%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%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{Solution of equations}

Consider,

  \begin{align*}

    3x + 2y - z  & = 1 \\

    2x - 2y + 4z  & = -2 \\

    -x + \frac{1}{2}y -z & = 0

  \end{align*}

Solution:

  \begin{align*}

    x & = 1 \\

    y & = -2 \\

    z & = -2

  \end{align*}

\end{frame}

\begin{frame}[fragile]

\frametitle{Scipy Methods - \typ{roots}}

\begin{itemize}

\item Calculates the roots of polynomials

\item To calculate the roots of $x^2-5x+6$ 

\end{itemize}

\begin{lstlisting}

  In []: coeffs = [1, -5, 6]

  In []: roots(coeffs)

  Out[]: array([3., 2.])

\end{lstlisting}

\vspace*{-.2in}

\begin{center}

\includegraphics[height=1.6in, interpolate=true]{data/roots}    

\end{center}

\end{frame}

\begin{frame}[fragile]

\frametitle{Scipy Methods - \typ{fsolve}}

\begin{small}

\begin{lstlisting}

  In []: from scipy.optimize import fsolve

\end{lstlisting}

\end{small}

\begin{itemize}

\item Finds the roots of a system of non-linear equations

\item Input arguments - Function and initial estimate

\item Returns the solution

\end{itemize}

\end{frame}

\begin{frame}[fragile]

  \frametitle{Summary}

  \begin{block}{}

    \begin{itemize}

    \item Solving linear equations

    \item Finding roots

    \item Roots of non linear equations

    \item Basics of Functions

    \end{itemize}

  \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}