Suite corrections expés

[rce2015.git] / paper.tex

diff --git a/paper.tex b/paper.tex
index ca172c0c7026b2fb7dd12850fd52563b05973dea..cb95155ce9eb3dd31616beb0ceb1b3882977226d 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -557,17 +557,28 @@ In what follows, we will present the test conditions, the output results and our
 \begin{center}
 \begin{tabular}{ll }
  \hline
 \begin{center}
 \begin{tabular}{ll }
  \hline

+<<<<<<< HEAD

  Grid architecture & 2$\times$16, 4$\times$8, 4$\times$16 and 8$\times$8\\ %\hline
  Grid architecture & 2$\times$16, 4$\times$8, 4$\times$16 and 8$\times$8\\ %\hline

- Network           & N1 : $bw$=1Gbits/s, $lat$=5.10$^{-5}$ \\ %\hline
+ Network           & N1 : $bw$=1Gbits/s, $lat$=5$\times$10$^{-5}$ \\ %\hline

  \multirow{2}{*}{Matrix size}  & N$_{x}$ $\times$ N$_{y}$ $\times$ N$_{z}$ =150 $\times$ 150 $\times$ 150\\ %\hline
   &  N$_{x}$ $\times$ N$_{y}$ $\times$ N$_{z}$  =170 $\times$ 170 $\times$ 170    \\ \hline
  \end{tabular}
 \caption{Test conditions: various grid configurations with the matrix sizes 150$^3$ or 170$^3$}
 \LZK{Ce sont les caractéristiques du réseau intra ou inter clusters? Ce n'est pas précisé...}
  \multirow{2}{*}{Matrix size}  & N$_{x}$ $\times$ N$_{y}$ $\times$ N$_{z}$ =150 $\times$ 150 $\times$ 150\\ %\hline
   &  N$_{x}$ $\times$ N$_{y}$ $\times$ N$_{z}$  =170 $\times$ 170 $\times$ 170    \\ \hline
  \end{tabular}
 \caption{Test conditions: various grid configurations with the matrix sizes 150$^3$ or 170$^3$}
 \LZK{Ce sont les caractéristiques du réseau intra ou inter clusters? Ce n'est pas précisé...}

+=======
+ Grid Architecture & 2 $\times$ 16, 4 $\times$ 8, 4 $\times$ 16 and 8 $\times$ 8\\ %\hline
+ Inter Network N2 & bw=1Gbits/s - lat=5.10$^{-5}$ \\ %\hline
+ Input matrix size & N$_{x}$ $\times$ N$_{y}$ $\times$ N$_{z}$ =150 $\times$ 150 $\times$ 150\\ %\hline
+ - &  N$_{x}$ $\times$ N$_{y}$ $\times$ N$_{z}$  =170 $\times$ 170 $\times$ 170    \\ \hline
+ \end{tabular}
+\caption{Test conditions: various grid configurations with the input matrix size N$_{x}$=N$_{y}$=N$_{z}$=150 or 170 \RC{N2 n'est pas défini..}\RC{Nx est défini, Ny? Nz?}
+\AG{La lettre 'x' n'est pas le symbole de la multiplication. Utiliser \texttt{\textbackslash times}.  Idem dans le texte, les figures, etc.}}
+>>>>>>> 2f78f080350308e2f46d8eff8d66a8e127fee583

 \label{tab:01}
 \end{center}
 \end{table}
 
 \label{tab:01}
 \end{center}
 \end{table}
 

+<<<<<<< HEAD

 In this section, we analyze the simulations conducted on various grid configurations presented in Table~\ref{tab:01}. Figure~\ref{fig:01} shows, for all grid configurations and a given matrix size, a non-variation in the number of iterations for the classical GMRES algorithm, which is not the case of the Krylov two-stage algorithm.
 %% First,  the results in  Figure~\ref{fig:01}
 %% show for all grid configurations the non-variation of the number of iterations of
 In this section, we analyze the simulations conducted on various grid configurations presented in Table~\ref{tab:01}. Figure~\ref{fig:01} shows, for all grid configurations and a given matrix size, a non-variation in the number of iterations for the classical GMRES algorithm, which is not the case of the Krylov two-stage algorithm.
 %% First,  the results in  Figure~\ref{fig:01}
 %% show for all grid configurations the non-variation of the number of iterations of


@@ -575,6 +586,20 @@ In this section, we analyze the simulations conducted on various grid configurat
 %% multisplitting method.
 \RC{CE attention tu n'as pas mis de label dans tes figures, donc c'est le bordel, j'en mets mais vérifie...}
 \RC{Les légendes ne sont pas explicites...}
 %% multisplitting method.
 \RC{CE attention tu n'as pas mis de label dans tes figures, donc c'est le bordel, j'en mets mais vérifie...}
 \RC{Les légendes ne sont pas explicites...}

+=======
+
+
+
+
+In this  section, we analyze the  performance of algorithms running  on various
+grid configurations  (2 $\times$ 16, 4 $\times$ 8, 4 $\times$ 16  and 8 $\times$ 8) and using an inter-network N2 defined in the test conditions in Table~\ref{tab:01}. First,  the results in  Figure~\ref{fig:01}
+show for all grid configurations the non-variation of the number of iterations of
+classical  GMRES for  a given  input matrix  size; it is not  the case  for the
+multisplitting method.
+
+%\RC{CE attention tu n'as pas mis de label dans tes figures, donc c'est le bordel, j'en mets mais vérifie...}
+%\RC{Les légendes ne sont pas explicites...}
+>>>>>>> 2f78f080350308e2f46d8eff8d66a8e127fee583

 
 \begin{figure} [ht!]
   \begin{center}
 
 \begin{figure} [ht!]
   \begin{center}


@@ -586,6 +611,7 @@ In this section, we analyze the simulations conducted on various grid configurat
   \label{fig:01}
 \end{figure}
 
   \label{fig:01}
 \end{figure}
 

+<<<<<<< HEAD

 The execution  times between  the two algorithms  is significant  with different
 grid architectures, even  with the same number of processors  (for example, 2x16
 and  4x8). We  can  observe  the low  sensitivity  of  the Krylov multisplitting  method
 The execution  times between  the two algorithms  is significant  with different
 grid architectures, even  with the same number of processors  (for example, 2x16
 and  4x8). We  can  observe  the low  sensitivity  of  the Krylov multisplitting  method


@@ -594,6 +620,14 @@ in the  grid: in  average, the GMRES  (resp. Multisplitting)  algorithm performs
 $40\%$ better (resp. $48\%$) when running from 2x16=32 to 8x8=64 processors. 
 \RC{pas très clair, c'est pas précis de dire qu'un algo perform mieux qu'un autre, selon quel critère?}
 \LZK{A revoir toute cette analyse... Le multi est plus performant que GMRES. Les temps d'exécution de multi sont sensibles au nombre de CLUSTERS. Il est moins performant pour un nombre grand de cluster. Avez vous d'autres remarques?}
 $40\%$ better (resp. $48\%$) when running from 2x16=32 to 8x8=64 processors. 
 \RC{pas très clair, c'est pas précis de dire qu'un algo perform mieux qu'un autre, selon quel critère?}
 \LZK{A revoir toute cette analyse... Le multi est plus performant que GMRES. Les temps d'exécution de multi sont sensibles au nombre de CLUSTERS. Il est moins performant pour un nombre grand de cluster. Avez vous d'autres remarques?}

+=======
+
+Secondly, the execution  times between  the two algorithms  is significant  with different
+grid architectures, even  with the same number of processors  (for example, 2 $\times$ 16
+and  4 $\times$ 8). We  can  observ  the sensitivity  of  the Krylov multisplitting  method
+(compared with the classical GMRES) when scaling up the number of the processors
+in the  grid: in  average, the reduction of the execution time for GMRES  (resp. Multisplitting)  algorithm is around $40\%$ (resp. around $48\%$) when running from 32 (grid 2 $\times$ 16) to 64 processors (grid 8 $\times$ 8) processors. \RC{pas très clair, c'est pas précis de dire qu'un algo perform mieux qu'un autre, selon quel critère?}
+>>>>>>> 2f78f080350308e2f46d8eff8d66a8e127fee583

 
 \subsubsection{Simulations for two different inter-clusters network speeds \\}
 
 
 \subsubsection{Simulations for two different inter-clusters network speeds \\}
 


@@ -601,20 +635,34 @@ $40\%$ better (resp. $48\%$) when running from 2x16=32 to 8x8=64 processors.
 \begin{center}
 \begin{tabular}{ll}
  \hline
 \begin{center}
 \begin{tabular}{ll}
  \hline

+<<<<<<< HEAD

  Grid architecture        & 2$\times$16, 4$\times$8\\ %\hline
  Grid architecture        & 2$\times$16, 4$\times$8\\ %\hline

- \multirow{2}{*}{Network} & N1: $bw$=1Gbs, $lat$=5.10$^{-5}$ \\ %\hline
-                          & N2: $bw$=10Gbs, $lat$=8.10$^{-6}$ \\
+ \multirow{2}{*}{Network} & N1: $bw$=1Gbs, $lat$=5$\times$10$^{-5}$ \\ %\hline
+                          & N2: $bw$=10Gbs, $lat$=8$\times$10$^{-6}$ \\

  Matrix size              & $N_{x} \times N_{y} \times N_{z} =150 \times 150 \times 150$\\ \hline
  \end{tabular}
 \caption{Test conditions: grid configurations 2$\times$16 and 4$\times$8 with networks N1 vs. N2}
  Matrix size              & $N_{x} \times N_{y} \times N_{z} =150 \times 150 \times 150$\\ \hline
  \end{tabular}
 \caption{Test conditions: grid configurations 2$\times$16 and 4$\times$8 with networks N1 vs. N2}

+=======
+ Grid Architecture & 2 $\times$ 16, 4 $\times$ 8\\ %\hline
+ Inter Networks & N1 : bw=10Gbs-lat=8.10$^{-6}$ \\ %\hline
+ - & N2 : bw=1Gbs-lat=5.10$^{-5}$ \\
+ Input matrix size & $N_{x} \times N_{y} \times N_{z} =150 \times 150 \times 150$\\ \hline
+ \end{tabular}
+\caption{Test conditions: grid 2 $\times$ 16 and 4 $\times$ 8 with  networks N1 vs N2}
+>>>>>>> 2f78f080350308e2f46d8eff8d66a8e127fee583

 \label{tab:02}
 \end{center}
 \end{table}
 
 \label{tab:02}
 \end{center}
 \end{table}
 

+<<<<<<< HEAD

 These experiments  compare the  behavior of  the algorithms  running first  on a
 slow inter-cluster  network (N1) and  also on  a more performant  network (N2). \RC{Il faut définir cela avant...}
 These experiments  compare the  behavior of  the algorithms  running first  on a
 slow inter-cluster  network (N1) and  also on  a more performant  network (N2). \RC{Il faut définir cela avant...}

+=======
+In this section, the experiments  compare the  behavior of  the algorithms  running on a
+speeder inter-cluster  network (N1) and  also on  a less performant  network (N2) respectively defined in the test conditions Table~\ref{tab:02}. \RC{Il faut définir cela avant...}
+>>>>>>> 2f78f080350308e2f46d8eff8d66a8e127fee583

 Figure~\ref{fig:02} shows that end users will reduce the execution time
 Figure~\ref{fig:02} shows that end users will reduce the execution time

-for  both  algorithms when using  a  grid  architecture  like  4x16 or  8x8: the reduction is about $2$. The results depict  also that when
+for  both  algorithms when using  a  grid  architecture  like  4 $\times$ 16 or  8 $\times$ 8: the reduction is about $2$. The results depict  also that when

 the  network speed  drops down (variation of 12.5\%), the  difference between  the two Multisplitting algorithms execution times can reach more than 25\%.
 
 
 the  network speed  drops down (variation of 12.5\%), the  difference between  the two Multisplitting algorithms execution times can reach more than 25\%.
 
 


@@ -623,7 +671,7 @@ the  network speed  drops down (variation of 12.5\%), the  difference between  t
 \begin{figure} [ht!]
 \centering
 \includegraphics[width=100mm]{cluster_x_nodes_n1_x_n2.pdf}
 \begin{figure} [ht!]
 \centering
 \includegraphics[width=100mm]{cluster_x_nodes_n1_x_n2.pdf}

-\caption{Grid 2x16 and 4x8 with networks N1 vs N2
+\caption{Grid 2 $\times$ 16 and 4 $\times$ 8 with networks N1 vs N2

 \AG{\np{8E-6}, \np{5E-6} au lieu de 8E-6, 5E-6}}
 \label{fig:02}
 \end{figure}
 \AG{\np{8E-6}, \np{5E-6} au lieu de 8E-6, 5E-6}}
 \label{fig:02}
 \end{figure}


@@ -636,7 +684,7 @@ the  network speed  drops down (variation of 12.5\%), the  difference between  t
 \centering
 \begin{tabular}{r c }
  \hline
 \centering
 \begin{tabular}{r c }
  \hline

- Grid Architecture & 2x16\\ %\hline
+ Grid Architecture & 2 $\times$ 16\\ %\hline

  Network & N1 : bw=1Gbs \\ %\hline
  Input matrix size & $N_{x} \times N_{y} \times N_{z} = 150 \times 150 \times 150$\\ \hline
  \end{tabular}
  Network & N1 : bw=1Gbs \\ %\hline
  Input matrix size & $N_{x} \times N_{y} \times N_{z} = 150 \times 150 \times 150$\\ \hline
  \end{tabular}


@@ -672,7 +720,7 @@ magnitude with a latency of $8.10^{-6}$.
 \centering
 \begin{tabular}{r c }
  \hline
 \centering
 \begin{tabular}{r c }
  \hline

- Grid Architecture & 2x16\\ %\hline
+ Grid Architecture & 2 $\times$ 16\\ %\hline

  Network & N1 : bw=1Gbs - lat=5.10$^{-5}$ \\ %\hline
  Input matrix size & $N_{x} \times N_{y} \times N_{z} =150 \times 150 \times 150$\\ \hline \\
  \end{tabular}
  Network & N1 : bw=1Gbs - lat=5.10$^{-5}$ \\ %\hline
  Input matrix size & $N_{x} \times N_{y} \times N_{z} =150 \times 150 \times 150$\\ \hline \\
  \end{tabular}


@@ -701,7 +749,7 @@ of $40\%$ which is only around $24\%$ for the classical GMRES.
 \centering
 \begin{tabular}{r c }
  \hline
 \centering
 \begin{tabular}{r c }
  \hline

- Grid Architecture & 4x8\\ %\hline
+ Grid Architecture & 4 $\times$ 8\\ %\hline

  Network & N2 : bw=1Gbs - lat=5.10$^{-5}$ \\
  Input matrix size & $N_{x}$ = From 40 to 200\\ \hline
  \end{tabular}
  Network & N2 : bw=1Gbs - lat=5.10$^{-5}$ \\
  Input matrix size & $N_{x}$ = From 40 to 200\\ \hline
  \end{tabular}


@@ -733,7 +781,7 @@ But the interesting results are:
 These  findings may  help a  lot end  users to  setup the  best and  the optimal
 targeted environment for the application deployment when focusing on the problem
 size scale up.  It  should be noticed that the same test has  been done with the
 These  findings may  help a  lot end  users to  setup the  best and  the optimal
 targeted environment for the application deployment when focusing on the problem
 size scale up.  It  should be noticed that the same test has  been done with the

-grid 2x16 leading to the same conclusion.
+grid 2 $\times$ 16 leading to the same conclusion.

 
 \subsubsection{CPU Power impacts on performance}
 
 
 \subsubsection{CPU Power impacts on performance}
 


@@ -741,7 +789,7 @@ grid 2x16 leading to the same conclusion.
 \centering
 \begin{tabular}{r c }
  \hline
 \centering
 \begin{tabular}{r c }
  \hline

- Grid architecture & 2x16\\ %\hline
+ Grid architecture & 2 $\times$ 16\\ %\hline

  Network & N2 : bw=1Gbs - lat=5.10$^{-5}$ \\ %\hline
  Input matrix size & $N_{x} = 150 \times 150 \times 150$\\ \hline
  \end{tabular}
  Network & N2 : bw=1Gbs - lat=5.10$^{-5}$ \\ %\hline
  Input matrix size & $N_{x} = 150 \times 150 \times 150$\\ \hline
  \end{tabular}


@@ -802,7 +850,7 @@ The test conditions are summarized in the table~\ref{tab:07}: \\
 \centering
 \begin{tabular}{r c }
  \hline
 \centering
 \begin{tabular}{r c }
  \hline

- Grid Architecture & 2x50 totaling 100 processors\\ %\hline
+ Grid Architecture & 2 $\times$ 50 totaling 100 processors\\ %\hline

  Processors Power & 1 GFlops to 1.5 GFlops\\
    Intra-Network & bw=1.25 Gbits - lat=5.10$^{-5}$ \\ %\hline
    Inter-Network & bw=5 Mbits - lat=2.10$^{-2}$\\
  Processors Power & 1 GFlops to 1.5 GFlops\\
    Intra-Network & bw=1.25 Gbits - lat=5.10$^{-5}$ \\ %\hline
    Inter-Network & bw=5 Mbits - lat=2.10$^{-2}$\\