diff -r f05b1c457120 -r df494695e061 day2/session5.tex --- a/day2/session5.tex Tue Nov 10 12:21:29 2009 +0530 +++ b/day2/session5.tex Tue Nov 10 16:26:47 2009 +0530 @@ -1,33 +1,48 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%Tutorial slides on Python. +% Tutorial slides on Python. % % Author: Prabhu Ramachandran % Copyright (c) 2005-2009, Prabhu Ramachandran %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\documentclass[14pt,compress]{beamer} -%\documentclass[draft]{beamer} -%\documentclass[compress,handout]{beamer} -%\usepackage{pgfpages} -%\pgfpagesuselayout{2 on 1}[a4paper,border shrink=5mm] +\documentclass[compress,14pt]{beamer} +% \documentclass[handout]{beamer} +% \usepackage{pgfpages} +% \pgfpagesuselayout{4 on 1}[a4paper,border, shrink=5mm,landscape] +\usepackage{tikz} +\newcommand{\hyperlinkmovie}{} +%\usepackage{movie15} -% Modified from: generic-ornate-15min-45min.de.tex +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Note that in presentation mode +% \paperwidth 364.19536pt +% \paperheight 273.14662pt +% h/w = 0.888 + + \mode { \usetheme{Warsaw} + %\usetheme{Boadilla} + %\usetheme{default} \useoutertheme{infolines} \setbeamercovered{transparent} } +% To remove navigation symbols +\setbeamertemplate{navigation symbols}{} + +\usepackage{amsmath} \usepackage[english]{babel} \usepackage[latin1]{inputenc} -%\usepackage{times} +\usepackage{times} \usepackage[T1]{fontenc} % Taken from Fernando's slides. \usepackage{ae,aecompl} \usepackage{mathpazo,courier,euler} \usepackage[scaled=.95]{helvet} +\usepackage{pgf} \definecolor{darkgreen}{rgb}{0,0.5,0} @@ -40,50 +55,65 @@ keywordstyle=\color{blue}\bfseries} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% Macros +% My Macros +\setbeamercolor{postit}{bg=yellow,fg=black} \setbeamercolor{emphbar}{bg=blue!20, fg=black} \newcommand{\emphbar}[1] {\begin{beamercolorbox}[rounded=true]{emphbar} {#1} \end{beamercolorbox} } +%{\centerline{\fcolorbox{gray!50} {blue!10}{ +%\begin{minipage}{0.9\linewidth} +% {#1} +%\end{minipage} +% }}} + +\newcommand{\myemph}[1]{\structure{\emph{#1}}} +\newcommand{\PythonCode}[1]{\lstinline{#1}} + +\newcommand{\tvtk}{\texttt{tvtk}} +\newcommand{\mlab}{\texttt{mlab}} + \newcounter{time} \setcounter{time}{0} -\newcommand{\inctime}[1]{\addtocounter{time}{#1}{\tiny \thetime\ m}} - -\newcommand{\typ}[1]{\texttt{#1}} - -\newcommand{\kwrd}[1]{ \texttt{\textbf{\color{blue}{#1}}} } +\newcommand{\inctime}[1]{\addtocounter{time}{#1}{\vspace*{0.1in}\tiny \thetime\ m}} -%%% This is from Fernando's setup. -% \usepackage{color} -% \definecolor{orange}{cmyk}{0,0.4,0.8,0.2} -% % Use and configure listings package for nicely formatted code -% \usepackage{listings} -% \lstset{ -% language=Python, -% basicstyle=\small\ttfamily, -% commentstyle=\ttfamily\color{blue}, -% stringstyle=\ttfamily\color{orange}, -% showstringspaces=false, -% breaklines=true, -% postbreak = \space\dots -% } +\newcommand\BackgroundPicture[1]{% + \setbeamertemplate{background}{% + \parbox[c][\paperheight]{\paperwidth}{% + \vfill \hfill + \hfill \vfill +}}} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Configuring the theme +%\setbeamercolor{normal text}{fg=white} +%\setbeamercolor{background canvas}{bg=black} + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Title page -\title[Exercises]{Exercises} +\title[3D Plotting]{3D data Visualization} \author[FOSSEE] {FOSSEE} \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay} \date[] {8 November, 2009\\Day 2, Session 5} + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo} -%\logo{\pgfuseimage{iitmlogo}} +%\pgfdeclareimage[height=0.75cm]{iitblogo}{iitblogo} +%\logo{\pgfuseimage{iitblogo}} +\AtBeginSection[] +{ + \begin{frame} + \frametitle{Outline} + \tableofcontents[currentsection,currentsubsection] + \end{frame} +} %% Delete this, if you do not want the table of contents to pop up at %% the beginning of each subsection: @@ -95,109 +125,434 @@ \end{frame} } - -% If you wish to uncover everything in a step-wise fashion, uncomment -% the following command: -%\beamerdefaultoverlayspecification{<+->} - -%\includeonlyframes{current,current1,current2,current3,current4,current5,current6} - +\AtBeginSection[] +{ + \begin{frame} + \frametitle{Outline} + \tableofcontents[currentsection,currentsubsection] + \end{frame} +} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % DOCUMENT STARTS \begin{document} \begin{frame} - \titlepage + \maketitle +\end{frame} + +\begin{frame} + \frametitle{Outline} + \tableofcontents + % You might wish to add the option [pausesections] \end{frame} -\begin{frame}{Problem 1.1} - The aliquot of a number is defined as: the sum of the \emph{proper} divisors of the number. \\For example: -\center{aliquot(12) = 1 + 2 + 3 + 4 + 6 = 16.}\\ - Write a function that returns the aliquot number of a given number. +\section{3D Data Visualization} + +\begin{frame} + \frametitle{What is visualization?} + \Large + \begin{center} + Visual representation of data + \end{center} \end{frame} -\begin{frame}{Problem 1.2} - Pair of numbers (a, b) is said to be \alert{amicable} if aliquot number of a is b and aliquot number of b is a.\\ - Example: \texttt{220, 284}\\ - Write a program that prints all four digit amicable pairs. - -\inctime{20} + +%% \begin{frame} +%% \frametitle{Is this new?} +%% \begin{center} +%% We have moved from: +%% \end{center} +%% \begin{columns} +%% \column{} +%% \hspace*{-1in} +%% \includegraphics[width=1.75in,height=1.75in, interpolate=true]{data/3832} +%% \column{}\hspace*{-0.25in} +%% To +%% \column{} +%% \hspace*{-1in} +%% \includegraphics[width=1.75in, height=1.75in, interpolate=true]{data/torus} +%% \end{columns} +%% \end{frame} + +\begin{frame} + \frametitle{3D visualization} + \Large + \begin{center} + Harder but important + \end{center} \end{frame} -%% \begin{frame}{Problem 2} -%% Given an empty chessboard and one Bishop placed in any s%quare, say (r, c), generate the list of all squares the Bi%shop could move to. - -%% \end{frame} +\begin{frame} + \frametitle{Is this Graphics?} + \Large + \begin{center} + Visualization is about data! + \end{center} +\end{frame} -\begin{frame}[fragile] - \frametitle{Problem Set 2} - Given a string like, ``1, 3-7, 12, 15, 18-21'', produce the list \\ - \begin{lstlisting} - [1,3,4,5,6,7,12,15,18,19,20,21] - \end{lstlisting} +\begin{frame} + \frametitle{Examples: trajectory in space} + \Large + \begin{center} + \pgfimage[width=2.5in]{MEDIA/m2/mlab/plot3d_ex} + \end{center} +\end{frame} + +\begin{frame} + \frametitle{Examples: Fire in a room} + \Large + \begin{center} + Demo of data + \end{center} \inctime{10} \end{frame} -\begin{frame} - \frametitle{Problem Set 3} - \begin{description} - \item[3.1] Count word frequencies in a file. -\end{description} -\inctime{5} +\section{Tools available} + +\subsection{mlab} + +\begin{frame} + {Overview} + \Large + \begin{itemize} + \item Simple + \item Convenient + \item Full-featured + \end{itemize} +\end{frame} + +\begin{frame}[fragile] + + \frametitle{Getting started} + \myemph{\Large Vanilla:} + \begin{lstlisting}[language=bash] + $ ipython -wthread + \end{lstlisting} + \myemph{\Large with Pylab:} + \begin{lstlisting}[language=bash] + $ ipython -pylab -wthread + \end{lstlisting} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Using mlab} + + \begin{lstlisting} +In []:from enthought.mayavi import mlab + \end{lstlisting} + + \vspace*{0.5in} + + \myemph{\Large Try these} + + \vspace*{0.25in} + + \begin{lstlisting} +In []: mlab.test_ +In []: mlab.test_contour3d() +In []: mlab.test_contour3d?? + \end{lstlisting} +\end{frame} + +\begin{frame} + {Exploring the view} + \begin{columns} + \column{0.6\textwidth} + \pgfimage[width=3in]{MEDIA/m2/contour3d} + \column{0.4\textwidth} + \begin{itemize} + \item Mouse + \item Keyboard + \item Toolbar + \item Mayavi icon\pgfimage[width=0.2in]{MEDIA/m2/m2_icon} + \end{itemize} + \end{columns} +\end{frame} + +\begin{frame}[fragile] + \frametitle{\mlab\ plotting functions} + \begin{columns} + \column{0.25\textwidth} + \myemph{\Large 0D data} + \column{0.5\textwidth} + \pgfimage[width=2in]{MEDIA/m2/mlab/points3d_ex} + \end{columns} + + \begin{lstlisting} +In []: t = linspace(0, 2*pi, 50) +In []: u = cos(t) * pi +In []: x, y, z = sin(u), cos(u), sin(t) + \end{lstlisting} + \emphbar{\PythonCode{In []: mlab.points3d(x, y, z)}} +\end{frame} + +\begin{frame} + \begin{columns} + \column{0.25\textwidth} + \myemph{\Large 1D data} + \column{0.5\textwidth} + \pgfimage[width=2.5in]{MEDIA/m2/mlab/plot3d_ex} + \end{columns} + \emphbar{\PythonCode{In []: mlab.plot3d(x, y, z, t)}} + + Plots lines between the points + +\end{frame} + +\begin{frame}[fragile] + \begin{columns} + \column{0.25\textwidth} + \myemph{\Large 2D data} + \column{0.5\textwidth} + \pgfimage[width=2in]{MEDIA/m2/mlab/surf_ex} + \end{columns} + \begin{lstlisting} +In []: x, y = mgrid[-3:3:100j,-3:3:100j] +In []: z = sin(x*x + y*y) + \end{lstlisting} + + \emphbar{\PythonCode{In []: mlab.surf(x, y, z)}} + + \alert{Assumes the points are rectilinear} + +\end{frame} + +\begin{frame}[fragile] + \frametitle{mgrid} + \begin{lstlisting} +In []: mgrid[0:3,0:3] +Out[]: +array([[[0, 0, 0], + [1, 1, 1], + [2, 2, 2]], + + [[0, 1, 2], + [0, 1, 2], + [0, 1, 2]]]) + +In []: mgrid[-1:1:5j] +Out[]: array([-1., -0.5, 0., 0.5, 1.]) +\end{lstlisting} \end{frame} \begin{frame}[fragile] - \frametitle{Problem set 4} - Central difference - \begin{equation*} - \frac{sin(x+h)-sin(x-h)}{2h} - \end{equation*} + \frametitle{Example} \begin{lstlisting} - In []: x = linspace(0, 2*pi, 100) - In []: y = sin(x) - In []: deltax = x[1] - x[0] - \end{lstlisting} +In []: x, y = mgrid[-1:1:5j, -1:1:5j] +In []: z = x*x + y*y + +In []: z +Out[]: +array([[ 2. , 1.25, 1. , 1.25, 2. ], + [ 1.25, 0.5 , 0.25, 0.5 , 1.25], + [ 1. , 0.25, 0. , 0.25, 1. ], + [ 1.25, 0.5 , 0.25, 0.5 , 1.25], + [ 2. , 1.25, 1. , 1.25, 2. ]]) +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] + \myemph{\Large 2D data: \texttt{mlab.mesh}} + \vspace*{0.25in} + + \emphbar{\PythonCode{In []: mlab.mesh(x, y, z)}} + + \alert{Points needn't be regular} + + \vspace*{0.25in} +\begin{lstlisting} +In []: phi, theta = mgrid[0:pi:20j, +... 0:2*pi:20j] +In []: x = sin(phi)*cos(theta) +In []: y = sin(phi)*sin(theta) +In []: z = cos(phi) +In []: mlab.mesh(x, y, z, +... representation= +... 'wireframe') +\end{lstlisting} + +\end{frame} + +\begin{frame}[fragile] + + \begin{columns} + \column{0.25\textwidth} + \myemph{\Large 3D data} + \column{0.5\textwidth} + \pgfimage[width=1.5in]{MEDIA/m2/mlab/contour3d}\\ + \end{columns} +\begin{lstlisting} +In []: x, y, z = mgrid[-5:5:64j, +... -5:5:64j, +... -5:5:64j] +In []: mlab.contour3d(x*x*0.5 + y*y + + z*z*2) +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] + + \myemph{\Large 3D vector data: \PythonCode{mlab.quiver3d}} + \vspace*{0.25in} + + \pgfimage[width=2in]{MEDIA/m2/mlab/quiver3d_ex}\\ + +\begin{lstlisting} +In []: mlab.test_quiver3d() +\end{lstlisting} + +\emphbar{\PythonCode{obj = mlab.quiver3d(x, y, z, u, v, w)}} +\inctime{20} +\end{frame} + + +\subsection{Mayavi2} + +\begin{frame} + \frametitle{Introduction to Mayavi} + \begin{itemize} + \item Most scientists not interested in details of visualization + \item Visualization of data files with a nice UI + \item Interactive visualization of data (think Matlab) + \item Embedding visualizations in applications + \item Customization + \end{itemize} \pause - \begin{enumerate} - \item Given this, get the finite difference of sin in the range 0 to 2*pi - \end{enumerate} + \begin{block}{The Goal} + Provide a \alert{flexible} library/app for all of these needs! + \end{block} +\end{frame} + +\begin{frame} + {Overview of features} + \vspace*{-0.3in} + \begin{center} + \hspace*{-0.2in}\pgfimage[width=5in]{MEDIA/m2/m2_app3_3} + \end{center} +\end{frame} + + +\begin{frame} + \frametitle{Mayavi in applications} + \vspace*{-0.3in} + \begin{center} + \hspace*{-0.2in}\pgfimage[width=4.5in]{MEDIA/m2/m2_envisage} + \end{center} \end{frame} \begin{frame} - \frametitle{Problem Set 5} - \begin{itemize} - \item[5.1] Write a function that plots any regular n-gon given \typ{n}. - \item[5.2] Consider the logistic map, $f(x) = kx(1-x)$, plot it for - $k=2.5, 3.5$ and $4$ in the same plot. -\end{itemize} + \frametitle{Live in your dialogs} + \vspace*{0.1in} + \begin{center} + \hspace*{-0.2in}\pgfimage[width=2.5in]{MEDIA/m2/mlab_tui} + \end{center} +\end{frame} + +\begin{frame} + {Exploring the documentation} + \begin{center} + \pgfimage[width=4in]{MEDIA/m2/m2_ug_doc} + \end{center} \end{frame} -\begin{frame}[fragile] -\frametitle{Problem Set 5} - \begin{columns} - \column{0.6\textwidth} - \small{ - \begin{itemize} - \item[3] Consider the iteration $x_{n+1} = f(x_n)$ where $f(x) = kx(1-x)$. Plot the successive iterates of this process as explained below. - \end{itemize}} - \column{0.35\textwidth} - \hspace*{-0.5in} - \includegraphics[height=1.6in, interpolate=true]{data/cobweb} -\end{columns} + +\begin{frame} + \frametitle{Summary} + \begin{itemize} + \item \url{http://code.enthought.com/projects/mayavi} + \item Uses VTK (\url{www.vtk.org}) + \item BSD license + \item Linux, win32 and Mac OS X + \item Highly scriptable + \item Embed in Traits UIs (wxPython and PyQt4) + \item Envisage Plugins + \item Debian/Ubuntu/Fedora + \item \alert{Pythonic} + \end{itemize} + + \inctime{10} + \end{frame} \begin{frame} - \frametitle{Problem Set 5.3} - Plot the cobweb plot as follows: - \begin{enumerate} - \item Start at $(x_0, 0)$ ($\implies$ i=0) - \item Draw a line to $(x_i, f(x_i))$ - \item Set $x_{i+1} = f(x_i)$ - \item Draw a line to $(x_{i+1}, x_{i+1})$ - \item $(i\implies i+1)$ - \item Repeat from 2 for as long as you want - \end{enumerate} + {Getting hands dirty!} + + \begin{block}{Motivational problem} + Atmospheric data of temperature over the surface of the earth. + Let temperature ($T$) vary linearly with height ($z$): + \begin{center} + $T = 288.15 - 6.5z$ + \end{center} + \end{block} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Simple solution} + + \begin{lstlisting} +lat = linspace(-89, 89, 37) +lon = linspace(0, 360, 37) +z = linspace(0, 100, 11) + \end{lstlisting} +\pause + \begin{lstlisting} +x, y, z = mgrid[0:360:37j,-89:89:37j, + 0:100:11j] +t = 288.15 - 6.5*z +mlab.contour3d(x, y, z, t) +mlab.outline() +mlab.colorbar() + \end{lstlisting} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Exercise: Lorenz equation} + \begin{columns} + \column{0.25\textwidth} + \begin{eqnarray*} + \frac{d x}{dt} &=& s (y-x)\\ + \frac{d y}{d t} &=& rx -y -xz\\ + \frac{d z}{d t} &=& xy - bz\\ + \end{eqnarray*} + \column{0.25\textwidth} + Let $s=10,$ + $r=28,$ + $b=8./3.$ + \end{columns} + \structure{\Large Region of interest} + \begin{lstlisting} +x, y, z = mgrid[-50:50:20j,-50:50:20j, + -10:60:20j] + \end{lstlisting} \inctime{20} + +\end{frame} +\begin{frame}[fragile] + \frametitle{Solution} + \begin{lstlisting} +def lorenz(x,y,z,s=10.,r=28.,b=8./3.): + u = s*(y-x) + v = r*x-y-x*z + w = x*y-b*z + return u,v,w +x,y,z = mgrid [-50:50:20j,-50:50:20j, + -10:60:20j ] +u,v,w = lorenz( x , y , z ) +# Your plot here +# +mlab.show() + + \end{lstlisting} +\end{frame} + +\begin{frame} + \frametitle{We have covered:} + \begin{itemize} + \item Need of visualization. + \item Using mlab to create 3 D plots. + \item Mayavi Toolkit. + \end{itemize} \end{frame} \end{document} +