz$ threads to define the values associated to the bordering vector elements along $y$-axis and, +\item a kernel executed by $NX\times ny$ threads to define the values associated to the bordering vector elements along $z$-axis. +\end{itemize*} +As mentioned before, we develop the \emph{synchronous} and \emph{asynchronous} algorithms of the projected Richardson method. Obviously, +in this scope, the synchronous or asynchronous communications refer to the communications between the CPU cores (MPI processes) on the +GPU cluster, in order to exchange the vector elements associated to subdomain boundaries. For the memory copies between a CPU core and +its GPU, we use the synchronous communication routines of the CUBLAS library: \verb+cublasSetVector()+ and \verb+cublasGetVector()+ +in the synchronous algorithm and the asynchronous ones: \verb+cublasSetVectorAsync()+ and \verb+cublasGetVectorAsync()+ in the +asynchronous algorithm. Moreover, we use the communication routines of the MPI library to carry out the data exchanges between the neighboring +nodes. We use the following communication routines: \verb+MPI_Isend()+ and \verb+MPI_Irecv()+ to perform non-blocking sends and receptions, +respectively. For the synchronous algorithm, we use the MPI routine \verb+MPI_Waitall()+ which puts the MPI process of a computing node +in blocking status until all data exchanges with neighboring nodes (sends and receptions) are completed. In contrast, for the asynchronous +algorithms, we use the MPI routine \verb+MPI_Test()+ which tests the completion of a data exchange (send or reception) without putting the +MPI process in blocking status. + +The function $Compute\_New\_Vector\_Elements()$ (line~$6$ in Algorithm~\ref{alg:02}) computes, at each iteration, the new elements +of the iterate vector $U$. Its general code is presented in Listing~\ref{list:01} (CPU function). The iterations of the projected +Richardson method, based on those of the Jacobi method, are defined as follows: +\begin{equation} +\begin{array}{ll} +u^{p+1}(x,y,z) =& \frac{1}{Center}(g(x,y,z) - (Center\cdot u^{p}(x,y,z) + \\ +& West\cdot u^{p}(x-h,y,z) + East\cdot u^{p}(x+h,y,z) + \\ +& South\cdot u^{p}(x,y-h,z) + North\cdot u^{p}(x,y+h,z) + \\ +& Rear\cdot u^{p}(x,y,z-h) + Front\cdot u^{p}(x,y,z+h))), +\end{array} +\label{eq:17} +\end{equation} +where $u^{p}(x,y,z)$ is an element of the iterate vector $U$ computed at the iteration $p$ and $g(x,y,z)$ is a vector element of the +right-hand side $G$. The scalars $Center$, $West$, $East$, $South$, $North$, $Rear$ and $Front$ define constant coefficients of the +block matrix $A$. Figure~\ref{fig:03} shows the positions of these coefficients in a three-dimensional domain. + +\begin{figure} +\centerline{\includegraphics[scale=0.35]{Chapters/chapter13/figures/matrix}} +\caption{Matrix constant coefficients in a three-dimensional domain.} +\label{fig:03} +\end{figure} + +The kernel implementations of the projected Richardson method on GPUs uses a perfect fine-grain multithreading parallelism. Since the +projected Richardson algorithm is implemented as a fixed point method, each kernel is executed by a large number of GPU threads such +that each thread is in charge of the computation of one element of the iterate vector $U$. Moreover, this method uses the vector elements +updates of the Jacobi method, which means that each thread $i$ computes the new value of its element $u_{i}^{p+1}$ independently of the +new values $u_{j}^{p+1}$, where $j\neq i$, of those computed in parallel by other threads at the same iteration $p+1$. Listing~\ref{list:02} +shows the GPU implementations of the main kernels of the projected Richardson method, which are: the matrix-vector multiplication +(\verb+MV_Multiplication()+) and the vector elements updates (\verb+Vector_Updates()+). The codes of these kernels are based on +that presented in Listing~\ref{list:01}. + +\lstinputlisting[label=list:02,caption=GPU kernels of the projected Richardson method]{Chapters/chapter13/ex2.cu} + +\begin{figure} +\centerline{\includegraphics[scale=0.3]{Chapters/chapter13/figures/points3D}} +\caption{Computation of a vector element with the projected Richardson method.} +\label{fig:04} +\end{figure} + +Each kernel is executed by $NX\times ny$ GPU threads so that $nz$ slices of $(NX\times ny)$ vector elements are computed in +a {\bf for} loop. In this case, each thread is in charge of one vector element from each slice (in total $nz$ vector elements +along $z$-axis). We can notice from the formula~(\ref{eq:17}) that the computation of a vector element $u^{p+1}(x,y,z)$, by +a thread at iteration $p+1$, requires seven vector elements computed at the previous iteration $p$: two vector elements in +each dimension plus the vector element at the intersection of the three axises $x$, $y$ and $z$ (see Figure~\ref{fig:04}). +So, to reduce the memory accesses to the high-latency global memory, the vector elements of the current slice can be stored +in the low-latency shared memories of thread blocks, as is described in~\cite{ref9}. Nevertheless, the fact that the computation +of a vector element requires only two elements in each dimension does not allow to maximize the data reuse from the shared memories. +The computation of a slice involves in total $(bx+2)\times(by+2)$ accesses to the global memory per thread block, to fill the +required vector elements in the shared memory where $bx$ and $by$ are the dimensions of a thread block. Then, in order to optimize +the memory accesses on GPUs, the elements of the iterate vector $U$ are filled in the cache texture memory (see~\cite{ref10}). +In new GPU generations as Fermi or Kepler, the global memory accesses are always cached in L1 and L2 caches. For example, for +a given kernel, we can favour the use of the L1 cache to that of the shared memory by using the function \verb+cudaFuncSetCacheConfig(Kernel,cudaFuncCachePreferL1)+. +So, the initial access to the global memory loads the vector elements required by the threads of a block into the cache memory +(texture or L1/L2 caches). Then, all the following memory accesses read from this cache memory. In Listing~\ref{list:02}, the +function \verb+fetch_double(v,i)+ is used to read from the texture memory the $i^{th}$ element of the double-precision vector +\verb+v+ (see Listing~\ref{list:03}). Moreover, the seven constant coefficients of matrix $A$ can be stored in the constant memory +but, since they are reused $nz$ times by each thread, it is more interesting to fill them on the low-latency registers of each thread. + +\lstinputlisting[label=list:03,caption=Memory access to the cache texture memory]{Chapters/chapter13/ex3.cu} + +The function $Convergence()$ (line~$11$ in Algorithm~\ref{alg:02}) allows to detect the convergence of the parallel iterative algorithm +and is based on the tolerance threshold $\varepsilon$ and the maximum number of relaxations $MaxRelax$. We take into account the number +of relaxations since that of iterations cannot be computed in the asynchronous case. Indeed, a relaxation is the update~(\ref{eq:13}) of +a local iterate vector $U_i$ according to $F_i$. Then, counting the number of relaxations is possible in both synchronous and asynchronous +cases. On the other hand, an iteration is the update of at least all vector components with $F_i$. + +In the synchronous algorithm, the global convergence is detected when the maximal value of the absolute error, $error$, is sufficiently small +and/or the maximum number of relaxations, $MaxRelax$, is reached, as follows: +$$ +\begin{array}{l} +error=\|U^{p}-U^{p+1}\|_{2}; \\ +AllReduce(error,\hspace{0.1cm}maxerror,\hspace{0.1cm}MAX); \\ +\text{if}((maxerror<\varepsilon)\hspace{0.2cm}\text{or}\hspace{0.2cm}(p\geq MaxRelax)) \\ +conv \leftarrow true; +\end{array} +$$ +where the function $AllReduce()$ uses the MPI reduction subroutine \verb+MPI_Allreduce()+ to compute the maximal value, $maxerror$, among the +local absolute errors, $error$, of all computing nodes and $p$ (in Algorithm~\ref{alg:02}) is used as a counter of the local relaxations carried +out by a computing node. In the asynchronous algorithms, the global convergence is detected when all computing nodes locally converge. For this, +we use a token ring architecture around which a boolean token travels, in one direction, from a computing node to another. Starting from node $0$, +the boolean token is set to $true$ by node $i$ if the local convergence is reached or to $false$ otherwise and, then, it is sent to node $i+1$. +Finally, the global convergence is detected when node $0$ receives from its neighbor node $S-1$, in the ring architecture, a token set to $true$. +In this case, node $0$ sends a stop message (end of parallel solving) to all computing nodes in the cluster. + + +%%--------------------------%% +%% SECTION 5 %% +%%--------------------------%% +\section{Experimental tests on a GPU cluster} +\label{sec:05} +The GPU cluster of tests, that we used in this chapter, is an $20Gbps$ Infiniband network of six machines. Each machine is a Quad-Core Xeon +E5530 CPU running at $2.4$GHz. It provides a RAM memory of $12$GB with a memory bandwidth of $25.6$GB/s and it is equipped with two Nvidia +Tesla C1060 GPUs. A Tesla GPU contains in total $240$ cores running at $1.3$GHz. It provides $4$GB of global memory with a memory bandwidth +of $102$GB/s, accessible by all its cores and also by the CPU through the PCI-Express 16x Gen 2.0 interface with a throughput of $8$GB/s. +Hence, the memory copy operations between the GPU and the CPU are about $12$ times slower than those of the Tesla GPU memory. We have performed +our simulations on a cluster of $24$ CPU cores and on a cluster of $12$ GPUs. Figure~\ref{fig:05} describes the components of the GPU cluster +of tests. + +\begin{figure} +\centerline{\includegraphics[scale=0.25]{Chapters/chapter13/figures/cluster}} +\caption{GPU cluster of tests composed of 12 computing nodes (six machines, each with two GPUs.} +\label{fig:05} +\end{figure} + +Linux cluster version 2.6.39 OS is installed on CPUs. C programming language is used for coding the parallel algorithms of the methods on both +GPU cluster and CPU cluster. CUDA version 4.0~\cite{ref12} is used for programming GPUs, using CUBLAS library~\cite{ref8} to deal with vector +operations in GPUs and, finally, MPI functions of OpenMPI 1.3.3 are used to carry out the synchronous and asynchronous communications between +CPU cores. Indeed, in our experiments, a computing node is managed by a MPI process and it is composed of one CPU core and one GPU card. + +All experimental results of the parallel projected Richardson algorithms are obtained from simulations made in double precision data. The obstacle +problems to be solved are defined in constant three-dimensional domain $\Omega\subset\mathbb{R}^{3}$. The numerical values of the parameters of the +obstacle problems are: $\eta=0.2$, $c=1.1$, $f$ is computed by formula~(\ref{eq:18}) and final time $T=0.02$. Moreover, three time steps ($NbSteps=3$) +are computed with $k=0.0066$. As the discretization matrix is constant along the time steps, the convergence properties of the iterative algorithms +do not change. Thus, the performance characteristics obtained with three time steps will still be valid for more time steps. The initial function +$u(0,x,y,z)$ of the obstacle problem~(\ref{eq:01}) is set to $0$, with a constraint $u\geq\phi=0$. The relaxation parameter $\gamma$ used by the +projected Richardson method is computed automatically thanks to the diagonal entries of the discretization matrix. The formula and its proof can be +found in~\cite{ref11}, Section~2.3. The convergence tolerance threshold $\varepsilon$ is set to $1e$-$04$ and the maximum number of relaxations is +limited to $10^{6}$ relaxations. Finally, the number of threads per block is set to $256$ threads, which gives, in general, good performances for +most GPU applications. We have performed some tests for the execution configurations and we have noticed that the best configuration of the $256$ +threads per block is an organization into two dimensions of sizes $(64,4)$. + +\begin{table}[!h] +\centering +\begin{tabular}{|c|c|c|c|c|c|} +\hline +\multirow{2}{*}{\bf Pb. size} & \multicolumn{2}{c|}{\bf Synchronous} & \multicolumn{2}{c|}{\bf Asynchronous} & \multirow{2}{*}{\bf Gain\%} \\ \cline{2-5} + + & $\mathbf{T_{cpu}}$ & {\bf \#relax.} & $\mathbf{T_{cpu}}$ & {\bf \#relax.} & \\ \hline \hline + +$256^{3}$ & $575.22$ & $198,288$ & $539.25$ & $198,613$ & $6.25$ \\ \hline \hline + +$512^{3}$ & $19,250.25$ & $750,912$ & $18,237.14$ & $769,611$ & $5.26$ \\ \hline \hline + +$768^{3}$ & $206,159.44$ & $1,635,264$ & $183,582.60$ & $1,577,004$ & $10.95$ \\ \hline \hline + +$800^{3}$ & $222,108.09$ & $1,769,232$ & $188,790.04$ & $1,701,735$ & $15.00$ \\ \hline +\end{tabular} +\vspace{0.5cm} +\caption{Execution times in seconds of the parallel projected Richardson method implemented on a cluster of 24 CPU cores.} +\label{tab:01} +\end{table} + +\begin{table}[!h] +\centering +\begin{tabular}{|c|c|c|c|c|c|c|c|} +\hline +\multirow{2}{*}{\bf Pb. size} & \multicolumn{3}{c|}{\bf Synchronous} & \multicolumn{3}{c|}{\bf Asynchronous} & \multirow{2}{*}{\bf Gain\%} \\ \cline{2-7} + + & $\mathbf{T_{gpu}}$ & {\bf \#relax.} & $\mathbf{\tau}$ & $\mathbf{T_{gpu}}$ & {\bf \#relax.} & $\mathbf{\tau}$ & \\ \hline \hline + +$256^{3}$ & $29.67$ & $100,692$ & $19.39$ & $18.00$ & $94,215$ & $29.96$ & $39.33$ \\ \hline \hline + +$512^{3}$ & $521.83$ & $381,300$ & $36.89$ & $425.15$ & $347,279$ & $42.89$ & $18.53$ \\ \hline \hline + +$768^{3}$ & $4,112.68$ & $831,144$ & $50.13$ & $3,313.87$ & $750,232$ & $55.40$ & $19.42$ \\ \hline \hline + +$800^{3}$ & $3,950.87$ & $899,088$ & $56.22$ & $3,636.57$ & $834,900$ & $51.91$ & $7.95$ \\ \hline +\end{tabular} +\vspace{0.5cm} +\caption{Execution times in seconds of the parallel projected Richardson method implemented on a cluster of 12 GPUs.} +\label{tab:02} +\end{table} + +The performance measures that we took into account are the execution times and the number of relaxations performed by the parallel iterative algorithms, +both synchronous and asynchronous versions, on the GPU and CPU clusters. These algorithms are used for solving nonlinear systems derived from the discretization +of obstacle problems of sizes $256^{3}$, $512^{3}$, $768^{3}$ and $800^{3}$. In Table~\ref{tab:01} and Table~\ref{tab:02}, we show the performances +of the parallel synchronous and asynchronous algorithms of the projected Richardson method implemented, respectively, on a cluster of $24$ CPU cores +and on a cluster of $12$ GPUs. In these tables, the execution time defines the time spent by the slowest computing node and the number of relaxations +is computed as the summation of those carried out by all computing nodes. + +In the sixth column of Table~\ref{tab:01} and in the eighth column of Table~\ref{tab:02}, we give the gains in $\%$ obtained by using an +asynchronous algorithm compared to a synchronous one. We can notice that the asynchronous version on CPU and GPU clusters is slightly faster +than the synchronous one for both methods. Indeed, the cluster of tests is composed of local and homogeneous nodes communicating via low-latency +connections. So, in the case of distant and/or heterogeneous nodes (or even with geographically distant clusters) the asynchronous version +would be faster than the synchronous one. However, the gains obtained on the GPU cluster are better than those obtained on the CPU cluster. +In fact, the computation times are reduced by accelerating the computations on GPUs while the communication times still unchanged. + +The fourth and seventh columns of Table~\ref{tab:02} show the relative gains obtained by executing the parallel algorithms on the cluster +of $12$ GPUs instead on the cluster of $24$ CPU cores. We compute the relative gain $\tau$ as a ratio between the execution time $T_{cpu}$ +spent on the CPU cluster over that $T_{gpu}$ spent on the GPU cluster: \[\tau=\frac{T_{cpu}}{T_{gpu}}.\] We can see from these ratios that +solving large obstacle problems is faster on the GPU cluster than on the CPU cluster. Indeed, the GPUs are more efficient than their +counterpart CPUs to execute large data-parallel operations. In addition, the projected Richardson method is implemented as a fixed point-based +iteration and uses the Jacobi vector updates that allow a well thread-parallelization on GPUs, such that each GPU thread is in charge +of one vector component at a time without being dependent on other vector components computed by other threads. Then, this allow to exploit +at best the high performance computing of the GPUs by using all the GPU resources and avoiding the idle cores. + +Finally, the number of relaxations performed by the parallel synchronous algorithm is different in the CPU and GPU versions, because the number +of computing nodes involved in the GPU cluster and in the CPU cluster is different. In the CPU case, $24$ computing nodes ($24$ CPU cores) are +considered, whereas in the GPU case, $12$ computing nodes ($12$ GPUs) are considered. As the number of relaxations depends on the domain decomposition, +consequently it also depends on the number of computing nodes. + + +%%--------------------------%% +%% SECTION 6 %% +%%--------------------------%% +\section{Red-Black ordering technique} +\label{sec:06} +As is well-known, the Jacobi method is characterized by a slow convergence rate compared to some iterative methods (for example Gauss-Seidel method). +So, in this section, we present some solutions to reduce the execution time and the number of relaxations and, more specifically, to speed up the +convergence of the parallel projected Richardson method on the GPU cluster. We propose to use the point red-black ordering technique to accelerate +the convergence. This technique is often used to increase the parallelism of iterative methods for solving linear systems~\cite{ref13,ref14,ref15}. +We apply it to the projected Richardson method as a compromise between the Jacobi and Gauss-Seidel iterative methods. + +The general principle of the red-black technique is as follows. Let $t$ be the summation of the integer $x$-, $y$- and $z$-coordinates of a vector +element $u(x,y,z)$ on a three-dimensional domain: $t=x+y+z$. As is shown in Figure~\ref{fig:06.01}, the red-black ordering technique consists in the +parallel computing of the red vector elements having even value $t$ by using the values of the black ones then, the parallel computing of the black +vector elements having odd values $t$ by using the new values of the red ones. + +\begin{figure} +\centering + \mbox{\subfigure[Red-black ordering on x, y and z axises]{\includegraphics[width=2.3in]{Chapters/chapter13/figures/rouge-noir}\label{fig:06.01}}\quad + \subfigure[Red-black ordering on y axis]{\includegraphics[width=2.3in]{Chapters/chapter13/figures/rouge-noir-y}\label{fig:06.02}}} +\caption{Red-black ordering for computing the iterate vector elements in a three-dimensional space.} +\end{figure} + +This technique can be implemented on the GPU in two different manners: +\begin{itemize*} +\item among all launched threads ($NX\times ny$ threads), only one thread out of two computes its red or black vector element at a time or, +\item all launched threads (on average half of $NX\times ny$ threads) compute the red vector elements first and, then, the black ones. +\end{itemize*} +However, in both solutions, for each memory transaction, only half of the memory segment addressed by a half-warp is used. So, the computation of the +red and black vector elements leads to use twice the initial number of memory transactions. Then, we apply the point red-black ordering accordingly to +the $y$-coordinate, as is shown in Figure~\ref{fig:06.02}. In this case, the vector elements having even $y$-coordinate are computed in parallel using +the values of those having odd $y$-coordinate and then vice-versa. Moreover, in the GPU implementation of the parallel projected Richardson method (Section~\ref{sec:04}), +we have shown that a sub-problem of size $(NX\times ny\times nz)$ is decomposed into $nz$ grids of size $(NX\times ny)$. Then, each kernel is executed +in parallel by $NX\times ny$ GPU threads, so that each thread is in charge of $nz$ vector elements along $z$-axis (one vector element in each grid of +the sub-problem). So, we propose to use the new values of the vector elements computed in grid $i$ to compute those of the vector elements in grid $i+1$. +Listing~\ref{list:04} describes the kernel of the matrix-vector multiplication and the kernel of the vector elements updates of the parallel projected +Richardson method using the red-black ordering technique. + +\lstinputlisting[label=list:04,caption=GPU kernels of the projected Richardson method using the red-black technique]{Chapters/chapter13/ex4.cu} + +Finally, we exploit the concurrent executions between the host functions and the GPU kernels provided by the GPU hardware and software. In fact, the kernel +launches are asynchronous (when this environment variable is not disabled on the GPUs), such that the control is returned to the host (MPI process) before +the GPU has completed the requested task (kernel)~\cite{ref12}. Therefore, all the kernels necessary to update the local vector elements, $u(x,y,z)$ where +$0>>(..., n, NX, ny, slices, stride, ...); + ... +} + diff --git a/BookGPU/Chapters/chapter13/ex2.cu b/BookGPU/Chapters/chapter13/ex2.cu new file mode 100644 index 0000000..f5d30ce --- /dev/null +++ b/BookGPU/Chapters/chapter13/ex2.cu @@ -0,0 +1,48 @@ +/* Kernel of the matrix-vector multiplication */ +__global__ void MV_Multiplication (..., double* U, double* Y) +{ + ... + //Matrix coefficients filled in registers + + for(int tz=0; tz>>(..., U, Y); + Vector_Updates<<>>(..., G, Y, U); +} diff --git a/BookGPU/Chapters/chapter13/ex3.cu b/BookGPU/Chapters/chapter13/ex3.cu new file mode 100644 index 0000000..6090907 --- /dev/null +++ b/BookGPU/Chapters/chapter13/ex3.cu @@ -0,0 +1,8 @@ +texture v; + +static __inline__ +__device__ double fetch_double(texture v, int i) +{ + int2 w = tex1Dfetch(v, i); + return __hiloint2double(w.y, w.x); +} diff --git a/BookGPU/Chapters/chapter13/ex4.cu b/BookGPU/Chapters/chapter13/ex4.cu new file mode 100644 index 0000000..738ca3d --- /dev/null +++ b/BookGPU/Chapters/chapter13/ex4.cu @@ -0,0 +1,54 @@ +/* Kernel of the matrix-vector multiplication */ +__global__ void MV_Multiplication(...,double*G,double*U,double*Y) +{ + ... + //Matrix coefficients filled in registers: + //Center, West, East, Front + + for(int tz=0; tz>>(..., G, U, Y); + Vector_Updates<<>>(..., red, Y, U); + Vector_Updates<<>>(..., black, Y, U); +} diff --git a/BookGPU/Chapters/chapter13/figures/bib.bib b/BookGPU/Chapters/chapter13/figures/bib.bib new file mode 100644 index 0000000..0262701 --- /dev/null +++ b/BookGPU/Chapters/chapter13/figures/bib.bib @@ -0,0 +1,358 @@ +@article{Zha07, + author = {Zhao, Y.}, + title = {Lattice {B}oltzmann {B}ased {PDE} {S}olver on the {GPU}}, + journal = {The Visual Computer}, + volume = {24}, + number = {5}, + pages = {323--333}, + year = {2008}, +} + +@article{Mar09, + author = {Maringanti, A. and Athavale, V. and Patkar, S. 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M. and Contassot-Vivier, S. and Couturier, R.}, + title = {Parallel {I}terative {A}lgorithms: from {S}equential to {G}rid {C}omputing}, + journal = {Chapman \& Hall/CRC, Numerical Analysis \& Scientific Computating 1 (2007)}, + volume = {}, + number = {}, + pages = {}, + year = {2007}, +} + +@article{Nvi10, + author = {Nvidia}, + title = {{NVIDIA} {CUDA} {C} {P}rogramming {G}uide}, + journal = {Version 4.0 (2011)}, + volume = {}, + number = {}, + pages = {}, + year = {2011}, +} + +@article{Nvid10, + author = {Nvidia}, + title = {{CUDA} {CUBLAS} {L}ibrary (2010)}, + journal = {}, + volume = {}, + number = {}, + pages = {}, + year = {2010}, +} + +@article{ref10, + author = {Micikevicius, P}, + title = {{3D} {F}inite {D}ifference {C}omputation on {GPUs} using {CUDA}}, + journal = {Proceedings of 2nd Workshop on General Purpose Processing on Graphics Processing Units}, + volume = {}, + number = {}, + pages = {79--84}, + year = {2009}, +} + +@article{ref11, + author = {Leist, A. and Playne, D. 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/BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ +sOXW#;]]f#$]3a'90!F"BA5Lg90YXI;Ur;M@RX8Pk_ +92!UM_eIP%*H:qH%HI_*f,L0`gA7rQmYJ4P2?>?NTnNF0GpI-<%D0lS)J`K/_RM4 ++OS@6,Jf]P7Q3OL`-S]u-G?2G[6N&>;I*MSqV:W(UZU<*K!D\V3'PG"Wo]Oc[=,T +s)"+_e.,U[0*Jl#O6eG4mZWm0MafGOAL*CDCD_,dA_d'2,XfkA1SIaiJ\05%8bqQ +=c;*:Kg=0>j_]H7j'Q-b+2N3!"C]\oe`$?(mT+mZ6mJ9Y:c?iGJ(GP30uUf>Y3/& +G*7'7q*[NoNY)jJd(Y79OiRjA(gUBS]:Z(^cXjO!XZ['ClmhV$J:X?]:6 +!Pdr@pWhugg=Y_u$4WLc0A +N!a7Vt/WA_YE*[P32nn6F45l+R)N&@26*%@"fgG!@52$A(NUIX)Z'Z +\;>S4X=k(CTgaioFV[%'+6'Zc!stc,@7)QH`VtP>0:UD\P9J;>.Q0&9K(^ +0a2kR8eJooDbT?KNLOt8o$BM)u_)tX*7O_IeXoZ>1gGN9>phrY,-B0M>T+^Zg3q2 +Q`-T"phRa*.r+usa*Ak-l(j(`JEO+62:hrUO'qA3pA;$VEW)+_ke/ZXh-"0pdH&C +*`^@U4lY/Q6k!)K$8WtqUMM7QUTdhK9OZ@4-1f0!c+Ga70,[*hd:W[p?1$uOfC,> +3W)HPB92>:aJq'?:\,I:!_E8EJjG;qt3G6?]2'XrE"Du<0f60Em\Zs3%P\Y'I +=.a>0Hr"i^1pT[-=SA;Z^uRiSZKL$ikY[ih[G.5,FX$.B;B.6B+2tQQ1`jPE5lL-\,LS5rro:VjHd`jR +P/a\7@^%4/4A7/otr5DG4u6=cOPM^Gq5UG9+;IlA1]F2VWG\M=DW4OtXtr\gNuN0 +5`te![8fm5U%C=3Sp9JCYG+XU]Y0g\k"\9Z5r@Fi9je[--GA(b]..HjuoUi2;kme +4:""bVA(YEk_36YmA%fh12PA!fj"<^N^krrH:2r*1fIJ0pk@'=78\7fK(2XZGu+@bM)lL3WH>]amM. +alH*Df%K6!499s_qZ1Mh639PU+k!Ve`JY$nJ]K,*A,YuY9.XfGP"'VTF?RJ2#oK6 +3%q4dJWL.nOFeZ%+Gbj[pf8?J@J1dp,4TjeB:05]VB0aNQ)CAUG[D$c?fX8$J("$ +PILZ$Gp'&#>&Z4t`R8)jg;sGPS&HkKm5nO_As4I~>restore grestore +% +% End Imported PIC File: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +% +% Polyline +% +% pen to black in case this eps object doesn't set color first +0 0 0 setrgbcolor +% Begin Imported JPEG File: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg + +n gs +10350 10350 tr +3.982301 -3.982301 sc +113 -113 tr +90 rot +0 0 tr +sa +/showpage {} def +% JPEG image follows: +113 113 sc +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: jpeg2ps 3.2 by Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +%%CreationDate: Mon Jan 14 14:35:51 2013 +%%BoundingBox: 0 0 113 113 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ +sOXW#;]]f#$]3a'90!F"BA5Lg90YXI;Ur;M@RX8Pk_ +92!UM_eIP%*H:qH%HI_*f,L0`gA7rQmYJ4P2?>?NTnNF0GpI-<%D0lS)J`K/_RM4 ++OS@6,Jf]P7Q3OL`-S]u-G?2G[6N&>;I*MSqV:W(UZU<*K!D\V3'PG"Wo]Oc[=,T +s)"+_e.,U[0*Jl#O6eG4mZWm0MafGOAL*CDCD_,dA_d'2,XfkA1SIaiJ\05%8bqQ +=c;*:Kg=0>j_]H7j'Q-b+2N3!"C]\oe`$?(mT+mZ6mJ9Y:c?iGJ(GP30uUf>Y3/& +G*7'7q*[NoNY)jJd(Y79OiRjA(gUBS]:Z(^cXjO!XZ['ClmhV$J:X?]:6 +!Pdr@pWhugg=Y_u$4WLc0A +N!a7Vt/WA_YE*[P32nn6F45l+R)N&@26*%@"fgG!@52$A(NUIX)Z'Z +\;>S4X=k(CTgaioFV[%'+6'Zc!stc,@7)QH`VtP>0:UD\P9J;>.Q0&9K(^ +0a2kR8eJooDbT?KNLOt8o$BM)u_)tX*7O_IeXoZ>1gGN9>phrY,-B0M>T+^Zg3q2 +Q`-T"phRa*.r+usa*Ak-l(j(`JEO+62:hrUO'qA3pA;$VEW)+_ke/ZXh-"0pdH&C +*`^@U4lY/Q6k!)K$8WtqUMM7QUTdhK9OZ@4-1f0!c+Ga70,[*hd:W[p?1$uOfC,> +3W)HPB92>:aJq'?:\,I:!_E8EJjG;qt3G6?]2'XrE"Du<0f60Em\Zs3%P\Y'I +=.a>0Hr"i^1pT[-=SA;Z^uRiSZKL$ikY[ih[G.5,FX$.B;B.6B+2tQQ1`jPE5lL-\,LS5rro:VjHd`jR +P/a\7@^%4/4A7/otr5DG4u6=cOPM^Gq5UG9+;IlA1]F2VWG\M=DW4OtXtr\gNuN0 +5`te![8fm5U%C=3Sp9JCYG+XU]Y0g\k"\9Z5r@Fi9je[--GA(b]..HjuoUi2;kme +4:""bVA(YEk_36YmA%fh12PA!fj"<^N^krrH:2r*1fIJ0pk@'=78\7fK(2XZGu+@bM)lL3WH>]amM. +alH*Df%K6!499s_qZ1Mh639PU+k!Ve`JY$nJ]K,*A,YuY9.XfGP"'VTF?RJ2#oK6 +3%q4dJWL.nOFeZ%+Gbj[pf8?J@J1dp,4TjeB:05]VB0aNQ)CAUG[D$c?fX8$J("$ +PILZ$Gp'&#>&Z4t`R8)jg;sGPS&HkKm5nO_As4I~>restore grestore +% +% End Imported PIC File: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +% +% Polyline +% +% pen to black in case this eps object doesn't set color first +0 0 0 setrgbcolor +% Begin Imported JPEG File: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg + +n gs +6750 3150 tr +3.982301 -3.982301 sc +113 -113 tr +90 rot +0 0 tr +sa +/showpage {} def +% JPEG image follows: +113 113 sc +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: jpeg2ps 3.2 by Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +%%CreationDate: Mon Jan 14 14:35:51 2013 +%%BoundingBox: 0 0 113 113 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ +sOXW#;]]f#$]3a'90!F"BA5Lg90YXI;Ur;M@RX8Pk_ +92!UM_eIP%*H:qH%HI_*f,L0`gA7rQmYJ4P2?>?NTnNF0GpI-<%D0lS)J`K/_RM4 ++OS@6,Jf]P7Q3OL`-S]u-G?2G[6N&>;I*MSqV:W(UZU<*K!D\V3'PG"Wo]Oc[=,T +s)"+_e.,U[0*Jl#O6eG4mZWm0MafGOAL*CDCD_,dA_d'2,XfkA1SIaiJ\05%8bqQ +=c;*:Kg=0>j_]H7j'Q-b+2N3!"C]\oe`$?(mT+mZ6mJ9Y:c?iGJ(GP30uUf>Y3/& +G*7'7q*[NoNY)jJd(Y79OiRjA(gUBS]:Z(^cXjO!XZ['ClmhV$J:X?]:6 +!Pdr@pWhugg=Y_u$4WLc0A +N!a7Vt/WA_YE*[P32nn6F45l+R)N&@26*%@"fgG!@52$A(NUIX)Z'Z +\;>S4X=k(CTgaioFV[%'+6'Zc!stc,@7)QH`VtP>0:UD\P9J;>.Q0&9K(^ +0a2kR8eJooDbT?KNLOt8o$BM)u_)tX*7O_IeXoZ>1gGN9>phrY,-B0M>T+^Zg3q2 +Q`-T"phRa*.r+usa*Ak-l(j(`JEO+62:hrUO'qA3pA;$VEW)+_ke/ZXh-"0pdH&C +*`^@U4lY/Q6k!)K$8WtqUMM7QUTdhK9OZ@4-1f0!c+Ga70,[*hd:W[p?1$uOfC,> +3W)HPB92>:aJq'?:\,I:!_E8EJjG;qt3G6?]2'XrE"Du<0f60Em\Zs3%P\Y'I +=.a>0Hr"i^1pT[-=SA;Z^uRiSZKL$ikY[ih[G.5,FX$.B;B.6B+2tQQ1`jPE5lL-\,LS5rro:VjHd`jR +P/a\7@^%4/4A7/otr5DG4u6=cOPM^Gq5UG9+;IlA1]F2VWG\M=DW4OtXtr\gNuN0 +5`te![8fm5U%C=3Sp9JCYG+XU]Y0g\k"\9Z5r@Fi9je[--GA(b]..HjuoUi2;kme +4:""bVA(YEk_36YmA%fh12PA!fj"<^N^krrH:2r*1fIJ0pk@'=78\7fK(2XZGu+@bM)lL3WH>]amM. +alH*Df%K6!499s_qZ1Mh639PU+k!Ve`JY$nJ]K,*A,YuY9.XfGP"'VTF?RJ2#oK6 +3%q4dJWL.nOFeZ%+Gbj[pf8?J@J1dp,4TjeB:05]VB0aNQ)CAUG[D$c?fX8$J("$ +PILZ$Gp'&#>&Z4t`R8)jg;sGPS&HkKm5nO_As4I~>restore grestore +% +% End Imported PIC File: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +% +% Polyline +% +% pen to black in case this eps object doesn't set color first +0 0 0 setrgbcolor +% Begin Imported JPEG File: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg + +n gs +8550 4950 tr +3.982301 -3.982301 sc +113 -113 tr +90 rot +0 0 tr +sa +/showpage {} def +% JPEG image follows: +113 113 sc +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: jpeg2ps 3.2 by Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +%%CreationDate: Mon Jan 14 14:35:51 2013 +%%BoundingBox: 0 0 113 113 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ +sOXW#;]]f#$]3a'90!F"BA5Lg90YXI;Ur;M@RX8Pk_ +92!UM_eIP%*H:qH%HI_*f,L0`gA7rQmYJ4P2?>?NTnNF0GpI-<%D0lS)J`K/_RM4 ++OS@6,Jf]P7Q3OL`-S]u-G?2G[6N&>;I*MSqV:W(UZU<*K!D\V3'PG"Wo]Oc[=,T +s)"+_e.,U[0*Jl#O6eG4mZWm0MafGOAL*CDCD_,dA_d'2,XfkA1SIaiJ\05%8bqQ +=c;*:Kg=0>j_]H7j'Q-b+2N3!"C]\oe`$?(mT+mZ6mJ9Y:c?iGJ(GP30uUf>Y3/& +G*7'7q*[NoNY)jJd(Y79OiRjA(gUBS]:Z(^cXjO!XZ['ClmhV$J:X?]:6 +!Pdr@pWhugg=Y_u$4WLc0A +N!a7Vt/WA_YE*[P32nn6F45l+R)N&@26*%@"fgG!@52$A(NUIX)Z'Z 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Imported JPEG File: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg + +n gs +10350 6750 tr +3.982301 -3.982301 sc +113 -113 tr +90 rot +0 0 tr +sa +/showpage {} def +% JPEG image follows: +113 113 sc +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: jpeg2ps 3.2 by Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +%%CreationDate: Mon Jan 14 14:35:51 2013 +%%BoundingBox: 0 0 113 113 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ +sOXW#;]]f#$]3a'90!F"BA5Lg90YXI;Ur;M@RX8Pk_ +92!UM_eIP%*H:qH%HI_*f,L0`gA7rQmYJ4P2?>?NTnNF0GpI-<%D0lS)J`K/_RM4 ++OS@6,Jf]P7Q3OL`-S]u-G?2G[6N&>;I*MSqV:W(UZU<*K!D\V3'PG"Wo]Oc[=,T +s)"+_e.,U[0*Jl#O6eG4mZWm0MafGOAL*CDCD_,dA_d'2,XfkA1SIaiJ\05%8bqQ +=c;*:Kg=0>j_]H7j'Q-b+2N3!"C]\oe`$?(mT+mZ6mJ9Y:c?iGJ(GP30uUf>Y3/& +G*7'7q*[NoNY)jJd(Y79OiRjA(gUBS]:Z(^cXjO!XZ['ClmhV$J:X?]:6 +!Pdr@pWhugg=Y_u$4WLc0A +N!a7Vt/WA_YE*[P32nn6F45l+R)N&@26*%@"fgG!@52$A(NUIX)Z'Z 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Imported JPEG File: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg + +n gs +8550 6750 tr +3.982301 -3.982301 sc +113 -113 tr +90 rot +0 0 tr +sa +/showpage {} def +% JPEG image follows: +113 113 sc +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: jpeg2ps 3.2 by Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +%%CreationDate: Mon Jan 14 14:35:51 2013 +%%BoundingBox: 0 0 113 113 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ +sOXW#;]]f#$]3a'90!F"BA5Lg90YXI;Ur;M@RX8Pk_ +92!UM_eIP%*H:qH%HI_*f,L0`gA7rQmYJ4P2?>?NTnNF0GpI-<%D0lS)J`K/_RM4 ++OS@6,Jf]P7Q3OL`-S]u-G?2G[6N&>;I*MSqV:W(UZU<*K!D\V3'PG"Wo]Oc[=,T +s)"+_e.,U[0*Jl#O6eG4mZWm0MafGOAL*CDCD_,dA_d'2,XfkA1SIaiJ\05%8bqQ +=c;*:Kg=0>j_]H7j'Q-b+2N3!"C]\oe`$?(mT+mZ6mJ9Y:c?iGJ(GP30uUf>Y3/& +G*7'7q*[NoNY)jJd(Y79OiRjA(gUBS]:Z(^cXjO!XZ['ClmhV$J:X?]:6 +!Pdr@pWhugg=Y_u$4WLc0A +N!a7Vt/WA_YE*[P32nn6F45l+R)N&@26*%@"fgG!@52$A(NUIX)Z'Z 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doesn't set color first +0 0 0 setrgbcolor +% Begin Imported JPEG File: /home/ziane/Desktop/Revision_PC_07_01_2013/noire.jpg + +n gs +6750 5850 tr +4.687500 -4.687500 sc +270 rot +0 0 tr +sa +/showpage {} def +% JPEG image follows: +96 96 sc +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: jpeg2ps 3.2 by Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/noire.jpg +%%CreationDate: Mon Jan 14 14:35:51 2013 +%%BoundingBox: 0 0 96 96 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/noire.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 96 + /Height 96 + /ImageMatrix [ 96 0 0 -96 0 96 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6'G(fi%h]Kd'bV8r(D.2g%2BB^&.f? +d&/?<&&02H'*[r-H0d@PO'H]C]0/G%.3%u's3C,bc5pn681][mi$3^S:%0ZnE.2W +[7.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4 +P;4!"fJ:?iXR:!?qLF&HMtG!WU(<)uos?!WrH(zz!!!3.!!NE,#Qk,-_uMP(!!*0 +(!7DatUj=?94I_GkBe-oEq +tGNO)85l@W_'?s!1^N'.3QAArMD,[KhHkr6L/]0fpFn[<,&aWkcJA;l;O_n7TI7/IS=%8E^*pg(QF5 +;nefo26+&g4&#DU(4h5;J_BF6$&o?9fok!,]:X";IbV)4aPZ4%=7mE5niFH_6M#. +pUo_@Zt,HDI%]l>QYO!)m"h-s;o3X:/F2/8-hJ'Zg*:B,E5c[Qi61_ia7V:])<0R +Mq!CUuG^##R@t^,V'tBNE6#FqG^SJ0uW;q^jq\P4"ne2Dh>VoVAG$K/4!0SNA#`? +@NNho0,4/E1FMC="IPMN^2doP/VP7t1CLdBuF=kC<$&+$I+TWVhq13f<0*/tJ=`f +=hh6!QsQhTl"%A;4<)LF+[F#(NVmVU#JYJ)=]=Ik$e;=*LZnEn8<>B4GE7r]r^tZ +I_a>.f-/t/FS\cpUTJ#c6q-R=ej@F-(`q_,9(cp,=P[CJ8e0i4WkjiW;%/<'huis +J9WD\[gh,dbJbSA5bbnqZ(;4Nk=po4NVW[p01+Q_jL'GUf1o<\T*$@]17YrM$Y!&q\SQ`Y!X5oms+IEOh(b;"`\P&6 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3.2 by Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/noire.jpg +%%CreationDate: Mon Jan 14 14:35:51 2013 +%%BoundingBox: 0 0 96 96 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/noire.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 96 + /Height 96 + /ImageMatrix [ 96 0 0 -96 0 96 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6'G(fi%h]Kd'bV8r(D.2g%2BB^&.f? +d&/?<&&02H'*[r-H0d@PO'H]C]0/G%.3%u's3C,bc5pn681][mi$3^S:%0ZnE.2W 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/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +%%CreationDate: Mon Jan 14 14:35:51 2013 +%%BoundingBox: 0 0 113 113 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o 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18022 7222 l gs col0 s gr +% Polyline +n 13949 4049 m + 17999 8099 l gs col0 s gr +% Polyline +n 13972 1372 m + 18022 5422 l gs col0 s gr +% Polyline +n 15975 2250 m + 15975 6300 l gs col0 s gr +% Polyline +% +% pen to black in case this eps object doesn't set color first +0 0 0 setrgbcolor +% Begin Imported JPEG File: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg + +n gs +13950 4050 tr +3.982301 -3.982301 sc +113 -113 tr +90 rot +0 0 tr +sa +/showpage {} def +% JPEG image follows: +113 113 sc +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: jpeg2ps 3.2 by Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +%%CreationDate: Mon Jan 14 14:35:51 2013 +%%BoundingBox: 0 0 113 113 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ +sOXW#;]]f#$]3a'90!F"BA5Lg90YXI;Ur;M@RX8Pk_ +92!UM_eIP%*H:qH%HI_*f,L0`gA7rQmYJ4P2?>?NTnNF0GpI-<%D0lS)J`K/_RM4 ++OS@6,Jf]P7Q3OL`-S]u-G?2G[6N&>;I*MSqV:W(UZU<*K!D\V3'PG"Wo]Oc[=,T +s)"+_e.,U[0*Jl#O6eG4mZWm0MafGOAL*CDCD_,dA_d'2,XfkA1SIaiJ\05%8bqQ +=c;*:Kg=0>j_]H7j'Q-b+2N3!"C]\oe`$?(mT+mZ6mJ9Y:c?iGJ(GP30uUf>Y3/& +G*7'7q*[NoNY)jJd(Y79OiRjA(gUBS]:Z(^cXjO!XZ['ClmhV$J:X?]:6 +!Pdr@pWhugg=Y_u$4WLc0A +N!a7Vt/WA_YE*[P32nn6F45l+R)N&@26*%@"fgG!@52$A(NUIX)Z'Z +\;>S4X=k(CTgaioFV[%'+6'Zc!stc,@7)QH`VtP>0:UD\P9J;>.Q0&9K(^ +0a2kR8eJooDbT?KNLOt8o$BM)u_)tX*7O_IeXoZ>1gGN9>phrY,-B0M>T+^Zg3q2 +Q`-T"phRa*.r+usa*Ak-l(j(`JEO+62:hrUO'qA3pA;$VEW)+_ke/ZXh-"0pdH&C +*`^@U4lY/Q6k!)K$8WtqUMM7QUTdhK9OZ@4-1f0!c+Ga70,[*hd:W[p?1$uOfC,> +3W)HPB92>:aJq'?:\,I:!_E8EJjG;qt3G6?]2'XrE"Du<0f60Em\Zs3%P\Y'I +=.a>0Hr"i^1pT[-=SA;Z^uRiSZKL$ikY[ih[G.5,FX$.B;B.6B+2tQQ1`jPE5lL-\,LS5rro:VjHd`jR +P/a\7@^%4/4A7/otr5DG4u6=cOPM^Gq5UG9+;IlA1]F2VWG\M=DW4OtXtr\gNuN0 +5`te![8fm5U%C=3Sp9JCYG+XU]Y0g\k"\9Z5r@Fi9je[--GA(b]..HjuoUi2;kme +4:""bVA(YEk_36YmA%fh12PA!fj"<^N^krrH:2r*1fIJ0pk@'=78\7fK(2XZGu+@bM)lL3WH>]amM. +alH*Df%K6!499s_qZ1Mh639PU+k!Ve`JY$nJ]K,*A,YuY9.XfGP"'VTF?RJ2#oK6 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/Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ +sOXW#;]]f#$]3a'90!F"BA5Lg90YXI;Ur;M@RX8Pk_ +92!UM_eIP%*H:qH%HI_*f,L0`gA7rQmYJ4P2?>?NTnNF0GpI-<%D0lS)J`K/_RM4 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'/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ +sOXW#;]]f#$]3a'90!F"BA5Lg90YXI;Ur;M@RX8Pk_ 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/noire.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 96 + /Height 96 + /ImageMatrix [ 96 0 0 -96 0 96 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6'G(fi%h]Kd'bV8r(D.2g%2BB^&.f? +d&/?<&&02H'*[r-H0d@PO'H]C]0/G%.3%u's3C,bc5pn681][mi$3^S:%0ZnE.2W +[7.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4 +P;4!"fJ:?iXR:!?qLF&HMtG!WU(<)uos?!WrH(zz!!!3.!!NE,#Qk,-_uMP(!!*0 +(!7DatUj=?94I_GkBe-oEq +tGNO)85l@W_'?s!1^N'.3QAArMD,[KhHkr6L/]0fpFn[<,&aWkcJA;l;O_n7TI7/IS=%8E^*pg(QF5 +;nefo26+&g4&#DU(4h5;J_BF6$&o?9fok!,]:X";IbV)4aPZ4%=7mE5niFH_6M#. 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RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 96 + /Height 96 + /ImageMatrix [ 96 0 0 -96 0 96 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6'G(fi%h]Kd'bV8r(D.2g%2BB^&.f? +d&/?<&&02H'*[r-H0d@PO'H]C]0/G%.3%u's3C,bc5pn681][mi$3^S:%0ZnE.2W +[7.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4 +P;4!"fJ:?iXR:!?qLF&HMtG!WU(<)uos?!WrH(zz!!!3.!!NE,#Qk,-_uMP(!!*0 +(!7DatUj=?94I_GkBe-oEq +tGNO)85l@W_'?s!1^N'.3QAArMD,[KhHkr6L/]0fpFn[<,&aWkcJA;l;O_n7TI7/IS=%8E^*pg(QF5 +;nefo26+&g4&#DU(4h5;J_BF6$&o?9fok!,]:X";IbV)4aPZ4%=7mE5niFH_6M#. +pUo_@Zt,HDI%]l>QYO!)m"h-s;o3X:/F2/8-hJ'Zg*:B,E5c[Qi61_ia7V:])<0R +Mq!CUuG^##R@t^,V'tBNE6#FqG^SJ0uW;q^jq\P4"ne2Dh>VoVAG$K/4!0SNA#`? +@NNho0,4/E1FMC="IPMN^2doP/VP7t1CLdBuF=kC<$&+$I+TWVhq13f<0*/tJ=`f +=hh6!QsQhTl"%A;4<)LF+[F#(NVmVU#JYJ)=]=Ik$e;=*LZnEn8<>B4GE7r]r^tZ 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def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ +sOXW#;]]f#$]3a'90!F"BA5Lg90YXI;Ur;M@RX8Pk_ +92!UM_eIP%*H:qH%HI_*f,L0`gA7rQmYJ4P2?>?NTnNF0GpI-<%D0lS)J`K/_RM4 ++OS@6,Jf]P7Q3OL`-S]u-G?2G[6N&>;I*MSqV:W(UZU<*K!D\V3'PG"Wo]Oc[=,T +s)"+_e.,U[0*Jl#O6eG4mZWm0MafGOAL*CDCD_,dA_d'2,XfkA1SIaiJ\05%8bqQ 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+PILZ$Gp'&#>&Z4t`R8)jg;sGPS&HkKm5nO_As4I~>restore grestore +% +% End Imported PIC File: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +% +% Polyline +% +% pen to black in case this eps object doesn't set color first +0 0 0 setrgbcolor +% Begin Imported JPEG File: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg + +n gs +7650 7650 tr +3.982301 -3.982301 sc +113 -113 tr +90 rot +0 0 tr +sa +/showpage {} def +% JPEG image follows: +113 113 sc +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: jpeg2ps 3.2 by Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +%%CreationDate: Mon Jan 14 14:35:51 2013 +%%BoundingBox: 0 0 113 113 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ +sOXW#;]]f#$]3a'90!F"BA5Lg90YXI;Ur;M@RX8Pk_ +92!UM_eIP%*H:qH%HI_*f,L0`gA7rQmYJ4P2?>?NTnNF0GpI-<%D0lS)J`K/_RM4 ++OS@6,Jf]P7Q3OL`-S]u-G?2G[6N&>;I*MSqV:W(UZU<*K!D\V3'PG"Wo]Oc[=,T +s)"+_e.,U[0*Jl#O6eG4mZWm0MafGOAL*CDCD_,dA_d'2,XfkA1SIaiJ\05%8bqQ +=c;*:Kg=0>j_]H7j'Q-b+2N3!"C]\oe`$?(mT+mZ6mJ9Y:c?iGJ(GP30uUf>Y3/& +G*7'7q*[NoNY)jJd(Y79OiRjA(gUBS]:Z(^cXjO!XZ['ClmhV$J:X?]:6 +!Pdr@pWhugg=Y_u$4WLc0A +N!a7Vt/WA_YE*[P32nn6F45l+R)N&@26*%@"fgG!@52$A(NUIX)Z'Z +\;>S4X=k(CTgaioFV[%'+6'Zc!stc,@7)QH`VtP>0:UD\P9J;>.Q0&9K(^ +0a2kR8eJooDbT?KNLOt8o$BM)u_)tX*7O_IeXoZ>1gGN9>phrY,-B0M>T+^Zg3q2 +Q`-T"phRa*.r+usa*Ak-l(j(`JEO+62:hrUO'qA3pA;$VEW)+_ke/ZXh-"0pdH&C +*`^@U4lY/Q6k!)K$8WtqUMM7QUTdhK9OZ@4-1f0!c+Ga70,[*hd:W[p?1$uOfC,> +3W)HPB92>:aJq'?:\,I:!_E8EJjG;qt3G6?]2'XrE"Du<0f60Em\Zs3%P\Y'I +=.a>0Hr"i^1pT[-=SA;Z^uRiSZKL$ikY[ih[G.5,FX$.B;B.6B+2tQQ1`jPE5lL-\,LS5rro:VjHd`jR +P/a\7@^%4/4A7/otr5DG4u6=cOPM^Gq5UG9+;IlA1]F2VWG\M=DW4OtXtr\gNuN0 +5`te![8fm5U%C=3Sp9JCYG+XU]Y0g\k"\9Z5r@Fi9je[--GA(b]..HjuoUi2;kme +4:""bVA(YEk_36YmA%fh12PA!fj"<^N^krrH:2r*1fIJ0pk@'=78\7fK(2XZGu+@bM)lL3WH>]amM. +alH*Df%K6!499s_qZ1Mh639PU+k!Ve`JY$nJ]K,*A,YuY9.XfGP"'VTF?RJ2#oK6 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findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 96 + /Height 96 + /ImageMatrix [ 96 0 0 -96 0 96 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6'G(fi%h]Kd'bV8r(D.2g%2BB^&.f? +d&/?<&&02H'*[r-H0d@PO'H]C]0/G%.3%u's3C,bc5pn681][mi$3^S:%0ZnE.2W +[7.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4 +P;4!"fJ:?iXR:!?qLF&HMtG!WU(<)uos?!WrH(zz!!!3.!!NE,#Qk,-_uMP(!!*0 +(!7DatUj=?94I_GkBe-oEq +tGNO)85l@W_'?s!1^N'.3QAArMD,[KhHkr6L/]0fpFn[<,&aWkcJA;l;O_n7TI7/IS=%8E^*pg(QF5 +;nefo26+&g4&#DU(4h5;J_BF6$&o?9fok!,]:X";IbV)4aPZ4%=7mE5niFH_6M#. +pUo_@Zt,HDI%]l>QYO!)m"h-s;o3X:/F2/8-hJ'Zg*:B,E5c[Qi61_ia7V:])<0R +Mq!CUuG^##R@t^,V'tBNE6#FqG^SJ0uW;q^jq\P4"ne2Dh>VoVAG$K/4!0SNA#`? 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object doesn't set color first +0 0 0 setrgbcolor +% Begin Imported JPEG File: /home/ziane/Desktop/Revision_PC_07_01_2013/noire.jpg + +n gs +6750 4050 tr +4.687500 -4.687500 sc +270 rot +0 0 tr +sa +/showpage {} def +% JPEG image follows: +96 96 sc +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: jpeg2ps 3.2 by Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/noire.jpg +%%CreationDate: Mon Jan 14 14:35:51 2013 +%%BoundingBox: 0 0 96 96 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/noire.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 96 + /Height 96 + /ImageMatrix [ 96 0 0 -96 0 96 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6'G(fi%h]Kd'bV8r(D.2g%2BB^&.f? +d&/?<&&02H'*[r-H0d@PO'H]C]0/G%.3%u's3C,bc5pn681][mi$3^S:%0ZnE.2W +[7.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4 +P;4!"fJ:?iXR:!?qLF&HMtG!WU(<)uos?!WrH(zz!!!3.!!NE,#Qk,-_uMP(!!*0 +(!7DatUj=?94I_GkBe-oEq +tGNO)85l@W_'?s!1^N'.3QAArMD,[KhHkr6L/]0fpFn[<,&aWkcJA;l;O_n7TI7/IS=%8E^*pg(QF5 +;nefo26+&g4&#DU(4h5;J_BF6$&o?9fok!,]:X";IbV)4aPZ4%=7mE5niFH_6M#. +pUo_@Zt,HDI%]l>QYO!)m"h-s;o3X:/F2/8-hJ'Zg*:B,E5c[Qi61_ia7V:])<0R +Mq!CUuG^##R@t^,V'tBNE6#FqG^SJ0uW;q^jq\P4"ne2Dh>VoVAG$K/4!0SNA#`? +@NNho0,4/E1FMC="IPMN^2doP/VP7t1CLdBuF=kC<$&+$I+TWVhq13f<0*/tJ=`f +=hh6!QsQhTl"%A;4<)LF+[F#(NVmVU#JYJ)=]=Ik$e;=*LZnEn8<>B4GE7r]r^tZ +I_a>.f-/t/FS\cpUTJ#c6q-R=ej@F-(`q_,9(cp,=P[CJ8e0i4WkjiW;%/<'huis 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0 tr +sa +/showpage {} def +% JPEG image follows: +113 113 sc +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: jpeg2ps 3.2 by Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +%%CreationDate: Mon Jan 14 14:35:51 2013 +%%BoundingBox: 0 0 113 113 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec 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+0 0 tr +sa +/showpage {} def +% JPEG image follows: +96 96 sc +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: jpeg2ps 3.2 by Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/noire.jpg +%%CreationDate: Mon Jan 14 14:35:51 2013 +%%BoundingBox: 0 0 96 96 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/noire.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 96 + /Height 96 + /ImageMatrix [ 96 0 0 -96 0 96 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec 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Mon Jan 14 14:35:51 2013 +%%BoundingBox: 0 0 113 113 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) 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+%%CreationDate: Mon Jan 14 14:35:51 2013 +%%BoundingBox: 0 0 96 96 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/noire.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 96 + /Height 96 + /ImageMatrix [ 96 0 0 -96 0 96 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6'G(fi%h]Kd'bV8r(D.2g%2BB^&.f? +d&/?<&&02H'*[r-H0d@PO'H]C]0/G%.3%u's3C,bc5pn681][mi$3^S:%0ZnE.2W +[7.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4 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ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ +sOXW#;]]f#$]3a'90!F"BA5Lg90YXI;Ur;M@RX8Pk_ 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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+n gs +9450 7695 tr +3.982301 -3.982301 sc +113 -113 tr +90 rot +0 0 tr +sa +/showpage {} def +% JPEG image follows: +113 113 sc +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: jpeg2ps 3.2 by Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +%%CreationDate: Mon Jan 14 14:35:51 2013 +%%BoundingBox: 0 0 113 113 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ +sOXW#;]]f#$]3a'90!F"BA5Lg90YXI;Ur;M@RX8Pk_ +92!UM_eIP%*H:qH%HI_*f,L0`gA7rQmYJ4P2?>?NTnNF0GpI-<%D0lS)J`K/_RM4 ++OS@6,Jf]P7Q3OL`-S]u-G?2G[6N&>;I*MSqV:W(UZU<*K!D\V3'PG"Wo]Oc[=,T +s)"+_e.,U[0*Jl#O6eG4mZWm0MafGOAL*CDCD_,dA_d'2,XfkA1SIaiJ\05%8bqQ +=c;*:Kg=0>j_]H7j'Q-b+2N3!"C]\oe`$?(mT+mZ6mJ9Y:c?iGJ(GP30uUf>Y3/& +G*7'7q*[NoNY)jJd(Y79OiRjA(gUBS]:Z(^cXjO!XZ['ClmhV$J:X?]:6 +!Pdr@pWhugg=Y_u$4WLc0A +N!a7Vt/WA_YE*[P32nn6F45l+R)N&@26*%@"fgG!@52$A(NUIX)Z'Z +\;>S4X=k(CTgaioFV[%'+6'Zc!stc,@7)QH`VtP>0:UD\P9J;>.Q0&9K(^ 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doesn't set color first +0 0 0 setrgbcolor +% Begin Imported JPEG File: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg + +n gs +7650 4050 tr +3.982301 -3.982301 sc +113 -113 tr +90 rot +0 0 tr +sa +/showpage {} def +% JPEG image follows: +113 113 sc +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: jpeg2ps 3.2 by Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +%%CreationDate: Mon Jan 14 14:35:51 2013 +%%BoundingBox: 0 0 113 113 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ +sOXW#;]]f#$]3a'90!F"BA5Lg90YXI;Ur;M@RX8Pk_ +92!UM_eIP%*H:qH%HI_*f,L0`gA7rQmYJ4P2?>?NTnNF0GpI-<%D0lS)J`K/_RM4 ++OS@6,Jf]P7Q3OL`-S]u-G?2G[6N&>;I*MSqV:W(UZU<*K!D\V3'PG"Wo]Oc[=,T +s)"+_e.,U[0*Jl#O6eG4mZWm0MafGOAL*CDCD_,dA_d'2,XfkA1SIaiJ\05%8bqQ +=c;*:Kg=0>j_]H7j'Q-b+2N3!"C]\oe`$?(mT+mZ6mJ9Y:c?iGJ(GP30uUf>Y3/& +G*7'7q*[NoNY)jJd(Y79OiRjA(gUBS]:Z(^cXjO!XZ['ClmhV$J:X?]:6 +!Pdr@pWhugg=Y_u$4WLc0A 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object doesn't set color first +0 0 0 setrgbcolor +% Begin Imported JPEG File: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg + +n gs +9450 5850 tr +3.982301 -3.982301 sc +113 -113 tr +90 rot +0 0 tr +sa +/showpage {} def +% JPEG image follows: +113 113 sc +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: jpeg2ps 3.2 by Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +%%CreationDate: Mon Jan 14 14:35:51 2013 +%%BoundingBox: 0 0 113 113 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ +sOXW#;]]f#$]3a'90!F"BA5Lg90YXI;Ur;M@RX8Pk_ +92!UM_eIP%*H:qH%HI_*f,L0`gA7rQmYJ4P2?>?NTnNF0GpI-<%D0lS)J`K/_RM4 ++OS@6,Jf]P7Q3OL`-S]u-G?2G[6N&>;I*MSqV:W(UZU<*K!D\V3'PG"Wo]Oc[=,T +s)"+_e.,U[0*Jl#O6eG4mZWm0MafGOAL*CDCD_,dA_d'2,XfkA1SIaiJ\05%8bqQ +=c;*:Kg=0>j_]H7j'Q-b+2N3!"C]\oe`$?(mT+mZ6mJ9Y:c?iGJ(GP30uUf>Y3/& +G*7'7q*[NoNY)jJd(Y79OiRjA(gUBS]:Z(^cXjO!XZ['ClmhV$J:X?]:6 +!Pdr@pWhugg=Y_u$4WLc0A 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object doesn't set color first +0 0 0 setrgbcolor +% Begin Imported JPEG File: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg + +n gs +12150 7200 tr +3.982301 -3.982301 sc +113 -113 tr +90 rot +0 0 tr +sa +/showpage {} def +% JPEG image follows: +113 113 sc +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: jpeg2ps 3.2 by Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +%%CreationDate: Mon Jan 14 14:35:51 2013 +%%BoundingBox: 0 0 113 113 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ +sOXW#;]]f#$]3a'90!F"BA5Lg90YXI;Ur;M@RX8Pk_ +92!UM_eIP%*H:qH%HI_*f,L0`gA7rQmYJ4P2?>?NTnNF0GpI-<%D0lS)J`K/_RM4 ++OS@6,Jf]P7Q3OL`-S]u-G?2G[6N&>;I*MSqV:W(UZU<*K!D\V3'PG"Wo]Oc[=,T +s)"+_e.,U[0*Jl#O6eG4mZWm0MafGOAL*CDCD_,dA_d'2,XfkA1SIaiJ\05%8bqQ +=c;*:Kg=0>j_]H7j'Q-b+2N3!"C]\oe`$?(mT+mZ6mJ9Y:c?iGJ(GP30uUf>Y3/& +G*7'7q*[NoNY)jJd(Y79OiRjA(gUBS]:Z(^cXjO!XZ['ClmhV$J:X?]:6 +!Pdr@pWhugg=Y_u$4WLc0A 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object doesn't set color first +0 0 0 setrgbcolor +% Begin Imported JPEG File: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg + +n gs +10350 5400 tr +3.982301 -3.982301 sc +113 -113 tr +90 rot +0 0 tr +sa +/showpage {} def +% JPEG image follows: +113 113 sc +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: jpeg2ps 3.2 by Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +%%CreationDate: Mon Jan 14 14:35:51 2013 +%%BoundingBox: 0 0 113 113 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ +sOXW#;]]f#$]3a'90!F"BA5Lg90YXI;Ur;M@RX8Pk_ +92!UM_eIP%*H:qH%HI_*f,L0`gA7rQmYJ4P2?>?NTnNF0GpI-<%D0lS)J`K/_RM4 ++OS@6,Jf]P7Q3OL`-S]u-G?2G[6N&>;I*MSqV:W(UZU<*K!D\V3'PG"Wo]Oc[=,T +s)"+_e.,U[0*Jl#O6eG4mZWm0MafGOAL*CDCD_,dA_d'2,XfkA1SIaiJ\05%8bqQ +=c;*:Kg=0>j_]H7j'Q-b+2N3!"C]\oe`$?(mT+mZ6mJ9Y:c?iGJ(GP30uUf>Y3/& +G*7'7q*[NoNY)jJd(Y79OiRjA(gUBS]:Z(^cXjO!XZ['ClmhV$J:X?]:6 +!Pdr@pWhugg=Y_u$4WLc0A 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object doesn't set color first +0 0 0 setrgbcolor +% Begin Imported JPEG File: /home/ziane/Desktop/Revision_PC_07_01_2013/noire.jpg + +n gs +10350 4500 tr +4.687500 -4.687500 sc +270 rot +0 0 tr +sa +/showpage {} def +% JPEG image follows: +96 96 sc +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: jpeg2ps 3.2 by Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/noire.jpg +%%CreationDate: Mon Jan 14 14:35:51 2013 +%%BoundingBox: 0 0 96 96 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/noire.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 96 + /Height 96 + /ImageMatrix [ 96 0 0 -96 0 96 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6'G(fi%h]Kd'bV8r(D.2g%2BB^&.f? +d&/?<&&02H'*[r-H0d@PO'H]C]0/G%.3%u's3C,bc5pn681][mi$3^S:%0ZnE.2W +[7.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4 +P;4!"fJ:?iXR:!?qLF&HMtG!WU(<)uos?!WrH(zz!!!3.!!NE,#Qk,-_uMP(!!*0 +(!7DatUj=?94I_GkBe-oEq +tGNO)85l@W_'?s!1^N'.3QAArMD,[KhHkr6L/]0fpFn[<,&aWkcJA;l;O_n7TI7/IS=%8E^*pg(QF5 +;nefo26+&g4&#DU(4h5;J_BF6$&o?9fok!,]:X";IbV)4aPZ4%=7mE5niFH_6M#. +pUo_@Zt,HDI%]l>QYO!)m"h-s;o3X:/F2/8-hJ'Zg*:B,E5c[Qi61_ia7V:])<0R +Mq!CUuG^##R@t^,V'tBNE6#FqG^SJ0uW;q^jq\P4"ne2Dh>VoVAG$K/4!0SNA#`? +@NNho0,4/E1FMC="IPMN^2doP/VP7t1CLdBuF=kC<$&+$I+TWVhq13f<0*/tJ=`f +=hh6!QsQhTl"%A;4<)LF+[F#(NVmVU#JYJ)=]=Ik$e;=*LZnEn8<>B4GE7r]r^tZ +I_a>.f-/t/FS\cpUTJ#c6q-R=ej@F-(`q_,9(cp,=P[CJ8e0i4WkjiW;%/<'huis 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+/showpage {} def +% JPEG image follows: +96 96 sc +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: jpeg2ps 3.2 by Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/noire.jpg +%%CreationDate: Mon Jan 14 14:35:51 2013 +%%BoundingBox: 0 0 96 96 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/noire.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 96 + /Height 96 + /ImageMatrix [ 96 0 0 -96 0 96 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec 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14:35:51 2013 +%%BoundingBox: 0 0 96 96 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/noire.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 96 + /Height 96 + /ImageMatrix [ 96 0 0 -96 0 96 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6'G(fi%h]Kd'bV8r(D.2g%2BB^&.f? +d&/?<&&02H'*[r-H0d@PO'H]C]0/G%.3%u's3C,bc5pn681][mi$3^S:%0ZnE.2W +[7.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/noire.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 96 + /Height 96 + /ImageMatrix [ 96 0 0 -96 0 96 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6'G(fi%h]Kd'bV8r(D.2g%2BB^&.f? +d&/?<&&02H'*[r-H0d@PO'H]C]0/G%.3%u's3C,bc5pn681][mi$3^S:%0ZnE.2W +[7.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4 +P;4!"fJ:?iXR:!?qLF&HMtG!WU(<)uos?!WrH(zz!!!3.!!NE,#Qk,-_uMP(!!*0 +(!7DatUj=?94I_GkBe-oEq +tGNO)85l@W_'?s!1^N'.3QAArMD,[KhHkr6L/]0fpFn[<,&aWkcJA;l;O_n7TI7/IS=%8E^*pg(QF5 +;nefo26+&g4&#DU(4h5;J_BF6$&o?9fok!,]:X";IbV)4aPZ4%=7mE5niFH_6M#. 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Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +%%CreationDate: Mon Jan 14 14:35:51 2013 +%%BoundingBox: 0 0 113 113 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o 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Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +%%CreationDate: Mon Jan 14 14:35:51 2013 +%%BoundingBox: 0 0 113 113 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o 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6919 l 9184 6782 l cp +eoclip +n 12211 5711 m + 9016 6926 l gs col0 s gr gr + +% arrowhead +15.000 slw +n 9184 6782 m 9036 6919 l 9237 6922 l 9176 6865 l 9184 6782 l + cp gs 0.00 setgray ef gr col0 s +% Polyline +% +% pen to black in case this eps object doesn't set color first +0 0 0 setrgbcolor +% Begin Imported JPEG File: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg + +n gs +14850 4950 tr +3.982301 -3.982301 sc +113 -113 tr +90 rot +0 0 tr +sa +/showpage {} def +% JPEG image follows: +113 113 sc +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: jpeg2ps 3.2 by Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +%%CreationDate: Mon Jan 14 14:35:51 2013 +%%BoundingBox: 0 0 113 113 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ +sOXW#;]]f#$]3a'90!F"BA5Lg90YXI;Ur;M@RX8Pk_ +92!UM_eIP%*H:qH%HI_*f,L0`gA7rQmYJ4P2?>?NTnNF0GpI-<%D0lS)J`K/_RM4 ++OS@6,Jf]P7Q3OL`-S]u-G?2G[6N&>;I*MSqV:W(UZU<*K!D\V3'PG"Wo]Oc[=,T 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findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 96 + /Height 96 + /ImageMatrix [ 96 0 0 -96 0 96 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6'G(fi%h]Kd'bV8r(D.2g%2BB^&.f? +d&/?<&&02H'*[r-H0d@PO'H]C]0/G%.3%u's3C,bc5pn681][mi$3^S:%0ZnE.2W +[7.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4 +P;4!"fJ:?iXR:!?qLF&HMtG!WU(<)uos?!WrH(zz!!!3.!!NE,#Qk,-_uMP(!!*0 +(!7DatUj=?94I_GkBe-oEq +tGNO)85l@W_'?s!1^N'.3QAArMD,[KhHkr6L/]0fpFn[<,&aWkcJA;l;O_n7TI7/IS=%8E^*pg(QF5 +;nefo26+&g4&#DU(4h5;J_BF6$&o?9fok!,]:X";IbV)4aPZ4%=7mE5niFH_6M#. +pUo_@Zt,HDI%]l>QYO!)m"h-s;o3X:/F2/8-hJ'Zg*:B,E5c[Qi61_ia7V:])<0R +Mq!CUuG^##R@t^,V'tBNE6#FqG^SJ0uW;q^jq\P4"ne2Dh>VoVAG$K/4!0SNA#`? 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object doesn't set color first +0 0 0 setrgbcolor +% Begin Imported JPEG File: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg + +n gs +16650 6750 tr +3.982301 -3.982301 sc +113 -113 tr +90 rot +0 0 tr +sa +/showpage {} def +% JPEG image follows: +113 113 sc +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: jpeg2ps 3.2 by Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +%%CreationDate: Mon Jan 14 14:35:51 2013 +%%BoundingBox: 0 0 113 113 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ +sOXW#;]]f#$]3a'90!F"BA5Lg90YXI;Ur;M@RX8Pk_ +92!UM_eIP%*H:qH%HI_*f,L0`gA7rQmYJ4P2?>?NTnNF0GpI-<%D0lS)J`K/_RM4 ++OS@6,Jf]P7Q3OL`-S]u-G?2G[6N&>;I*MSqV:W(UZU<*K!D\V3'PG"Wo]Oc[=,T +s)"+_e.,U[0*Jl#O6eG4mZWm0MafGOAL*CDCD_,dA_d'2,XfkA1SIaiJ\05%8bqQ +=c;*:Kg=0>j_]H7j'Q-b+2N3!"C]\oe`$?(mT+mZ6mJ9Y:c?iGJ(GP30uUf>Y3/& +G*7'7q*[NoNY)jJd(Y79OiRjA(gUBS]:Z(^cXjO!XZ['ClmhV$J:X?]:6 +!Pdr@pWhugg=Y_u$4WLc0A 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object doesn't set color first +0 0 0 setrgbcolor +% Begin Imported JPEG File: /home/ziane/Desktop/Revision_PC_07_01_2013/noire.jpg + +n gs +16650 5850 tr +4.687500 -4.687500 sc +270 rot +0 0 tr +sa +/showpage {} def +% JPEG image follows: +96 96 sc +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: jpeg2ps 3.2 by Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/noire.jpg +%%CreationDate: Mon Jan 14 14:35:51 2013 +%%BoundingBox: 0 0 96 96 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/noire.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 96 + /Height 96 + /ImageMatrix [ 96 0 0 -96 0 96 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6'G(fi%h]Kd'bV8r(D.2g%2BB^&.f? +d&/?<&&02H'*[r-H0d@PO'H]C]0/G%.3%u's3C,bc5pn681][mi$3^S:%0ZnE.2W +[7.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4 +P;4!"fJ:?iXR:!?qLF&HMtG!WU(<)uos?!WrH(zz!!!3.!!NE,#Qk,-_uMP(!!*0 +(!7DatUj=?94I_GkBe-oEq +tGNO)85l@W_'?s!1^N'.3QAArMD,[KhHkr6L/]0fpFn[<,&aWkcJA;l;O_n7TI7/IS=%8E^*pg(QF5 +;nefo26+&g4&#DU(4h5;J_BF6$&o?9fok!,]:X";IbV)4aPZ4%=7mE5niFH_6M#. +pUo_@Zt,HDI%]l>QYO!)m"h-s;o3X:/F2/8-hJ'Zg*:B,E5c[Qi61_ia7V:])<0R +Mq!CUuG^##R@t^,V'tBNE6#FqG^SJ0uW;q^jq\P4"ne2Dh>VoVAG$K/4!0SNA#`? +@NNho0,4/E1FMC="IPMN^2doP/VP7t1CLdBuF=kC<$&+$I+TWVhq13f<0*/tJ=`f +=hh6!QsQhTl"%A;4<)LF+[F#(NVmVU#JYJ)=]=Ik$e;=*LZnEn8<>B4GE7r]r^tZ +I_a>.f-/t/FS\cpUTJ#c6q-R=ej@F-(`q_,9(cp,=P[CJ8e0i4WkjiW;%/<'huis 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+/showpage {} def +% JPEG image follows: +96 96 sc +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: jpeg2ps 3.2 by Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/noire.jpg +%%CreationDate: Mon Jan 14 14:35:51 2013 +%%BoundingBox: 0 0 96 96 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/noire.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 96 + /Height 96 + /ImageMatrix [ 96 0 0 -96 0 96 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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+%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ 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+%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 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'/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ +sOXW#;]]f#$]3a'90!F"BA5Lg90YXI;Ur;M@RX8Pk_ 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/noire.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 96 + /Height 96 + /ImageMatrix [ 96 0 0 -96 0 96 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6'G(fi%h]Kd'bV8r(D.2g%2BB^&.f? +d&/?<&&02H'*[r-H0d@PO'H]C]0/G%.3%u's3C,bc5pn681][mi$3^S:%0ZnE.2W +[7.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4 +P;4!"fJ:?iXR:!?qLF&HMtG!WU(<)uos?!WrH(zz!!!3.!!NE,#Qk,-_uMP(!!*0 +(!7DatUj=?94I_GkBe-oEq +tGNO)85l@W_'?s!1^N'.3QAArMD,[KhHkr6L/]0fpFn[<,&aWkcJA;l;O_n7TI7/IS=%8E^*pg(QF5 +;nefo26+&g4&#DU(4h5;J_BF6$&o?9fok!,]:X";IbV)4aPZ4%=7mE5niFH_6M#. 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/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg + +n gs +13050 8100 tr +3.982301 -3.982301 sc +113 -113 tr +90 rot +0 0 tr +sa +/showpage {} def +% JPEG image follows: +113 113 sc +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: jpeg2ps 3.2 by Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +%%CreationDate: Mon Jan 14 14:37:45 2013 +%%BoundingBox: 0 0 113 113 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ +sOXW#;]]f#$]3a'90!F"BA5Lg90YXI;Ur;M@RX8Pk_ +92!UM_eIP%*H:qH%HI_*f,L0`gA7rQmYJ4P2?>?NTnNF0GpI-<%D0lS)J`K/_RM4 ++OS@6,Jf]P7Q3OL`-S]u-G?2G[6N&>;I*MSqV:W(UZU<*K!D\V3'PG"Wo]Oc[=,T +s)"+_e.,U[0*Jl#O6eG4mZWm0MafGOAL*CDCD_,dA_d'2,XfkA1SIaiJ\05%8bqQ +=c;*:Kg=0>j_]H7j'Q-b+2N3!"C]\oe`$?(mT+mZ6mJ9Y:c?iGJ(GP30uUf>Y3/& +G*7'7q*[NoNY)jJd(Y79OiRjA(gUBS]:Z(^cXjO!XZ['ClmhV$J:X?]:6 +!Pdr@pWhugg=Y_u$4WLc0A +N!a7Vt/WA_YE*[P32nn6F45l+R)N&@26*%@"fgG!@52$A(NUIX)Z'Z +\;>S4X=k(CTgaioFV[%'+6'Zc!stc,@7)QH`VtP>0:UD\P9J;>.Q0&9K(^ 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col0 s gr gr + +% arrowhead +15.000 slw +n 9152 6787 m 9004 6924 l 9205 6927 l 9144 6870 l 9152 6787 l + cp gs 0.00 setgray ef gr col0 s +% Polyline +% +% pen to black in case this eps object doesn't set color first +0 0 0 setrgbcolor +% Begin Imported JPEG File: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg + +n gs +13950 6300 tr +3.982301 -3.982301 sc +113 -113 tr +90 rot +0 0 tr +sa +/showpage {} def +% JPEG image follows: +113 113 sc +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: jpeg2ps 3.2 by Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +%%CreationDate: Mon Jan 14 14:37:45 2013 +%%BoundingBox: 0 0 113 113 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ +sOXW#;]]f#$]3a'90!F"BA5Lg90YXI;Ur;M@RX8Pk_ +92!UM_eIP%*H:qH%HI_*f,L0`gA7rQmYJ4P2?>?NTnNF0GpI-<%D0lS)J`K/_RM4 ++OS@6,Jf]P7Q3OL`-S]u-G?2G[6N&>;I*MSqV:W(UZU<*K!D\V3'PG"Wo]Oc[=,T +s)"+_e.,U[0*Jl#O6eG4mZWm0MafGOAL*CDCD_,dA_d'2,XfkA1SIaiJ\05%8bqQ 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showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ +sOXW#;]]f#$]3a'90!F"BA5Lg90YXI;Ur;M@RX8Pk_ +92!UM_eIP%*H:qH%HI_*f,L0`gA7rQmYJ4P2?>?NTnNF0GpI-<%D0lS)J`K/_RM4 ++OS@6,Jf]P7Q3OL`-S]u-G?2G[6N&>;I*MSqV:W(UZU<*K!D\V3'PG"Wo]Oc[=,T 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findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 96 + /Height 96 + /ImageMatrix [ 96 0 0 -96 0 96 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6'G(fi%h]Kd'bV8r(D.2g%2BB^&.f? +d&/?<&&02H'*[r-H0d@PO'H]C]0/G%.3%u's3C,bc5pn681][mi$3^S:%0ZnE.2W +[7.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4 +P;4!"fJ:?iXR:!?qLF&HMtG!WU(<)uos?!WrH(zz!!!3.!!NE,#Qk,-_uMP(!!*0 +(!7DatUj=?94I_GkBe-oEq +tGNO)85l@W_'?s!1^N'.3QAArMD,[KhHkr6L/]0fpFn[<,&aWkcJA;l;O_n7TI7/IS=%8E^*pg(QF5 +;nefo26+&g4&#DU(4h5;J_BF6$&o?9fok!,]:X";IbV)4aPZ4%=7mE5niFH_6M#. +pUo_@Zt,HDI%]l>QYO!)m"h-s;o3X:/F2/8-hJ'Zg*:B,E5c[Qi61_ia7V:])<0R +Mq!CUuG^##R@t^,V'tBNE6#FqG^SJ0uW;q^jq\P4"ne2Dh>VoVAG$K/4!0SNA#`? 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object doesn't set color first +0 0 0 setrgbcolor +% Begin Imported JPEG File: /home/ziane/Desktop/Revision_PC_07_01_2013/noire.jpg + +n gs +13950 9000 tr +4.687500 -4.687500 sc +270 rot +0 0 tr +sa +/showpage {} def +% JPEG image follows: +96 96 sc +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: jpeg2ps 3.2 by Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/noire.jpg +%%CreationDate: Mon Jan 14 14:37:45 2013 +%%BoundingBox: 0 0 96 96 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/noire.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 96 + /Height 96 + /ImageMatrix [ 96 0 0 -96 0 96 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6'G(fi%h]Kd'bV8r(D.2g%2BB^&.f? +d&/?<&&02H'*[r-H0d@PO'H]C]0/G%.3%u's3C,bc5pn681][mi$3^S:%0ZnE.2W +[7.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4 +P;4!"fJ:?iXR:!?qLF&HMtG!WU(<)uos?!WrH(zz!!!3.!!NE,#Qk,-_uMP(!!*0 +(!7DatUj=?94I_GkBe-oEq +tGNO)85l@W_'?s!1^N'.3QAArMD,[KhHkr6L/]0fpFn[<,&aWkcJA;l;O_n7TI7/IS=%8E^*pg(QF5 +;nefo26+&g4&#DU(4h5;J_BF6$&o?9fok!,]:X";IbV)4aPZ4%=7mE5niFH_6M#. +pUo_@Zt,HDI%]l>QYO!)m"h-s;o3X:/F2/8-hJ'Zg*:B,E5c[Qi61_ia7V:])<0R +Mq!CUuG^##R@t^,V'tBNE6#FqG^SJ0uW;q^jq\P4"ne2Dh>VoVAG$K/4!0SNA#`? +@NNho0,4/E1FMC="IPMN^2doP/VP7t1CLdBuF=kC<$&+$I+TWVhq13f<0*/tJ=`f +=hh6!QsQhTl"%A;4<)LF+[F#(NVmVU#JYJ)=]=Ik$e;=*LZnEn8<>B4GE7r]r^tZ +I_a>.f-/t/FS\cpUTJ#c6q-R=ej@F-(`q_,9(cp,=P[CJ8e0i4WkjiW;%/<'huis 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13950 450 m + 18000 4500 l gs col0 s gr +% Polyline +n 13950 2250 m + 18000 6300 l gs col0 s gr +% Polyline +n 13972 3172 m + 18022 7222 l gs col0 s gr +% Polyline +n 13949 4049 m + 17999 8099 l gs col0 s gr +% Polyline +n 13972 1372 m + 18022 5422 l gs col0 s gr +% Polyline +n 15975 2250 m + 15975 6300 l gs col0 s gr +% Polyline +% +% pen to black in case this eps object doesn't set color first +0 0 0 setrgbcolor +% Begin Imported JPEG File: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg + +n gs +13950 4050 tr +3.982301 -3.982301 sc +113 -113 tr +90 rot +0 0 tr +sa +/showpage {} def +% JPEG image follows: +113 113 sc +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: jpeg2ps 3.2 by Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +%%CreationDate: Mon Jan 14 14:37:45 2013 +%%BoundingBox: 0 0 113 113 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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+4:""bVA(YEk_36YmA%fh12PA!fj"<^N^krrH:2r*1fIJ0pk@'=78\7fK(2XZGu+@bM)lL3WH>]amM. +alH*Df%K6!499s_qZ1Mh639PU+k!Ve`JY$nJ]K,*A,YuY9.XfGP"'VTF?RJ2#oK6 +3%q4dJWL.nOFeZ%+Gbj[pf8?J@J1dp,4TjeB:05]VB0aNQ)CAUG[D$c?fX8$J("$ +PILZ$Gp'&#>&Z4t`R8)jg;sGPS&HkKm5nO_As4I~>restore grestore +% +% End Imported PIC File: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +% +% Polyline +% +% pen to black in case this eps object doesn't set color first +0 0 0 setrgbcolor +% Begin Imported JPEG File: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg + +n gs +14850 4050 tr +3.982301 -3.982301 sc +113 -113 tr +90 rot +0 0 tr +sa +/showpage {} def +% JPEG image follows: +113 113 sc +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: jpeg2ps 3.2 by Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +%%CreationDate: Mon Jan 14 14:37:45 2013 +%%BoundingBox: 0 0 113 113 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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+4:""bVA(YEk_36YmA%fh12PA!fj"<^N^krrH:2r*1fIJ0pk@'=78\7fK(2XZGu+@bM)lL3WH>]amM. +alH*Df%K6!499s_qZ1Mh639PU+k!Ve`JY$nJ]K,*A,YuY9.XfGP"'VTF?RJ2#oK6 +3%q4dJWL.nOFeZ%+Gbj[pf8?J@J1dp,4TjeB:05]VB0aNQ)CAUG[D$c?fX8$J("$ +PILZ$Gp'&#>&Z4t`R8)jg;sGPS&HkKm5nO_As4I~>restore grestore +% +% End Imported PIC File: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +% +% Polyline +% +% pen to black in case this eps object doesn't set color first +0 0 0 setrgbcolor +% Begin Imported JPEG File: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg + +n gs +14850 2250 tr +3.982301 -3.982301 sc +113 -113 tr +90 rot +0 0 tr +sa +/showpage {} def +% JPEG image follows: +113 113 sc +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: jpeg2ps 3.2 by Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +%%CreationDate: Mon Jan 14 14:37:45 2013 +%%BoundingBox: 0 0 113 113 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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+4:""bVA(YEk_36YmA%fh12PA!fj"<^N^krrH:2r*1fIJ0pk@'=78\7fK(2XZGu+@bM)lL3WH>]amM. +alH*Df%K6!499s_qZ1Mh639PU+k!Ve`JY$nJ]K,*A,YuY9.XfGP"'VTF?RJ2#oK6 +3%q4dJWL.nOFeZ%+Gbj[pf8?J@J1dp,4TjeB:05]VB0aNQ)CAUG[D$c?fX8$J("$ +PILZ$Gp'&#>&Z4t`R8)jg;sGPS&HkKm5nO_As4I~>restore grestore +% +% End Imported PIC File: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +% +% Polyline +% +% pen to black in case this eps object doesn't set color first +0 0 0 setrgbcolor +% Begin Imported JPEG File: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg + +n gs +15750 2250 tr +3.982301 -3.982301 sc +113 -113 tr +90 rot +0 0 tr +sa +/showpage {} def +% JPEG image follows: +113 113 sc +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: jpeg2ps 3.2 by Thomas Merz +%%Title: /home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg +%%CreationDate: Mon Jan 14 14:37:45 2013 +%%BoundingBox: 0 0 113 113 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%EndComments +%%BeginProlog +%%EndProlog +%%Page: 1 1 +/languagelevel where {pop languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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languagelevel 2 lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/rouge.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 113 + /Height 113 + /ImageMatrix [ 113 0 0 -113 0 113 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6&J,Kc%hB3^$kop&/#Tl)^ZUB)($79&g&kP0./2%/3"@o1,Ua83$p.,2$"!j$4[IS(Cq#p.3o +r[/h/_-2)-O//1EG6.Pr\02)R6B0.eV12(^[C.PNA,/i>C?.lAk32(U1-1,UU?2) +YEL!"fJ:E<'t\!?qLF&HMtG!WU(<)up!>!WrH(!<<*"z!!!!&"p4u5#QY#,_uMh0 +!!*3&!X8f6$3L8.z!<<0'"9fAA+Yc8[@0[DYJWV-36=OqTZ,%+i,;W4rJt\pE'dQ +0H_uL_W!!*6(!<<*"zz"TST+"9o)3s24mj&HDh6!WrW0"p4i*z!!!$$!sB2>&g8G +R5uDWq"u9V<',6S6dGZl`Z.@ 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lt}{true} ifelse { + (JPEG file '/home/ziane/Desktop/Revision_PC_07_01_2013/noire.jpg' needs PostScript Level 2!\n) dup print flush + /Helvetica findfont 20 scalefont setfont 100 100 moveto show showpage stop +} if +save +/RawData currentfile /ASCII85Decode filter def +/Data RawData << >> /DCTDecode filter def +/DeviceRGB setcolorspace +{ << /ImageType 1 + /Width 96 + /Height 96 + /ImageMatrix [ 96 0 0 -96 0 96 ] + /DataSource Data + /BitsPerComponent 8 + /Decode [0 1 0 1 0 1] + >> image + Data closefile + RawData flushfile + showpage + restore +} exec +s4IA0!"_al8O`[\!<<*#!!*'"s4[O,!!ri6'G(fi%h]Kd'bV8r(D.2g%2BB^&.f? +d&/?<&&02H'*[r-H0d@PO'H]C]0/G%.3%u's3C,bc5pn681][mi$3^S:%0ZnE.2W +[7.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4H\p.4 +P;4!"fJ:?iXR:!?qLF&HMtG!WU(<)uos?!WrH(zz!!!3.!!NE,#Qk,-_uMP(!!*0 +(!7DatUj=?94I_GkBe-oEq +tGNO)85l@W_'?s!1^N'.3QAArMD,[KhHkr6L/]0fpFn[<,&aWkcJA;l;O_n7TI7/IS=%8E^*pg(QF5 +;nefo26+&g4&#DU(4h5;J_BF6$&o?9fok!,]:X";IbV)4aPZ4%=7mE5niFH_6M#. 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z#l^x2q67SEp0x8k|<8t{gYS_r|4>4^Jc9y>^!pIO{Y-xNekv&q$Af%i|hCC)PJ1YosJwt44 zknS%C968AVRuMfnW9}WC{N*VF|spA0A7HwJATH6SI-A2?SvYrxUP) zAxw>#tzl3*7NpXCQ-UQ_;J3uD+JJwz_zx=jMM7FNQd@vO_6z|`s{hjS-)rdK8zmCy zmY>e?b{qT;%-cWt@P0RI`hT)&2INuk)>4querqfAqCB^T1_XiFLF{atzif;S2&6-@ zA#L%0;ZVKR7X4rK@O%3(JNp0Clo8e>}+WiC{J`l?m0qXsoPU zNXOyrLuLIh8XJ&{6X~D(3k}H1%8GPf{f!0$BPZyuG$8OcsNi2|tU%=P{qHn3@PG7y z45;uQG*)(wztdR39LN#;wLMl2AoqXJz+AWP> matrix makepattern +/Pat1 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke + 0 4 M 4 8 L 8 4 L 4 0 L 0 4 L stroke} +>> matrix makepattern +/Pat2 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop 0 0 M 0 8 L + 8 8 L 8 0 L 0 0 L fill} +>> matrix makepattern +/Pat3 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop -4 8 M 8 -4 L + 0 12 M 12 0 L stroke} +>> matrix makepattern +/Pat4 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop -4 0 M 8 12 L + 0 -4 M 12 8 L stroke} +>> matrix makepattern +/Pat5 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop -2 8 M 4 -4 L + 0 12 M 8 -4 L 4 12 M 10 0 L stroke} +>> matrix makepattern +/Pat6 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop -2 0 M 4 12 L + 0 -4 M 8 12 L 4 -4 M 10 8 L stroke} +>> matrix makepattern +/Pat7 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop 8 -2 M -4 4 L + 12 0 M -4 8 L 12 4 M 0 10 L stroke} +>> matrix makepattern +/Pat8 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop 0 -2 M 12 4 L + -4 0 M 12 8 L -4 4 M 8 10 L stroke} +>> matrix makepattern +/Pat9 exch def +/Pattern1 {PatternBgnd KeepColor Pat1 setpattern} bind def +/Pattern2 {PatternBgnd KeepColor Pat2 setpattern} bind def +/Pattern3 {PatternBgnd KeepColor Pat3 setpattern} bind def +/Pattern4 {PatternBgnd KeepColor Landscape {Pat5} {Pat4} ifelse setpattern} bind def +/Pattern5 {PatternBgnd KeepColor Landscape {Pat4} {Pat5} ifelse setpattern} bind def +/Pattern6 {PatternBgnd KeepColor Landscape {Pat9} {Pat6} ifelse setpattern} bind def +/Pattern7 {PatternBgnd KeepColor Landscape {Pat8} {Pat7} ifelse setpattern} bind def +} def +% +% +%End of PostScript Level 2 code +% +/PatternBgnd { + TransparentPatterns {} {gsave 1 setgray fill grestore} ifelse +} def +% +% Substitute for Level 2 pattern fill codes with +% grayscale if Level 2 support is not selected. +% +/Level1PatternFill { +/Pattern1 {0.250 Density} bind def +/Pattern2 {0.500 Density} bind def +/Pattern3 {0.750 Density} bind def +/Pattern4 {0.125 Density} bind def +/Pattern5 {0.375 Density} bind def +/Pattern6 {0.625 Density} bind def +/Pattern7 {0.875 Density} bind def +} def +% +% Now test for support of Level 2 code +% +Level1 {Level1PatternFill} {Level2PatternFill} ifelse +% +/Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont +dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall +currentdict end definefont pop +/MFshow { + { dup 5 get 3 ge + { 5 get 3 eq {gsave} {grestore} ifelse } + {dup dup 0 get findfont exch 1 get scalefont setfont + [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6 + get exch 4 get {Gshow} {stringwidth pop 0 R} ifelse }if dup 5 get 0 eq + {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5 + get 1 eq {dup 2 get exch dup 3 get exch 6 get stringwidth pop -2 div + dup 0 R} {dup 6 get stringwidth pop -2 div 0 R 6 get + show 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop + pop aload pop M} ifelse }ifelse }ifelse } + ifelse } + forall} def +/Gswidth {dup type /stringtype eq {stringwidth} {pop (n) stringwidth} ifelse} def +/MFwidth {0 exch { dup 5 get 3 ge { 5 get 3 eq { 0 } { pop } ifelse } + {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont + 6 get Gswidth pop add} {pop} ifelse} ifelse} forall} def +/MLshow { currentpoint stroke M + 0 exch R + Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def +/MRshow { currentpoint stroke M + exch dup MFwidth neg 3 -1 roll R + Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def 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