day1/session3.tex
author Madhusudan.C.S <madhusudancs@gmail.com>
Wed, 28 Oct 2009 20:32:06 +0530
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Fixed typos and hanging words in 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{infolines}
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  \setbeamercovered{transparent}
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}
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\usepackage[english]{babel}
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\usepackage[latin1]{inputenc}
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%\usepackage{times}
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\usepackage[T1]{fontenc}
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% Taken from Fernando's slides.
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\usepackage{ae,aecompl}
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\usepackage{mathpazo,courier,euler}
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\usepackage[scaled=.95]{helvet}
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\usepackage{amsmath}
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\definecolor{darkgreen}{rgb}{0,0.5,0}
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\usepackage{listings}
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\lstset{language=Python,
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    basicstyle=\ttfamily\bfseries,
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    commentstyle=\color{red}\itshape,
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  stringstyle=\color{darkgreen},
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  showstringspaces=false,
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  keywordstyle=\color{blue}\bfseries}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Macros
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\setbeamercolor{emphbar}{bg=blue!20, fg=black}
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\newcommand{\emphbar}[1]
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{\begin{beamercolorbox}[rounded=true]{emphbar} 
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      {#1}
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 \end{beamercolorbox}
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}
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\newcounter{time}
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\setcounter{time}{0}
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\newcommand{\inctime}[1]{\addtocounter{time}{#1}{\tiny \thetime\ m}}
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\newcommand{\typ}[1]{\lstinline{#1}}
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\newcommand{\kwrd}[1]{ \texttt{\textbf{\color{blue}{#1}}}  }
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%%% This is from Fernando's setup.
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% \usepackage{color}
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% \definecolor{orange}{cmyk}{0,0.4,0.8,0.2}
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% % Use and configure listings package for nicely formatted code
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% \usepackage{listings}
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% \lstset{
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%    language=Python,
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%    basicstyle=\small\ttfamily,
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%    commentstyle=\ttfamily\color{blue},
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%    stringstyle=\ttfamily\color{orange},
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%    showstringspaces=false,
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%    breaklines=true,
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%    postbreak = \space\dots
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% }
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Title page
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\title[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{Processing voluminous data}
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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: Problem statement}
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  Read the data supplied in \emph{sslc1.txt} and carry out the following:
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  \begin{enumerate}
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    \item Draw a pie chart representing the proportion of students who scored more than 90\% in each region in Science.
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    \item Draw a pie chart representing the proportion of students who scored more than 90\% in each subject across regions.
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    \item Print mean, median, mode and standard deviation of math scores for all regions combined.
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  \end{enumerate}
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\end{frame}
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\begin{frame}
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  \frametitle{Problem statement: explanation}
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    \emphbar{Draw a pie chart representing the proportion of students who scored more than 90\% in each region in Science.}
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    \begin{enumerate}
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      \item Complete(100\%) data - Number of students who scored more than 90\% in Science
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      \item Each slice - Number of students who scored more than 90\% in Science in one region
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    \end{enumerate}
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\end{frame}
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\begin{frame}
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  \frametitle{Problem statement: explanation}
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    \emphbar{Draw a pie chart representing the proportion of students who scored more than 90\% in each subject across regions.}
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    \begin{enumerate}
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      \item Complete(100\%) data - Number of students who scored more than 90\% across all regions
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      \item Each slice - Number of students who scored more than 90\% in each subject across all regions
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    \end{enumerate}
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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 One line in file corresponds to a student's details
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    \item aka record
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    \item Each record consists of fields separated by ';'
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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}
229
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  \inctime{5}
120
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\end{frame}
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229
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\subsection{Data processing}
120
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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
120
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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]
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  \end{lstlisting}
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\end{frame}
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\begin{frame}[fragile]
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  \frametitle{Back to lists: Iterating}
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  \begin{itemize}
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    \item Python's \kwrd{for} loop iterates through list items
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    \item In other languages (C/C++) we run through indices and pick items from the array using these indices
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    \item In Python, while iterating through list items current position is not available
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  \end{itemize}
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  \begin{block}{Iterating through indices}
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    What if we want the index of an item of a list?
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  \end{block}
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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{Continuing with our Dictionary}
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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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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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  \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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   324
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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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249
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\subsection{Visualizing data}
204
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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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   338
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}
204
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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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   357
216
c6704d4a18bd Removed multiplication of list with * operator.
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   358
scores = [[], [], [], [], []]
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ninety_percents = [{}, {}, {}, {}, {}]
204
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  \end{lstlisting}
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\end{frame}
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\begin{frame}[fragile]
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   364
  \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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   369
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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
125
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   377
  \begin{lstlisting}
184
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for i, field in enumerate(fields[3:8]):
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   379
    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()
204
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   383
    score = int(score_str) if
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   384
      score_str != 'AA' else 0
125
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204
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   386
    scores[i].append(score)
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   387
184
9efa777af2e2 Reworked on Session 3 day 1 slides.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 178
diff changeset
   388
    if score > 90:
9efa777af2e2 Reworked on Session 3 day 1 slides.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 178
diff changeset
   389
        ninety_percents[i][region_code] += 1
125
99ca3cb18fd2 Session 3 Day 1, sslc data parsing obtaining statistics.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 120
diff changeset
   390
  \end{lstlisting}
99ca3cb18fd2 Session 3 Day 1, sslc data parsing obtaining statistics.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 120
diff changeset
   391
\end{frame}
120
055b199c46c2 Added NumPy array operations to session3 day1 for sslc1.txt.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 117
diff changeset
   392
125
99ca3cb18fd2 Session 3 Day 1, sslc data parsing obtaining statistics.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 120
diff changeset
   393
\begin{frame}[fragile]
184
9efa777af2e2 Reworked on Session 3 day 1 slides.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 178
diff changeset
   394
  \frametitle{Consolidating data}
125
99ca3cb18fd2 Session 3 Day 1, sslc data parsing obtaining statistics.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 120
diff changeset
   395
  \begin{lstlisting}
184
9efa777af2e2 Reworked on Session 3 day 1 slides.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 178
diff changeset
   396
subj_total = []
9efa777af2e2 Reworked on Session 3 day 1 slides.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 178
diff changeset
   397
for subject in ninety_percents:
9efa777af2e2 Reworked on Session 3 day 1 slides.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 178
diff changeset
   398
    subj_total.append(sum(
9efa777af2e2 Reworked on Session 3 day 1 slides.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 178
diff changeset
   399
         subject.values()))
170
36ed5cdf5fde Reorganized the slides for sslc1.txt.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 167
diff changeset
   400
  \end{lstlisting}
36ed5cdf5fde Reorganized the slides for sslc1.txt.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 167
diff changeset
   401
\end{frame}
36ed5cdf5fde Reorganized the slides for sslc1.txt.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 167
diff changeset
   402
36ed5cdf5fde Reorganized the slides for sslc1.txt.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 167
diff changeset
   403
\begin{frame}[fragile]
184
9efa777af2e2 Reworked on Session 3 day 1 slides.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 178
diff changeset
   404
  \frametitle{Pie charts}
9efa777af2e2 Reworked on Session 3 day 1 slides.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 178
diff changeset
   405
  \begin{lstlisting}
9efa777af2e2 Reworked on Session 3 day 1 slides.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 178
diff changeset
   406
figure(2)
9efa777af2e2 Reworked on Session 3 day 1 slides.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 178
diff changeset
   407
pie(subj_total, labels=['English',
9efa777af2e2 Reworked on Session 3 day 1 slides.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 178
diff changeset
   408
    'Hindi', 'Maths', 'Science',
9efa777af2e2 Reworked on Session 3 day 1 slides.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 178
diff changeset
   409
    'Social'])
9efa777af2e2 Reworked on Session 3 day 1 slides.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 178
diff changeset
   410
title('Students scoring more than
9efa777af2e2 Reworked on Session 3 day 1 slides.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 178
diff changeset
   411
      90% by subject(All regions
9efa777af2e2 Reworked on Session 3 day 1 slides.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 178
diff changeset
   412
      combined).')
9efa777af2e2 Reworked on Session 3 day 1 slides.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 178
diff changeset
   413
savefig('/tmp/all_regions.png')
120
055b199c46c2 Added NumPy array operations to session3 day1 for sslc1.txt.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 117
diff changeset
   414
  \end{lstlisting}
055b199c46c2 Added NumPy array operations to session3 day1 for sslc1.txt.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 117
diff changeset
   415
\end{frame}
055b199c46c2 Added NumPy array operations to session3 day1 for sslc1.txt.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 117
diff changeset
   416
166
ddfd95133adc Taken task based approach for Session 3, day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 161
diff changeset
   417
\begin{frame}[fragile]
184
9efa777af2e2 Reworked on Session 3 day 1 slides.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 178
diff changeset
   418
  \frametitle{Pie charts}
9efa777af2e2 Reworked on Session 3 day 1 slides.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 178
diff changeset
   419
  \includegraphics[height=3in, interpolate=true]{data/all_regions}
166
ddfd95133adc Taken task based approach for Session 3, day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 161
diff changeset
   420
\end{frame}
ddfd95133adc Taken task based approach for Session 3, day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 161
diff changeset
   421
249
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   422
\subsection{Obtaining statistics}
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   423
\begin{frame}[fragile]
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   424
  \frametitle{Obtaining statistics}
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   425
  \begin{block}{Statistics: Mean}
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   426
    Obtain the mean of Math scores
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   427
  \end{block}
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   428
\end{frame}
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   429
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   430
\begin{frame}[fragile]
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   431
  \frametitle{Obtaining statistics: Solution}
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   432
  \begin{block}{Statistics: Mean}
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   433
    Obtain the mean of Math scores
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   434
  \end{block}
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   435
  \begin{lstlisting}
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   436
math_scores = scores[2]
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   437
total = 0
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   438
for i, score in enumerate(math_scores):
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   439
    total += score
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   440
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   441
mean = total / (i + 1)
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   442
print "Mean: ", mean
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   443
  \end{lstlisting}
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   444
\end{frame}
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   445
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   446
\begin{frame}[fragile]
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   447
  \frametitle{Obtaining statistics: Another solution}
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   448
  \begin{block}{Statistics: Mean}
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   449
    Obtain the mean of Math scores
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   450
  \end{block}
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   451
  \begin{lstlisting}
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   452
math_scores = scores[2]
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   453
mean = sum(math_scores) /
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   454
          len(math_scores)
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   455
  \end{lstlisting}
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   456
\end{frame}
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   457
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   458
\begin{frame}[fragile]
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   459
\frametitle{NumPy arrays}
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   460
  \begin{itemize}
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   461
    \item NumPy provides arrays
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   462
    \item arrays are very efficient and powerful 
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   463
    \item Very easy to perform element-wise operations - \typ{+, -, *, /, \%}
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   464
    \begin{lstlisting}
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   465
In [1]: a = array([1, 2, 3])
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   466
In [2]: b = array([4, 5, 6])
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   467
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   468
In [3]: a + b
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   469
Out[3]: array([5, 7, 9])
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   470
    \end{lstlisting}
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   471
    \item Very easy to compute statistics
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   472
  \end{itemize}
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   473
\end{frame}
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   474
174
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   475
\begin{frame}[fragile]
204
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   476
  \frametitle{Obtaining statistics}
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   477
  \begin{lstlisting}
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   478
math_scores = array(scores[2])
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   479
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   480
print "Mean: ", mean(math_scores)
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   481
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   482
print "Median: ", median(math_scores)
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   483
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   484
print "Mode: ", stats.mode(math_scores)
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   485
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   486
print "Standard Deviation: ",
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   487
              std(math_scores)
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   488
  \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
   489
  \inctime{15}
204
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   490
\end{frame}
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   491
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   492
\begin{frame}[fragile]
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   493
  \frametitle{What tools did we use?}
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   494
  \begin{itemize}
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   495
   \item Dictionaries for storing data
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   496
   \item Facilities for drawing pie charts
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   497
   \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
   498
   \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
   499
  \end{itemize}
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   500
\end{frame}
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 192
diff changeset
   501
249
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   502
\section{Least square fit}
208
c663c8daa109 Reorganized slides of session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 205
diff changeset
   503
\begin{frame}
c663c8daa109 Reorganized slides of session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 205
diff changeset
   504
\frametitle{L vs $T^2$ \ldots}
c663c8daa109 Reorganized slides of session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 205
diff changeset
   505
Let's go back to the L vs $T^2$ plot
c663c8daa109 Reorganized slides of session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 205
diff changeset
   506
\begin{itemize}
c663c8daa109 Reorganized slides of session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 205
diff changeset
   507
\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
   508
\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
   509
\end{itemize}
c663c8daa109 Reorganized slides of session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 205
diff changeset
   510
\end{frame}
c663c8daa109 Reorganized slides of session 3 day 1.
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diff changeset
   511
204
87f914f38ba1 Session 3 day 1, Statistical operations finalized.
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parents: 192
diff changeset
   512
\begin{frame}[fragile]
178
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
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diff changeset
   513
\frametitle{Dealing with data whole-sale}
174
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parents: 170
diff changeset
   514
\begin{lstlisting}
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parents: 170
diff changeset
   515
In []: for t in T:
185
e59ab9ab1a89 Manual Merge with Mainline.
Puneeth Chaganti <punchagan@fossee.in>
parents: 184
diff changeset
   516
 ....:     TSq.append(t*t)
174
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   517
\end{lstlisting}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   518
\begin{itemize}
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   519
\item This is not very efficient
178
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   520
\item We are squaring element after element
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   521
\item We use arrays to make this efficient
174
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   522
\end{itemize}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   523
\begin{lstlisting}
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   524
In []: L = array(L)
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   525
In []: T = array(T)
185
e59ab9ab1a89 Manual Merge with Mainline.
Puneeth Chaganti <punchagan@fossee.in>
parents: 184
diff changeset
   526
In []: TSq = T*T
174
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   527
\end{lstlisting}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   528
\end{frame}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   529
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   530
\begin{frame}[fragile]
178
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   531
\frametitle{Least Squares Fit}
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   532
\vspace{-0.15in}
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   533
\begin{figure}
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   534
\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
   535
\end{figure}
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   536
\end{frame}
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   537
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   538
\begin{frame}[fragile]
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   539
\frametitle{Least Squares Fit}
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   540
\vspace{-0.15in}
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   541
\begin{figure}
210
2d41487bc6fe Added an image for scatter plot of L vs T^2.
Puneeth Chaganti <punchagan@fossee.in>
parents: 203
diff changeset
   542
\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
   543
\end{figure}
2d41487bc6fe Added an image for scatter plot of L vs T^2.
Puneeth Chaganti <punchagan@fossee.in>
parents: 203
diff changeset
   544
\end{frame}
2d41487bc6fe Added an image for scatter plot of L vs T^2.
Puneeth Chaganti <punchagan@fossee.in>
parents: 203
diff changeset
   545
2d41487bc6fe Added an image for scatter plot of L vs T^2.
Puneeth Chaganti <punchagan@fossee.in>
parents: 203
diff changeset
   546
\begin{frame}[fragile]
2d41487bc6fe Added an image for scatter plot of L vs T^2.
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parents: 203
diff changeset
   547
\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
   548
\vspace{-0.15in}
2d41487bc6fe Added an image for scatter plot of L vs T^2.
Puneeth Chaganti <punchagan@fossee.in>
parents: 203
diff changeset
   549
\begin{figure}
178
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   550
\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
   551
\end{figure}
8a3a9d98fa84 Changed functions section and some minor edits.
Puneeth Chaganti <punchagan@fossee.in>
parents: 174
diff changeset
   552
\end{frame}
8a3a9d98fa84 Changed functions section and some minor edits.
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parents: 174
diff changeset
   553
174
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parents: 170
diff changeset
   554
\begin{frame}
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   555
\frametitle{Least Square Fit Curve}
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parents: 170
diff changeset
   556
\begin{itemize}
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   557
\item $T^2$ and $L$ have a linear relationship
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   558
\item Hence, Least Square Fit Curve is a line
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   559
\item we shall use the \typ{lstsq} function
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   560
\end{itemize}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   561
\end{frame}
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   562
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   563
\begin{frame}[fragile]
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   564
\frametitle{\typ{lstsq}}
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   565
\begin{itemize}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   566
\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
   567
\item The equation can be re-written as $T^2 = A \cdot p$
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   568
\item where A is   
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   569
  $\begin{bmatrix}
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   570
  L_1 & 1 \\
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   571
  L_2 & 1 \\
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   572
  \vdots & \vdots\\
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   573
  L_N & 1 \\
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   574
  \end{bmatrix}$
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   575
  and p is 
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   576
  $\begin{bmatrix}
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   577
  m\\
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   578
  c\\
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   579
  \end{bmatrix}$
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   580
\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
   581
\end{itemize}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   582
\end{frame}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   583
249
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   584
\subsection{Van der Monde matrix generation}
174
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   585
\begin{frame}[fragile]
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   586
\frametitle{Van der Monde Matrix}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   587
\begin{itemize}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   588
\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
   589
\item It can be generated using \typ{vander}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   590
\end{itemize}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   591
Van der Monde matrix of order M
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   592
\begin{equation*}
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   593
  \begin{bmatrix}
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   594
  l_1^{M-1} & \ldots & l_1 & 1 \\
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   595
  l_2^{M-1} & \ldots &l_2 & 1 \\
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   596
  \vdots & \ldots & \vdots & \vdots\\
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   597
  l_N^{M-1} & \ldots & l_N & 1 \\
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   598
  \end{bmatrix}
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   599
\end{equation*}
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   600
\begin{lstlisting}
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   601
In []: A = vander(L,2)
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   602
\end{lstlisting}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   603
\end{frame}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   604
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   605
\begin{frame}[fragile]
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   606
\frametitle{\typ{lstsq} \ldots}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   607
\begin{itemize}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   608
\item Now use the \typ{lstsq} function
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   609
\item Along with a lot of things, it returns the least squares solution
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   610
\end{itemize}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   611
\begin{lstlisting}
185
e59ab9ab1a89 Manual Merge with Mainline.
Puneeth Chaganti <punchagan@fossee.in>
parents: 184
diff changeset
   612
In []: coef, res, r, s = lstsq(A,TSq)
174
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   613
\end{lstlisting}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   614
\end{frame}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   615
249
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   616
\subsection{Plotting}
174
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parents: 170
diff changeset
   617
\begin{frame}[fragile]
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   618
\frametitle{Least Square Fit Line \ldots}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   619
We get the points of the line from \typ{coef}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   620
\begin{lstlisting}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   621
In []: Tline = coef[0]*L + coef[1]
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   622
\end{lstlisting}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   623
\begin{itemize}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   624
\item Now plot Tline vs. L, to get the Least squares fit line. 
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   625
\end{itemize}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   626
\begin{lstlisting}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   627
In []: plot(L, Tline)
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   628
\end{lstlisting}
a43832c1edc2 Reordered Session 3 Day 1.
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parents: 170
diff changeset
   629
\end{frame}
a43832c1edc2 Reordered Session 3 Day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 170
diff changeset
   630
249
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   631
\begin{frame}[fragile]
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   632
  \frametitle{What did we learn?}
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   633
  \begin{itemize}
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   634
   \item Least square fit
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   635
   \item Van der Monde matrix generation
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   636
   \item Plotting the least square fit curve
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   637
  \end{itemize}
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   638
\end{frame}
135062d6f91f Fixed typos and hanging words in Session 3 day 1.
Madhusudan.C.S <madhusudancs@gmail.com>
parents: 240
diff changeset
   639
115
66709e58f765 Added session3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   640
\end{document}