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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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\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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\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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% Title page
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\title{Python for Scientific Computing : Least Square Fit}
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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{}
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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{About the Session}
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\begin{block}{Goal}
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Finding least square fit of given data-set
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\end{block}
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\begin{block}{Checklist}
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\begin{itemize}
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\item pendulum.txt
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\end{itemize}
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\end{block}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{$L$ vs. $T^2$ - Scatter}
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\vspace{-0.15in}
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\begin{figure}
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\includegraphics[width=4in]{data/L-Tsq-points}
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\end{figure}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{$L$ vs. $T^2$ - Line}
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\vspace{-0.15in}
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\begin{figure}
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\includegraphics[width=4in]{data/L-Tsq-Line}
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\end{figure}
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\end{frame}
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\begin{frame}[fragile]
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\frametitle{$L$ vs. $T^2$ }
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\frametitle{$L$ vs. $T^2$ - Least Square 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}
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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{center}
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\begin{itemize}
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\item $L \alpha T^2$
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\item Best Fit Curve $\rightarrow$ Linear
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\begin{itemize}
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\item Least Square Fit
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\end{itemize}
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\item \typ{lstsq()}
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\end{itemize}
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\end{center}
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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 In matrix form, the equation can be represented as $T_{sq} = A \cdot p$, where $T_{sq}$ is
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$\begin{bmatrix}
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T^2_1 \\
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T^2_2 \\
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\vdots\\
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T^2_N \\
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\end{bmatrix}$
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, 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{Summary}
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\begin{block}{}
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\end{block}
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\end{frame}
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\begin{frame}
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\frametitle{Thank you!}
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\begin{block}{}
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This session is part of \textcolor{blue}{FOSSEE} project funded by:
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\begin{center}
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\textcolor{blue}{NME through ICT from MHRD, Govt. of India}.
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\end{center}
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\end{block}
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\end{frame}
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\end{document}
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