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     2 %Tutorial slides on Python.

     3 %

     4 % Author: FOSSEE 

     5 % Copyright (c) 2009, FOSSEE, IIT Bombay

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     7 

     8 \documentclass[14pt,compress]{beamer}

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    14 % Modified from: generic-ornate-15min-45min.de.tex

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    27 % Taken from Fernando's slides.

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    32 \definecolor{darkgreen}{rgb}{0,0.5,0}

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    34 \usepackage{listings}

    35 \lstset{language=Python,

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    43 % Macros

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    54 \newcommand{\typ}[1]{\lstinline{#1}}

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    56 \newcommand{\kwrd}[1]{ \texttt{\textbf{\color{blue}{#1}}}  }

    57 

    58 % Title page

    59 \title{Python for Scientific Computing : Least Square Fit}

    60 

    61 \author[FOSSEE] {FOSSEE}

    62 

    63 \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}

    64 \date{}

    65 

    66 % DOCUMENT STARTS

    67 \begin{document}

    68 

    69 \begin{frame}

    70   \maketitle

    71 \end{frame}

    72 

    73 \begin{frame}

    74   \frametitle{About the Session}

    75   \begin{block}{Goal}

    76 Finding least square fit of given data-set

    77   \end{block}

    78   \begin{block}{Checklist}

    79     \begin{itemize}

    80     \item pendulum.txt

    81   \end{itemize}

    82   \end{block}

    83 \end{frame}

    84 

    85 \begin{frame}[fragile]

    86   \frametitle{$L$ vs. $T^2$ - Scatter}

    87   \vspace{-0.15in}

    88   \begin{figure}

    89     \includegraphics[width=4in]{data/L-Tsq-points}

    90   \end{figure}

    91 \end{frame}

    92 

    93 \begin{frame}[fragile]

    94   \frametitle{$L$ vs. $T^2$ - Line}

    95   \vspace{-0.15in}

    96   \begin{figure}

    97     \includegraphics[width=4in]{data/L-Tsq-Line}

    98   \end{figure}

    99 \end{frame}

   100 

   101 \begin{frame}[fragile]

   102   \frametitle{$L$ vs. $T^2$ }

   103   \frametitle{$L$ vs. $T^2$ - Least Square Fit}

   104   \vspace{-0.15in}

   105   \begin{figure}

   106     \includegraphics[width=4in]{data/least-sq-fit}

   107   \end{figure}

   108 \end{frame}

   109 

   110 \begin{frame}

   111   \frametitle{Least Square Fit Curve}

   112   \begin{center}

   113     \begin{itemize}

   114     \item $L \alpha T^2$

   115     \item Best Fit Curve $\rightarrow$ Linear

   116   \begin{itemize}

   117   \item Least Square Fit

   118   \end{itemize}

   119 \item \typ{lstsq()} 

   120     \end{itemize}

   121   \end{center}

   122 \end{frame}

   123 

   124 \begin{frame}[fragile]

   125   \frametitle{\typ{lstsq}}

   126   \begin{itemize}

   127   \item We need to fit a line through points for the equation $T^2 = m \cdot L+c$

   128   \item In matrix form, the equation can be represented as $T_{sq} = A \cdot p$, where $T_{sq}$ is

   129   $\begin{bmatrix}

   130   T^2_1 \\

   131   T^2_2 \\

   132   \vdots\\

   133   T^2_N \\

   134   \end{bmatrix}$

   135 , A is   

   136   $\begin{bmatrix}

   137   L_1 & 1 \\

   138   L_2 & 1 \\

   139   \vdots & \vdots\\

   140   L_N & 1 \\

   141   \end{bmatrix}$

   142   and p is 

   143   $\begin{bmatrix}

   144   m\\

   145   c\\

   146   \end{bmatrix}$

   147   \item We need to find $p$ to plot the line

   148   \end{itemize}

   149 \end{frame}

   150 

   151 \begin{frame}[fragile]

   152   \frametitle{Summary}

   153   \begin{block}{}

   154     Obtaining the least fit curve from a data set

   155   \end{block}    

   156 \end{frame}

   157 

   158 \begin{frame}

   159   \frametitle{Thank you!}  

   160   \begin{block}{}

   161   This session is part of \textcolor{blue}{FOSSEE} project funded by:

   162   \begin{center}

   163     \textcolor{blue}{NME through ICT from MHRD, Govt. of India}.

   164   \end{center}  

   165   \end{block}

   166 \end{frame}

   167 

   168 \end{document}