From 754635f587b2438535b38afaa98a86cdbb2ef85a Mon Sep 17 00:00:00 2001 From: Riccardo Murri Date: Thu, 14 Jul 2016 13:05:59 +0200 Subject: [PATCH] New part 10: advanced workflow constructs --- .../tutorials/workflows/fig/3n+1.fig | 84 +++++++++ .../tutorials/workflows/fig/3n+1.pdf | Bin 0 -> 5788 bytes .../programmers/tutorials/workflows/fig/A.fig | 23 +++ .../programmers/tutorials/workflows/fig/A.pdf | Bin 0 -> 4189 bytes .../programmers/tutorials/workflows/fig/S.fig | 45 +++++ .../programmers/tutorials/workflows/fig/S.pdf | Bin 0 -> 5443 bytes .../tutorials/workflows/part10.pdf | Bin 97962 -> 153022 bytes .../tutorials/workflows/part10.tex | 160 ++++++++++++++++++ 8 files changed, 312 insertions(+) create mode 100644 docs/programmers/tutorials/workflows/fig/3n+1.fig create mode 100644 docs/programmers/tutorials/workflows/fig/3n+1.pdf create mode 100644 docs/programmers/tutorials/workflows/fig/A.fig create mode 100644 docs/programmers/tutorials/workflows/fig/A.pdf create mode 100644 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z4rVTH31$v%2{Cp~4o(p<5dq@=f63=AaQ`cjS-Fy!oM`}pX=(W&Bb1PBT2oa>Ng;g4 zUN1sN^)=6LyXvyKX*JAOm>a!hTd3{f@ZY|rK6Z6@DIXnIbLJGf3Q}NT8NsGdm_5U4 z4GR;(DIV+m=B=e_yCE2n&TC0jFy=PL8SX{>w}q|!$p&`>qrnbnnD>f<2xdlrI{A%R zPeR>GlO+n^4Cb2h0|Of{F};wgMr+1^ZfRlMngLoTjRbZO``aiP zHQ?nn&?hxunG36ue5-XEbO}wB8xDm8Cl>-UReE+3EA=|dQZM&?3WX3YA#^Qac$R&Y rZ<-37`7ghLkbbiJ|9i#2ba6FucJ*{NGl%2mWaDImqo5F1kbwIyU^et( diff --git a/docs/programmers/tutorials/workflows/part10.tex b/docs/programmers/tutorials/workflows/part10.tex index 7964d42d..f093c28d 100644 --- a/docs/programmers/tutorials/workflows/part10.tex +++ b/docs/programmers/tutorials/workflows/part10.tex @@ -143,6 +143,166 @@ \+ \ldots specifying dependencies among them. \end{frame} + + + \begin{frame} + \frametitle{The \emph{3n+1} conjecture, a fictitious use case} + \label{sec:7a} + + \+ + \begin{columns}[c] + \column{0.5\linewidth} + \includegraphics[height=0.8\textheight]{fig/3n+1} + + \column{0.5\linewidth} + Define a function $f$, for $n$ positive integer: + \begin{itemize} + \item if $n$ is even, then $f(n) = n / 2$, + \item if $n$ is odd, then $f(n) = 3n+1$, + \end{itemize} + + \+ + For every positive integer $n$, form the sequence $S(n)$: + $n \to f(n) \to f(f(n)) \to f(f(f(n))) \to \ldots$ + + \+ + \textbf{Conjecture:} For every positive integer $n$, the sequence $S(n)$ + eventually hits $1$. + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{The \emph{3n+1} conjecture, \emph{(I)}} + \label{sec:7} + + \+ + \begin{columns}[c] + \column{0.5\linewidth} + \includegraphics[height=0.8\textheight]{fig/3n+1_A} + + \column{0.5\linewidth} + A computational job $J(n,k)$, applies + function $f$ to the result of $J(n,k)$. + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{The \emph{3n+1} conjecture, \emph{(II)}} + \label{sec:7b} + + \+ + \begin{columns}[c] + \column{0.5\linewidth} + \includegraphics[height=0.8\textheight]{fig/3n+1_S} + + \column{0.5\linewidth} + A sequence $H(n)$ of jobs computes the chain $n \to f(n) \to + ... \to 1$. + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{The \emph{3n+1} conjecture, \emph{(III)}} + \label{sec:7c} + + \+ + \begin{columns}[c] + \column{0.5\linewidth} + \includegraphics[height=0.8\textheight]{fig/3n+1_P} + + \column{0.5\linewidth} + Run one sequence $H(n)$ per each $n = 1, \ldots, N$. + + \+ + The can all run in \textbf{parallel}. + \end{columns} + \end{frame} + +\begin{frame}[fragile] +\frametitle{The \emph{3n+1} conjecture (IV)} +\label{sec:10} + +\begin{columns} + \column{0.3\linewidth} + \begin{center} + \includegraphics[height=0.8\textheight]{fig/A} + \end{center} + + \column{0.7\linewidth} + Let's define the simple application that computes~$f$: +\begin{lstlisting} +class HotpoApplication(Application): + def __init__(self, n): + Application.__init__( + self, + executable = '/usr/bin/expr', + arguments = ( + # run `expr n / 2` if n is even + [n, '/', n] if n % 2 == 0 + # run `expr 1 + 3 * n` if n is odd + else [1, '+', 3, '*', n]), + stdout = "stdout.txt", + ) +\end{lstlisting} + \end{columns} +\end{frame} + +\begin{frame}[fragile] +\frametitle{The \emph{3n+1} conjecture (V)} +\label{sec:14} + +\begin{columns} + \column{0.2\linewidth} + \begin{center} + \includegraphics[height=0.8\textheight]{fig/S} + \end{center} + + \column{0.8\linewidth} + Now string together applications to compute a + single sequence: +\begin{lstlisting} +class HotpoSequence(SequentialTask): + + def __init__(self, n): + # compute first iteration of $f$ + self.tasks = [ HotpoApplication(n) ] + SequentialTask.__init__(self, self.tasks) + + def next(self, k): + last = self.tasks[k].result + if last == 1: + return TERMINATED + else: + self.tasks.append(MyApplication(last) + return RUNNING +\end{lstlisting} + \end{columns} +\end{frame} + +\begin{frame}[fragile] + \frametitle{The \emph{3n+1} conjecture (VI)} + \label{sec:15} + + \begin{columns} + \column{0.5\linewidth} + \begin{center} + \includegraphics[height=0.8\textheight]{fig/3n+1_P} + \end{center} + + \column{0.5\linewidth} + Parallel tasks are independent by definition, so it's even easier to + create a collection: +\begin{lstlisting} +tasks = + ParallelTaskCollection([ + HotpoSequence(n) + for n in range(1, N) ]) +\end{lstlisting} + + We can run such a collection like any other \texttt{Task}. + \end{columns} +\end{frame} + \end{document} %%% Local Variables: