diff -r 76fd286276f7 -r fa5c77536e4e presentations/least-square.tex --- a/presentations/least-square.tex Mon Sep 13 18:35:56 2010 +0530 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,168 +0,0 @@ -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%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 -\mode -{ - \usetheme{Warsaw} - \useoutertheme{infolines} - \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 -\setbeamercolor{emphbar}{bg=blue!20, fg=black} -\newcommand{\emphbar}[1] -{\begin{beamercolorbox}[rounded=true]{emphbar} - {#1} - \end{beamercolorbox} -} -\newcounter{time} -\setcounter{time}{0} -\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}