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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Tutorial slides on Python.
%
% Author: FOSSEE
% Copyright (c) 2009, FOSSEE, IIT Bombay
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\documentclass[14pt,compress]{beamer}
%\documentclass[draft]{beamer}
%\documentclass[compress,handout]{beamer}
%\usepackage{pgfpages}
%\pgfpagesuselayout{2 on 1}[a4paper,border shrink=5mm]
% Modified from: generic-ornate-15min-45min.de.tex
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\setbeamercovered{transparent}
}
\usepackage[english]{babel}
\usepackage[latin1]{inputenc}
%\usepackage{times}
\usepackage[T1]{fontenc}
% Taken from Fernando's slides.
\usepackage{ae,aecompl}
\usepackage{mathpazo,courier,euler}
\usepackage[scaled=.95]{helvet}
\definecolor{darkgreen}{rgb}{0,0.5,0}
\usepackage{listings}
\lstset{language=Python,
basicstyle=\ttfamily\bfseries,
commentstyle=\color{red}\itshape,
stringstyle=\color{darkgreen},
showstringspaces=false,
keywordstyle=\color{blue}\bfseries}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Macros
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{\begin{beamercolorbox}[rounded=true]{emphbar}
{#1}
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\newcommand{\inctime}[1]{\addtocounter{time}{#1}{\tiny \thetime\ m}}
\newcommand{\typ}[1]{\lstinline{#1}}
\newcommand{\kwrd}[1]{ \texttt{\textbf{\color{blue}{#1}}} }
% Title page
\title{Python for Scientific Computing : Least Square Fit}
\author[FOSSEE] {FOSSEE}
\institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
\date{}
% DOCUMENT STARTS
\begin{document}
\begin{frame}
\maketitle
\end{frame}
\begin{frame}
\frametitle{About the Session}
\begin{block}{Goal}
Finding least square fit of given data-set
\end{block}
\begin{block}{Checklist}
\begin{itemize}
\item pendulum.txt
\end{itemize}
\end{block}
\end{frame}
\begin{frame}[fragile]
\frametitle{$L$ vs. $T^2$ - Scatter}
\vspace{-0.15in}
\begin{figure}
\includegraphics[width=4in]{data/L-Tsq-points}
\end{figure}
\end{frame}
\begin{frame}[fragile]
\frametitle{$L$ vs. $T^2$ - Line}
\vspace{-0.15in}
\begin{figure}
\includegraphics[width=4in]{data/L-Tsq-Line}
\end{figure}
\end{frame}
\begin{frame}[fragile]
\frametitle{$L$ vs. $T^2$ }
\frametitle{$L$ vs. $T^2$ - Least Square Fit}
\vspace{-0.15in}
\begin{figure}
\includegraphics[width=4in]{data/least-sq-fit}
\end{figure}
\end{frame}
\begin{frame}
\frametitle{Least Square Fit Curve}
\begin{center}
\begin{itemize}
\item $L \alpha T^2$
\item Best Fit Curve $\rightarrow$ Linear
\begin{itemize}
\item Least Square Fit
\end{itemize}
\item \typ{lstsq()}
\end{itemize}
\end{center}
\end{frame}
\begin{frame}[fragile]
\frametitle{\typ{lstsq}}
\begin{itemize}
\item We need to fit a line through points for the equation $T^2 = m \cdot L+c$
\item In matrix form, the equation can be represented as $T_{sq} = A \cdot p$, where $T_{sq}$ is
$\begin{bmatrix}
T^2_1 \\
T^2_2 \\
\vdots\\
T^2_N \\
\end{bmatrix}$
, A is
$\begin{bmatrix}
L_1 & 1 \\
L_2 & 1 \\
\vdots & \vdots\\
L_N & 1 \\
\end{bmatrix}$
and p is
$\begin{bmatrix}
m\\
c\\
\end{bmatrix}$
\item We need to find $p$ to plot the line
\end{itemize}
\end{frame}
\begin{frame}[fragile]
\frametitle{Summary}
\begin{block}{}
Obtaining the least fit curve from a data set
\end{block}
\end{frame}
\begin{frame}
\frametitle{Thank you!}
\begin{block}{}
This session is part of \textcolor{blue}{FOSSEE} project funded by:
\begin{center}
\textcolor{blue}{NME through ICT from MHRD, Govt. of India}.
\end{center}
\end{block}
\end{frame}
\end{document}
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