Reorganized last 3 sessions of day 2 again.

1 files changed, 460 insertions, 105 deletions

diff --git a/day2/session6.tex b/day2/session6.tex
index ddb1599..70e66e5 100644
--- a/day2/session6.tex
+++ b/day2/session6.tex
@@ -1,33 +1,48 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%Tutorial slides on Python.
+% Tutorial slides on Python.
 %
 % Author: Prabhu Ramachandran <prabhu at aero.iitb.ac.in>
 % 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}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Note that in presentation mode 
+% \paperwidth  364.19536pt
+% \paperheight 273.14662pt
+% h/w = 0.888
+
 
-% Modified from: generic-ornate-15min-45min.de.tex
 \mode<presentation>
 {
   \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{\inctime}[1]{\addtocounter{time}{#1}{\vspace*{0.1in}\tiny \thetime\ m}}
 
-\newcommand{\typ}[1]{\texttt{#1}}
+\newcommand\BackgroundPicture[1]{%
+  \setbeamertemplate{background}{%
+      \parbox[c][\paperheight]{\paperwidth}{%
+      \vfill \hfill
+ \hfill \vfill
+}}}
 
-\newcommand{\kwrd}[1]{ \texttt{\textbf{\color{blue}{#1}}}  }
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Configuring the theme
+%\setbeamercolor{normal text}{fg=white}
+%\setbeamercolor{background canvas}{bg=black}
 
-%%% 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
-% }
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % Title page
-\title[Exercises]{Exercises}
+\title[3D Plotting]{3D data Visualization}
 
 \author[FOSSEE] {FOSSEE}
 
 \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
-\date[] {1 November, 2009\\Day 2, Session 4}
+\date[] {8 November, 2009\\Day 2, Session 6}
+
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-%\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo}
-%\logo{\pgfuseimage{iitmlogo}}
+%\pgfdeclareimage[height=0.75cm]{iitblogo}{iitblogo}
+%\logo{\pgfuseimage{iitblogo}}
 
+\AtBeginSection[]
+{
+  \begin{frame}<beamer>
+    \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}<beamer>
+    \frametitle{Outline}
+    \tableofcontents[currentsection,currentsubsection]
+  \end{frame}
+}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % DOCUMENT STARTS
 \begin{document}
 
 \begin{frame}
-  \titlepage
+  \maketitle
 \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. 
+\begin{frame}
+  \frametitle{Outline}
+  \tableofcontents
+  % You might wish to add the option [pausesections]
 \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}
+\section{3D Data Visualization}
+
+\begin{frame}
+    \frametitle{What is visualization?}
+    \Large
+    \begin{center}
+    Visual representation of data
+    \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.
 
+%% \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}[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{3D visualization}
+    \Large
+    \begin{center}
+        Harder but important
+    \end{center}
+\end{frame}
+
+\begin{frame}
+    \frametitle{Is this Graphics?}
+    \Large
+    \begin{center}
+        Visualization is about data!
+    \end{center}
+\end{frame}
+
+\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{Problem set 4}
-  Central difference
-  \begin{equation*}
-  \frac{sin(x+h)-sin(x-h)}{2h}
-  \end{equation*}
+    \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_<TAB>
+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 []: x = linspace(0, 2*pi, 100)
-  In []: y = sin(x)
-  In []: deltax = x[1] - x[0]
-  \end{lstlisting}
-  \pause
-    \begin{enumerate}
-      \item Given this, get the finite difference of sin in the range 0 to 2*pi
-    \end{enumerate}
+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{Example}
+  \begin{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{Problem Set 5}
+  \frametitle{Introduction to Mayavi}
   \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}
+  \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{block}{The Goal}
+      Provide a \alert{flexible} library/app for all of these needs!
+  \end{block}
 \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}
-\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}
+\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{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}
+  \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}
+    {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}
+