1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
2 %Tutorial slides on Python. |
2 % Tutorial slides on Python. |
3 % |
3 % |
4 % Author: Prabhu Ramachandran <prabhu at aero.iitb.ac.in> |
4 % Author: Prabhu Ramachandran <prabhu at aero.iitb.ac.in> |
5 % Copyright (c) 2005-2009, Prabhu Ramachandran |
5 % Copyright (c) 2005-2009, Prabhu Ramachandran |
6 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
6 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
7 |
7 |
8 \documentclass[14pt,compress]{beamer} |
8 \documentclass[compress,14pt]{beamer} |
9 %\documentclass[draft]{beamer} |
9 % \documentclass[handout]{beamer} |
10 %\documentclass[compress,handout]{beamer} |
10 % \usepackage{pgfpages} |
11 %\usepackage{pgfpages} |
11 % \pgfpagesuselayout{4 on 1}[a4paper,border, shrink=5mm,landscape] |
12 %\pgfpagesuselayout{2 on 1}[a4paper,border shrink=5mm] |
12 \usepackage{tikz} |
13 |
13 \newcommand{\hyperlinkmovie}{} |
14 % Modified from: generic-ornate-15min-45min.de.tex |
14 %\usepackage{movie15} |
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15 |
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17 % Note that in presentation mode |
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18 % \paperwidth 364.19536pt |
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19 % \paperheight 273.14662pt |
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20 % h/w = 0.888 |
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21 |
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22 |
15 \mode<presentation> |
23 \mode<presentation> |
16 { |
24 { |
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25 \usetheme{Warsaw} |
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27 %\usetheme{default} |
18 \useoutertheme{infolines} |
28 \useoutertheme{infolines} |
19 \setbeamercovered{transparent} |
29 \setbeamercovered{transparent} |
20 } |
30 } |
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31 |
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32 % To remove navigation symbols |
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33 \setbeamertemplate{navigation symbols}{} |
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34 |
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35 \usepackage{amsmath} |
22 \usepackage[english]{babel} |
36 \usepackage[english]{babel} |
23 \usepackage[latin1]{inputenc} |
37 \usepackage[latin1]{inputenc} |
24 %\usepackage{times} |
38 \usepackage{times} |
25 \usepackage[T1]{fontenc} |
39 \usepackage[T1]{fontenc} |
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40 |
27 % Taken from Fernando's slides. |
41 % Taken from Fernando's slides. |
28 \usepackage{ae,aecompl} |
42 \usepackage{ae,aecompl} |
29 \usepackage{mathpazo,courier,euler} |
43 \usepackage{mathpazo,courier,euler} |
30 \usepackage[scaled=.95]{helvet} |
44 \usepackage[scaled=.95]{helvet} |
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45 \usepackage{pgf} |
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46 |
32 \definecolor{darkgreen}{rgb}{0,0.5,0} |
47 \definecolor{darkgreen}{rgb}{0,0.5,0} |
33 |
48 |
34 \usepackage{listings} |
49 \usepackage{listings} |
35 \lstset{language=Python, |
50 \lstset{language=Python, |
38 stringstyle=\color{darkgreen}, |
53 stringstyle=\color{darkgreen}, |
39 showstringspaces=false, |
54 showstringspaces=false, |
40 keywordstyle=\color{blue}\bfseries} |
55 keywordstyle=\color{blue}\bfseries} |
41 |
56 |
42 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
57 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
43 % Macros |
58 % My Macros |
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59 \setbeamercolor{postit}{bg=yellow,fg=black} |
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60 \setbeamercolor{emphbar}{bg=blue!20, fg=black} |
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47 {#1} |
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49 } |
65 } |
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68 % {#1} |
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69 %\end{minipage} |
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70 % }}} |
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71 |
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72 \newcommand{\myemph}[1]{\structure{\emph{#1}}} |
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73 \newcommand{\PythonCode}[1]{\lstinline{#1}} |
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74 |
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75 \newcommand{\tvtk}{\texttt{tvtk}} |
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76 \newcommand{\mlab}{\texttt{mlab}} |
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77 |
50 \newcounter{time} |
78 \newcounter{time} |
51 \setcounter{time}{0} |
79 \setcounter{time}{0} |
52 \newcommand{\inctime}[1]{\addtocounter{time}{#1}{\tiny \thetime\ m}} |
80 \newcommand{\inctime}[1]{\addtocounter{time}{#1}{\vspace*{0.1in}\tiny \thetime\ m}} |
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81 |
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56 \newcommand{\kwrd}[1]{ \texttt{\textbf{\color{blue}{#1}}} } |
84 \parbox[c][\paperheight]{\paperwidth}{% |
57 |
85 \vfill \hfill |
58 %%% This is from Fernando's setup. |
86 \hfill \vfill |
59 % \usepackage{color} |
87 }}} |
60 % \definecolor{orange}{cmyk}{0,0.4,0.8,0.2} |
88 |
61 % % Use and configure listings package for nicely formatted code |
89 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
62 % \usepackage{listings} |
90 % Configuring the theme |
63 % \lstset{ |
91 %\setbeamercolor{normal text}{fg=white} |
64 % language=Python, |
92 %\setbeamercolor{background canvas}{bg=black} |
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69 % breaklines=true, |
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70 % postbreak = \space\dots |
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71 % } |
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72 |
94 |
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74 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
96 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
75 % Title page |
97 % Title page |
76 \title[Exercises]{Exercises} |
98 \title[3D Plotting]{3D data Visualization} |
77 |
99 |
78 \author[FOSSEE] {FOSSEE} |
100 \author[FOSSEE] {FOSSEE} |
79 |
101 |
80 \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay} |
102 \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay} |
81 \date[] {8 November, 2009\\Day 2, Session 5} |
103 \date[] {8 November, 2009\\Day 2, Session 5} |
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104 |
82 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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106 |
84 %\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo} |
107 %\pgfdeclareimage[height=0.75cm]{iitblogo}{iitblogo} |
85 %\logo{\pgfuseimage{iitmlogo}} |
108 %\logo{\pgfuseimage{iitblogo}} |
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109 |
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110 \AtBeginSection[] |
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111 { |
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112 \begin{frame}<beamer> |
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113 \frametitle{Outline} |
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114 \tableofcontents[currentsection,currentsubsection] |
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115 \end{frame} |
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116 } |
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117 |
88 %% Delete this, if you do not want the table of contents to pop up at |
118 %% Delete this, if you do not want the table of contents to pop up at |
89 %% the beginning of each subsection: |
119 %% the beginning of each subsection: |
90 \AtBeginSubsection[] |
120 \AtBeginSubsection[] |
91 { |
121 { |
93 \frametitle{Outline} |
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94 \tableofcontents[currentsection,currentsubsection] |
124 \tableofcontents[currentsection,currentsubsection] |
95 \end{frame} |
125 \end{frame} |
96 } |
126 } |
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98 |
128 \AtBeginSection[] |
99 % If you wish to uncover everything in a step-wise fashion, uncomment |
129 { |
100 % the following command: |
130 \begin{frame}<beamer> |
101 %\beamerdefaultoverlayspecification{<+->} |
131 \frametitle{Outline} |
102 |
132 \tableofcontents[currentsection,currentsubsection] |
103 %\includeonlyframes{current,current1,current2,current3,current4,current5,current6} |
133 \end{frame} |
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134 } |
105 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
135 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
106 % DOCUMENT STARTS |
136 % DOCUMENT STARTS |
107 \begin{document} |
137 \begin{document} |
108 |
138 |
109 \begin{frame} |
139 \begin{frame} |
110 \titlepage |
140 \maketitle |
111 \end{frame} |
141 \end{frame} |
112 |
142 |
113 \begin{frame}{Problem 1.1} |
143 \begin{frame} |
114 The aliquot of a number is defined as: the sum of the \emph{proper} divisors of the number. \\For example: |
144 \frametitle{Outline} |
115 \center{aliquot(12) = 1 + 2 + 3 + 4 + 6 = 16.}\\ |
145 \tableofcontents |
116 Write a function that returns the aliquot number of a given number. |
146 % You might wish to add the option [pausesections] |
117 \end{frame} |
147 \end{frame} |
118 |
148 |
119 \begin{frame}{Problem 1.2} |
149 \section{3D Data Visualization} |
120 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.\\ |
150 |
121 Example: \texttt{220, 284}\\ |
151 \begin{frame} |
122 Write a program that prints all four digit amicable pairs. |
152 \frametitle{What is visualization?} |
123 |
153 \Large |
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154 \begin{center} |
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155 Visual representation of data |
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156 \end{center} |
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157 \end{frame} |
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158 |
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159 |
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160 %% \begin{frame} |
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161 %% \frametitle{Is this new?} |
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162 %% \begin{center} |
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163 %% We have moved from: |
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164 %% \end{center} |
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165 %% \begin{columns} |
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166 %% \column{} |
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167 %% \hspace*{-1in} |
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168 %% \includegraphics[width=1.75in,height=1.75in, interpolate=true]{data/3832} |
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169 %% \column{}\hspace*{-0.25in} |
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170 %% To |
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171 %% \column{} |
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172 %% \hspace*{-1in} |
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173 %% \includegraphics[width=1.75in, height=1.75in, interpolate=true]{data/torus} |
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174 %% \end{columns} |
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175 %% \end{frame} |
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176 |
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177 \begin{frame} |
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178 \frametitle{3D visualization} |
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179 \Large |
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180 \begin{center} |
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181 Harder but important |
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182 \end{center} |
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183 \end{frame} |
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184 |
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185 \begin{frame} |
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186 \frametitle{Is this Graphics?} |
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187 \Large |
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188 \begin{center} |
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189 Visualization is about data! |
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190 \end{center} |
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191 \end{frame} |
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192 |
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193 \begin{frame} |
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194 \frametitle{Examples: trajectory in space} |
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195 \Large |
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196 \begin{center} |
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197 \pgfimage[width=2.5in]{MEDIA/m2/mlab/plot3d_ex} |
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198 \end{center} |
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199 \end{frame} |
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200 |
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201 \begin{frame} |
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202 \frametitle{Examples: Fire in a room} |
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203 \Large |
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204 \begin{center} |
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205 Demo of data |
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206 \end{center} |
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207 \inctime{10} |
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208 \end{frame} |
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209 |
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210 \section{Tools available} |
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211 |
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212 \subsection{mlab} |
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213 |
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214 \begin{frame} |
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215 {Overview} |
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216 \Large |
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217 \begin{itemize} |
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218 \item Simple |
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219 \item Convenient |
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220 \item Full-featured |
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221 \end{itemize} |
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222 \end{frame} |
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223 |
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224 \begin{frame}[fragile] |
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225 |
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226 \frametitle{Getting started} |
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227 \myemph{\Large Vanilla:} |
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228 \begin{lstlisting}[language=bash] |
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229 $ ipython -wthread |
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230 \end{lstlisting} |
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231 \myemph{\Large with Pylab:} |
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232 \begin{lstlisting}[language=bash] |
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233 $ ipython -pylab -wthread |
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234 \end{lstlisting} |
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235 \end{frame} |
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236 |
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237 \begin{frame}[fragile] |
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238 \frametitle{Using mlab} |
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239 |
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240 \begin{lstlisting} |
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241 In []:from enthought.mayavi import mlab |
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242 \end{lstlisting} |
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243 |
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244 \vspace*{0.5in} |
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245 |
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246 \myemph{\Large Try these} |
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247 |
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248 \vspace*{0.25in} |
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249 |
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250 \begin{lstlisting} |
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251 In []: mlab.test_<TAB> |
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252 In []: mlab.test_contour3d() |
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253 In []: mlab.test_contour3d?? |
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254 \end{lstlisting} |
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255 \end{frame} |
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256 |
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257 \begin{frame} |
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258 {Exploring the view} |
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259 \begin{columns} |
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260 \column{0.6\textwidth} |
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261 \pgfimage[width=3in]{MEDIA/m2/contour3d} |
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262 \column{0.4\textwidth} |
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263 \begin{itemize} |
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264 \item Mouse |
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265 \item Keyboard |
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266 \item Toolbar |
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267 \item Mayavi icon\pgfimage[width=0.2in]{MEDIA/m2/m2_icon} |
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268 \end{itemize} |
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269 \end{columns} |
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270 \end{frame} |
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271 |
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272 \begin{frame}[fragile] |
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273 \frametitle{\mlab\ plotting functions} |
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274 \begin{columns} |
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275 \column{0.25\textwidth} |
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276 \myemph{\Large 0D data} |
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277 \column{0.5\textwidth} |
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278 \pgfimage[width=2in]{MEDIA/m2/mlab/points3d_ex} |
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279 \end{columns} |
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280 |
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281 \begin{lstlisting} |
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282 In []: t = linspace(0, 2*pi, 50) |
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283 In []: u = cos(t) * pi |
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284 In []: x, y, z = sin(u), cos(u), sin(t) |
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285 \end{lstlisting} |
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286 \emphbar{\PythonCode{In []: mlab.points3d(x, y, z)}} |
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287 \end{frame} |
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288 |
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289 \begin{frame} |
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290 \begin{columns} |
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291 \column{0.25\textwidth} |
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292 \myemph{\Large 1D data} |
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293 \column{0.5\textwidth} |
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294 \pgfimage[width=2.5in]{MEDIA/m2/mlab/plot3d_ex} |
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295 \end{columns} |
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296 \emphbar{\PythonCode{In []: mlab.plot3d(x, y, z, t)}} |
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297 |
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298 Plots lines between the points |
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299 |
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300 \end{frame} |
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301 |
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302 \begin{frame}[fragile] |
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303 \begin{columns} |
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304 \column{0.25\textwidth} |
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305 \myemph{\Large 2D data} |
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306 \column{0.5\textwidth} |
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307 \pgfimage[width=2in]{MEDIA/m2/mlab/surf_ex} |
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308 \end{columns} |
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309 \begin{lstlisting} |
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310 In []: x, y = mgrid[-3:3:100j,-3:3:100j] |
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311 In []: z = sin(x*x + y*y) |
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312 \end{lstlisting} |
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313 |
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314 \emphbar{\PythonCode{In []: mlab.surf(x, y, z)}} |
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315 |
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316 \alert{Assumes the points are rectilinear} |
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317 |
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318 \end{frame} |
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319 |
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320 \begin{frame}[fragile] |
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321 \frametitle{mgrid} |
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322 \begin{lstlisting} |
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323 In []: mgrid[0:3,0:3] |
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324 Out[]: |
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325 array([[[0, 0, 0], |
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326 [1, 1, 1], |
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327 [2, 2, 2]], |
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328 |
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329 [[0, 1, 2], |
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330 [0, 1, 2], |
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331 [0, 1, 2]]]) |
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332 |
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333 In []: mgrid[-1:1:5j] |
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334 Out[]: array([-1., -0.5, 0., 0.5, 1.]) |
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335 \end{lstlisting} |
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336 \end{frame} |
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337 |
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338 \begin{frame}[fragile] |
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339 \frametitle{Example} |
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340 \begin{lstlisting} |
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341 In []: x, y = mgrid[-1:1:5j, -1:1:5j] |
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342 In []: z = x*x + y*y |
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343 |
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344 In []: z |
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345 Out[]: |
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346 array([[ 2. , 1.25, 1. , 1.25, 2. ], |
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347 [ 1.25, 0.5 , 0.25, 0.5 , 1.25], |
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348 [ 1. , 0.25, 0. , 0.25, 1. ], |
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349 [ 1.25, 0.5 , 0.25, 0.5 , 1.25], |
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350 [ 2. , 1.25, 1. , 1.25, 2. ]]) |
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351 \end{lstlisting} |
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352 \end{frame} |
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353 |
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354 \begin{frame}[fragile] |
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355 \myemph{\Large 2D data: \texttt{mlab.mesh}} |
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356 \vspace*{0.25in} |
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357 |
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358 \emphbar{\PythonCode{In []: mlab.mesh(x, y, z)}} |
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359 |
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360 \alert{Points needn't be regular} |
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361 |
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362 \vspace*{0.25in} |
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363 \begin{lstlisting} |
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364 In []: phi, theta = mgrid[0:pi:20j, |
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365 ... 0:2*pi:20j] |
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366 In []: x = sin(phi)*cos(theta) |
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367 In []: y = sin(phi)*sin(theta) |
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368 In []: z = cos(phi) |
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369 In []: mlab.mesh(x, y, z, |
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370 ... representation= |
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371 ... 'wireframe') |
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372 \end{lstlisting} |
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373 |
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374 \end{frame} |
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375 |
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376 \begin{frame}[fragile] |
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377 |
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378 \begin{columns} |
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379 \column{0.25\textwidth} |
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380 \myemph{\Large 3D data} |
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381 \column{0.5\textwidth} |
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382 \pgfimage[width=1.5in]{MEDIA/m2/mlab/contour3d}\\ |
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383 \end{columns} |
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384 \begin{lstlisting} |
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385 In []: x, y, z = mgrid[-5:5:64j, |
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386 ... -5:5:64j, |
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387 ... -5:5:64j] |
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388 In []: mlab.contour3d(x*x*0.5 + y*y + |
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389 z*z*2) |
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390 \end{lstlisting} |
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391 \end{frame} |
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392 |
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393 \begin{frame}[fragile] |
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394 |
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395 \myemph{\Large 3D vector data: \PythonCode{mlab.quiver3d}} |
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396 \vspace*{0.25in} |
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397 |
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398 \pgfimage[width=2in]{MEDIA/m2/mlab/quiver3d_ex}\\ |
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399 |
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400 \begin{lstlisting} |
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401 In []: mlab.test_quiver3d() |
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402 \end{lstlisting} |
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403 |
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404 \emphbar{\PythonCode{obj = mlab.quiver3d(x, y, z, u, v, w)}} |
124 \inctime{20} |
405 \inctime{20} |
125 \end{frame} |
406 \end{frame} |
126 |
407 |
127 %% \begin{frame}{Problem 2} |
408 |
128 %% 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. |
409 \subsection{Mayavi2} |
129 |
410 |
130 %% \end{frame} |
411 \begin{frame} |
131 |
412 \frametitle{Introduction to Mayavi} |
132 \begin{frame}[fragile] |
413 \begin{itemize} |
133 \frametitle{Problem Set 2} |
414 \item Most scientists not interested in details of visualization |
134 Given a string like, ``1, 3-7, 12, 15, 18-21'', produce the list \\ |
415 \item Visualization of data files with a nice UI |
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416 \item Interactive visualization of data (think Matlab) |
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417 \item Embedding visualizations in applications |
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418 \item Customization |
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419 \end{itemize} |
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420 \pause |
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421 \begin{block}{The Goal} |
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422 Provide a \alert{flexible} library/app for all of these needs! |
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423 \end{block} |
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424 \end{frame} |
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425 |
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426 \begin{frame} |
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427 {Overview of features} |
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428 \vspace*{-0.3in} |
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429 \begin{center} |
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430 \hspace*{-0.2in}\pgfimage[width=5in]{MEDIA/m2/m2_app3_3} |
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431 \end{center} |
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432 \end{frame} |
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433 |
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434 |
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435 \begin{frame} |
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436 \frametitle{Mayavi in applications} |
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437 \vspace*{-0.3in} |
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438 \begin{center} |
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439 \hspace*{-0.2in}\pgfimage[width=4.5in]{MEDIA/m2/m2_envisage} |
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440 \end{center} |
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441 \end{frame} |
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442 |
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443 \begin{frame} |
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444 \frametitle{Live in your dialogs} |
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445 \vspace*{0.1in} |
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446 \begin{center} |
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447 \hspace*{-0.2in}\pgfimage[width=2.5in]{MEDIA/m2/mlab_tui} |
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448 \end{center} |
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449 \end{frame} |
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450 |
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451 \begin{frame} |
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452 {Exploring the documentation} |
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453 \begin{center} |
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454 \pgfimage[width=4in]{MEDIA/m2/m2_ug_doc} |
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455 \end{center} |
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456 \end{frame} |
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457 |
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458 |
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459 \begin{frame} |
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460 \frametitle{Summary} |
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461 \begin{itemize} |
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462 \item \url{http://code.enthought.com/projects/mayavi} |
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463 \item Uses VTK (\url{www.vtk.org}) |
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464 \item BSD license |
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465 \item Linux, win32 and Mac OS X |
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466 \item Highly scriptable |
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467 \item Embed in Traits UIs (wxPython and PyQt4) |
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468 \item Envisage Plugins |
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469 \item Debian/Ubuntu/Fedora |
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470 \item \alert{Pythonic} |
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471 \end{itemize} |
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472 |
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473 \inctime{10} |
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474 |
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475 \end{frame} |
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476 |
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477 \begin{frame} |
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478 {Getting hands dirty!} |
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479 |
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480 \begin{block}{Motivational problem} |
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481 Atmospheric data of temperature over the surface of the earth. |
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482 Let temperature ($T$) vary linearly with height ($z$): |
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483 \begin{center} |
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484 $T = 288.15 - 6.5z$ |
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485 \end{center} |
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486 \end{block} |
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487 \end{frame} |
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488 |
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489 \begin{frame}[fragile] |
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490 \frametitle{Simple solution} |
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491 |
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492 \begin{lstlisting} |
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493 lat = linspace(-89, 89, 37) |
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494 lon = linspace(0, 360, 37) |
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495 z = linspace(0, 100, 11) |
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496 \end{lstlisting} |
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497 \pause |
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498 \begin{lstlisting} |
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499 x, y, z = mgrid[0:360:37j,-89:89:37j, |
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500 0:100:11j] |
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501 t = 288.15 - 6.5*z |
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502 mlab.contour3d(x, y, z, t) |
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503 mlab.outline() |
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504 mlab.colorbar() |
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505 \end{lstlisting} |
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506 \end{frame} |
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507 |
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508 \begin{frame}[fragile] |
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509 \frametitle{Exercise: Lorenz equation} |
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510 \begin{columns} |
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511 \column{0.25\textwidth} |
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512 \begin{eqnarray*} |
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513 \frac{d x}{dt} &=& s (y-x)\\ |
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514 \frac{d y}{d t} &=& rx -y -xz\\ |
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515 \frac{d z}{d t} &=& xy - bz\\ |
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516 \end{eqnarray*} |
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517 \column{0.25\textwidth} |
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518 Let $s=10,$ |
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519 $r=28,$ |
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520 $b=8./3.$ |
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521 \end{columns} |
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522 \structure{\Large Region of interest} |
135 \begin{lstlisting} |
523 \begin{lstlisting} |
136 [1,3,4,5,6,7,12,15,18,19,20,21] |
524 x, y, z = mgrid[-50:50:20j,-50:50:20j, |
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525 -10:60:20j] |
137 \end{lstlisting} |
526 \end{lstlisting} |
138 \inctime{10} |
527 \inctime{20} |
139 \end{frame} |
528 |
140 |
529 \end{frame} |
141 \begin{frame} |
530 \begin{frame}[fragile] |
142 \frametitle{Problem Set 3} |
531 \frametitle{Solution} |
143 \begin{description} |
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144 \item[3.1] Count word frequencies in a file. |
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145 \end{description} |
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146 \inctime{5} |
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147 \end{frame} |
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148 |
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149 \begin{frame}[fragile] |
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150 \frametitle{Problem set 4} |
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151 Central difference |
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152 \begin{equation*} |
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153 \frac{sin(x+h)-sin(x-h)}{2h} |
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154 \end{equation*} |
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155 \begin{lstlisting} |
532 \begin{lstlisting} |
156 In []: x = linspace(0, 2*pi, 100) |
533 def lorenz(x,y,z,s=10.,r=28.,b=8./3.): |
157 In []: y = sin(x) |
534 u = s*(y-x) |
158 In []: deltax = x[1] - x[0] |
535 v = r*x-y-x*z |
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536 w = x*y-b*z |
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537 return u,v,w |
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538 x,y,z = mgrid [-50:50:20j,-50:50:20j, |
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539 -10:60:20j ] |
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540 u,v,w = lorenz( x , y , z ) |
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541 # Your plot here |
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542 # |
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543 mlab.show() |
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544 |
159 \end{lstlisting} |
545 \end{lstlisting} |
160 \pause |
546 \end{frame} |
161 \begin{enumerate} |
547 |
162 \item Given this, get the finite difference of sin in the range 0 to 2*pi |
548 \begin{frame} |
163 \end{enumerate} |
549 \frametitle{We have covered:} |
164 \end{frame} |
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165 |
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166 \begin{frame} |
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167 \frametitle{Problem Set 5} |
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168 \begin{itemize} |
550 \begin{itemize} |
169 \item[5.1] Write a function that plots any regular n-gon given \typ{n}. |
551 \item Need of visualization. |
170 \item[5.2] Consider the logistic map, $f(x) = kx(1-x)$, plot it for |
552 \item Using mlab to create 3 D plots. |
171 $k=2.5, 3.5$ and $4$ in the same plot. |
553 \item Mayavi Toolkit. |
172 \end{itemize} |
554 \end{itemize} |
173 \end{frame} |
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174 |
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175 \begin{frame}[fragile] |
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176 \frametitle{Problem Set 5} |
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177 \begin{columns} |
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178 \column{0.6\textwidth} |
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179 \small{ |
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180 \begin{itemize} |
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181 \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. |
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182 \end{itemize}} |
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183 \column{0.35\textwidth} |
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184 \hspace*{-0.5in} |
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185 \includegraphics[height=1.6in, interpolate=true]{data/cobweb} |
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186 \end{columns} |
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187 \end{frame} |
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188 |
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189 \begin{frame} |
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190 \frametitle{Problem Set 5.3} |
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191 Plot the cobweb plot as follows: |
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192 \begin{enumerate} |
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193 \item Start at $(x_0, 0)$ ($\implies$ i=0) |
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194 \item Draw a line to $(x_i, f(x_i))$ |
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195 \item Set $x_{i+1} = f(x_i)$ |
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196 \item Draw a line to $(x_{i+1}, x_{i+1})$ |
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197 \item $(i\implies i+1)$ |
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198 \item Repeat from 2 for as long as you want |
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199 \end{enumerate} |
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200 \inctime{20} |
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201 \end{frame} |
555 \end{frame} |
202 |
556 |
203 \end{document} |
557 \end{document} |
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558 |