1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

     2 %Tutorial slides on Python.

     3 %

     4 % Author: Prabhu Ramachandran <prabhu at aero.iitb.ac.in>

     5 % Copyright (c) 2005-2009, Prabhu Ramachandran

     6 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

     7 

     8 \documentclass[14pt,compress]{beamer}

     9 %\documentclass[draft]{beamer}

    10 %\documentclass[compress,handout]{beamer}

    11 %\usepackage{pgfpages} 

    12 %\pgfpagesuselayout{2 on 1}[a4paper,border shrink=5mm]

    13 

    14 % Modified from: generic-ornate-15min-45min.de.tex

    15 \mode<presentation>

    16 {

    17   \usetheme{Warsaw}

    18   \useoutertheme{infolines}

    19   \setbeamercovered{transparent}

    20 }

    21 

    22 \usepackage[english]{babel}

    23 \usepackage[latin1]{inputenc}

    24 %\usepackage{times}

    25 \usepackage[T1]{fontenc}

    26 

    27 % Taken from Fernando's slides.

    28 \usepackage{ae,aecompl}

    29 \usepackage{mathpazo,courier,euler}

    30 \usepackage[scaled=.95]{helvet}

    31 

    32 \definecolor{darkgreen}{rgb}{0,0.5,0}

    33 

    34 \usepackage{listings}

    35 \lstset{language=Python,

    36     basicstyle=\ttfamily\bfseries,

    37     commentstyle=\color{red}\itshape,

    38   stringstyle=\color{darkgreen},

    39   showstringspaces=false,

    40   keywordstyle=\color{blue}\bfseries}

    41 

    42 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    43 % Macros

    44 \setbeamercolor{emphbar}{bg=blue!20, fg=black}

    45 \newcommand{\emphbar}[1]

    46 {\begin{beamercolorbox}[rounded=true]{emphbar} 

    47       {#1}

    48  \end{beamercolorbox}

    49 }

    50 \newcounter{time}

    51 \setcounter{time}{0}

    52 \newcommand{\inctime}[1]{\addtocounter{time}{#1}{\tiny \thetime\ m}}

    53 

    54 \newcommand{\typ}[1]{\texttt{#1}}

    55 

    56 \newcommand{\kwrd}[1]{ \texttt{\textbf{\color{blue}{#1}}}  }

    57 

    58 %%% This is from Fernando's setup.

    59 % \usepackage{color}

    60 % \definecolor{orange}{cmyk}{0,0.4,0.8,0.2}

    61 % % Use and configure listings package for nicely formatted code

    62 % \usepackage{listings}

    63 % \lstset{

    64 %    language=Python,

    65 %    basicstyle=\small\ttfamily,

    66 %    commentstyle=\ttfamily\color{blue},

    67 %    stringstyle=\ttfamily\color{orange},

    68 %    showstringspaces=false,

    69 %    breaklines=true,

    70 %    postbreak = \space\dots

    71 % }

    72 

    73 

    74 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    75 % Title page

    76 \title[Exercises]{Exercises}

    77 

    78 \author[FOSSEE] {FOSSEE}

    79 

    80 \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}

    81 \date[] {11 January, 2010\\Day 1, Session 5}

    82 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    83 

    84 %\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo}

    85 %\logo{\pgfuseimage{iitmlogo}}

    86 

    87 

    88 %% Delete this, if you do not want the table of contents to pop up at

    89 %% the beginning of each subsection:

    90 \AtBeginSubsection[]

    91 {

    92   \begin{frame}<beamer>

    93     \frametitle{Outline}

    94     \tableofcontents[currentsection,currentsubsection]

    95   \end{frame}

    96 }

    97 

    98 

    99 % If you wish to uncover everything in a step-wise fashion, uncomment

   100 % the following command: 

   101 %\beamerdefaultoverlayspecification{<+->}

   102 

   103 %\includeonlyframes{current,current1,current2,current3,current4,current5,current6}

   104 

   105 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   106 % DOCUMENT STARTS

   107 \begin{document}

   108 

   109 \begin{frame}

   110   \titlepage

   111 \end{frame}

   112 

   113 

   114 \begin{frame}[fragile]

   115   \frametitle{Problem 1}

   116   \begin{columns}

   117     \column{0.5\textwidth}

   118     \hspace*{-0.5in}

   119     \includegraphics[height=2in, interpolate=true]{data/L-Tsq.png}

   120     \column{0.45\textwidth}

   121     \begin{block}{Example code}

   122     \tiny

   123     \begin{lstlisting}

   124 l = []

   125 t = []

   126 for line in open('pendulum.txt'):

   127     point = line.split()

   128     l.append(float(point[0]))

   129     t.append(float(point[1]))

   130 tsq = []

   131 for time in t:

   132     tsq.append(time*time)

   133 plot(l, tsq, '.')

   134     \end{lstlisting}

   135     \end{block}

   136   \end{columns}

   137   \begin{block}{Problem Statement}

   138     Tweak above code to plot data in file 'location.txt'.

   139   \end{block}

   140 \end{frame}

   141 

   142 \begin{frame}

   143   \frametitle{Problem 1 cont...}

   144   \begin{itemize}

   145   \item Label both the axes.

   146   \item What kind of motion is this?

   147   \item Title the graph accordingly.

   148   \item Annotate the position where vertical velocity is zero.

   149   \end{itemize}

   150 \end{frame}

   151 

   152 \begin{frame}[fragile]

   153   \frametitle{Problem 2}

   154   \begin{columns}

   155     \column{0.5\textwidth}

   156     \hspace*{-0.5in}

   157     \includegraphics[height=2in, interpolate=true]{data/points}

   158     \column{0.45\textwidth}

   159     \begin{block}{Line between two points}

   160     \tiny

   161     \begin{lstlisting}

   162 In []: x = [1, 5]

   163 In []: y = [1, 4]

   164 In []: plot(x, y)

   165     \end{lstlisting}

   166     \end{block}

   167   \end{columns}

   168   Line can be plotted using arrays of coordinates.

   169   \pause

   170   \begin{block}{Problem statement}

   171     Write a Program that plots a regular n-gon(Let n = 5).

   172   \end{block}  

   173 \end{frame}

   174 

   175 

   176 \begin{frame}[fragile]

   177   \frametitle{Problem 3}

   178   \begin{columns}

   179     \column{0.5\textwidth}

   180     \hspace*{-0.5in}

   181     \includegraphics[height=2in, interpolate=true]{data/damp}

   182     \column{0.45\textwidth}

   183     \begin{block}{Damped Oscillation}

   184     \tiny

   185     \begin{lstlisting}

   186 In []: x = linspace(0, 4*pi)

   187 In []: plot(x, exp(x/10)*sin(x))

   188     \end{lstlisting}

   189     \end{block}

   190   \end{columns}

   191 \end{frame}

   192 

   193 \begin{frame}[fragile]

   194   \frametitle{Problem 3 cont...}

   195 Create a sequence of images in which the damped oscillator($e^{x/10}sin(x)$) slowly evolves over time.

   196 \begin{columns}

   197 \column{0.35\textwidth}

   198 \includegraphics[width=1.5in,height=1.5in, interpolate=true]{data/plot2}

   199 \column{0.35\textwidth}

   200 \includegraphics[width=1.5in,height=1.5in, interpolate=true]{data/plot4}

   201 \column{0.35\textwidth}

   202 \includegraphics[width=1.5in,height=1.5in, interpolate=true]{data/plot6}

   203 \end{columns}

   204 \begin{block}{Hint}

   205 \small

   206   \begin{lstlisting}

   207 savefig('plot'+str(i)+'.png') #i is int variable  

   208   \end{lstlisting}  

   209 \end{block}

   210 \end{frame}

   211 

   212 \begin{frame}[fragile]

   213   \frametitle{Problem 4}

   214   \begin{lstlisting}

   215 In []: x = imread('smoothing.png')

   216 In []: x.shape

   217 Out[]: (256, 256)

   218 In []: imshow(x,cmap=cm.gray)

   219   \end{lstlisting}

   220 \emphbar{Replace each pixel with mean of neighboring pixels}

   221   \begin{center}

   222   \includegraphics[height=1in, interpolate=true]{data/neighbour}

   223   \end{center}

   224 \end{frame}

   225 

   226 \begin{frame}

   227   \begin{center}

   228     \includegraphics[height=3in, interpolate=true]{data/smoothing}    

   229   \end{center}

   230 \end{frame}

   231 

   232 \begin{frame}[fragile]

   233   \frametitle{Problem 4: Approach}

   234   For \typ{y} being resultant image:

   235   \begin{lstlisting}

   236 y[1, 1] = x[0, 1]/4 + x[1, 0]/4 

   237           + x[2, 1]/4 + x[1, 2]/4    

   238   \end{lstlisting}

   239    \begin{columns}

   240     \column{0.45\textwidth}

   241     \hspace*{-0.5in}

   242     \includegraphics[height=1.5in, interpolate=true]{data/smoothing}

   243     \column{0.45\textwidth}

   244     \hspace*{-0.5in}

   245     \includegraphics[height=1.5in, interpolate=true]{data/after-filter}

   246   \end{columns}

   247    \begin{block}{Hint:}

   248      Use array Slicing.

   249    \end{block}

   250 \end{frame}

   251 

   252 \begin{frame}[fragile]

   253   \frametitle{Solution}

   254   \begin{lstlisting}

   255 In []: y = zeros_like(x)

   256 In []: y[1:-1,1:-1] = x[:-2,1:-1]/4+

   257                       x[2:,1:-1]/4+

   258                       x[1:-1,2:]/4+

   259                       x[1:-1,:-2]/4

   260 In []: imshow(y,cmap=cm.gray)

   261   \end{lstlisting}

   262 \end{frame}

   263 

   264 

   265 \end{document}

   266 

   267 %% \begin{frame}

   268 %%   \frametitle{Problem 4}

   269 %%   Legendre polynomials $P_n(x)$ are defined by the following recurrence relation

   270 

   271 %% \center{$(n+1)P_{n+1}(x) - (2n+1)xP_n(x) + nP_{n-1}(x) = 0$}\\

   272 

   273 %% with $P_0(x) = 1$, $P_1(x) = x$ and $P_2(x) = (3x^2 - 1)/2$. Compute the next three 

   274 %%    Legendre polynomials and plot all 6 over the interval [-1,1].

   275 %% \end{frame}

   276 

   277 %% \begin{frame}[fragile] 

   278 %% \frametitle{Problem Set 5}

   279 %%   \begin{columns}

   280 %%     \column{0.6\textwidth}

   281 %%     \small{

   282 %%     \begin{itemize}

   283 %%       \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. 

   284 %%     \end{itemize}}

   285 %%     \column{0.35\textwidth}

   286 %%     \hspace*{-0.5in}

   287 %%   \includegraphics[height=1.6in, interpolate=true]{data/cobweb}  

   288 %% \end{columns}

   289 %% \end{frame}

   290 

   291 %% \begin{frame}

   292 %%   \frametitle{Problem Set 5.3}

   293 %%   Plot the cobweb plot as follows:

   294 %%   \begin{enumerate}

   295 %%     \item Start at $(x_0, 0)$ ($\implies$ i=0)

   296 %%     \item Draw a line to $(x_i, f(x_i))$

   297 %%     \item Set $x_{i+1} = f(x_i)$

   298 %%     \item Draw a line to $(x_{i+1}, x_{i+1})$

   299 %%     \item $(i\implies i+1)$ 

   300 %%     \item Repeat from 2 for as long as you want 

   301 %%   \end{enumerate}

   302 %% \inctime{20}

   303 %% \end{frame}