day1/session3.tex
author Madhusudan.C.S <madhusudancs@gmail.com>
Wed, 28 Oct 2009 16:01:13 +0530
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Added sections, subsections and time estimates for session 3 day 1.
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%Tutorial slides on Python.
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%
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% Author: FOSSEE
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% Copyright (c) 2009, FOSSEE, IIT Bombay
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\documentclass[14pt,compress]{beamer}
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%\documentclass[draft]{beamer}
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%\documentclass[compress,handout]{beamer}
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%\usepackage{pgfpages} 
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%\pgfpagesuselayout{2 on 1}[a4paper,border shrink=5mm]
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% Modified from: generic-ornate-15min-45min.de.tex
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\mode<presentation>
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{
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  \usetheme{Warsaw}
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  \useoutertheme{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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\usepackage{amsmath}
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\definecolor{darkgreen}{rgb}{0,0.5,0}
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\usepackage{listings}
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\lstset{language=Python,
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    basicstyle=\ttfamily\bfseries,
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    commentstyle=\color{red}\itshape,
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  stringstyle=\color{darkgreen},
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  showstringspaces=false,
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  keywordstyle=\color{blue}\bfseries}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Macros
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\setbeamercolor{emphbar}{bg=blue!20, fg=black}
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\newcommand{\emphbar}[1]
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{\begin{beamercolorbox}[rounded=true]{emphbar} 
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      {#1}
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 \end{beamercolorbox}
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}
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\newcounter{time}
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\setcounter{time}{0}
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\newcommand{\inctime}[1]{\addtocounter{time}{#1}{\tiny \thetime\ m}}
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\newcommand{\typ}[1]{\lstinline{#1}}
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\newcommand{\kwrd}[1]{ \texttt{\textbf{\color{blue}{#1}}}  }
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%%% This is from Fernando's setup.
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% \usepackage{color}
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% \definecolor{orange}{cmyk}{0,0.4,0.8,0.2}
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% % Use and configure listings package for nicely formatted code
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% \usepackage{listings}
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% \lstset{
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%    language=Python,
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%    basicstyle=\small\ttfamily,
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%    commentstyle=\ttfamily\color{blue},
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%    stringstyle=\ttfamily\color{orange},
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%    showstringspaces=false,
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%    breaklines=true,
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%    postbreak = \space\dots
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% }
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Title page
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\title[Statistics]{Python for Science and Engg. Statistics}
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\author[FOSSEE] {FOSSEE}
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\institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
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\date[] {31, October 2009\\Day 1, Session 3}
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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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\newcommand{\num}{\texttt{numpy}}
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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{Statistics}
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\begin{frame}
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  \frametitle{More on data processing}
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  \begin{block}{}
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    We have a huge--1m records--data file.\\How do we do \emph{efficient} statistical computations, that is find mean, median, mode, standard deveiation etc; draw pie charts?
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  \end{block}
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\end{frame}
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\begin{frame}
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  \frametitle{Statistical Analysis and Parsing}
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  Read the data supplied in \emph{sslc1.txt} and obtain the following statistics:
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  \begin{itemize}
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    \item Draw a pie chart representing the number of students who scored more than 90\% in Science per region.
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    \item Draw a pie chart representing the number of students who scored more than 90\% per subject(All regions combined).
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    \item Print mean, median, mode and standard deviation of math scores for all regions combined.
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  \end{itemize}
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\end{frame}
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\begin{frame}
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  \frametitle{Statistical Analysis and Parsing \ldots}
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  Machinery Required -
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  \begin{itemize}
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    \item File reading
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    \item Parsing
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    \item Dictionaries
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    \item NumPy arrays
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    \item Statistical operations
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  \end{itemize}
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\end{frame}
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\begin{frame}
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  \frametitle{File reading and parsing}
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  Understanding the structure of sslc1.txt
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  \begin{itemize}
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    \item Each line in the file corresponds to one student's details
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    \item aka record
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    \item Each record consists of several fields separated by a ';'
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  \end{itemize}
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\end{frame}
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\begin{frame}
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  \frametitle{File reading and parsing \ldots}
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  Each record consists of:
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  \begin{itemize}
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    \item Region Code
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    \item Roll Number
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    \item Name
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    \item Marks of 5 subjects: English, Hindi, Maths, Science, Social
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    \item Total marks
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    \item Pass/Fail (P/F)
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    \item Withdrawn (W)
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  \end{itemize}
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  \inctime{5}
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\end{frame}
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229
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\subsection{Data processing}
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\begin{frame}[fragile]
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  \frametitle{File reading and parsing \ldots}
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  \begin{lstlisting}
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for record in open('sslc1.txt'):
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    fields = record.split(';')
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  \end{lstlisting}
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\end{frame}
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229
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\subsection{Dictionary}
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\begin{frame}[fragile]
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  \frametitle{Dictionary: Introduction}
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  \begin{itemize}
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    \item lists index: 0 \ldots n
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    \item dictionaries index using strings
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  \end{itemize}
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  \begin{block}{Example}
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d = \{ ``Hitchhiker's guide'' : 42,
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     ``Terminator'' : ``I'll be back''\}\\
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d[``Terminator''] => ``I'll be back''
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  \end{block}
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\end{frame}
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\begin{frame}[fragile]
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  \frametitle{Dictionary: Introduction}
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  \begin{lstlisting}
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In [1]: d = {"Hitchhiker's guide" : 42,
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      "Terminator" : "I'll be back"}
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In [2]: d["Hitchhiker's guide"]
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Out[2]: 42
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In [3]: "Hitchhiker's guide" in d
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Out[3]: True
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In [4]: "Guido" in d
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Out[4]: False
229
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  \end{lstlisting}
120
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\end{frame}
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\begin{frame}[fragile]
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  \frametitle{Dictionary: Introduction}
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  \begin{lstlisting}
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In [5]: d.keys()
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Out[5]: ['Terminator', "Hitchhiker's 
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                              guide"]
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In [6]: d.values()
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Out[6]: ["I'll be back", 42]
229
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  \end{lstlisting}
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\end{frame}
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\begin{frame}[fragile]
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  \frametitle{enumerate: Iterating through list indices}
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  \begin{lstlisting}
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In [1]: names = ["Guido","Alex", "Tim"]
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In [2]: for i, name in enumerate(names):
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   ...:     print i, name
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   ...: 
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0 Guido
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1 Alex
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2 Tim
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  \end{lstlisting}
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  \inctime{5}
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\end{frame}
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\begin{frame}[fragile]
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  \frametitle{Dictionary: Building parsed data}
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  Let our dictionary be:
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  \begin{lstlisting}
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science = {} # is an empty dictionary
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  \end{lstlisting}
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\end{frame}
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\begin{frame}[fragile]
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  \frametitle{Dictionary - Building parsed data}
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  \begin{itemize}
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    \item \emph{Keys} of \emph{science} will be region codes
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    \item Value of a \emph{science} will be the number students who scored more than 90\% in that region
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  \end{itemize}
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\end{frame}
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\begin{frame}[fragile]
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  \frametitle{Building parsed data \ldots}
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  \begin{lstlisting}
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from pylab import pie
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204
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science = {}
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for record in open('sslc1.txt'):
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    record = record.strip()
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    fields = record.split(';')
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    region_code = fields[0].strip()
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  \end{lstlisting}
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\end{frame}
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\begin{frame}[fragile]
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  \frametitle{Building parsed data \ldots}
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  \begin{lstlisting}
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if region_code not in science:
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    science[region_code] = 0
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score_str = fields[4].strip()
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score = int(score_str) if
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    score_str != 'AA' else 0
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if score > 90:
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    science[region_code] += 1
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  \end{lstlisting}
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\end{frame}
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\subsection{Visualizing the data}
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\begin{frame}[fragile]
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  \frametitle{Pie charts}
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  \small
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  \begin{lstlisting}
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figure(1)
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pie(science.values(), 
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    labels=science.keys())
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title('Students scoring 90% and above 
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      in science by region')
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savefig('/tmp/science.png')
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  \end{lstlisting}
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\begin{columns}
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    \column{5.25\textwidth}
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    \hspace*{1.1in}
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\includegraphics[height=2in, interpolate=true]{data/science}
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    \column{0.8\textwidth}
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\end{columns}
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  \inctime{5}
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\end{frame}
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\begin{frame}[fragile]
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  \frametitle{Building data for all subjects \ldots}
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  \begin{lstlisting}
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from pylab import pie
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from scipy import mean, median, std
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from scipy import stats
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216
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scores = [[], [], [], [], []]
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ninety_percents = [{}, {}, {}, {}, {}]
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  \end{lstlisting}
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\end{frame}
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\begin{frame}[fragile]
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  \frametitle{Building data for all subjects \ldots}
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  \begin{lstlisting}
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for record in open('sslc1.txt'):
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    record = record.strip()
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    fields = record.split(';')
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    region_code = fields[0].strip()
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  \end{lstlisting}
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\end{frame}
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\begin{frame}[fragile]
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  \frametitle{Building data for all subjects \ldots}
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  \small
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  \begin{lstlisting}
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for i, field in enumerate(fields[3:8]):
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    if region_code not in ninety_percents[i]:
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        ninety_percents[i][region_code] = 0
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    score_str = field.strip()
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    score = int(score_str) if
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      score_str != 'AA' else 0
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204
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    scores[i].append(score)
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    if score > 90:
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        ninety_percents[i][region_code] += 1
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  \end{lstlisting}
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\end{frame}
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125
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\begin{frame}[fragile]
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  \frametitle{Consolidating data}
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  \begin{lstlisting}
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subj_total = []
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for subject in ninety_percents:
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    subj_total.append(sum(
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         subject.values()))
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  \end{lstlisting}
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\end{frame}
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\begin{frame}[fragile]
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  \frametitle{Pie charts}
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  \begin{lstlisting}
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figure(2)
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pie(subj_total, labels=['English',
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    'Hindi', 'Maths', 'Science',
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    'Social'])
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title('Students scoring more than
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      90% by subject(All regions
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      combined).')
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savefig('/tmp/all_regions.png')
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  \end{lstlisting}
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\end{frame}
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166
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\begin{frame}[fragile]
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  \frametitle{Pie charts}
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  \includegraphics[height=3in, interpolate=true]{data/all_regions}
166
ddfd95133adc Taken task based approach for Session 3, day 1.
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parents: 161
diff changeset
   389
\end{frame}
ddfd95133adc Taken task based approach for Session 3, day 1.
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parents: 161
diff changeset
   390
229
5541c47bc2e8 Added sections, subsections and time estimates for session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 216
diff changeset
   391
\subsection{Obtaining stastics}
174
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   392
\begin{frame}[fragile]
204
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
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parents: 192
diff changeset
   393
  \frametitle{Obtaining statistics}
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
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parents: 192
diff changeset
   394
  \begin{lstlisting}
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
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parents: 192
diff changeset
   395
math_scores = array(scores[2])
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
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parents: 192
diff changeset
   396
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
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parents: 192
diff changeset
   397
print "Mean: ", mean(math_scores)
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
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parents: 192
diff changeset
   398
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
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parents: 192
diff changeset
   399
print "Median: ", median(math_scores)
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   400
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
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parents: 192
diff changeset
   401
print "Mode: ", stats.mode(math_scores)
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   402
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   403
print "Standard Deviation: ",
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   404
              std(math_scores)
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
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parents: 192
diff changeset
   405
  \end{lstlisting}
229
5541c47bc2e8 Added sections, subsections and time estimates for session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 216
diff changeset
   406
  \inctime{15}
204
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
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parents: 192
diff changeset
   407
\end{frame}
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
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parents: 192
diff changeset
   408
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   409
\begin{frame}[fragile]
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
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parents: 192
diff changeset
   410
  \frametitle{What tools did we use?}
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
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parents: 192
diff changeset
   411
  \begin{itemize}
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
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parents: 192
diff changeset
   412
   \item Dictionaries for storing data
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
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parents: 192
diff changeset
   413
   \item Facilities for drawing pie charts
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   414
   \item NumPy arrays for efficient array manipulations
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   415
   \item Functions for statistical computations - mean, median, mode, standard deviation
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   416
  \end{itemize}
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   417
\end{frame}
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   418
208
c663c8daa109 Reorganized slides of session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 205
diff changeset
   419
\begin{frame}
c663c8daa109 Reorganized slides of session 3 day 1.
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parents: 205
diff changeset
   420
\frametitle{L vs $T^2$ \ldots}
c663c8daa109 Reorganized slides of session 3 day 1.
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parents: 205
diff changeset
   421
Let's go back to the L vs $T^2$ plot
c663c8daa109 Reorganized slides of session 3 day 1.
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parents: 205
diff changeset
   422
\begin{itemize}
c663c8daa109 Reorganized slides of session 3 day 1.
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parents: 205
diff changeset
   423
\item We first look at obtaining $T^2$ from T
c663c8daa109 Reorganized slides of session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 205
diff changeset
   424
\item Then, we look at plotting a Least Squares fit
c663c8daa109 Reorganized slides of session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 205
diff changeset
   425
\end{itemize}
c663c8daa109 Reorganized slides of session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 205
diff changeset
   426
\end{frame}
c663c8daa109 Reorganized slides of session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 205
diff changeset
   427
204
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
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parents: 192
diff changeset
   428
\begin{frame}[fragile]
178
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   429
\frametitle{Dealing with data whole-sale}
174
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   430
\begin{lstlisting}
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   431
In []: for t in T:
185
e59ab9ab1a89 Manual Merge with Mainline.
Puneeth Chaganti <punchagan@fossee.in>
parents: 184
diff changeset
   432
 ....:     TSq.append(t*t)
174
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   433
\end{lstlisting}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   434
\begin{itemize}
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   435
\item This is not very efficient
178
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   436
\item We are squaring element after element
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   437
\item We use arrays to make this efficient
174
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   438
\end{itemize}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   439
\begin{lstlisting}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   440
In []: L = array(L)
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   441
In []: T = array(T)
185
e59ab9ab1a89 Manual Merge with Mainline.
Puneeth Chaganti <punchagan@fossee.in>
parents: 184
diff changeset
   442
In []: TSq = T*T
174
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   443
\end{lstlisting}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   444
\end{frame}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   445
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   446
\begin{frame}[fragile]
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   447
\frametitle{Arrays}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   448
\begin{itemize}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   449
\item \typ{T} and \typ{L} are now arrays
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   450
\item arrays are very efficient and powerful 
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   451
\item Very easy to perform element-wise operations
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   452
\item \typ{+, -, *, /, \%}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   453
\item More about arrays later
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   454
\end{itemize}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   455
\end{frame}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   456
178
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   457
\begin{frame}[fragile]
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   458
\frametitle{Least Squares Fit}
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   459
\vspace{-0.15in}
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   460
\begin{figure}
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   461
\includegraphics[width=4in]{data/L-Tsq-Line.png}
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   462
\end{figure}
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   463
\end{frame}
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   464
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   465
\begin{frame}[fragile]
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   466
\frametitle{Least Squares Fit}
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   467
\vspace{-0.15in}
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   468
\begin{figure}
210
2d41487bc6fe Added an image for scatter plot of L vs T^2.
Puneeth Chaganti <punchagan@fossee.in>
parents: 203
diff changeset
   469
\includegraphics[width=4in]{data/L-Tsq-points.png}
2d41487bc6fe Added an image for scatter plot of L vs T^2.
Puneeth Chaganti <punchagan@fossee.in>
parents: 203
diff changeset
   470
\end{figure}
2d41487bc6fe Added an image for scatter plot of L vs T^2.
Puneeth Chaganti <punchagan@fossee.in>
parents: 203
diff changeset
   471
\end{frame}
2d41487bc6fe Added an image for scatter plot of L vs T^2.
Puneeth Chaganti <punchagan@fossee.in>
parents: 203
diff changeset
   472
2d41487bc6fe Added an image for scatter plot of L vs T^2.
Puneeth Chaganti <punchagan@fossee.in>
parents: 203
diff changeset
   473
\begin{frame}[fragile]
2d41487bc6fe Added an image for scatter plot of L vs T^2.
Puneeth Chaganti <punchagan@fossee.in>
parents: 203
diff changeset
   474
\frametitle{Least Squares Fit}
2d41487bc6fe Added an image for scatter plot of L vs T^2.
Puneeth Chaganti <punchagan@fossee.in>
parents: 203
diff changeset
   475
\vspace{-0.15in}
2d41487bc6fe Added an image for scatter plot of L vs T^2.
Puneeth Chaganti <punchagan@fossee.in>
parents: 203
diff changeset
   476
\begin{figure}
178
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   477
\includegraphics[width=4in]{data/least-sq-fit.png}
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   478
\end{figure}
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   479
\end{frame}
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   480
174
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   481
\begin{frame}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   482
\frametitle{Least Square Fit Curve}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   483
\begin{itemize}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   484
\item $T^2$ and $L$ have a linear relationship
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   485
\item Hence, Least Square Fit Curve is a line
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   486
\item we shall use the \typ{lstsq} function
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   487
\end{itemize}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   488
\end{frame}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   489
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   490
\begin{frame}[fragile]
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   491
\frametitle{\typ{lstsq}}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   492
\begin{itemize}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   493
\item We need to fit a line through points for the equation $T^2 = m \cdot L+c$
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   494
\item The equation can be re-written as $T^2 = A \cdot p$
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   495
\item where A is   
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   496
  $\begin{bmatrix}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   497
  L_1 & 1 \\
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   498
  L_2 & 1 \\
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   499
  \vdots & \vdots\\
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   500
  L_N & 1 \\
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   501
  \end{bmatrix}$
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   502
  and p is 
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   503
  $\begin{bmatrix}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   504
  m\\
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   505
  c\\
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   506
  \end{bmatrix}$
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   507
\item We need to find $p$ to plot the line
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   508
\end{itemize}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   509
\end{frame}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   510
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   511
\begin{frame}[fragile]
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   512
\frametitle{Van der Monde Matrix}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   513
\begin{itemize}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   514
\item A is also called a Van der Monde matrix
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   515
\item It can be generated using \typ{vander}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   516
\end{itemize}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   517
Van der Monde matrix of order M
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\begin{equation*}
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  \begin{bmatrix}
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  l_1^{M-1} & \ldots & l_1 & 1 \\
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  l_2^{M-1} & \ldots &l_2 & 1 \\
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  \vdots & \ldots & \vdots & \vdots\\
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  l_N^{M-1} & \ldots & l_N & 1 \\
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  \end{bmatrix}
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\end{equation*}
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\begin{lstlisting}
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In []: A = vander(L,2)
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\end{lstlisting}
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\end{frame}
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   530
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\begin{frame}[fragile]
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\frametitle{\typ{lstsq} \ldots}
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\begin{itemize}
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\item Now use the \typ{lstsq} function
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\item Along with a lot of things, it returns the least squares solution
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\end{itemize}
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\begin{lstlisting}
185
e59ab9ab1a89 Manual Merge with Mainline.
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In []: coef, res, r, s = lstsq(A,TSq)
174
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\end{lstlisting}
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\end{frame}
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   541
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   542
\begin{frame}[fragile]
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\frametitle{Least Square Fit Line \ldots}
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We get the points of the line from \typ{coef}
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\begin{lstlisting}
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In []: Tline = coef[0]*L + coef[1]
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\end{lstlisting}
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\begin{itemize}
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\item Now plot Tline vs. L, to get the Least squares fit line. 
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\end{itemize}
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\begin{lstlisting}
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In []: plot(L, Tline)
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\end{lstlisting}
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\end{frame}
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115
66709e58f765 Added session3.
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\end{document}