hpcs-17-subord

git clone https://git.igankevich.com/hpcs-17-subord.git
Log | Files | Refs

commit 492f9cb2b2734fb5cd600ee265c19553679a6a8a
parent 33e444cb0f929734d10d70dd42fec8b913f26603
Author: Ivan Gankevich <igankevich@ya.ru>
Date:   Fri, 14 Jul 2017 20:38:12 +0300

Add wavy surface.

Diffstat:
figures/wavy.eps | 76286+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
slides.tex | 196+++++++++++++++++++++++++++++++++++++++++++++++++++++++++----------------------
2 files changed, 76427 insertions(+), 55 deletions(-)

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S +930.48 205.039 m 949.68 205.039 l 976.559 225.84 m 957.359 225.84 l 957.367 + 225.84 l S +BT +32 0 0 32 994.479 216.241006 Tm +/f-0-0 1 Tf +(2)Tj +ET +930.48 225.84 m 949.68 225.84 l 976.559 246.722 m 957.359 246.722 l 957.367 + 246.722 l S +930.48 246.722 m 949.688 246.722 l S +Q Q +showpage +%%Trailer +end restore +%%EOF diff --git a/slides.tex b/slides.tex @@ -26,10 +26,12 @@ \tikzset{Process/.style={ellipse,draw=spbuGreen,line width=3pt,dashed}} \tikzset{ProcessEdge/.style={draw=spbuGreen,line width=3pt,solid}} \tikzset{Node/.style={rectangle,draw=spbuDarkGray,thick}} -\tikzset{Task/.style={Process,anchor=center,draw=spbuGreen}} -\tikzset{TaskEdge/.style={ProcessEdge,draw=spbuGreen,solid,->}} +\tikzset{Task/.style={Process,anchor=center,draw=spbuGreen,text=spbuGreen}} +\tikzset{Kernel/.style={Task,solid,line width=2pt}} +\tikzset{TaskEdge/.style={ProcessEdge,draw=spbuGreen,solid,->,line width=2pt}} \tikzset{Label/.style={label distance=0.1cm,text=spbuTerracotta}} \tikzset{TaskLabel/.style={label distance=0.1cm,text=spbuGreen}} +\tikzset{KernelPool/.style={rectangle,draw=spbuDarkGray,minimum width=4.5cm,minimum height=0.9cm,line width=2pt,thick}} \begin{document} @@ -65,7 +67,7 @@ \end{itemize} \end{column} \begin{column}{0.55\textwidth} - \begin{tikzpicture}[remember picture,x=2.5cm,y=-1cm] + \begin{tikzpicture}[x=2.5cm,y=-1cm] \node[Node] (M) at (2,0) {\texttt{10.0.0.1}}; \node[Node] (S1) at (1.25,1) {\texttt{10.0.0.2}}; \node[Node] (S2) at (2.75,1) {\texttt{10.0.0.3}}; @@ -113,16 +115,56 @@ \section{Kernel processing algorithm} -\begin{frame} - \frametitle{Hierarchical dependence between tasks} - \bigskip\bigskip% - \includegraphics<1>[width=\textwidth]{figures/tasks-and-queue} - \includegraphics<2>[width=\textwidth]{figures/tasks-and-queue-1} - \includegraphics<3>[width=\textwidth]{figures/tasks-and-queue-2} - \includegraphics<4>[width=\textwidth]{figures/tasks-and-queue-3} - \includegraphics<5>[width=\textwidth]{figures/tasks-and-queue-4} - \includegraphics<6>[width=\textwidth]{figures/tasks-and-queue-5} - \includegraphics<7>[width=\textwidth]{figures/tasks-and-queue-6} +\begin{frame}{Example} + \begin{tikzpicture}[x=3cm,y=-0.9cm] + \node (dummy) at (0,0) {}; + + \node<1-5>[Kernel] (task1) at (2,0) {Task1}; + \node<1>[KernelPool] (pool0) at (4,0) {Task1::act()}; + \node<1>[KernelPool] (pool1) at (4,1) {}; + \node<1>[KernelPool] (pool2) at (4,2) {}; + \node<1>[KernelPool] (pool3) at (4,3) {}; + \node<1>[KernelPool] (pool4) at (4,4) {}; + + \node<2-5>[Kernel] (sub1) at (1.25,1.5) {Sub1}; + \node<2-4>[Kernel] (sub2) at (2.75,1.5) {Sub2}; + \path<2-5>[TaskEdge] (task1) edge (sub1); + \path<2-4>[TaskEdge] (task1) edge (sub2); + \node<2>[KernelPool] (pool0) at (4,0) {Sub1::act()}; + \node<2>[KernelPool] (pool1) at (4,1) {Sub2::act()}; + \node<2>[KernelPool] (pool2) at (4,2) {}; + \node<2>[KernelPool] (pool3) at (4,3) {}; + \node<2>[KernelPool] (pool4) at (4,4) {}; + + \node<3-4>[Kernel] (subsub1) at (0.75,3) {SubSub1}; + \node<3-4>[Kernel] (subsub2) at (1.75,3) {SubSub2}; + \path<3-4>[TaskEdge] (sub1) edge (subsub1); + \path<3-4>[TaskEdge] (sub1) edge (subsub2); + \node<3>[KernelPool] (pool0) at (4,0) {Sub2::act()}; + \node<3>[KernelPool] (pool1) at (4,1) {SubSub1::act()}; + \node<3>[KernelPool] (pool2) at (4,2) {SubSub2::act()}; + \node<3>[KernelPool] (pool3) at (4,3) {}; + \node<3>[KernelPool] (pool4) at (4,4) {}; + + \path<4>[TaskEdge] (subsub1) edge[bend left] (sub1); + \path<4>[TaskEdge] (subsub2) edge[bend right] (sub1); + \path<4>[TaskEdge] (sub2) edge[bend right] (task1); + \node<4>[KernelPool] (pool0) at (4,0) {Task1::react(Sub2)}; + \node<4>[KernelPool] (pool1) at (4,1) {Sub1::react(SubSub1)}; + \node<4>[KernelPool] (pool2) at (4,2) {Sub1::react(SubSub2)}; + \node<4>[KernelPool] (pool3) at (4,3) {}; + \node<4>[KernelPool] (pool4) at (4,4) {}; + + \path<5>[TaskEdge] (sub1) edge[bend left] (task1); + \node<5>[KernelPool] (pool0) at (4,0) {Task1::react(Sub1)}; + \node<5>[KernelPool] (pool1) at (4,1) {}; + \node<5>[KernelPool] (pool2) at (4,2) {}; + \node<5>[KernelPool] (pool3) at (4,3) {}; + \node<5>[KernelPool] (pool4) at (4,4) {}; + + \node<6> (task1) at (2,0) {\[Programme ends\]}; + + \end{tikzpicture} \note<1>{ \begin{itemize} \item Left --- kernels, right --- execution queue (pool). Animation shows how kernels create subordinates and collect results from them. @@ -131,50 +173,19 @@ } \end{frame} -\section{Evaluation} - -\begin{frame}{Case study: Ocean wavy surface generator} -\end{frame} - -\begin{frame} - \frametitle{Case study: NDBC dataset preprocessing} +\begin{frame}{Kernel processing algorithm: summary} + \begin{itemize} + \item It is like procedure calls, but asynchronous. + \end{itemize} + \vfill \begin{center} - \begin{tabular}{ll} - \toprule - Dataset size & 144MB \\ - Dataset size (uncompressed) & 770MB \\ - No.~of wave stations & 24 \\ - Time span & 3 years (2010--2012) \\ - Total no.~of spectra & 445422 \\ - \bottomrule - \end{tabular} + The purpose of kernel hierarchy is to decouple the number of parallel + tasks from the number of cluster nodes. \end{center} - \vfill - Spectrum reconstruction formula: - \begin{equation*} - S(\omega, \theta) = \frac{1}{\pi}\! - \left[ - \frac{1}{2} + - r_1 \cos \left( \theta - \alpha_1 \right) + - r_2 \sin \left( 2 \left( \theta - \alpha_2 \right) \right) - \right]\! - S_0(\omega). - \end{equation*} - \note{ - Master node fail over technique is evaluated on the example of wave energy spectra processing application. This programme uses NDBC (\href{http://www.ndbc.noaa.gov/}{National Data Buoy Center}) dataset to reconstruct frequency-directional spectra from wave rider buoy measurements and compute variance. Each spectrum is reconstructed from five variables using the following formula. - \begin{equation*} - S(\omega, \theta) = \frac{1}{\pi} - \left[ - \frac{1}{2} + - r_1 \cos \left( \theta - \alpha_1 \right) + - r_2 \sin \left( 2 \left( \theta - \alpha_2 \right) \right) - \right] - S_0(\omega). - \end{equation*} - Here $\omega$ denotes frequency, $\theta$ is wave direction, $r_{1,2}$ and $\alpha_{1,2}$ are parameters of spectrum decomposition and $S_0$ is non-directional spectrum; $r_{1,2}$, $\alpha_{1,2}$ and $S_0$ are acquired through measurements. Properties of the dataset which is used in evaluation are listed in Table. - } \end{frame} +\section{Recovery from master node failure} + \begin{frame} \frametitle{Handling master node failure} \centering @@ -228,17 +239,86 @@ } \end{frame} +\begin{frame}{Case study: ARMA ocean wavy surface generator} + \begin{columns} + \begin{column}{0.25\textwidth} + MA model: + \begin{equation*} + \zeta_{\vec{x}} = + \sum\limits_{\vec{y}=\vec{0}}^{N} + \Theta_{\vec{y}}\,\epsilon_{\vec{x} - \vec{y}} + \end{equation*} + \vfill + Coefficients: + \begin{equation*} + K_{i,j,k} = + \left[ + \displaystyle + \sum\limits_{l=i}^{q_1} + \sum\limits_{m=j}^{q_2} + \sum\limits_{n=k}^{q_3} + \Theta_{l,m,n}\Theta_{l-i,m-j,n-k} + \right] + \Var{\epsilon} + \end{equation*} + \end{column} + \begin{column}{0.65\textwidth} + \includegraphics[width=\linewidth]{figures/wavy.eps} + \end{column} + \end{columns} +\end{frame} -\begin{frame}{Performance in case of master node failure} +\begin{frame}{Performance with master node failure (ARMA)} \centering \includegraphics[width=0.9\linewidth]{figures/mpp-time-color.eps} \end{frame} -\begin{frame}{Performance in case of master node failure} +\begin{frame} + \frametitle{Case study: NDBC dataset preprocessing} + \begin{center} + \begin{tabular}{ll} + \toprule + Dataset size & 144MB \\ + Dataset size (uncompressed) & 770MB \\ + No.~of wave stations & 24 \\ + Time span & 3 years (2010--2012) \\ + Total no.~of spectra & 445422 \\ + \bottomrule + \end{tabular} + \end{center} + \vfill + Spectrum reconstruction formula: + \begin{equation*} + S(\omega, \theta) = \frac{1}{\pi}\! + \left[ + \frac{1}{2} + + r_1 \cos \left( \theta - \alpha_1 \right) + + r_2 \sin \left( 2 \left( \theta - \alpha_2 \right) \right) + \right]\! + S_0(\omega). + \end{equation*} + \note{ + Master node fail over technique is evaluated on the example of wave energy spectra processing application. This programme uses NDBC (\href{http://www.ndbc.noaa.gov/}{National Data Buoy Center}) dataset to reconstruct frequency-directional spectra from wave rider buoy measurements and compute variance. Each spectrum is reconstructed from five variables using the following formula. + \begin{equation*} + S(\omega, \theta) = \frac{1}{\pi} + \left[ + \frac{1}{2} + + r_1 \cos \left( \theta - \alpha_1 \right) + + r_2 \sin \left( 2 \left( \theta - \alpha_2 \right) \right) + \right] + S_0(\omega). + \end{equation*} + Here $\omega$ denotes frequency, $\theta$ is wave direction, $r_{1,2}$ and $\alpha_{1,2}$ are parameters of spectrum decomposition and $S_0$ is non-directional spectrum; $r_{1,2}$, $\alpha_{1,2}$ and $S_0$ are acquired through measurements. Properties of the dataset which is used in evaluation are listed in Table. + } +\end{frame} + +\begin{frame}{Performance with master node failure (NDBC)} \centering \includegraphics[width=0.9\linewidth]{figures/mpp-time-color-ndbc.eps} \end{frame} +\section{Recovery from multiple node failures} + \begin{frame}{Overhead of recovery from multiple node failures} \begin{columns}[T] \begin{column}{0.45\textwidth} @@ -264,4 +344,10 @@ \end{itemize} \end{frame} +\begin{frame} + \centering% + \vspace{1.0cm}% + \Large\textbf{Thank you for attention!} +\end{frame} + \end{document}