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%Tutorial slides on Python.

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

% Copyright (c) 2005-2009, Prabhu Ramachandran

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% Taken from Fernando's slides.

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\usepackage[scaled=.95]{helvet}

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\usepackage{listings}

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%%% This is from Fernando's setup.

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% Title page

\title[Exercises]{Exercises}

\author[FOSSEE] {FOSSEE}

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

\date[] {12 February, 2010\\Day 1, Session 5}

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

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

%% the beginning of each subsection:

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{

  \begin{frame}<beamer>

    \frametitle{Outline}

    \tableofcontents[currentsection,currentsubsection]

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

% the following command: 

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

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% DOCUMENT STARTS

\begin{document}

\begin{frame}

  \titlepage

\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]))

plot(l, t, '.')

    \end{lstlisting}

    \end{block}

  \end{columns}

  \begin{block}{Problem Statement}

    Tweak above code to plot data in file `pos.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}