day2/session1.tex
author Madhusudan.C.S <madhusudancs@gmail.com>
Wed, 07 Oct 2009 00:43:37 +0530
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% Tutorial slides on Python.
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%
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% Author: Prabhu Ramachandran <prabhu at aero.iitb.ac.in>
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% Copyright (c) 2005-2009, Prabhu Ramachandran
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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{split}
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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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\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[]{Matrices and Arrays\\ \& \\2D Plotting}
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\author[FOSSEE Team] {Asokan Pichai\\Prabhu Ramachandran}
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\institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
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\date[] {11, October 2009}
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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{Matrices and Arrays}
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\subsection{Basic \typ{numpy} }
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\newcommand{\num}{\texttt{numpy}}
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\begin{frame}
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  \frametitle{The \num\ module}
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  \begin{itemize}
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      \item Why?
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  \item What:
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    \begin{itemize}
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    \item An efficient and powerful array type for various common data
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      types
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    \item Abstracts out the most commonly used standard operations on
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      arrays
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    \end{itemize}
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  \end{itemize}
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\end{frame}
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\begin{frame}[fragile]
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  \frametitle{Examples of \num}
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\begin{lstlisting}
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# Simple array math example
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>>> from numpy import *
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>>> a = array([1,2,3,4])
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>>> b = array([2,3,4,5])
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>>> a*2 + b + 1 # Basic math!
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array([5, 8, 11, 14])
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# Pi and e are defined.
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>>> x = linspace(0.0, 10.0, 1000)
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>>> x *= 2*pi/10 # inplace.
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# apply functions to array.
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>>> y = sin(x)
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\end{lstlisting}
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\inctime{5}
3
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\end{frame}
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\begin{frame}
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  \frametitle{Basic concepts}
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  \begin{itemize}
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  \item fixed size (\typ{arr.size});
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  \item Same type (\typ{arr.dtype}) of data
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  \item arbitrary dimensionality
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  \item \typ{arr.shape}: size in each dimension
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  \item \alert{Note:} \typ{len(arr) != arr.size} in general
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  \item \alert{Note:} By default array operations are performed
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    \alert{elementwise}
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  \end{itemize}
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\end{frame}
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\begin{frame}[fragile]
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  \frametitle{More examples of \num}
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\vspace*{-8pt}
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\begin{lstlisting}
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>>> x = array([1., 2, 3, 4])
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>>> size(x)
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4
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>>> x.dtype # What is a.dtype?
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dtype('float64')
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>>> x.shape
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(4,)
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>>> print rank(x), x.itemsize
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1 8
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>>> x[0] = 10
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>>> print x[0], x[-1]
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10.0 4.0
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\end{lstlisting}
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\end{frame}
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\begin{frame}[fragile]
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  \frametitle{Multi-dimensional arrays}
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\begin{lstlisting}
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>>> a = array([[ 0, 1, 2, 3],
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...            [10,11,12,13]])
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>>> a.shape # (rows, columns)
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(2, 4)
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# Accessing and setting values
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>>> a[1,3] 
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13
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>>> a[1,3] = -1
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>>> a[1] # The second row
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array([10,11,12,-1])
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\end{lstlisting}
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\end{frame}
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\begin{frame}[fragile]
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  \frametitle{Array math}
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  \begin{itemize}
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  \item Basic \alert{elementwise} math (given two arrays \typ{a, b}):
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      \typ{+, -, *, /, \%}
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  \item Inplace operators: \typ{a += b}, or \typ{add(a, b, a)} etc. 
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  \item \typ{sum(x, axis=0)}, 
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        \typ{product(x, axis=0)},
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        \typ{dot(a, bp)}   
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  \end{itemize}
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\end{frame}
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\begin{frame}[fragile]
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  \frametitle{Array math cont.}
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  \begin{itemize}
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  \item Logical operations: \typ{equal (==)}, \typ{not\_equal (!=)},
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    \typ{less (<)}, \typ{greater (>)} etc.
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  \item Trig and other functions: \typ{sin(x),}
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        \typ{arcsin(x), sinh(x),}
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      \typ{exp(x), sqrt(x)} etc.
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  \end{itemize}
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\inctime{10}
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\end{frame}
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\subsection{Array Creation \& Slicing, Striding Arrays}
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\begin{frame}[fragile]
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  \frametitle{Array creation functions}
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  \begin {block}{\typ{array(object, dtype=None, ...)}}
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  \begin{lstlisting}
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  >>> array( [2,3,4] )  
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  array([2, 3, 4])
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  \end{lstlisting}
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  \end {block}
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  \begin{block}{\typ{linspace(start, stop, num=50, ...)}}
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  \begin{lstlisting}
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  >>> linspace( 0, 2, 4 )   
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  array([0.,0.6666667,1.3333333,2.])
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  \end{lstlisting}
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  \end{block}
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  \begin{itemize}
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  \item also try \typ{arange} command
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  \end{itemize}
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\end{frame}
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\begin{frame}[fragile]
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  \frametitle{Array creation functions cont.}
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  \begin{itemize}  
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  \item \typ{ones(shape, dtype=None, ...)}  
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  \begin{lstlisting} 
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  >>>ones([2,2])
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  array([[ 1.,  1.],
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       [ 1.,  1.]])
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  \end{lstlisting}  
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  \item \typ{identity(n)} 
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  \item \typ{ones\_like(x)}  
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  \begin{lstlisting} 
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  >>>a = array([[1,2,3],[4,5,6]])
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  >>>ones_like(a)
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    array([[1, 1, 1],
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           [1, 1, 1]])
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  \end{lstlisting}
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  \item check out \typ{zeros, zeros\_like, empty}
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  \end{itemize}
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\end{frame}
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\begin{frame}[fragile]
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  \frametitle{Slicing arrays}
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\begin{lstlisting}
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>>> a = array([[1,2,3], [4,5,6], 
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               [7,8,9]])
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>>> a[0,1:3]
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array([2, 3])
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>>> a[1:,1:]
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array([[5, 6],
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       [8, 9]])
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>>> a[:,2]
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array([3, 6, 9])
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>>> a[...,2]
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array([3, 6, 9])
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\end{lstlisting}
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\end{frame}
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\begin{frame}[fragile]
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  \frametitle{Striding arrays}
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\begin{lstlisting}
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>>> a[0::2,0::2]
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array([[1, 3],
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       [7, 9]])
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# Slices are references to the 
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# same memory!
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\end{lstlisting}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{Random Numbers}
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\begin{lstlisting}
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>>> np.random.rand(3,2)
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array([[ 0.96276665,  0.77174861],
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       [ 0.35138557,  0.61462271],
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       [ 0.16789255,  0.43848811]])
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>>> np.random.randint(1,100)
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42
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\end{lstlisting}
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\inctime{15}
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\end{frame}
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\begin{frame}[fragile]
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  \frametitle{Problem Set}
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  \begin{lstlisting}
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    >>> from scipy import misc
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    >>> A=misc.imread(name)
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    >>> misc.imshow(A)
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  \end{lstlisting}
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    \begin{enumerate}
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    \item Convert an RGB image to Grayscale. $ Y = 0.5R + 0.25G + 0.25B $
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    \item Scale the image to 50\%
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    \item Introduce some random noise
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    \item Smooth the image using a mean filter
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      \\\small{Take the mean of all the neighbouring elements}
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      \\\small{How fast can you do it?}
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    \end{enumerate}
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\inctime{15}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3
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\section{2D Plotting}
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\subsection{Getting Started}
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\begin{frame}
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    {IPython's \typ{pylab} mode}
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\begin{block}{Immediate use:}
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 \typ{\$ ipython -pylab}
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\end{block}
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\begin{itemize}
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    \item \typ{pylab}: convenient 2D plotting interface to MPL    
3
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    \item Imports all of pylab for you!
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    \item Allows for interactive plotting
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\end{itemize}
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\end{frame}
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\begin{frame}[fragile]
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    \frametitle{Basic 2D plotting}
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\begin{lstlisting}
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>>> x = linspace(0, 2*pi, 1000)
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>>> plot(x, sin(x)) 
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>>> plot(x, sin(x), 'ro')
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>>> xlabel(r'$\chi$', color='g')
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# LaTeX markup!
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>>> ylabel(r'sin($\chi$)', color='r')
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>>> title('Simple figure', fontsize=20)
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>>> savefig('/tmp/test.eps')
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\end{lstlisting}
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\begin{itemize}
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  \item Also: PNG, PDF, PS, EPS, SVG, PDF
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\end{itemize}
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\inctime{5}
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\end{frame}
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\subsection{Plots - Lines, Labels and Legends}
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\begin{frame}[fragile]
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  \frametitle{Tweaking plots}
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\begin{lstlisting}
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# Set properties of objects:
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>>> l, = plot(x, sin(x))
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# Why "l,"?
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>>> setp(l, linewidth=2.0, color='r')
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>>> l.set_linewidth(2.0)
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>>> draw() # Redraw.
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>>> setp(l) # Print properties.
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>>> clf() # Clear figure.
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>>> close() # Close figure.
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\end{lstlisting}
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\end{frame}
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\begin{frame}[fragile]
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   \frametitle{Working with text \ldots}
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%\begin{itemize}
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%  \item We already saw LaTeX markup support!
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%\end{itemize}
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\begin{lstlisting}
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>>> w = arange(-2,2,.1)
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>>> plot(w,exp(-(w*w))*cos)
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>>> ylabel('$f(\omega)$')
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>>> xlabel('$\omega$')
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>>> title(r"$f(\omega)=e^{-\omega^2}
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            cos({\omega^2})$")
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>>> annotate('maxima',xy=(0, 1), 
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             xytext=(1, 0.8), 
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             arrowprops=dict(
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             facecolor='black', 
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             shrink=0.05))
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\end{lstlisting}
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7
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\end{frame}
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\begin{frame}[fragile]
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  \frametitle{Legends}
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\begin{lstlisting}
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>>> x = linspace(0, 2*pi, 1000)
8
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>>> plot(x, cos(5*x), 'r--', 
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         label='cosine')
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>>> plot(x, sin(5*x), 'g--', 
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         label='sine')
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>>> legend() 
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# Or use:
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>>> legend(['cosine', 'sine'])
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\end{lstlisting}
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diff changeset
   420
\end{frame}
41bdf277c755 Added legend() section.
Shantanu <shantanu@fossee.in>
parents: 7
diff changeset
   421
41bdf277c755 Added legend() section.
Shantanu <shantanu@fossee.in>
parents: 7
diff changeset
   422
\begin{frame}[fragile]
3
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   423
    \frametitle{Multiple figures}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   424
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   425
\begin{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   426
>>> figure(1)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   427
>>> plot(x, sin(x))
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   428
>>> figure(2)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   429
>>> plot(x, tanh(x))
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   430
>>> figure(1)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   431
>>> title('Easy as 1,2,3')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   432
\end{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   433
    
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   434
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   435
\end{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   436
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   437
\begin{frame}[fragile]
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   438
    \frametitle{Note: \typ{pylab} in Python scripts}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   439
\begin{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   440
import pylab
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   441
x = pylab.linspace(0, 20, 1000)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   442
pylab.plot(x, pylab.sin(x))
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   443
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   444
# Can also use:
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   445
from pylab import linspace, sin, plot
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   446
\end{lstlisting}
12
996fb264fbe2 Corrected screwed up merge.
Shantanu <shantanu@fossee.in>
parents: 10
diff changeset
   447
\inctime{5}
3
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   448
\end{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   449
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   450
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   451
\subsection{Types of Plots}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   452
\begin{frame}[fragile]
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   453
  \frametitle{X-Y plot}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   454
  \begin{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   455
    \column{0.5\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   456
    \hspace*{-0.5in}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   457
    \includegraphics[height=2in, interpolate=true]{data/xyplot}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   458
    \column{0.45\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   459
    \begin{block}{Example code}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   460
    \tiny
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   461
\begin{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   462
t1 = arange(0.0, 5.0, 0.1)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   463
t2 = arange(0.0, 5.0, 0.02)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   464
t3 = arange(0.0, 2.0, 0.01)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   465
subplot(211)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   466
plot(t1, cos(2*pi*t1)*exp(-t1), 'bo', 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   467
     t2, cos(2*pi*t2)*exp(-t2), 'k')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   468
grid(True)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   469
title('A tale of 2 subplots')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   470
ylabel('Damped')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   471
subplot(212)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   472
plot(t3, cos(2*pi*t3), 'r--')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   473
grid(True)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   474
xlabel('time (s)')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   475
ylabel('Undamped')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   476
\end{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   477
    \end{block}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   478
  \end{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   479
\end{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   480
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   481
\begin{frame}[fragile] \frametitle{Semi-log and log-log plots}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   482
  \begin{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   483
    \column{0.5\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   484
    \hspace*{-0.5in}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   485
  \includegraphics[height=2in, interpolate=true]{data/log}  
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   486
    \column{0.45\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   487
    \begin{block}{Example code}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   488
    \tiny
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   489
\begin{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   490
dt = 0.01
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   491
t = arange(dt, 20.0, dt)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   492
subplot(311)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   493
semilogy(t, exp(-t/5.0))
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   494
ylabel('semilogy')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   495
grid(True)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   496
subplot(312)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   497
semilogx(t, sin(2*pi*t))
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   498
ylabel('semilogx')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   499
grid(True)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   500
# minor grid on too
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   501
gca().xaxis.grid(True, which='minor')  
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   502
subplot(313)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   503
loglog(t, 20*exp(-t/10.0), basex=4)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   504
grid(True)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   505
ylabel('loglog base 4 on x')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   506
\end{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   507
  \end{block}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   508
\end{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   509
\end{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   510
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   511
\begin{frame}[fragile] \frametitle{Errorbar}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   512
  \begin{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   513
    \column{0.5\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   514
    \hspace*{-0.5in}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   515
  \includegraphics[height=2in, interpolate=true]{data/errorbar}  
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   516
    \column{0.45\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   517
    \begin{block}{Example code}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   518
    \tiny
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   519
\begin{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   520
t = arange(0.1, 4, 0.1)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   521
s = exp(-t)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   522
e = 0.1*abs(randn(len(s)))
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   523
f = 0.1*abs(randn(len(s)))
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   524
g = 2*e
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   525
h = 2*f
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   526
errorbar(t, s, [e,g], f, fmt='o')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   527
xlabel('Distance (m)')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   528
ylabel('Height (m)')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   529
title('Mean and standard error '\
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   530
      'as a function of distance')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   531
\end{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   532
  \end{block}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   533
\end{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   534
\end{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   535
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   536
\begin{frame}[fragile] \frametitle{Histogram}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   537
  \begin{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   538
    \column{0.5\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   539
    \hspace*{-0.5in}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   540
  \includegraphics[height=2in, interpolate=true]{data/histogram}  
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   541
    \column{0.45\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   542
    \begin{block}{Example code}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   543
    \tiny
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   544
\begin{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   545
mu, sigma = 100, 15
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   546
x = mu + sigma*randn(10000)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   547
# the histogram of the data
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   548
n, bins, patches = hist(x, 100, normed=1)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   549
# add a 'best fit' line
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   550
y = normpdf( bins, mu, sigma)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   551
l = plot(bins, y, 'r--', linewidth=2)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   552
xlim(40, 160)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   553
xlabel('Smarts')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   554
ylabel('P')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   555
title(r'$\rm{IQ:}\/ \mu=100,\/ \sigma=15$')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   556
\end{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   557
  \end{block}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   558
\end{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   559
\end{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   560
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   561
\begin{frame}[fragile] \frametitle{Bar charts}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   562
  \begin{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   563
    \column{0.5\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   564
    \hspace*{-0.5in}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   565
  \includegraphics[height=2in, interpolate=true]{data/barchart}  
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   566
    \column{0.45\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   567
    \begin{block}{Example code}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   568
    \tiny
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   569
\begin{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   570
N = 5
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   571
menMeans = (20, 35, 30, 35, 27)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   572
menStd =   ( 2,  3,  4,  1,  2)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   573
# the x locations for the groups
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   574
ind = arange(N) 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   575
# the width of the bars
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   576
width = 0.35       
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   577
p1 = bar(ind, menMeans, width, 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   578
         color='r', yerr=menStd)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   579
womenMeans = (25, 32, 34, 20, 25)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   580
womenStd =   ( 3,  5,  2,  3,  3)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   581
p2 = bar(ind+width, womenMeans, width, 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   582
         color='y', yerr=womenStd)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   583
ylabel('Scores')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   584
title('Scores by group and gender')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   585
xticks(ind+width, 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   586
       ('G1', 'G2', 'G3', 'G4', 'G5'))
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   587
xlim(-width,len(ind))
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   588
yticks(arange(0,41,10))
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   589
legend((p1[0], p2[0]), 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   590
       ('Men', 'Women'), shadow=True)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   591
\end{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   592
  \end{block}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   593
\end{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   594
\end{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   595
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   596
\begin{frame}[fragile] \frametitle{Pie charts}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   597
  \begin{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   598
    \column{0.5\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   599
    \hspace*{-0.4in}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   600
  \includegraphics[height=2.0in, interpolate=true]{data/piechart}  
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   601
    \column{0.45\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   602
    \begin{block}{Example code}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   603
    \tiny
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   604
\begin{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   605
# make a square figure and axes
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   606
figure(1, figsize=(8,8))
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   607
ax = axes([0.1, 0.1, 0.8, 0.8])
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   608
labels = 'Frogs', 'Hogs', 'Dogs', 'Logs'
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   609
fracs = [15,30,45, 10]
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   610
explode=(0, 0.05, 0, 0)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   611
pie(fracs, explode=explode, labels=labels, 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   612
    autopct='%1.1f%%', shadow=True)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   613
title('Raining Hogs and Dogs', 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   614
      bbox={'facecolor':'0.8', 'pad':5})
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   615
\end{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   616
  \end{block}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   617
\end{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   618
\end{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   619
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   620
\begin{frame}[fragile] \frametitle{Scatter plots}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   621
  \begin{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   622
    \column{0.5\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   623
    \hspace*{-0.4in}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   624
  \includegraphics[height=2in, interpolate=true]{data/scatter}  
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   625
    \column{0.45\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   626
    \begin{block}{Example code}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   627
    \tiny
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   628
\begin{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   629
N = 30
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   630
x = 0.9*rand(N)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   631
y = 0.9*rand(N)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   632
# 0 to 10 point radiuses
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   633
area = pi*(10 * rand(N))**2 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   634
volume = 400 + rand(N)*450
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   635
scatter(x,y,s=area, marker='o', c=volume, 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   636
        alpha=0.75)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   637
xlabel(r'$\Delta_i$', size='x-large')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   638
ylabel(r'$\Delta_{i+1}$', size='x-large')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   639
title(r'Volume and percent change')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   640
grid(True)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   641
colorbar()
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   642
savefig('scatter')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   643
\end{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   644
  \end{block}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   645
\end{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   646
\end{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   647
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   648
\begin{frame}[fragile] \frametitle{Polar}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   649
  \begin{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   650
    \column{0.5\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   651
    \hspace*{-0.5in}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   652
  \includegraphics[height=2in, interpolate=true]{data/polar}  
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   653
    \column{0.45\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   654
    \begin{block}{Example code}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   655
    \tiny
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   656
\begin{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   657
figure(figsize=(8,8))
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   658
ax = axes([0.1, 0.1, 0.8, 0.8], 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   659
          polar=True, 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   660
          axisbg='#d5de9c')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   661
r = arange(0,1,0.001)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   662
theta = 2*2*pi*r
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   663
polar(theta, r, color='#ee8d18', lw=3)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   664
# the radius of the grid labels
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   665
setp(ax.thetagridlabels, y=1.075) 
4
e5047bcbb608 Moved Array Math, Creation slides around; Added time counters.
Puneeth Chaganti <punchagan@fossee.in>
parents: 3
diff changeset
   666
title(r'$\theta=4\pi r$', fontsize=20)
3
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   667
\end{lstlisting}
4
e5047bcbb608 Moved Array Math, Creation slides around; Added time counters.
Puneeth Chaganti <punchagan@fossee.in>
parents: 3
diff changeset
   668
3
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   669
  \end{block}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   670
\end{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   671
\end{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   672
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   673
\begin{frame}[fragile] \frametitle{Contours}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   674
  \begin{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   675
    \column{0.45\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   676
    \hspace*{-0.5in}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   677
  \includegraphics[height=2in, interpolate=true]{data/contour}  
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   678
    \column{0.525\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   679
    \begin{block}{Example code}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   680
    \tiny
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   681
\begin{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   682
x = arange(-3.0, 3.0, 0.025)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   683
y = arange(-2.0, 2.0, 0.025)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   684
X, Y = meshgrid(x, y)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   685
Z1 = bivariate_normal(X, Y, 1.0, 1.0, 0.0, 0.0)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   686
Z2 = bivariate_normal(X, Y, 1.5, 0.5, 1, 1)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   687
# difference of Gaussians
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   688
Z = 10.0 * (Z2 - Z1)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   689
im = imshow(Z, interpolation='bilinear', 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   690
            origin='lower',
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   691
            cmap=cm.gray, extent=(-3,3,-2,2))
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   692
levels = arange(-1.2, 1.6, 0.2)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   693
# label every second level
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   694
clabel(CS, levels[1::2],  inline=1,
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   695
       fmt='%1.1f', fontsize=14)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   696
CS = contour(Z, levels,
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   697
             origin='lower',
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   698
             linewidths=2,
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   699
             extent=(-3,3,-2,2))
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   700
# make a colorbar for the contour lines
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   701
CB = colorbar(CS, shrink=0.8, extend='both')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   702
title('Lines with colorbar')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   703
hot(); flag()
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   704
\end{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   705
  \end{block}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   706
\end{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   707
\end{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   708
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   709
\begin{frame}[fragile] \frametitle{Velocity vectors}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   710
  \begin{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   711
    \column{0.5\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   712
    \hspace*{-0.5in}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   713
  \includegraphics[height=2in, interpolate=true]{data/quiver}  
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   714
    \column{0.45\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   715
    \begin{block}{Example code}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   716
    \tiny
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   717
\begin{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   718
X,Y = meshgrid(arange(0,2*pi,.2),
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   719
               arange(0,2*pi,.2) )
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   720
U = cos(X)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   721
V = sin(Y)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   722
Q = quiver(X[::3, ::3], Y[::3, ::3], 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   723
           U[::3, ::3], V[::3, ::3],
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   724
           color='r', units='x', 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   725
           linewidths=(2,), 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   726
           edgecolors=('k'), 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   727
           headaxislength=5 )
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   728
qk = quiverkey(Q, 0.5, 0.03, 1, '1 m/s', 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   729
               fontproperties=
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   730
               {'weight': 'bold'})
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   731
axis([-1, 7, -1, 7])
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   732
title('triangular head; scale '\
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   733
      'with x view; black edges')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   734
\end{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   735
  \end{block}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   736
\end{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   737
\end{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   738
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   739
\begin{frame}[fragile] \frametitle{Maps}
8
41bdf277c755 Added legend() section.
Shantanu <shantanu@fossee.in>
parents: 7
diff changeset
   740
  \includegraphics[height=2.3in, interpolate=true]{data/plotmap}  
3
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   741
  \begin{center}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   742
    \tiny
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   743
    For details see \url{http://matplotlib.sourceforge.net/screenshots/plotmap.py}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   744
  \end{center}
12
996fb264fbe2 Corrected screwed up merge.
Shantanu <shantanu@fossee.in>
parents: 10
diff changeset
   745
\inctime{5}
3
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   746
\end{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   747
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   748
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   749
\begin{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   750
  \frametitle{More information}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   751
  \begin{itemize}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   752
  \item More information here: \url{http://matplotlib.sf.net}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   753
  \item \url{http://matplotlib.sf.net/tutorial.html}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   754
  \item \url{http://matplotlib.sf.net/screenshots.html}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   755
  \end{itemize}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   756
\end{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   757
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   758
\begin{frame}
9
2281002b579b Edited Problem Sets - Added cobweb plot; Removed Koch.
Puneeth Chaganti <punchagan@fossee.in>
parents: 6
diff changeset
   759
  \frametitle{Problem Set}
3
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   760
  \begin{enumerate}
20
84458ebb6951 Modified numpy array parts.
Shantanu <shantanu@fossee.in>
parents: 12
diff changeset
   761
      \item Write a function that plots any regular n-gon given \typ{n}.
3
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   762
      \item Consider the logistic map, $f(x) = kx(1-x)$, plot it for
20
84458ebb6951 Modified numpy array parts.
Shantanu <shantanu@fossee.in>
parents: 12
diff changeset
   763
          $k=2.5, 3.5$ and $4$ in the same plot.
3
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   764
\end{enumerate}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   765
\end{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   766
9
2281002b579b Edited Problem Sets - Added cobweb plot; Removed Koch.
Puneeth Chaganti <punchagan@fossee.in>
parents: 6
diff changeset
   767
\begin{frame}[fragile] 
2281002b579b Edited Problem Sets - Added cobweb plot; Removed Koch.
Puneeth Chaganti <punchagan@fossee.in>
parents: 6
diff changeset
   768
\frametitle{Problem Set}
2281002b579b Edited Problem Sets - Added cobweb plot; Removed Koch.
Puneeth Chaganti <punchagan@fossee.in>
parents: 6
diff changeset
   769
  \begin{columns}
2281002b579b Edited Problem Sets - Added cobweb plot; Removed Koch.
Puneeth Chaganti <punchagan@fossee.in>
parents: 6
diff changeset
   770
    \column{0.6\textwidth}
2281002b579b Edited Problem Sets - Added cobweb plot; Removed Koch.
Puneeth Chaganti <punchagan@fossee.in>
parents: 6
diff changeset
   771
    \small{
2281002b579b Edited Problem Sets - Added cobweb plot; Removed Koch.
Puneeth Chaganti <punchagan@fossee.in>
parents: 6
diff changeset
   772
    \begin{enumerate}
3
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   773
      \item Consider the iteration $x_{n+1} = f(x_n)$ where $f(x) =
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   774
          kx(1-x)$.  Plot the successive iterates of this process.
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   775
      \item Plot this using a cobweb plot as follows:
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   776
          \begin{enumerate}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   777
              \item Start at $(x_0, 0)$
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   778
              \item Draw line to $(x_i, f(x_i))$; 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   779
              \item Set $x_{i+1} = f(x_i)$
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   780
              \item Draw line to $(x_i, x_i)$
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   781
              \item Repeat from 2 for as long as you want 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   782
          \end{enumerate}
9
2281002b579b Edited Problem Sets - Added cobweb plot; Removed Koch.
Puneeth Chaganti <punchagan@fossee.in>
parents: 6
diff changeset
   783
    \end{enumerate}}
2281002b579b Edited Problem Sets - Added cobweb plot; Removed Koch.
Puneeth Chaganti <punchagan@fossee.in>
parents: 6
diff changeset
   784
    \column{0.35\textwidth}
2281002b579b Edited Problem Sets - Added cobweb plot; Removed Koch.
Puneeth Chaganti <punchagan@fossee.in>
parents: 6
diff changeset
   785
    \hspace*{-0.5in}
2281002b579b Edited Problem Sets - Added cobweb plot; Removed Koch.
Puneeth Chaganti <punchagan@fossee.in>
parents: 6
diff changeset
   786
  \includegraphics[height=1.6in, interpolate=true]{data/cobweb}  
2281002b579b Edited Problem Sets - Added cobweb plot; Removed Koch.
Puneeth Chaganti <punchagan@fossee.in>
parents: 6
diff changeset
   787
\end{columns}
2281002b579b Edited Problem Sets - Added cobweb plot; Removed Koch.
Puneeth Chaganti <punchagan@fossee.in>
parents: 6
diff changeset
   788
\inctime{20}
3
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   789
\end{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   790
\end{document}