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Diffstat (limited to 'day1/session5.tex')
| -rw-r--r-- | day1/session5.tex | 210 |
1 files changed, 192 insertions, 18 deletions
diff --git a/day1/session5.tex b/day1/session5.tex index 326e8fe..3fe435e 100644 --- a/day1/session5.tex +++ b/day1/session5.tex @@ -1,8 +1,8 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Tutorial slides on Python. % -% Author: FOSSEE -% Copyright (c) 2009, FOSSEE, IIT Bombay +% Author: Prabhu Ramachandran <prabhu at aero.iitb.ac.in> +% Copyright (c) 2005-2009, Prabhu Ramachandran %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \documentclass[14pt,compress]{beamer} @@ -23,7 +23,6 @@ \usepackage[latin1]{inputenc} %\usepackage{times} \usepackage[T1]{fontenc} -\usepackage{amsmath} % Taken from Fernando's slides. \usepackage{ae,aecompl} @@ -52,7 +51,7 @@ \setcounter{time}{0} \newcommand{\inctime}[1]{\addtocounter{time}{#1}{\tiny \thetime\ m}} -\newcommand{\typ}[1]{\lstinline{#1}} +\newcommand{\typ}[1]{\texttt{#1}} \newcommand{\kwrd}[1]{ \texttt{\textbf{\color{blue}{#1}}} } @@ -74,12 +73,12 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Title page -\title[]{} +\title[Exercises]{Exercises} \author[FOSSEE] {FOSSEE} \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay} -\date[] {11, January 2010\\Day 1, Session 5} +\date[] {11 January, 2010\\Day 1, Session 5} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo} @@ -96,13 +95,6 @@ \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: @@ -118,12 +110,194 @@ \titlepage \end{frame} -%% \begin{frame} -%% \frametitle{Outline} -%% \tableofcontents -%% % \pausesections -%% \end{frame} + +\begin{frame}[fragile] + \frametitle{Problem 1} + \begin{columns} + \column{0.5\textwidth} + \hspace*{-0.5in} + \includegraphics[height=2in, interpolate=true]{data/L-Tsq.png} + \column{0.45\textwidth} + \begin{block}{Example code} + \tiny + \begin{lstlisting} +l = [] +t = [] +for line in open('pendulum.txt'): + point = line.split() + l.append(float(point[0])) + t.append(float(point[1])) +tsq = [] +for time in t: + tsq.append(time*time) +plot(l, tsq, '.') + \end{lstlisting} + \end{block} + \end{columns} + \begin{block}{Problem Statement} + Tweak above code to plot data in file 'location.txt'. + \end{block} +\end{frame} + +\begin{frame} + \frametitle{Problem 1 cont...} + \begin{itemize} + \item Label both the axes. + \item What kind of motion is this? + \item Title the graph accordingly. + \item Annotate the position where vertical velocity is zero. + \end{itemize} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Problem 2} + \begin{columns} + \column{0.5\textwidth} + \hspace*{-0.5in} + \includegraphics[height=2in, interpolate=true]{data/points} + \column{0.45\textwidth} + \begin{block}{Line between two points} + \tiny + \begin{lstlisting} +In []: x = [1, 5] +In []: y = [1, 4] +In []: plot(x, y) + \end{lstlisting} + \end{block} + \end{columns} + Line can be plotted using arrays of coordinates. + \pause + \begin{block}{Problem statement} + Write a Program that plots a regular n-gon(Let n = 5). + \end{block} +\end{frame} + + +\begin{frame}[fragile] + \frametitle{Problem 3} + \begin{columns} + \column{0.5\textwidth} + \hspace*{-0.5in} + \includegraphics[height=2in, interpolate=true]{data/damp} + \column{0.45\textwidth} + \begin{block}{Damped Oscillation} + \tiny + \begin{lstlisting} +In []: x = linspace(0, 4*pi) +In []: plot(x, exp(x/10)*sin(x)) + \end{lstlisting} + \end{block} + \end{columns} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Problem 3 cont...} +Create a sequence of images in which the damped oscillator($e^{x/10}sin(x)$) slowly evolves over time. +\begin{columns} +\column{0.35\textwidth} +\includegraphics[width=1.5in,height=1.5in, interpolate=true]{data/plot2} +\column{0.35\textwidth} +\includegraphics[width=1.5in,height=1.5in, interpolate=true]{data/plot4} +\column{0.35\textwidth} +\includegraphics[width=1.5in,height=1.5in, interpolate=true]{data/plot6} +\end{columns} +\begin{block}{Hint} +\small + \begin{lstlisting} +savefig('plot'+str(i)+'.png') #i is int variable + \end{lstlisting} +\end{block} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Problem 4} + \begin{lstlisting} +In []: x = imread('smoothing.png') +In []: x.shape +Out[]: (256, 256) +In []: imshow(x,cmap=cm.gray) + \end{lstlisting} +\emphbar{Replace each pixel with mean of neighboring pixels} + \begin{center} + \includegraphics[height=1in, interpolate=true]{data/neighbour} + \end{center} +\end{frame} + +\begin{frame} + \begin{center} + \includegraphics[height=3in, interpolate=true]{data/smoothing} + \end{center} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Problem 4: Approach} + For \typ{y} being resultant image: + \begin{lstlisting} +y[1, 1] = x[0, 1]/4 + x[1, 0]/4 + + x[2, 1]/4 + x[1, 2]/4 + \end{lstlisting} + \begin{columns} + \column{0.45\textwidth} + \hspace*{-0.5in} + \includegraphics[height=1.5in, interpolate=true]{data/smoothing} + \column{0.45\textwidth} + \hspace*{-0.5in} + \includegraphics[height=1.5in, interpolate=true]{data/after-filter} + \end{columns} + \begin{block}{Hint:} + Use array Slicing. + \end{block} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Solution} + \begin{lstlisting} +In []: y = zeros_like(x) +In []: y[1:-1,1:-1] = x[:-2,1:-1]/4+ + x[2:,1:-1]/4+ + x[1:-1,2:]/4+ + x[1:-1,:-2]/4 +In []: imshow(y,cmap=cm.gray) + \end{lstlisting} +\end{frame} \end{document} +%% \begin{frame} +%% \frametitle{Problem 4} +%% Legendre polynomials $P_n(x)$ are defined by the following recurrence relation + +%% \center{$(n+1)P_{n+1}(x) - (2n+1)xP_n(x) + nP_{n-1}(x) = 0$}\\ + +%% with $P_0(x) = 1$, $P_1(x) = x$ and $P_2(x) = (3x^2 - 1)/2$. Compute the next three +%% Legendre polynomials and plot all 6 over the interval [-1,1]. +%% \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} +%% \inctime{20} +%% \end{frame} |