
diff -r e9961fb16c58 -r 22e3480e4794 day2/session5.tex
--- a/day2/session5.tex	Sun Jan 10 17:43:28 2010 +0530
+++ b/day2/session5.tex	Sun Jan 10 17:49:23 2010 +0530
@@ -1,48 +1,33 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Tutorial slides on Python.
+%Tutorial slides on Python.
 %
 % Author: Prabhu Ramachandran <prabhu at aero.iitb.ac.in>
 % Copyright (c) 2005-2009, Prabhu Ramachandran
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-\documentclass[compress,14pt]{beamer}
-% \documentclass[handout]{beamer}
-% \usepackage{pgfpages}
-% \pgfpagesuselayout{4 on 1}[a4paper,border, shrink=5mm,landscape]
-\usepackage{tikz}
-\newcommand{\hyperlinkmovie}{}
-%\usepackage{movie15}
+\documentclass[14pt,compress]{beamer}
+%\documentclass[draft]{beamer}
+%\documentclass[compress,handout]{beamer}
+%\usepackage{pgfpages} 
+%\pgfpagesuselayout{2 on 1}[a4paper,border shrink=5mm]
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% 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}
 
@@ -55,65 +40,50 @@
   keywordstyle=\color{blue}\bfseries}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% My Macros
-\setbeamercolor{postit}{bg=yellow,fg=black}
+% Macros
 \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}{\vspace*{0.1in}\tiny \thetime\ m}}
+\newcommand{\inctime}[1]{\addtocounter{time}{#1}{\tiny \thetime\ m}}
+
+\newcommand{\typ}[1]{\texttt{#1}}
+
+\newcommand{\kwrd}[1]{ \texttt{\textbf{\color{blue}{#1}}}  }
 
-\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}
-
+%%% 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[3D Plotting]{3D data Visualization}
+\title[Exercises]{Exercises}
 
 \author[FOSSEE] {FOSSEE}
 
 \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
 \date[] {12 January, 2010\\Day 2, Session 5}
-
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-%\pgfdeclareimage[height=0.75cm]{iitblogo}{iitblogo}
-%\logo{\pgfuseimage{iitblogo}}
+%\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo}
+%\logo{\pgfuseimage{iitmlogo}}
 
-\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:
@@ -125,434 +95,107 @@
   \end{frame}
 }
 
-\AtBeginSection[]
-{
-  \begin{frame}<beamer>
-    \frametitle{Outline}
-    \tableofcontents[currentsection,currentsubsection]
-  \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}
+
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % DOCUMENT STARTS
 \begin{document}
 
 \begin{frame}
-  \maketitle
-\end{frame}
-
-\begin{frame}
-  \frametitle{Outline}
-  \tableofcontents
-  % You might wish to add the option [pausesections]
+  \titlepage
 \end{frame}
 
-\section{3D Data Visualization}
-
-\begin{frame}
-    \frametitle{What is visualization?}
-    \Large
-    \begin{center}
-    Visual representation of data
-    \end{center}
+\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:\\
+aliquot(12) = 1 + 2 + 3 + 4 + 6 = 16.\\
+  Write a function that returns the aliquot number of a given number. 
 \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}
+\end{frame}
 
-%% \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}
+%% \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{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}
+\begin{frame}[fragile]
+  \frametitle{Problem 2}
+  Given a string of numbers like, ``1, 3-7, 12, 15, 18-21'', produce the following list \\
+  \begin{lstlisting}
+    [1,3,4,5,6,7,12,15,18,19,20,21]
+  \end{lstlisting}
 \inctime{10}
 \end{frame}
 
-\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_<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 []: 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}
+\begin{frame} 
+  \frametitle{Problem 3}
+  Count frequencies of words in a file.
+\inctime{25}
 \end{frame}
 
 \begin{frame}[fragile]
-  \frametitle{Example}
+  \frametitle{Problem set 4}
+  Central difference
+  \begin{equation*}
+  \frac{sin(x+h)-sin(x-h)}{2h}
+  \end{equation*}
   \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{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}
+  In []: x = linspace(0, 2*pi, 100)
+  In []: y = sin(x)
+  In []: deltax = x[1] - x[0]
+  \end{lstlisting}
   \pause
-  \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}
+    \begin{enumerate}
+      \item Given this, get the finite difference of sin in the range 0 to 2*pi
+    \end{enumerate}
 \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}
+  \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}
 \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}
-
+\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}
-    {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}
+  \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}
 \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}
-




