day2/session1.tex
author Puneeth Chaganti <punchagan@fossee.in>
Fri, 02 Oct 2009 18:02:38 +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) 2005-2008, 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]{\texttt{#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[Asokan \& Prabhu] {Asokan Pichai\\Prabhu Ramachandran}
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\institute[FOSSEE] {FOSSEE Team}
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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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\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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  \item Indices, slicing: just like lists 
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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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\inctime{10}
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\end{frame}
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\begin{frame}
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    {More Numpy}
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    \begin{itemize}
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        \item Multi-dimensional arrays
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        \item Random number generation
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    \end{itemize}
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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{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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\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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\subsection{Array creation }
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\begin{frame}[fragile]
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  \frametitle{Array creation functions}
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  \begin{itemize}
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  \item \typ{array(object, dtype=None, \ldots)}
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  \item \typ{arange(start, stop=None, step=1 \ldots)}
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  \item \typ{linspace(start, stop, num=50, \ldots)}
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  \item \typ{ones(shape, dtype=None, \ldots)}
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  \item \typ{zeros(shape, dtype=float,\ldots)}
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  \item \typ{identity(n)}
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  \item \typ{empty(shape, dtype=float,\ldots)}
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  \item \typ{ones\_like(x)}, 
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  \item \typ{zeros\_like(x)}, \typ{empty\_like(x)}
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  \end{itemize}
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\end{frame}
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\subsection{Array math}
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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,
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      a)} etc.
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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), arcsin(x), sinh(x),
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      exp(x), sqrt(x)} etc.
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  \item \typ{sum(x, axis=0), product(x, axis=0)} 
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  \item \typ{dot(a, bp)}
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  \end{itemize}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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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{itemize}
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    \item \typ{pylab}: convenient 2D plotting interface to MPL
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    \item Immediate use: \typ{ipython -pylab}
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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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\end{frame}
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\subsection{Playing with lines}
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\begin{frame}[fragile]
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  \frametitle{Basic plotting \ldots}
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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{Multiple figures}
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\begin{lstlisting}
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>>> figure(1)
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>>> plot(x, sin(x))
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>>> figure(2)
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>>> plot(x, tanh(x))
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>>> figure(1)
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>>> title('Easy as 1,2,3')
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\end{lstlisting}
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\end{frame}
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\subsection{Handling Text}
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\begin{frame}[fragile]
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  \frametitle{Legends and Annotation}
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\begin{lstlisting}
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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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# Annotation:
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>>> text(1,0, '(1,0)')
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\end{lstlisting}
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\end{frame}
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\begin{frame}[fragile]
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    \frametitle{More commands \ldots}
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    \begin{lstlisting}
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# semilog, loglog 
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>>> x = 10.**(-arange(100)*0.1)
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>>> semilogx(x, x)
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>>> semilogy(x, x)
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>>> loglog(x, x)
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>>> loglog(x, x*x)
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    \end{lstlisting}
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\end{frame}
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\begin{frame}[fragile]
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    \frametitle{More plots \ldots}
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    \begin{lstlisting}
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>>> clf()
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>>> t = arange(0.1, 4, 0.1)
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>>> s = exp(-t)
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>>> e = 0.1*abs(randn(len(s)))
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>>> errorbar(t, s, e)
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# Scatter plots
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>>> clf()
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>>> t = randn(len(e))
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>>> scatter(t, e, c=s)
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    \end{lstlisting}
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\end{frame}
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\begin{frame}[fragile]
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    \frametitle{Note: \typ{pylab} in Python scripts}
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\begin{lstlisting}
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import pylab
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x = pylab.linspace(0, 20, 1000)
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pylab.plot(x, pylab.sin(x))
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   397
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# Can also use:
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   399
from pylab import linspace, sin, plot
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\end{lstlisting}
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\end{frame}
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   402
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   403
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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   404
\subsection{Types of Plots}
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\begin{frame}[fragile]
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   406
  \frametitle{X-Y plot}
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   407
  \begin{columns}
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   408
    \column{0.5\textwidth}
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   409
    \hspace*{-0.5in}
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   410
    \includegraphics[height=2in, interpolate=true]{data/xyplot}
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   411
    \column{0.45\textwidth}
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   412
    \begin{block}{Example code}
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   413
    \tiny
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   414
\begin{lstlisting}
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   415
t1 = arange(0.0, 5.0, 0.1)
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   416
t2 = arange(0.0, 5.0, 0.02)
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   417
t3 = arange(0.0, 2.0, 0.01)
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   418
subplot(211)
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   419
plot(t1, cos(2*pi*t1)*exp(-t1), 'bo', 
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   420
     t2, cos(2*pi*t2)*exp(-t2), 'k')
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   421
grid(True)
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   422
title('A tale of 2 subplots')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   423
ylabel('Damped')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   424
subplot(212)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   425
plot(t3, cos(2*pi*t3), 'r--')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   426
grid(True)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   427
xlabel('time (s)')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   428
ylabel('Undamped')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   429
\end{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   430
    \end{block}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   431
  \end{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   432
\end{frame}
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
\begin{frame}[fragile] \frametitle{Semi-log and log-log plots}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   435
  \begin{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   436
    \column{0.5\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   437
    \hspace*{-0.5in}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   438
  \includegraphics[height=2in, interpolate=true]{data/log}  
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   439
    \column{0.45\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   440
    \begin{block}{Example code}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   441
    \tiny
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   442
\begin{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   443
dt = 0.01
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   444
t = arange(dt, 20.0, dt)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   445
subplot(311)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   446
semilogy(t, exp(-t/5.0))
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   447
ylabel('semilogy')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   448
grid(True)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   449
subplot(312)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   450
semilogx(t, sin(2*pi*t))
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   451
ylabel('semilogx')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   452
grid(True)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   453
# minor grid on too
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   454
gca().xaxis.grid(True, which='minor')  
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   455
subplot(313)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   456
loglog(t, 20*exp(-t/10.0), basex=4)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   457
grid(True)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   458
ylabel('loglog base 4 on x')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   459
\end{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   460
  \end{block}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   461
\end{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   462
\end{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   463
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   464
\begin{frame}[fragile] \frametitle{Errorbar}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   465
  \begin{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   466
    \column{0.5\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   467
    \hspace*{-0.5in}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   468
  \includegraphics[height=2in, interpolate=true]{data/errorbar}  
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   469
    \column{0.45\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   470
    \begin{block}{Example code}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   471
    \tiny
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   472
\begin{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   473
t = arange(0.1, 4, 0.1)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   474
s = exp(-t)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   475
e = 0.1*abs(randn(len(s)))
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   476
f = 0.1*abs(randn(len(s)))
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   477
g = 2*e
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   478
h = 2*f
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   479
errorbar(t, s, [e,g], f, fmt='o')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   480
xlabel('Distance (m)')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   481
ylabel('Height (m)')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   482
title('Mean and standard error '\
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   483
      'as a function of distance')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   484
\end{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   485
  \end{block}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   486
\end{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   487
\end{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   488
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   489
\begin{frame}[fragile] \frametitle{Histogram}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   490
  \begin{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   491
    \column{0.5\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   492
    \hspace*{-0.5in}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   493
  \includegraphics[height=2in, interpolate=true]{data/histogram}  
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   494
    \column{0.45\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   495
    \begin{block}{Example code}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   496
    \tiny
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   497
\begin{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   498
mu, sigma = 100, 15
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   499
x = mu + sigma*randn(10000)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   500
# the histogram of the data
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   501
n, bins, patches = hist(x, 100, normed=1)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   502
# add a 'best fit' line
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   503
y = normpdf( bins, mu, sigma)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   504
l = plot(bins, y, 'r--', linewidth=2)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   505
xlim(40, 160)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   506
xlabel('Smarts')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   507
ylabel('P')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   508
title(r'$\rm{IQ:}\/ \mu=100,\/ \sigma=15$')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   509
\end{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   510
  \end{block}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   511
\end{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   512
\end{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   513
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   514
\begin{frame}[fragile] \frametitle{Bar charts}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   515
  \begin{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   516
    \column{0.5\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   517
    \hspace*{-0.5in}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   518
  \includegraphics[height=2in, interpolate=true]{data/barchart}  
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   519
    \column{0.45\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   520
    \begin{block}{Example code}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   521
    \tiny
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   522
\begin{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   523
N = 5
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   524
menMeans = (20, 35, 30, 35, 27)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   525
menStd =   ( 2,  3,  4,  1,  2)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   526
# the x locations for the groups
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   527
ind = arange(N) 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   528
# the width of the bars
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   529
width = 0.35       
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   530
p1 = bar(ind, menMeans, width, 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   531
         color='r', yerr=menStd)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   532
womenMeans = (25, 32, 34, 20, 25)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   533
womenStd =   ( 3,  5,  2,  3,  3)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   534
p2 = bar(ind+width, womenMeans, width, 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   535
         color='y', yerr=womenStd)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   536
ylabel('Scores')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   537
title('Scores by group and gender')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   538
xticks(ind+width, 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   539
       ('G1', 'G2', 'G3', 'G4', 'G5'))
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   540
xlim(-width,len(ind))
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   541
yticks(arange(0,41,10))
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   542
legend((p1[0], p2[0]), 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   543
       ('Men', 'Women'), shadow=True)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   544
\end{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   545
  \end{block}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   546
\end{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   547
\end{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   548
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   549
\begin{frame}[fragile] \frametitle{Pie charts}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   550
  \begin{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   551
    \column{0.5\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   552
    \hspace*{-0.4in}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   553
  \includegraphics[height=2.0in, interpolate=true]{data/piechart}  
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   554
    \column{0.45\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   555
    \begin{block}{Example code}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   556
    \tiny
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   557
\begin{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   558
# make a square figure and axes
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   559
figure(1, figsize=(8,8))
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   560
ax = axes([0.1, 0.1, 0.8, 0.8])
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   561
labels = 'Frogs', 'Hogs', 'Dogs', 'Logs'
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   562
fracs = [15,30,45, 10]
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   563
explode=(0, 0.05, 0, 0)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   564
pie(fracs, explode=explode, labels=labels, 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   565
    autopct='%1.1f%%', shadow=True)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   566
title('Raining Hogs and Dogs', 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   567
      bbox={'facecolor':'0.8', 'pad':5})
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   568
\end{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   569
  \end{block}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   570
\end{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   571
\end{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   572
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   573
\begin{frame}[fragile] \frametitle{Scatter plots}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   574
  \begin{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   575
    \column{0.5\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   576
    \hspace*{-0.4in}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   577
  \includegraphics[height=2in, interpolate=true]{data/scatter}  
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   578
    \column{0.45\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   579
    \begin{block}{Example code}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   580
    \tiny
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   581
\begin{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   582
N = 30
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   583
x = 0.9*rand(N)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   584
y = 0.9*rand(N)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   585
# 0 to 10 point radiuses
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   586
area = pi*(10 * rand(N))**2 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   587
volume = 400 + rand(N)*450
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   588
scatter(x,y,s=area, marker='o', c=volume, 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   589
        alpha=0.75)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   590
xlabel(r'$\Delta_i$', size='x-large')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   591
ylabel(r'$\Delta_{i+1}$', size='x-large')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   592
title(r'Volume and percent change')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   593
grid(True)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   594
colorbar()
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   595
savefig('scatter')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   596
\end{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   597
  \end{block}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   598
\end{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   599
\end{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   600
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   601
\begin{frame}[fragile] \frametitle{Polar}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   602
  \begin{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   603
    \column{0.5\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   604
    \hspace*{-0.5in}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   605
  \includegraphics[height=2in, interpolate=true]{data/polar}  
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   606
    \column{0.45\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   607
    \begin{block}{Example code}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   608
    \tiny
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   609
\begin{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   610
figure(figsize=(8,8))
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   611
ax = axes([0.1, 0.1, 0.8, 0.8], 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   612
          polar=True, 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   613
          axisbg='#d5de9c')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   614
r = arange(0,1,0.001)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   615
theta = 2*2*pi*r
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   616
polar(theta, r, color='#ee8d18', lw=3)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   617
# the radius of the grid labels
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   618
setp(ax.thetagridlabels, y=1.075) 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   619
title(r"$\theta=4\pi r", fontsize=20)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   620
\end{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   621
  \end{block}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   622
\end{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   623
\end{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   624
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   625
\begin{frame}[fragile] \frametitle{Contours}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   626
  \begin{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   627
    \column{0.45\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   628
    \hspace*{-0.5in}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   629
  \includegraphics[height=2in, interpolate=true]{data/contour}  
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   630
    \column{0.525\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   631
    \begin{block}{Example code}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   632
    \tiny
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   633
\begin{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   634
x = arange(-3.0, 3.0, 0.025)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   635
y = arange(-2.0, 2.0, 0.025)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   636
X, Y = meshgrid(x, y)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   637
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
   638
Z2 = bivariate_normal(X, Y, 1.5, 0.5, 1, 1)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   639
# difference of Gaussians
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   640
Z = 10.0 * (Z2 - Z1)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   641
im = imshow(Z, interpolation='bilinear', 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   642
            origin='lower',
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   643
            cmap=cm.gray, extent=(-3,3,-2,2))
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   644
levels = arange(-1.2, 1.6, 0.2)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   645
# label every second level
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   646
clabel(CS, levels[1::2],  inline=1,
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   647
       fmt='%1.1f', fontsize=14)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   648
CS = contour(Z, levels,
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   649
             origin='lower',
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   650
             linewidths=2,
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   651
             extent=(-3,3,-2,2))
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   652
# make a colorbar for the contour lines
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   653
CB = colorbar(CS, shrink=0.8, extend='both')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   654
title('Lines with colorbar')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   655
hot(); flag()
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   656
\end{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   657
  \end{block}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   658
\end{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   659
\end{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   660
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   661
\begin{frame}[fragile] \frametitle{Velocity vectors}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   662
  \begin{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   663
    \column{0.5\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   664
    \hspace*{-0.5in}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   665
  \includegraphics[height=2in, interpolate=true]{data/quiver}  
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   666
    \column{0.45\textwidth}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   667
    \begin{block}{Example code}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   668
    \tiny
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   669
\begin{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   670
X,Y = meshgrid(arange(0,2*pi,.2),
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   671
               arange(0,2*pi,.2) )
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   672
U = cos(X)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   673
V = sin(Y)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   674
Q = quiver(X[::3, ::3], Y[::3, ::3], 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   675
           U[::3, ::3], V[::3, ::3],
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   676
           color='r', units='x', 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   677
           linewidths=(2,), 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   678
           edgecolors=('k'), 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   679
           headaxislength=5 )
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   680
qk = quiverkey(Q, 0.5, 0.03, 1, '1 m/s', 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   681
               fontproperties=
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   682
               {'weight': 'bold'})
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   683
axis([-1, 7, -1, 7])
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   684
title('triangular head; scale '\
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   685
      'with x view; black edges')
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   686
\end{lstlisting}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   687
  \end{block}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   688
\end{columns}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   689
\end{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   690
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   691
\begin{frame}[fragile] \frametitle{Maps}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   692
  \includegraphics[height=2.5in, interpolate=true]{data/plotmap}  
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   693
  \begin{center}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   694
    \tiny
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   695
    For details see \url{http://matplotlib.sourceforge.net/screenshots/plotmap.py}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   696
  \end{center}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   697
\end{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   698
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   699
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   700
\begin{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   701
  \frametitle{More information}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   702
  \begin{itemize}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   703
  \item More information here: \url{http://matplotlib.sf.net}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   704
  \item \url{http://matplotlib.sf.net/tutorial.html}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   705
  \item \url{http://matplotlib.sf.net/screenshots.html}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   706
  \end{itemize}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   707
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   708
  \inctime{25}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   709
\end{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   710
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   711
\begin{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   712
  \frametitle{Problem set 1.0}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   713
  \begin{enumerate}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   714
      \item Write a function that plots any n-gon given \typ{n}.
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   715
      \item Consider the logistic map, $f(x) = kx(1-x)$, plot it for
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   716
          $k=2.5, 3.5$ and $4$
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   717
\end{enumerate}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   718
\end{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   719
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   720
\begin{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   721
  \frametitle{Problem set 1.1}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   722
  \begin{enumerate}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   723
      \item Consider the iteration $x_{n+1} = f(x_n)$ where $f(x) =
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   724
          kx(1-x)$.  Plot the successive iterates of this process.
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   725
      \item Plot this using a cobweb plot as follows:
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   726
          \begin{enumerate}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   727
              \item Start at $(x_0, 0)$
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   728
              \item Draw line to $(x_i, f(x_i))$; 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   729
              \item Set $x_{i+1} = f(x_i)$
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   730
              \item Draw line to $(x_i, x_i)$
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   731
              \item Repeat from 2 for as long as you want 
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   732
          \end{enumerate}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   733
    \end{enumerate}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   734
\end{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   735
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   736
\begin{frame}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   737
  \frametitle{Problem set 1.2}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   738
  \begin{enumerate}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   739
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   740
      \item Plot the Koch snowflake.  Write a function to generate the
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   741
          necessary points given the two points constituting a line.
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   742
          \pause
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   743
          \begin{enumerate}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   744
              \item Split the line into 4 segments.
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   745
              \item The first and last segments are trivial.
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   746
              \item To rotate the point you can use complex numbers,
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   747
                  recall that $z e^{j \theta}$ rotates a point $z$ in 2D
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   748
                  by $\theta$.
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   749
              \item Do this for all line segments till everything is
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   750
                  done.
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   751
          \end{enumerate}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   752
      \item Show rate of convergence for a first and second order finite
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   753
          difference of sin(x)
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   754
\end{enumerate}
18a010e4caa0 Added day2 session1.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   755
\inctime{30}
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
\end{document}