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diff --git a/day2/session5.tex b/day2/session5.tex
index 1d0612c..c5809c5 100644
--- a/day2/session5.tex
+++ b/day2/session5.tex
@@ -1,48 +1,33 @@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Tutorial slides on Python.
+%Tutorial slides on Python.
%
% Author: Prabhu Ramachandran <prabhu at aero.iitb.ac.in>
% Copyright (c) 2005-2009, Prabhu Ramachandran
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\documentclass[compress,14pt]{beamer}
-% \documentclass[handout]{beamer}
-% \usepackage{pgfpages}
-% \pgfpagesuselayout{4 on 1}[a4paper,border, shrink=5mm,landscape]
-\usepackage{tikz}
-\newcommand{\hyperlinkmovie}{}
-%\usepackage{movie15}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Note that in presentation mode
-% \paperwidth 364.19536pt
-% \paperheight 273.14662pt
-% h/w = 0.888
-
+\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}
- %\usetheme{Boadilla}
- %\usetheme{default}
\useoutertheme{infolines}
\setbeamercovered{transparent}
}
-% To remove navigation symbols
-\setbeamertemplate{navigation symbols}{}
-
-\usepackage{amsmath}
\usepackage[english]{babel}
\usepackage[latin1]{inputenc}
-\usepackage{times}
+%\usepackage{times}
\usepackage[T1]{fontenc}
% Taken from Fernando's slides.
\usepackage{ae,aecompl}
\usepackage{mathpazo,courier,euler}
\usepackage[scaled=.95]{helvet}
-\usepackage{pgf}
\definecolor{darkgreen}{rgb}{0,0.5,0}
@@ -55,65 +40,50 @@
keywordstyle=\color{blue}\bfseries}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% My Macros
-\setbeamercolor{postit}{bg=yellow,fg=black}
+% Macros
\setbeamercolor{emphbar}{bg=blue!20, fg=black}
\newcommand{\emphbar}[1]
{\begin{beamercolorbox}[rounded=true]{emphbar}
{#1}
\end{beamercolorbox}
}
-%{\centerline{\fcolorbox{gray!50} {blue!10}{
-%\begin{minipage}{0.9\linewidth}
-% {#1}
-%\end{minipage}
-% }}}
-
-\newcommand{\myemph}[1]{\structure{\emph{#1}}}
-\newcommand{\PythonCode}[1]{\lstinline{#1}}
-
-\newcommand{\tvtk}{\texttt{tvtk}}
-\newcommand{\mlab}{\texttt{mlab}}
-
\newcounter{time}
\setcounter{time}{0}
-\newcommand{\inctime}[1]{\addtocounter{time}{#1}{\vspace*{0.1in}\tiny \thetime\ m}}
+\newcommand{\inctime}[1]{\addtocounter{time}{#1}{\tiny \thetime\ m}}
-\newcommand\BackgroundPicture[1]{%
- \setbeamertemplate{background}{%
- \parbox[c][\paperheight]{\paperwidth}{%
- \vfill \hfill
- \hfill \vfill
-}}}
+\newcommand{\typ}[1]{\texttt{#1}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Configuring the theme
-%\setbeamercolor{normal text}{fg=white}
-%\setbeamercolor{background canvas}{bg=black}
+\newcommand{\kwrd}[1]{ \texttt{\textbf{\color{blue}{#1}}} }
+%%% This is from Fernando's setup.
+% \usepackage{color}
+% \definecolor{orange}{cmyk}{0,0.4,0.8,0.2}
+% % Use and configure listings package for nicely formatted code
+% \usepackage{listings}
+% \lstset{
+% language=Python,
+% basicstyle=\small\ttfamily,
+% commentstyle=\ttfamily\color{blue},
+% stringstyle=\ttfamily\color{orange},
+% showstringspaces=false,
+% breaklines=true,
+% postbreak = \space\dots
+% }
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Title page
-\title[3D Plotting]{3D data Visualization}
+\title[Exercises]{Exercises}
\author[FOSSEE] {FOSSEE}
\institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
\date[] {12 January, 2010\\Day 2, Session 5}
-
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%\pgfdeclareimage[height=0.75cm]{iitblogo}{iitblogo}
-%\logo{\pgfuseimage{iitblogo}}
+%\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo}
+%\logo{\pgfuseimage{iitmlogo}}
-\AtBeginSection[]
-{
- \begin{frame}<beamer>
- \frametitle{Outline}
- \tableofcontents[currentsection,currentsubsection]
- \end{frame}
-}
%% Delete this, if you do not want the table of contents to pop up at
%% the beginning of each subsection:
@@ -125,434 +95,107 @@
\end{frame}
}
-\AtBeginSection[]
-{
- \begin{frame}<beamer>
- \frametitle{Outline}
- \tableofcontents[currentsection,currentsubsection]
- \end{frame}
-}
+
+% If you wish to uncover everything in a step-wise fashion, uncomment
+% the following command:
+%\beamerdefaultoverlayspecification{<+->}
+
+%\includeonlyframes{current,current1,current2,current3,current4,current5,current6}
+
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% DOCUMENT STARTS
\begin{document}
\begin{frame}
- \maketitle
+ \titlepage
\end{frame}
-\begin{frame}
- \frametitle{Outline}
- \tableofcontents
- % You might wish to add the option [pausesections]
+\begin{frame}{Problem 1.1}
+ The aliquot of a number is defined as: the sum of the \emph{proper} divisors of the number. For example:\\
+aliquot(12) = 1 + 2 + 3 + 4 + 6 = 16.\\
+ Write a function that returns the aliquot number of a given number.
\end{frame}
-\section{3D Data Visualization}
-
-\begin{frame}
- \frametitle{What is visualization?}
- \Large
- \begin{center}
- Visual representation of data
- \end{center}
+\begin{frame}{Problem 1.2}
+ Pair of numbers (a, b) is said to be \alert{amicable} if aliquot number of a is b and aliquot number of b is a.\\
+ Example: \texttt{220, 284}\\
+ Write a program that prints all four digit amicable pairs.
+
+\inctime{20}
\end{frame}
+%% \begin{frame}{Problem 2}
+%% Given an empty chessboard and one Bishop placed in any s%quare, say (r, c), generate the list of all squares the Bi%shop could move to.
-%% \begin{frame}
-%% \frametitle{Is this new?}
-%% \begin{center}
-%% We have moved from:
-%% \end{center}
-%% \begin{columns}
-%% \column{}
-%% \hspace*{-1in}
-%% \includegraphics[width=1.75in,height=1.75in, interpolate=true]{data/3832}
-%% \column{}\hspace*{-0.25in}
-%% To
-%% \column{}
-%% \hspace*{-1in}
-%% \includegraphics[width=1.75in, height=1.75in, interpolate=true]{data/torus}
-%% \end{columns}
%% \end{frame}
-\begin{frame}
- \frametitle{3D visualization}
- \Large
- \begin{center}
- Harder but important
- \end{center}
-\end{frame}
-
-\begin{frame}
- \frametitle{Is this Graphics?}
- \Large
- \begin{center}
- Visualization is about data!
- \end{center}
-\end{frame}
-
-\begin{frame}
- \frametitle{Examples: trajectory in space}
- \Large
- \begin{center}
- \pgfimage[width=2.5in]{MEDIA/m2/mlab/plot3d_ex}
- \end{center}
-\end{frame}
-
-\begin{frame}
- \frametitle{Examples: Fire in a room}
- \Large
- \begin{center}
- Demo of data
- \end{center}
-\inctime{10}
-\end{frame}
-
-\section{Tools available}
-
-\subsection{mlab}
-
-\begin{frame}
- {Overview}
- \Large
- \begin{itemize}
- \item Simple
- \item Convenient
- \item Full-featured
- \end{itemize}
-\end{frame}
-
-\begin{frame}[fragile]
-
- \frametitle{Getting started}
- \myemph{\Large Vanilla:}
- \begin{lstlisting}[language=bash]
- $ ipython -wthread
- \end{lstlisting}
- \myemph{\Large with Pylab:}
- \begin{lstlisting}[language=bash]
- $ ipython -pylab -wthread
- \end{lstlisting}
-\end{frame}
-
\begin{frame}[fragile]
- \frametitle{Using mlab}
-
- \begin{lstlisting}
-In []:from enthought.mayavi import mlab
- \end{lstlisting}
-
- \vspace*{0.5in}
-
- \myemph{\Large Try these}
-
- \vspace*{0.25in}
-
- \begin{lstlisting}
-In []: mlab.test_<TAB>
-In []: mlab.test_contour3d()
-In []: mlab.test_contour3d??
- \end{lstlisting}
-\end{frame}
-
-\begin{frame}
- {Exploring the view}
- \begin{columns}
- \column{0.6\textwidth}
- \pgfimage[width=3in]{MEDIA/m2/contour3d}
- \column{0.4\textwidth}
- \begin{itemize}
- \item Mouse
- \item Keyboard
- \item Toolbar
- \item Mayavi icon\pgfimage[width=0.2in]{MEDIA/m2/m2_icon}
- \end{itemize}
- \end{columns}
-\end{frame}
-
-\begin{frame}[fragile]
- \frametitle{\mlab\ plotting functions}
- \begin{columns}
- \column{0.25\textwidth}
- \myemph{\Large 0D data}
- \column{0.5\textwidth}
- \pgfimage[width=2in]{MEDIA/m2/mlab/points3d_ex}
- \end{columns}
-
- \begin{lstlisting}
-In []: t = linspace(0, 2*pi, 50)
-In []: u = cos(t) * pi
-In []: x, y, z = sin(u), cos(u), sin(t)
- \end{lstlisting}
- \emphbar{\PythonCode{In []: mlab.points3d(x, y, z)}}
-\end{frame}
-
-\begin{frame}
- \begin{columns}
- \column{0.25\textwidth}
- \myemph{\Large 1D data}
- \column{0.5\textwidth}
- \pgfimage[width=2.5in]{MEDIA/m2/mlab/plot3d_ex}
- \end{columns}
- \emphbar{\PythonCode{In []: mlab.plot3d(x, y, z, t)}}
-
- Plots lines between the points
-
-\end{frame}
-
-\begin{frame}[fragile]
- \begin{columns}
- \column{0.25\textwidth}
- \myemph{\Large 2D data}
- \column{0.5\textwidth}
- \pgfimage[width=2in]{MEDIA/m2/mlab/surf_ex}
- \end{columns}
- \begin{lstlisting}
-In []: x, y = mgrid[-3:3:100j,-3:3:100j]
-In []: z = sin(x*x + y*y)
- \end{lstlisting}
-
- \emphbar{\PythonCode{In []: mlab.surf(x, y, z)}}
-
- \alert{Assumes the points are rectilinear}
-
-\end{frame}
-
-\begin{frame}[fragile]
- \frametitle{mgrid}
+ \frametitle{Problem 2}
+ Given a string of numbers like, ``1, 3-7, 12, 15, 18-21'', produce the following list \\
\begin{lstlisting}
-In []: mgrid[0:3,0:3]
-Out[]:
-array([[[0, 0, 0],
- [1, 1, 1],
- [2, 2, 2]],
-
- [[0, 1, 2],
- [0, 1, 2],
- [0, 1, 2]]])
-
-In []: mgrid[-1:1:5j]
-Out[]: array([-1., -0.5, 0., 0.5, 1.])
-\end{lstlisting}
-\end{frame}
-
-\begin{frame}[fragile]
- \frametitle{Example}
- \begin{lstlisting}
-In []: x, y = mgrid[-1:1:5j, -1:1:5j]
-In []: z = x*x + y*y
-
-In []: z
-Out[]:
-array([[ 2. , 1.25, 1. , 1.25, 2. ],
- [ 1.25, 0.5 , 0.25, 0.5 , 1.25],
- [ 1. , 0.25, 0. , 0.25, 1. ],
- [ 1.25, 0.5 , 0.25, 0.5 , 1.25],
- [ 2. , 1.25, 1. , 1.25, 2. ]])
-\end{lstlisting}
+ [1,3,4,5,6,7,12,15,18,19,20,21]
+ \end{lstlisting}
+\inctime{10}
\end{frame}
-\begin{frame}[fragile]
- \myemph{\Large 2D data: \texttt{mlab.mesh}}
- \vspace*{0.25in}
-
- \emphbar{\PythonCode{In []: mlab.mesh(x, y, z)}}
-
- \alert{Points needn't be regular}
-
- \vspace*{0.25in}
-\begin{lstlisting}
-In []: phi, theta = mgrid[0:pi:20j,
-... 0:2*pi:20j]
-In []: x = sin(phi)*cos(theta)
-In []: y = sin(phi)*sin(theta)
-In []: z = cos(phi)
-In []: mlab.mesh(x, y, z,
-... representation=
-... 'wireframe')
-\end{lstlisting}
-
+\begin{frame}
+ \frametitle{Problem 3}
+ Count frequencies of words in a file.
+\inctime{25}
\end{frame}
\begin{frame}[fragile]
-
- \begin{columns}
- \column{0.25\textwidth}
- \myemph{\Large 3D data}
- \column{0.5\textwidth}
- \pgfimage[width=1.5in]{MEDIA/m2/mlab/contour3d}\\
- \end{columns}
-\begin{lstlisting}
-In []: x, y, z = mgrid[-5:5:64j,
-... -5:5:64j,
-... -5:5:64j]
-In []: mlab.contour3d(x*x*0.5 + y*y +
- z*z*2)
-\end{lstlisting}
-\end{frame}
-
-\begin{frame}[fragile]
-
- \myemph{\Large 3D vector data: \PythonCode{mlab.quiver3d}}
- \vspace*{0.25in}
-
- \pgfimage[width=2in]{MEDIA/m2/mlab/quiver3d_ex}\\
-
-\begin{lstlisting}
-In []: mlab.test_quiver3d()
-\end{lstlisting}
-
-\emphbar{\PythonCode{obj = mlab.quiver3d(x, y, z, u, v, w)}}
-\inctime{20}
-\end{frame}
-
-
-\subsection{Mayavi2}
-
-\begin{frame}
- \frametitle{Introduction to Mayavi}
- \begin{itemize}
- \item Most scientists not interested in details of visualization
- \item Visualization of data files with a nice UI
- \item Interactive visualization of data (think Matlab)
- \item Embedding visualizations in applications
- \item Customization
- \end{itemize}
+ \frametitle{Problem set 4}
+ Central difference
+ \begin{equation*}
+ \frac{sin(x+h)-sin(x-h)}{2h}
+ \end{equation*}
+ \begin{lstlisting}
+ In []: x = linspace(0, 2*pi, 100)
+ In []: y = sin(x)
+ In []: deltax = x[1] - x[0]
+ \end{lstlisting}
\pause
- \begin{block}{The Goal}
- Provide a \alert{flexible} library/app for all of these needs!
- \end{block}
+ \begin{enumerate}
+ \item Given this, get the finite difference of sin in the range 0 to 2*pi
+ \end{enumerate}
\end{frame}
\begin{frame}
- {Overview of features}
- \vspace*{-0.3in}
- \begin{center}
- \hspace*{-0.2in}\pgfimage[width=5in]{MEDIA/m2/m2_app3_3}
- \end{center}
-\end{frame}
-
-
-\begin{frame}
- \frametitle{Mayavi in applications}
- \vspace*{-0.3in}
- \begin{center}
- \hspace*{-0.2in}\pgfimage[width=4.5in]{MEDIA/m2/m2_envisage}
- \end{center}
-\end{frame}
-
-\begin{frame}
- \frametitle{Live in your dialogs}
- \vspace*{0.1in}
- \begin{center}
- \hspace*{-0.2in}\pgfimage[width=2.5in]{MEDIA/m2/mlab_tui}
- \end{center}
-\end{frame}
-
-\begin{frame}
- {Exploring the documentation}
- \begin{center}
- \pgfimage[width=4in]{MEDIA/m2/m2_ug_doc}
- \end{center}
-\end{frame}
-
-
-\begin{frame}
- \frametitle{Summary}
- \begin{itemize}
- \item \url{http://code.enthought.com/projects/mayavi}
- \item Uses VTK (\url{www.vtk.org})
- \item BSD license
- \item Linux, win32 and Mac OS X
- \item Highly scriptable
- \item Embed in Traits UIs (wxPython and PyQt4)
- \item Envisage Plugins
- \item Debian/Ubuntu/Fedora
- \item \alert{Pythonic}
- \end{itemize}
-
- \inctime{10}
-
-\end{frame}
-
-\begin{frame}
- {Getting hands dirty!}
-
- \begin{block}{Motivational problem}
- Atmospheric data of temperature over the surface of the earth.
- Let temperature ($T$) vary linearly with height ($z$):
- \begin{center}
- $T = 288.15 - 6.5z$
- \end{center}
- \end{block}
-\end{frame}
-
-\begin{frame}[fragile]
- \frametitle{Simple solution}
-
- \begin{lstlisting}
-lat = linspace(-89, 89, 37)
-lon = linspace(0, 360, 37)
-z = linspace(0, 100, 11)
- \end{lstlisting}
-\pause
- \begin{lstlisting}
-x, y, z = mgrid[0:360:37j,-89:89:37j,
- 0:100:11j]
-t = 288.15 - 6.5*z
-mlab.contour3d(x, y, z, t)
-mlab.outline()
-mlab.colorbar()
- \end{lstlisting}
+ \frametitle{Problem Set 5}
+ \begin{itemize}
+ \item[5.1] Write a function that plots any regular n-gon given \typ{n}.
+ \item[5.2] Consider the logistic map, $f(x) = kx(1-x)$, plot it for
+ $k=2.5, 3.5$ and $4$ in the same plot.
+\end{itemize}
\end{frame}
-\begin{frame}[fragile]
- \frametitle{Exercise: Lorenz equation}
- \begin{columns}
- \column{0.25\textwidth}
- \begin{eqnarray*}
- \frac{d x}{dt} &=& s (y-x)\\
- \frac{d y}{d t} &=& rx -y -xz\\
- \frac{d z}{d t} &=& xy - bz\\
- \end{eqnarray*}
- \column{0.25\textwidth}
- Let $s=10,$
- $r=28,$
- $b=8./3.$
- \end{columns}
- \structure{\Large Region of interest}
- \begin{lstlisting}
-x, y, z = mgrid[-50:50:20j,-50:50:20j,
- -10:60:20j]
- \end{lstlisting}
+\begin{frame}[fragile]
+\frametitle{Problem Set 5}
+ \begin{columns}
+ \column{0.6\textwidth}
+ \small{
+ \begin{itemize}
+ \item[3] Consider the iteration $x_{n+1} = f(x_n)$ where $f(x) = kx(1-x)$. Plot the successive iterates of this process as explained below.
+ \end{itemize}}
+ \column{0.35\textwidth}
+ \hspace*{-0.5in}
+ \includegraphics[height=1.6in, interpolate=true]{data/cobweb}
+\end{columns}
+\end{frame}
+
+\begin{frame}
+ \frametitle{Problem Set 5.3}
+ Plot the cobweb plot as follows:
+ \begin{enumerate}
+ \item Start at $(x_0, 0)$ ($\implies$ i=0)
+ \item Draw a line to $(x_i, f(x_i))$
+ \item Set $x_{i+1} = f(x_i)$
+ \item Draw a line to $(x_{i+1}, x_{i+1})$
+ \item $(i\implies i+1)$
+ \item Repeat from 2 for as long as you want
+ \end{enumerate}
\inctime{20}
-
-\end{frame}
-\begin{frame}[fragile]
- \frametitle{Solution}
- \begin{lstlisting}
-def lorenz(x,y,z,s=10.,r=28.,b=8./3.):
- u = s*(y-x)
- v = r*x-y-x*z
- w = x*y-b*z
- return u,v,w
-x,y,z = mgrid [-50:50:20j,-50:50:20j,
- -10:60:20j ]
-u,v,w = lorenz( x , y , z )
-# Your plot here
-#
-mlab.show()
-
- \end{lstlisting}
-\end{frame}
-
-\begin{frame}
- \frametitle{We have covered:}
- \begin{itemize}
- \item Need of visualization.
- \item Using mlab to create 3 D plots.
- \item Mayavi Toolkit.
- \end{itemize}
\end{frame}
\end{document}
-
generated by cgit (git 2.34.1) at 2024-12-20 11:19:04 +0000