day1/session6.tex
author Santosh G. Vattam <vattam.santosh@gmail.com>
Mon, 08 Mar 2010 20:45:33 +0530
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permissions -rwxr-xr-x
Updated for day1 of GRD workshop.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%Tutorial slides on Python.
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%
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% Author: FOSSEE
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% Copyright (c) 2009, FOSSEE, IIT Bombay
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\documentclass[14pt,compress]{beamer}
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%\documentclass[draft]{beamer}
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%\documentclass[compress,handout]{beamer}
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%\usepackage{pgfpages} 
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%\pgfpagesuselayout{2 on 1}[a4paper,border shrink=5mm]
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% Modified from: generic-ornate-15min-45min.de.tex
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\mode<presentation>
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{
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  \usetheme{Warsaw}
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  \useoutertheme{infolines}
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  \setbeamercovered{transparent}
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}
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\usepackage[english]{babel}
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\usepackage[latin1]{inputenc}
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%\usepackage{times}
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\usepackage[T1]{fontenc}
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% Taken from Fernando's slides.
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\usepackage{ae,aecompl}
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\usepackage{mathpazo,courier,euler}
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\usepackage[scaled=.95]{helvet}
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\usepackage{amsmath}
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\definecolor{darkgreen}{rgb}{0,0.5,0}
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\usepackage{listings}
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\lstset{language=Python,
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    basicstyle=\ttfamily\bfseries,
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    commentstyle=\color{red}\itshape,
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  stringstyle=\color{darkgreen},
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  showstringspaces=false,
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  keywordstyle=\color{blue}\bfseries}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Macros
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\setbeamercolor{emphbar}{bg=blue!20, fg=black}
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\newcommand{\emphbar}[1]
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{\begin{beamercolorbox}[rounded=true]{emphbar} 
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      {#1}
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 \end{beamercolorbox}
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}
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\newcounter{time}
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\setcounter{time}{0}
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\newcommand{\inctime}[1]{\addtocounter{time}{#1}{\tiny \thetime\ m}}
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\newcommand{\typ}[1]{\lstinline{#1}}
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\newcommand{\kwrd}[1]{ \texttt{\textbf{\color{blue}{#1}}}  }
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%%% This is from Fernando's setup.
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% \usepackage{color}
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% \definecolor{orange}{cmyk}{0,0.4,0.8,0.2}
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% % Use and configure listings package for nicely formatted code
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% \usepackage{listings}
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% \lstset{
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%    language=Python,
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%    basicstyle=\small\ttfamily,
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%    commentstyle=\ttfamily\color{blue},
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%    stringstyle=\ttfamily\color{orange},
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%    showstringspaces=false,
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%    breaklines=true,
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%    postbreak = \space\dots
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% }
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Title page
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\title[Solving Equations \& ODEs]{Python for Science and Engg:\\Solving Equations \& ODEs}
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\author[FOSSEE] {FOSSEE}
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\institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
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\date[] {08 March, 2010\\Day 1, Session 6}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo}
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%\logo{\pgfuseimage{iitmlogo}}
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%% Delete this, if you do not want the table of contents to pop up at
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%% the beginning of each subsection:
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\AtBeginSubsection[]
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{
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  \begin{frame}<beamer>
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    \frametitle{Outline}
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    \tableofcontents[currentsection,currentsubsection]
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  \end{frame}
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}
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\AtBeginSection[]
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{
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  \begin{frame}<beamer>
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    \frametitle{Outline}
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    \tableofcontents[currentsection,currentsubsection]
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  \end{frame}
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}
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% If you wish to uncover everything in a step-wise fashion, uncomment
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% the following command: 
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%\beamerdefaultoverlayspecification{<+->}
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%\includeonlyframes{current,current1,current2,current3,current4,current5,current6}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% DOCUMENT STARTS
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\begin{document}
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\begin{frame}
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  \maketitle
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\end{frame}
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%% \begin{frame}
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%%   \frametitle{Outline}
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%%   \tableofcontents
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%%   % You might wish to add the option [pausesections]
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%% \end{frame}
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\section{Solving linear equations}
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\begin{frame}[fragile]
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\frametitle{Solution of equations}
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Consider,
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  \begin{align*}
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    3x + 2y - z  & = 1 \\
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    2x - 2y + 4z  & = -2 \\
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    -x + \frac{1}{2}y -z & = 0
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  \end{align*}
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Solution:
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  \begin{align*}
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    x & = 1 \\
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    y & = -2 \\
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    z & = -2
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  \end{align*}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{Solving using Matrices}
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Let us now look at how to solve this using \kwrd{matrices}
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  \begin{lstlisting}
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    In []: A = array([[3,2,-1],
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                      [2,-2,4],                   
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                      [-1, 0.5, -1]])
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    In []: b = array([1, -2, 0])
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    In []: x = solve(A, b)
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  \end{lstlisting}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{Solution:}
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\begin{lstlisting}
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In []: x
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Out[]: array([ 1., -2., -2.])
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\end{lstlisting}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{Let's check!}
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\begin{lstlisting}
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In []: Ax = dot(A, x)
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In []: Ax
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Out[]: array([  1.00000000e+00,  -2.00000000e+00,  -1.11022302e-16])
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\end{lstlisting}
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\begin{block}{}
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The last term in the matrix is actually \alert{0}!\\
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We can use \kwrd{allclose()} to check.
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\end{block}
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\begin{lstlisting}
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In []: allclose(Ax, b)
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Out[]: True
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\end{lstlisting}
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\inctime{15}
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\end{frame}
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\subsection{Exercises}
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\begin{frame}[fragile]
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\frametitle{Problem}
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Solve the set of equations:
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\begin{align*}
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  x + y + 2z -w & = 3\\
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  2x + 5y - z - 9w & = -3\\
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  2x + y -z + 3w & = -11 \\
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  x - 3y + 2z + 7w & = -5\\
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\end{align*}
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\inctime{10}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{Solution}
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Use \kwrd{solve()}
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\begin{align*}
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  x & = -5\\
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  y & = 2\\
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  z & = 3\\
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  w & = 0\\
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\end{align*}
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\end{frame}
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\section{Finding Roots}
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\begin{frame}[fragile]
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\frametitle{Scipy Methods - \typ{roots}}
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\begin{itemize}
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\item Calculates the roots of polynomials
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\item To calculate the roots of $x^2-5x+6$ 
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\end{itemize}
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\begin{lstlisting}
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  In []: coeffs = [1, -5, 6]
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  In []: roots(coeffs)
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  Out[]: array([3., 2.])
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\end{lstlisting}
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\vspace*{-.2in}
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\begin{center}
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\includegraphics[height=1.6in, interpolate=true]{data/roots}    
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\end{center}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{Scipy Methods - \typ{fsolve}}
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\begin{small}
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\begin{lstlisting}
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  In []: from scipy.optimize import fsolve
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\end{lstlisting}
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\end{small}
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\begin{itemize}
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\item Finds the roots of a system of non-linear equations
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\item Input arguments - Function and initial estimate
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\item Returns the solution
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\end{itemize}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{\typ{fsolve}}
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Find the root of $sin(x)+cos^2(x)$ nearest to $0$
358
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\vspace{-0.1in}
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\begin{center}
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\includegraphics[height=2.8in, interpolate=true]{data/fsolve}    
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\end{center}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{\typ{fsolve}}
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Root of $sin(x)+cos^2(x)$ nearest to $0$
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\begin{lstlisting}
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In []: fsolve(sin(x)+cos(x)*cos(x), 0)
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NameError: name 'x' is not defined
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\end{lstlisting}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{\typ{fsolve}}
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\begin{lstlisting}
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In []: x = linspace(-pi, pi)
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In []: fsolve(sin(x)+cos(x)*cos(x), 0)
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\end{lstlisting}
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\begin{small}
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\alert{\typ{TypeError:}}
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\typ{'numpy.ndarray' object is not callable}
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\end{small}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{Functions - Definition}
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We have been using them all along. Now let's see how to define them.
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\begin{lstlisting}
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In []: def f(x):
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           return sin(x)+cos(x)*cos(x)
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\end{lstlisting}
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\begin{itemize}
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\item \typ{def}
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\item name
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\item arguments
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\item \typ{return}
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\end{itemize}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{Functions - Calling them}
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\begin{lstlisting}
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In [15]: f()
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---------------------------------------
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\end{lstlisting}
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\alert{\typ{TypeError:}}\typ{f() takes exactly 1 argument}
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\typ{(0 given)}
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\begin{lstlisting}
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In []: f(0)
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Out[]: 1.0
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In []: f(1)
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Out[]: 1.1333975665343254
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\end{lstlisting}
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More on Functions later \ldots
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{\typ{fsolve} \ldots}
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Find the root of $sin(x)+cos^2(x)$ nearest to $0$
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\begin{lstlisting}
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In []: fsolve(f, 0)
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Out[]: -0.66623943249251527
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\end{lstlisting}
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\begin{center}
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\includegraphics[height=2in, interpolate=true]{data/fsolve}    
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\end{center}
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\end{frame}
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\begin{frame}[fragile]
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  \frametitle{Exercise Problem}
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  Find the root of the equation $x^2 - sin(x) + cos^2(x)$ nearest to $0$
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\end{frame}
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\begin{frame}[fragile]
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  \frametitle{Solution}
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  \begin{small}
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  \begin{lstlisting}
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    def f(x):
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        return x**2 - sin(x) + cos(x)*cos(x)
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    fsolve(f, 0)
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  \end{lstlisting}
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  \end{small}
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  \begin{center}
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\includegraphics[height=2in, interpolate=true]{data/fsolve_tanx}
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  \end{center}
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\end{frame}
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%% \begin{frame}[fragile]
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%% \frametitle{Scipy Methods \dots}
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%% \begin{small}
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%% \begin{lstlisting}
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%% In []: from scipy.optimize import fixed_point
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%% In []: from scipy.optimize import bisect
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%% In []: from scipy.optimize import newton
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%% \end{lstlisting}
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%% \end{small}
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%% \end{frame}
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\section{ODEs}
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221
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\begin{frame}[fragile]
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\frametitle{Solving ODEs using SciPy}
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\begin{itemize}
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\item Let's consider the spread of an epidemic in a population
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\item $\frac{dy}{dt} = ky(L-y)$ gives the spread of the disease
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\item L is the total population.
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\item Use L = 25000, k = 0.00003, y(0) = 250
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\item Define a function as below
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\end{itemize}
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\begin{lstlisting}
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In []: from scipy.integrate import odeint
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In []: def epid(y, t):
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  ....     k = 0.00003
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  ....     L = 25000
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  ....     return k*y*(L-y)
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  ....
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\end{lstlisting}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{Solving ODEs using SciPy \ldots}
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\begin{lstlisting}
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In []: t = linspace(0, 12, 61)
293
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In []: y = odeint(epid, 250, t)
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In []: plot(t, y)
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\end{lstlisting}
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%Insert Plot
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\end{frame}
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\begin{frame}[fragile]
330
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\frametitle{Result}
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\begin{center}
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\includegraphics[height=2in, interpolate=true]{data/image}  
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\end{center}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{ODEs - Simple Pendulum}
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We shall use the simple ODE of a simple pendulum. 
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\begin{equation*}
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\ddot{\theta} = -\frac{g}{L}sin(\theta)
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\end{equation*}
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   393
\begin{itemize}
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diff changeset
   394
\item This equation can be written as a system of two first order ODEs
9ed9539446bc Updated day1 session5 and session6.
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diff changeset
   395
\end{itemize}
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diff changeset
   396
\begin{align}
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   397
\dot{\theta} &= \omega \\
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diff changeset
   398
\dot{\omega} &= -\frac{g}{L}sin(\theta) \\
9ed9539446bc Updated day1 session5 and session6.
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diff changeset
   399
 \text{At}\ t &= 0 : \nonumber \\
263
8a4a1e5aec85 Changes made for Goa workshop .
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diff changeset
   400
 \theta = \theta_0(10^o)\quad & \&\quad  \omega = 0\ (Initial\ values)\nonumber 
221
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diff changeset
   401
\end{align}
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diff changeset
   402
\end{frame}
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diff changeset
   403
9ed9539446bc Updated day1 session5 and session6.
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diff changeset
   404
\begin{frame}[fragile]
293
f7d7b5565232 Added another ODE example to session6.
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diff changeset
   405
\frametitle{ODEs - Simple Pendulum \ldots}
221
9ed9539446bc Updated day1 session5 and session6.
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parents: 142
diff changeset
   406
\begin{itemize}
293
f7d7b5565232 Added another ODE example to session6.
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diff changeset
   407
\item Use \typ{odeint} to do the integration
221
9ed9539446bc Updated day1 session5 and session6.
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parents: 142
diff changeset
   408
\end{itemize}
9ed9539446bc Updated day1 session5 and session6.
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diff changeset
   409
\begin{lstlisting}
263
8a4a1e5aec85 Changes made for Goa workshop .
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diff changeset
   410
In []: def pend_int(initial, t):
359
cb17c87b090e Fixed errors found during REC workshop.
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diff changeset
   411
  ....     theta = initial[0]
cb17c87b090e Fixed errors found during REC workshop.
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diff changeset
   412
  ....     omega = initial[1]
cb17c87b090e Fixed errors found during REC workshop.
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diff changeset
   413
  ....     g = 9.81
cb17c87b090e Fixed errors found during REC workshop.
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diff changeset
   414
  ....     L = 0.2
221
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diff changeset
   415
  ....     f=[omega, -(g/L)*sin(theta)]
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diff changeset
   416
  ....     return f
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diff changeset
   417
  ....
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diff changeset
   418
\end{lstlisting}
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diff changeset
   419
\end{frame}
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diff changeset
   420
9ed9539446bc Updated day1 session5 and session6.
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diff changeset
   421
\begin{frame}[fragile]
293
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   422
\frametitle{ODEs - Simple Pendulum \ldots}
221
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   423
\begin{itemize}
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   424
\item \typ{t} is the time variable \\ 
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   425
\item \typ{initial} has the initial values
9ed9539446bc Updated day1 session5 and session6.
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diff changeset
   426
\end{itemize}
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diff changeset
   427
\begin{lstlisting}
359
cb17c87b090e Fixed errors found during REC workshop.
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diff changeset
   428
In []: t = linspace(0, 20, 101)
221
9ed9539446bc Updated day1 session5 and session6.
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parents: 142
diff changeset
   429
In []: initial = [10*2*pi/360, 0]
263
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diff changeset
   430
\end{lstlisting} 
221
9ed9539446bc Updated day1 session5 and session6.
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diff changeset
   431
\end{frame}
9ed9539446bc Updated day1 session5 and session6.
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diff changeset
   432
9ed9539446bc Updated day1 session5 and session6.
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diff changeset
   433
\begin{frame}[fragile]
293
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   434
\frametitle{ODEs - Simple Pendulum \ldots}
263
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   435
%%\begin{small}
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   436
\typ{In []: from scipy.integrate import odeint}
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   437
%%\end{small}
221
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diff changeset
   438
\begin{lstlisting}
9ed9539446bc Updated day1 session5 and session6.
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diff changeset
   439
In []: pend_sol = odeint(pend_int, 
263
8a4a1e5aec85 Changes made for Goa workshop .
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diff changeset
   440
                         initial,t)
221
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   441
\end{lstlisting}
9ed9539446bc Updated day1 session5 and session6.
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diff changeset
   442
\end{frame}
9ed9539446bc Updated day1 session5 and session6.
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diff changeset
   443
330
46533051b9d3 commited changes made for scipy and cheatsheats.
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diff changeset
   444
\begin{frame}[fragile]
46533051b9d3 commited changes made for scipy and cheatsheats.
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diff changeset
   445
\frametitle{Result}
46533051b9d3 commited changes made for scipy and cheatsheats.
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diff changeset
   446
\begin{center}
46533051b9d3 commited changes made for scipy and cheatsheats.
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diff changeset
   447
\includegraphics[height=2in, interpolate=true]{data/ode}  
46533051b9d3 commited changes made for scipy and cheatsheats.
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diff changeset
   448
\end{center}
46533051b9d3 commited changes made for scipy and cheatsheats.
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parents: 319
diff changeset
   449
\end{frame}
133
578db74dfea0 Added Day1 Session6 - Finding Roots.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   450
223
081600805dde Minor edits to sessions 5 and 6.
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diff changeset
   451
\begin{frame}
081600805dde Minor edits to sessions 5 and 6.
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diff changeset
   452
  \frametitle{Things we have learned}
081600805dde Minor edits to sessions 5 and 6.
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diff changeset
   453
  \begin{itemize}
283
5d7ca20e955f Added functions to session6.
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diff changeset
   454
  \item Solving Linear Equations
5d7ca20e955f Added functions to session6.
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diff changeset
   455
  \item Defining Functions
5d7ca20e955f Added functions to session6.
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parents: 281
diff changeset
   456
  \item Finding Roots
223
081600805dde Minor edits to sessions 5 and 6.
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parents: 221
diff changeset
   457
  \item Solving ODEs
081600805dde Minor edits to sessions 5 and 6.
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parents: 221
diff changeset
   458
  \end{itemize}
081600805dde Minor edits to sessions 5 and 6.
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parents: 221
diff changeset
   459
\end{frame}
133
578db74dfea0 Added Day1 Session6 - Finding Roots.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   460
578db74dfea0 Added Day1 Session6 - Finding Roots.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   461
\end{document}
343
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   462
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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   463
%% Questions for Quiz %%
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   464
%% ------------------ %%
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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diff changeset
   465
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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   466
\begin{frame}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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   467
\frametitle{\incqno }
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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parents: 339
diff changeset
   468
Given a 4x4 matrix \texttt{A} and a 4-vector \texttt{b}, what command do
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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parents: 339
diff changeset
   469
you use to solve for the equation \\
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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parents: 339
diff changeset
   470
\texttt{Ax = b}?
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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diff changeset
   471
\end{frame}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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diff changeset
   472
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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diff changeset
   473
\begin{frame}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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   474
\frametitle{\incqno }
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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parents: 339
diff changeset
   475
What command will you use if you wish to integrate a system of ODEs?
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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parents: 339
diff changeset
   476
\end{frame}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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diff changeset
   477
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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diff changeset
   478
\begin{frame}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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diff changeset
   479
\frametitle{\incqno }
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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parents: 339
diff changeset
   480
How do you calculate the roots of the polynomial, $y = 1 + 6x + 8x^2 +
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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parents: 339
diff changeset
   481
x^3$?
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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parents: 339
diff changeset
   482
\end{frame}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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parents: 339
diff changeset
   483
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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parents: 339
diff changeset
   484
\begin{frame}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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diff changeset
   485
\frametitle{\incqno }
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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parents: 339
diff changeset
   486
Two arrays \lstinline+a+ and \lstinline+b+ are numerically almost equal, what command
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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parents: 339
diff changeset
   487
do you use to check if this is true?
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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diff changeset
   488
\end{frame}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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diff changeset
   489
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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diff changeset
   490
%% \begin{frame}[fragile]
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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diff changeset
   491
%% \frametitle{\incqno }
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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   492
%% \begin{lstlisting}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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   493
%%   In []: x = arange(0, 1, 0.25)
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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diff changeset
   494
%%   In []: print x
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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diff changeset
   495
%% \end{lstlisting}
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diff changeset
   496
%% What will be printed?
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diff changeset
   497
%% \end{frame}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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diff changeset
   498
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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diff changeset
   499
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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   500
%% \begin{frame}[fragile]
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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diff changeset
   501
%% \frametitle{\incqno }
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   502
%% \begin{lstlisting}
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diff changeset
   503
%% from scipy.integrate import quad
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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   504
%% def f(x):
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   505
%%     res = x*cos(x)
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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diff changeset
   506
%% quad(f, 0, 1)
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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diff changeset
   507
%% \end{lstlisting}
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diff changeset
   508
%% What changes will you make to the above code to make it work?
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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parents: 339
diff changeset
   509
%% \end{frame}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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diff changeset
   510
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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diff changeset
   511
%% \begin{frame}
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diff changeset
   512
%% \frametitle{\incqno }
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diff changeset
   513
%% What two commands will you use to create and evaluate a spline given
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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diff changeset
   514
%% some data?
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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diff changeset
   515
%% \end{frame}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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diff changeset
   516
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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diff changeset
   517
%% \begin{frame}[fragile]
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
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diff changeset
   518
%% \frametitle{\incqno }
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diff changeset
   519
%% What would be the result?
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   520
%% \begin{lstlisting}
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   521
%%   In []: x
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   522
%%   array([[0, 1, 2],
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   523
%%          [3, 4, 5],
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   524
%%          [6, 7, 8]])
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   525
%%   In []: x[::-1,:]
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   526
%% \end{lstlisting}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   527
%% Hint:
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   528
%% \begin{lstlisting}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   529
%%   In []: x = arange(9)
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   530
%%   In []: x[::-1]
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   531
%%   array([8, 7, 6, 5, 4, 3, 2, 1, 0])
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   532
%% \end{lstlisting}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   533
%% \end{frame}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   534
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   535
%% \begin{frame}[fragile]
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   536
%% \frametitle{\incqno }
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   537
%% What would be the result?
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   538
%% \begin{lstlisting}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   539
%%   In []: y = arange(3)
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   540
%%   In []: x = linspace(0,3,3)
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   541
%%   In []: x-y
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   542
%% \end{lstlisting}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   543
%% \end{frame}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   544
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   545
%% \begin{frame}[fragile]
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   546
%% \frametitle{\incqno }
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   547
%% \begin{lstlisting}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   548
%%   In []: x
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   549
%%   array([[ 0, 1, 2, 3],
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   550
%%          [ 4, 5, 6, 7],
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   551
%%          [ 8, 9, 10, 11],
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   552
%%          [12, 13, 14, 15]])
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   553
%% \end{lstlisting}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   554
%% How will you get the following \lstinline+x+?
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   555
%% \begin{lstlisting}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   556
%%   array([[ 5, 7],
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   557
%%          [ 9, 11]])
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   558
%% \end{lstlisting}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   559
%% \end{frame}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   560
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   561
%% \begin{frame}[fragile]
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   562
%% \frametitle{\incqno }
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   563
%% What would be the output?
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   564
%% \begin{lstlisting}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   565
%%   In []: y = arange(4)
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   566
%%   In []: x = array(([1,2,3,2],[1,3,6,0]))
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   567
%%   In []: x + y
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   568
%% \end{lstlisting}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   569
%% \end{frame}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   570
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   571
%% \begin{frame}[fragile]
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   572
%% \frametitle{\incqno }
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   573
%% \begin{lstlisting}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   574
%%   In []: line = plot(x, sin(x))
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   575
%% \end{lstlisting}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   576
%% Use the \lstinline+set_linewidth+ method to set width of \lstinline+line+ to 2.
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   577
%% \end{frame}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   578
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   579
%% \begin{frame}[fragile]
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   580
%% \frametitle{\incqno }
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   581
%% What would be the output?
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   582
%% \begin{lstlisting}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   583
%%   In []: x = arange(9)
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   584
%%   In []: y = arange(9.)
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   585
%%   In []: x == y
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   586
%% \end{lstlisting}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   587
%% \end{frame}
adb85e126341 Moved all day1 quiz questions to end of day1-sessions.
Puneeth Chaganti <punchagan@fossee.in>
parents: 339
diff changeset
   588