day1/session3.tex
author Puneeth Chaganti <punchagan@fossee.in>
Tue, 27 Oct 2009 14:24:49 +0530
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Added a slide for transition from sslc to lstsq in session3.
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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[]{Least Squares Fit\\Statistical Plotting}
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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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\begin{frame}
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  \frametitle{More on data processing}
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  \begin{block}{}
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    What do we do if we want to draw Pie charts for the data in a huge data file?
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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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  \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 and parsing
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    \item Dictionaries
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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, i.e each row of a file is a single record.
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    \item Each record corresponds to a record of a single student
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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
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    \item Total marks
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    \item Pass (P)
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    \item Withdrawn (W)
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    \item Fail (F)
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  \end{itemize}
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\end{frame}
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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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\begin{frame}[fragile]
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ddfd95133adc Taken task based approach for Session 3, day 1.
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  \frametitle{Dictionary - Building parsed data}
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  \begin{itemize}
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    \item Let the parsed data be stored in list of dictionaries.
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    \item d = \{\} is an empty dictionary
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  \end{itemize}
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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{lstlisting}
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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{Dictionary - Building parsed data}
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  \begin{itemize}
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    \item Index of a dictionary is called a \emph{key}
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    \item \emph{Keys} of these dictionaries are strings - region codes
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  \end{itemize}
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\end{frame}
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\begin{frame}[fragile]
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  \frametitle{Dictionary - Building parsed data \ldots}
184
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  \begin{itemize}
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    \item Value of a \emph{key} can be any legal Python value
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    \item In this problem let the value of a \emph{key} be another an integer
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    \item This dictionary contains:
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  \end{itemize}
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'region code': Number of students who scored more than 90\% in this region for this subject
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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 *
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ninety_percents = [{}, {}, {}, {}, {}]
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120
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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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  \small
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  \begin{lstlisting}
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for i, field in enumerate(fields[3:8]):
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184
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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 = 0 if score_str == 'AA' else 
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                         int(score_str)
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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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\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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  \small
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  \begin{lstlisting}
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figure(1)
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pie(ninety_percents[4].values(), 
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    labels=ninety_percents[1].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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\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}
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\end{frame}
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\begin{frame}
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\frametitle{L vs $T^2$ \ldots}
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Let's go back to the L vs $T^2$ plot
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\begin{itemize}
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\item We first look at obtaining $T^2$ from T
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\item Then, we look at plotting a Least Squares fit
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\end{itemize}
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\end{frame}
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174
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\begin{frame}[fragile]
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\frametitle{Dealing with data whole-sale}
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\begin{lstlisting}
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In []: for t in T:
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 ....:     TSq.append(t*t)
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\end{lstlisting}
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\begin{itemize}
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\item This is not very efficient
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\item We are squaring element after element
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\item We use arrays to make this efficient
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\end{itemize}
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\begin{lstlisting}
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In []: L = array(L)
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In []: T = array(T)
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In []: TSq = T*T
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\end{lstlisting}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{Arrays}
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\begin{itemize}
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\item \typ{T} and \typ{L} are now arrays
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\item arrays are very efficient and powerful 
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\item Very easy to perform element-wise operations
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\item \typ{+, -, *, /, \%}
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\item More about arrays later
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\end{itemize}
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\end{frame}
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178
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\begin{frame}[fragile]
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\frametitle{Least Squares Fit}
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\vspace{-0.15in}
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\begin{figure}
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\includegraphics[width=4in]{data/L-Tsq-Line.png}
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\end{figure}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{Least Squares Fit}
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\vspace{-0.15in}
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\begin{figure}
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\includegraphics[width=4in]{data/least-sq-fit.png}
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\end{figure}
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\end{frame}
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\begin{frame}
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\frametitle{Least Square Fit Curve}
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\begin{itemize}
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\item $T^2$ and $L$ have a linear relationship
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\item Hence, Least Square Fit Curve is a line
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\item we shall use the \typ{lstsq} function
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\end{itemize}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{\typ{lstsq}}
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\begin{itemize}
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\item We need to fit a line through points for the equation $T^2 = m \cdot L+c$
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\item The equation can be re-written as $T^2 = A \cdot p$
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\item where A is   
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  $\begin{bmatrix}
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  L_1 & 1 \\
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  L_2 & 1 \\
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  \vdots & \vdots\\
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  L_N & 1 \\
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  \end{bmatrix}$
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  and p is 
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  $\begin{bmatrix}
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  m\\
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  c\\
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  \end{bmatrix}$
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\item We need to find $p$ to plot the line
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\end{itemize}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{Van der Monde Matrix}
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\begin{itemize}
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\item A is also called a Van der Monde matrix
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\item It can be generated using \typ{vander}
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\end{itemize}
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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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\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}
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In []: coef, res, r, s = lstsq(A,TSq)
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\end{lstlisting}
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\end{frame}
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\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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\begin{frame}[fragile]
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  \frametitle{What did we learn?}
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  \begin{itemize}
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   \item Dictionaries
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   \item Drawing pie charts
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   \item Arrays
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   \item Least Square fitting
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   \item Intro to Matrices
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  \end{itemize}
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\end{frame}
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\end{document}