# HG changeset patch
# User Shantanu <shantanu@fossee.in>
# Date 1271399461 -19800
# Node ID bc3f351aeec96a4391376e605db97a793993128e
# Parent  fe5d3fb8359718cd4d27f321bf8f2e0656c42114
Added least-square.tex.

diff -r fe5d3fb83597 -r bc3f351aeec9 presentations/arrays.tex
--- a/presentations/arrays.tex	Thu Apr 15 15:30:59 2010 +0530
+++ b/presentations/arrays.tex	Fri Apr 16 12:01:01 2010 +0530
@@ -73,8 +73,10 @@
 \begin{frame}
   \frametitle{About the Session}
   \begin{block}{Goal}
-Perform efficient matrix operations.
-Basic Image processing. 
+    \begin{itemize}
+    \item Perform efficient matrix operations.
+    \item Basic Image processing. 
+    \end{itemize}
   \end{block}
   \begin{block}{Checklist}
     \begin{itemize}
diff -r fe5d3fb83597 -r bc3f351aeec9 presentations/least-square.tex
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/presentations/least-square.tex	Fri Apr 16 12:01:01 2010 +0530
@@ -0,0 +1,168 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%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<presentation>
+{
+  \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}{}
+        
+  \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}