| author | Shantanu <shantanu@fossee.in> |
| Thu, 29 Apr 2010 17:58:22 +0530 | |
| changeset 117 | d3005da44457 |
| parent 79 | 3893bac8e424 |
| permissions | -rw-r--r-- |
| 71 | 1 |
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%Tutorial slides on Python. |
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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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\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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79
3893bac8e424
Added presentation for solving-equations.
Shantanu <shantanu@fossee.in>
parents:
77
diff
changeset
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\begin{block}{}
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| 77 | 154 |
Obtaining the least fit curve from a data set |
|
79
3893bac8e424
Added presentation for solving-equations.
Shantanu <shantanu@fossee.in>
parents:
77
diff
changeset
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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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