1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

     2 % Tutorial slides on Python.

     3 %

     4 % Author: Prabhu Ramachandran <prabhu at aero.iitb.ac.in>

     5 % Copyright (c) 2005-2008, Prabhu Ramachandran

     6 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

     7 

     8 \documentclass[14pt,compress]{beamer}

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    14 % Modified from: generic-ornate-15min-45min.de.tex

    15 \mode<presentation>

    16 {

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    22 \usepackage[english]{babel}

    23 \usepackage[latin1]{inputenc}

    24 %\usepackage{times}

    25 \usepackage[T1]{fontenc}

    26 

    27 % Taken from Fernando's slides.

    28 \usepackage{ae,aecompl}

    29 \usepackage{mathpazo,courier,euler}

    30 \usepackage[scaled=.95]{helvet}

    31 

    32 \definecolor{darkgreen}{rgb}{0,0.5,0}

    33 

    34 \usepackage{listings}

    35 \lstset{language=Python,

    36     basicstyle=\ttfamily\bfseries,

    37     commentstyle=\color{red}\itshape,

    38   stringstyle=\color{darkgreen},

    39   showstringspaces=false,

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    41 

    42 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    43 % Macros

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    56 \newcommand{\kwrd}[1]{ \texttt{\textbf{\color{blue}{#1}}}  }

    57 

    58 %%% This is from Fernando's setup.

    59 % \usepackage{color}

    60 % \definecolor{orange}{cmyk}{0,0.4,0.8,0.2}

    61 % % Use and configure listings package for nicely formatted code

    62 % \usepackage{listings}

    63 % \lstset{

    64 %    language=Python,

    65 %    basicstyle=\small\ttfamily,

    66 %    commentstyle=\ttfamily\color{blue},

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    70 %    postbreak = \space\dots

    71 % }

    72 

    73 

    74 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    75 % Title page

    76 \title[Basic Python]{Python,\\a great programming toolkit:\\

    77 numerics and plotting}

    78 

    79 \author[Asokan \& Prabhu] {Asokan Pichai\\Prabhu Ramachandran}

    80 

    81 \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}

    82 \date[] {26, July 2009}

    83 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    84 

    85 %\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo}

    86 %\logo{\pgfuseimage{iitmlogo}}

    87 

    88 

    89 %% Delete this, if you do not want the table of contents to pop up at

    90 %% the beginning of each subsection:

    91 \AtBeginSubsection[]

    92 {

    93   \begin{frame}<beamer>

    94     \frametitle{Outline}

    95     \tableofcontents[currentsection,currentsubsection]

    96   \end{frame}

    97 }

    98 

    99 \AtBeginSection[]

   100 {

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   102     \frametitle{Outline}

   103     \tableofcontents[currentsection,currentsubsection]

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   105 }

   106 

   107 % If you wish to uncover everything in a step-wise fashion, uncomment

   108 % the following command: 

   109 %\beamerdefaultoverlayspecification{<+->}

   110 

   111 %\includeonlyframes{current,current1,current2,current3,current4,current5,current6}

   112 

   113 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   114 % DOCUMENT STARTS

   115 \begin{document}

   116 

   117 \begin{frame}

   118   \titlepage

   119 \end{frame}

   120 \begin{frame}

   121   {Acknowledgements}

   122   \begin{center}

   123   This program is conducted by\\

   124   IIT, Bombay\\

   125   through CDEEP\\

   126   as part of  the open source initiatives\\

   127   under the aegis of\\

   128   \alert{National Mission on Education through ICT,} \\

   129   Ministry of HRD.

   130   \end{center}

   131 \end{frame}

   132 

   133 \begin{frame}

   134   \frametitle{Outline}

   135   \tableofcontents

   136   % You might wish to add the option [pausesections]

   137 \end{frame}

   138 

   139 \begin{frame}{Goal of the Workshop}

   140 

   141         At the end of this program, successful participants will be able

   142         to use python as their scripting and problem solving language.

   143         Aimed at Engg. students--focus on basic numerics and plotting--

   144         but should serve a similar purpose for others.\\

   145 

   146         At the minimum you will be able to use Python for your plotting immediately.

   147 

   148 \end{frame}

   149 

   150 \begin{frame}{Checklist}

   151     

   152   \begin{description}

   153 	\item[pylab] matplotlib interface 

   154 	\item[numpy] Array computing

   155         \item[scipy] numerical work

   156         \item[mayavi] \typ{enthought.mayavi}: 3D viz.

   157   \end{description}

   158 \end{frame}

   159 

   160 \section{30000 feet view}

   161 \begin{frame}{Lets see what we can do!}

   162   \huge

   163   Hold on to your seatbelts

   164 \end{frame}

   165 

   166 \begin{frame}

   167   {That was done by\ldots}

   168   \begin{description}[CalisthenicsIsAnArt]

   169       \item[Arrays] 2--3 lines; 5 minutes to learn

   170       \item[2D plots] 5 lines; 10 minutes to learn

   171       \item[Simple 3D plots] 5 lines; 10 minutes to learn; GUI

   172           exploration!

   173       \item[Complex plots] relatively short (10-15 lines); more time to master; 

   174   \end{description}

   175   \inctime{15}

   176 \end{frame}

   177 

   178 \section{Matplotlib}

   179 

   180 \subsection{Basic \typ{numpy} }

   181 

   182 \newcommand{\num}{\texttt{numpy}}

   183 

   184 \begin{frame}

   185   \frametitle{The \num\ module}

   186   \begin{itemize}

   187       \item Why?

   188   \item What:

   189     \begin{itemize}

   190     \item An efficient and powerful array type for various common data

   191       types

   192     \item Abstracts out the most commonly used standard operations on

   193       arrays

   194     \end{itemize}

   195   \end{itemize}

   196 \end{frame}

   197 

   198 \begin{frame}[fragile]

   199   \frametitle{Examples of \num}

   200 \begin{lstlisting}

   201 # Simple array math example

   202 >>> from numpy import *

   203 >>> a = array([1,2,3,4])

   204 >>> b = array([2,3,4,5])

   205 >>> a*2 + b + 1 # Basic math!

   206 array([5, 8, 11, 14])

   207 # Pi and e are defined.

   208 >>> x = linspace(0.0, 10.0, 1000)

   209 >>> x *= 2*pi/10 # inplace.

   210 # apply functions to array.

   211 >>> y = sin(x)

   212 \end{lstlisting}

   213 \end{frame}

   214 

   215 \begin{frame}

   216   \frametitle{Basic concepts}

   217   \begin{itemize}

   218   \item fixed size (\typ{arr.size});

   219   \item Same type (\typ{arr.dtype}) of data

   220   \item arbitrary dimensionality

   221   \item \typ{arr.shape}: size in each dimension

   222   \item \alert{Note:} \typ{len(arr) != arr.size} in general

   223   \item \alert{Note:} By default array operations are performed

   224     \alert{elementwise}

   225   \item Indices, slicing: just like lists 

   226   \end{itemize}

   227 \end{frame}

   228 

   229 

   230 \begin{frame}[fragile]

   231   \frametitle{More examples of \num}

   232 \vspace*{-8pt}

   233 \begin{lstlisting}

   234 >>> x = array([1., 2, 3, 4])

   235 >>> size(x)

   236 4

   237 >>> x.dtype # What is a.dtype?

   238 dtype('float64')

   239 >>> x.shape

   240 (4,)

   241 >>> print rank(x), x.itemsize

   242 1 8

   243 >>> x[0] = 10

   244 >>> print x[0], x[-1]

   245 10.0 4.0

   246 \end{lstlisting}

   247     

   248 \inctime{10}

   249 \end{frame}

   250 

   251 

   252 

   253 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   254 \subsection{Plotting with \typ{pylab}}

   255 

   256 \begin{frame}

   257     {IPython's \typ{pylab} mode}

   258 \begin{itemize}

   259     \item \typ{pylab}: convenient 2D plotting interface to MPL

   260     \item Immediate use: \typ{ipython -pylab}

   261     \item Imports all of pylab for you!

   262     \item Allows for interactive plotting

   263 \end{itemize}

   264 \end{frame}

   265 

   266 \begin{frame}[fragile]

   267     \frametitle{Basic 2D plotting}

   268 

   269 \begin{lstlisting}

   270 >>> x = linspace(0, 2*pi, 1000)

   271 >>> plot(x, sin(x)) 

   272 >>> plot(x, sin(x), 'ro')

   273 >>> xlabel(r'$\chi$', color='g')

   274 # LaTeX markup!

   275 >>> ylabel(r'sin($\chi$)', color='r')

   276 >>> title('Simple figure', fontsize=20)

   277 >>> savefig('/tmp/test.eps')

   278 \end{lstlisting}

   279 \begin{itemize}

   280   \item Also: PNG, PDF, PS, EPS, SVG, PDF

   281 \end{itemize}

   282 \end{frame}

   283        

   284 

   285 \begin{frame}[fragile]

   286   \frametitle{Basic plotting \ldots}

   287 \begin{lstlisting}

   288 # Set properties of objects:

   289 >>> l, = plot(x, sin(x))

   290 # Why "l,"?

   291 >>> setp(l, linewidth=2.0, color='r')

   292 >>> l.set_linewidth(2.0)

   293 >>> draw() # Redraw.

   294 >>> setp(l) # Print properties

   295 >>> clf() # Clear figure.

   296 >>> close() # Close figure.

   297 \end{lstlisting}

   298 \end{frame}

   299 

   300 \begin{frame}[fragile]

   301     \frametitle{Multiple figures}

   302 

   303 \begin{lstlisting}

   304 >>> figure(1)

   305 >>> plot(x, sin(x))

   306 >>> figure(2)

   307 >>> plot(x, tanh(x))

   308 >>> figure(1)

   309 >>> title('Easy as 1,2,3')

   310 \end{lstlisting}

   311     

   312 \end{frame}

   313 

   314 

   315 \begin{frame}[fragile]

   316   \frametitle{Legends and Annotation}

   317 \begin{lstlisting}

   318 >>> plot(x, cos(5*x), 'r--', 

   319          label='cosine')

   320 >>> plot(x, sin(5*x), 'g--', 

   321          label='sine')

   322 >>> legend() 

   323 # Or use:

   324 >>> legend(['cosine', 'sine'])

   325 # Annotation:

   326 >>> text(1,0, '(1,0)')

   327 \end{lstlisting}

   328 \end{frame}

   329 

   330 \begin{frame}[fragile]

   331     \frametitle{More commands \ldots}

   332     \begin{lstlisting}

   333 # semilog, loglog 

   334 >>> x = 10.**(-arange(100)*0.1)

   335 >>> semilogx(x, x)

   336 >>> semilogy(x, x)

   337 >>> loglog(x, x)

   338 >>> loglog(x, x*x)

   339     \end{lstlisting}

   340 \end{frame}

   341 

   342 \begin{frame}[fragile]

   343     \frametitle{More plots \ldots}

   344     \begin{lstlisting}

   345 >>> clf()

   346 >>> t = arange(0.1, 4, 0.1)

   347 >>> s = exp(-t)

   348 >>> e = 0.1*abs(randn(len(s)))

   349 >>> errorbar(t, s, e)

   350 # Scatter plots

   351 >>> clf()

   352 >>> t = randn(len(e))

   353 >>> scatter(t, e, c=s)

   354     \end{lstlisting}

   355 \end{frame}

   356 

   357 \begin{frame}[fragile]

   358     \frametitle{Note: \typ{pylab} in Python scripts}

   359 \begin{lstlisting}

   360 import pylab

   361 x = pylab.linspace(0, 20, 1000)

   362 pylab.plot(x, pylab.sin(x))

   363 

   364 # Can also use:

   365 from pylab import linspace, sin, plot

   366 \end{lstlisting}

   367 \end{frame}

   368 

   369 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   370 

   371 \begin{frame}[fragile]

   372   \frametitle{X-Y plot}

   373   \begin{columns}

   374     \column{0.5\textwidth}

   375     \hspace*{-0.5in}

   376     \includegraphics[height=2in, interpolate=true]{data/xyplot}

   377     \column{0.45\textwidth}

   378     \begin{block}{Example code}

   379     \tiny

   380 \begin{lstlisting}

   381 t1 = arange(0.0, 5.0, 0.1)

   382 t2 = arange(0.0, 5.0, 0.02)

   383 t3 = arange(0.0, 2.0, 0.01)

   384 subplot(211)

   385 plot(t1, cos(2*pi*t1)*exp(-t1), 'bo', 

   386      t2, cos(2*pi*t2)*exp(-t2), 'k')

   387 grid(True)

   388 title('A tale of 2 subplots')

   389 ylabel('Damped')

   390 subplot(212)

   391 plot(t3, cos(2*pi*t3), 'r--')

   392 grid(True)

   393 xlabel('time (s)')

   394 ylabel('Undamped')

   395 \end{lstlisting}

   396     \end{block}

   397   \end{columns}

   398 \end{frame}

   399 

   400 \begin{frame}[fragile] \frametitle{Semi-log and log-log plots}

   401   \begin{columns}

   402     \column{0.5\textwidth}

   403     \hspace*{-0.5in}

   404   \includegraphics[height=2in, interpolate=true]{data/log}  

   405     \column{0.45\textwidth}

   406     \begin{block}{Example code}

   407     \tiny

   408 \begin{lstlisting}

   409 dt = 0.01

   410 t = arange(dt, 20.0, dt)

   411 subplot(311)

   412 semilogy(t, exp(-t/5.0))

   413 ylabel('semilogy')

   414 grid(True)

   415 subplot(312)

   416 semilogx(t, sin(2*pi*t))

   417 ylabel('semilogx')

   418 grid(True)

   419 # minor grid on too

   420 gca().xaxis.grid(True, which='minor')  

   421 subplot(313)

   422 loglog(t, 20*exp(-t/10.0), basex=4)

   423 grid(True)

   424 ylabel('loglog base 4 on x')

   425 \end{lstlisting}

   426   \end{block}

   427 \end{columns}

   428 \end{frame}

   429 

   430 \begin{frame}[fragile] \frametitle{Errorbar}

   431   \begin{columns}

   432     \column{0.5\textwidth}

   433     \hspace*{-0.5in}

   434   \includegraphics[height=2in, interpolate=true]{data/errorbar}  

   435     \column{0.45\textwidth}

   436     \begin{block}{Example code}

   437     \tiny

   438 \begin{lstlisting}

   439 t = arange(0.1, 4, 0.1)

   440 s = exp(-t)

   441 e = 0.1*abs(randn(len(s)))

   442 f = 0.1*abs(randn(len(s)))

   443 g = 2*e

   444 h = 2*f

   445 errorbar(t, s, [e,g], f, fmt='o')

   446 xlabel('Distance (m)')

   447 ylabel('Height (m)')

   448 title('Mean and standard error '\

   449       'as a function of distance')

   450 \end{lstlisting}

   451   \end{block}

   452 \end{columns}

   453 \end{frame}

   454 

   455 \begin{frame}[fragile] \frametitle{Histogram}

   456   \begin{columns}

   457     \column{0.5\textwidth}

   458     \hspace*{-0.5in}

   459   \includegraphics[height=2in, interpolate=true]{data/histogram}  

   460     \column{0.45\textwidth}

   461     \begin{block}{Example code}

   462     \tiny

   463 \begin{lstlisting}

   464 mu, sigma = 100, 15

   465 x = mu + sigma*randn(10000)

   466 # the histogram of the data

   467 n, bins, patches = hist(x, 100, normed=1)

   468 # add a 'best fit' line

   469 y = normpdf( bins, mu, sigma)

   470 l = plot(bins, y, 'r--', linewidth=2)

   471 xlim(40, 160)

   472 xlabel('Smarts')

   473 ylabel('P')

   474 title(r'$\rm{IQ:}\/ \mu=100,\/ \sigma=15$')

   475 \end{lstlisting}

   476   \end{block}

   477 \end{columns}

   478 \end{frame}

   479 

   480 \begin{frame}[fragile] \frametitle{Bar charts}

   481   \begin{columns}

   482     \column{0.5\textwidth}

   483     \hspace*{-0.5in}

   484   \includegraphics[height=2in, interpolate=true]{data/barchart}  

   485     \column{0.45\textwidth}

   486     \begin{block}{Example code}

   487     \tiny

   488 \begin{lstlisting}

   489 N = 5

   490 menMeans = (20, 35, 30, 35, 27)

   491 menStd =   ( 2,  3,  4,  1,  2)

   492 # the x locations for the groups

   493 ind = arange(N) 

   494 # the width of the bars

   495 width = 0.35       

   496 p1 = bar(ind, menMeans, width, 

   497          color='r', yerr=menStd)

   498 womenMeans = (25, 32, 34, 20, 25)

   499 womenStd =   ( 3,  5,  2,  3,  3)

   500 p2 = bar(ind+width, womenMeans, width, 

   501          color='y', yerr=womenStd)

   502 ylabel('Scores')

   503 title('Scores by group and gender')

   504 xticks(ind+width, 

   505        ('G1', 'G2', 'G3', 'G4', 'G5'))

   506 xlim(-width,len(ind))

   507 yticks(arange(0,41,10))

   508 legend((p1[0], p2[0]), 

   509        ('Men', 'Women'), shadow=True)

   510 \end{lstlisting}

   511   \end{block}

   512 \end{columns}

   513 \end{frame}

   514 

   515 \begin{frame}[fragile] \frametitle{Pie charts}

   516   \begin{columns}

   517     \column{0.5\textwidth}

   518     \hspace*{-0.4in}

   519   \includegraphics[height=2.0in, interpolate=true]{data/piechart}  

   520     \column{0.45\textwidth}

   521     \begin{block}{Example code}

   522     \tiny

   523 \begin{lstlisting}

   524 # make a square figure and axes

   525 figure(1, figsize=(8,8))

   526 ax = axes([0.1, 0.1, 0.8, 0.8])

   527 labels = 'Frogs', 'Hogs', 'Dogs', 'Logs'

   528 fracs = [15,30,45, 10]

   529 explode=(0, 0.05, 0, 0)

   530 pie(fracs, explode=explode, labels=labels, 

   531     autopct='%1.1f%%', shadow=True)

   532 title('Raining Hogs and Dogs', 

   533       bbox={'facecolor':'0.8', 'pad':5})

   534 \end{lstlisting}

   535   \end{block}

   536 \end{columns}

   537 \end{frame}

   538 

   539 \begin{frame}[fragile] \frametitle{Scatter plots}

   540   \begin{columns}

   541     \column{0.5\textwidth}

   542     \hspace*{-0.4in}

   543   \includegraphics[height=2in, interpolate=true]{data/scatter}  

   544     \column{0.45\textwidth}

   545     \begin{block}{Example code}

   546     \tiny

   547 \begin{lstlisting}

   548 N = 30

   549 x = 0.9*rand(N)

   550 y = 0.9*rand(N)

   551 # 0 to 10 point radiuses

   552 area = pi*(10 * rand(N))**2 

   553 volume = 400 + rand(N)*450

   554 scatter(x,y,s=area, marker='o', c=volume, 

   555         alpha=0.75)

   556 xlabel(r'$\Delta_i$', size='x-large')

   557 ylabel(r'$\Delta_{i+1}$', size='x-large')

   558 title(r'Volume and percent change')

   559 grid(True)

   560 colorbar()

   561 savefig('scatter')

   562 \end{lstlisting}

   563   \end{block}

   564 \end{columns}

   565 \end{frame}

   566 

   567 \begin{frame}[fragile] \frametitle{Polar}

   568   \begin{columns}

   569     \column{0.5\textwidth}

   570     \hspace*{-0.5in}

   571   \includegraphics[height=2in, interpolate=true]{data/polar}  

   572     \column{0.45\textwidth}

   573     \begin{block}{Example code}

   574     \tiny

   575 \begin{lstlisting}

   576 figure(figsize=(8,8))

   577 ax = axes([0.1, 0.1, 0.8, 0.8], 

   578           polar=True, 

   579           axisbg='#d5de9c')

   580 r = arange(0,1,0.001)

   581 theta = 2*2*pi*r

   582 polar(theta, r, color='#ee8d18', lw=3)

   583 # the radius of the grid labels

   584 setp(ax.thetagridlabels, y=1.075) 

   585 title(r"$\theta=4\pi r", fontsize=20)

   586 \end{lstlisting}

   587   \end{block}

   588 \end{columns}

   589 \end{frame}

   590 

   591 \begin{frame}[fragile] \frametitle{Contours}

   592   \begin{columns}

   593     \column{0.45\textwidth}

   594     \hspace*{-0.5in}

   595   \includegraphics[height=2in, interpolate=true]{data/contour}  

   596     \column{0.525\textwidth}

   597     \begin{block}{Example code}

   598     \tiny

   599 \begin{lstlisting}

   600 x = arange(-3.0, 3.0, 0.025)

   601 y = arange(-2.0, 2.0, 0.025)

   602 X, Y = meshgrid(x, y)

   603 Z1 = bivariate_normal(X, Y, 1.0, 1.0, 0.0, 0.0)

   604 Z2 = bivariate_normal(X, Y, 1.5, 0.5, 1, 1)

   605 # difference of Gaussians

   606 Z = 10.0 * (Z2 - Z1)

   607 im = imshow(Z, interpolation='bilinear', 

   608             origin='lower',

   609             cmap=cm.gray, extent=(-3,3,-2,2))

   610 levels = arange(-1.2, 1.6, 0.2)

   611 # label every second level

   612 clabel(CS, levels[1::2],  inline=1,

   613        fmt='%1.1f', fontsize=14)

   614 CS = contour(Z, levels,

   615              origin='lower',

   616              linewidths=2,

   617              extent=(-3,3,-2,2))

   618 # make a colorbar for the contour lines

   619 CB = colorbar(CS, shrink=0.8, extend='both')

   620 title('Lines with colorbar')

   621 hot(); flag()

   622 \end{lstlisting}

   623   \end{block}

   624 \end{columns}

   625 \end{frame}

   626 

   627 \begin{frame}[fragile] \frametitle{Velocity vectors}

   628   \begin{columns}

   629     \column{0.5\textwidth}

   630     \hspace*{-0.5in}

   631   \includegraphics[height=2in, interpolate=true]{data/quiver}  

   632     \column{0.45\textwidth}

   633     \begin{block}{Example code}

   634     \tiny

   635 \begin{lstlisting}

   636 X,Y = meshgrid(arange(0,2*pi,.2),

   637                arange(0,2*pi,.2) )

   638 U = cos(X)

   639 V = sin(Y)

   640 Q = quiver(X[::3, ::3], Y[::3, ::3], 

   641            U[::3, ::3], V[::3, ::3],

   642            color='r', units='x', 

   643            linewidths=(2,), 

   644            edgecolors=('k'), 

   645            headaxislength=5 )

   646 qk = quiverkey(Q, 0.5, 0.03, 1, '1 m/s', 

   647                fontproperties=

   648                {'weight': 'bold'})

   649 axis([-1, 7, -1, 7])

   650 title('triangular head; scale '\

   651       'with x view; black edges')

   652 \end{lstlisting}

   653   \end{block}

   654 \end{columns}

   655 \end{frame}

   656 

   657 \begin{frame}[fragile] \frametitle{Maps}

   658   \includegraphics[height=2.5in, interpolate=true]{data/plotmap}  

   659   \begin{center}

   660     \tiny

   661     For details see \url{http://matplotlib.sourceforge.net/screenshots/plotmap.py}

   662   \end{center}

   663 \end{frame}

   664 

   665 

   666 \begin{frame}

   667   \frametitle{More information}

   668   \begin{itemize}

   669   \item More information here: \url{http://matplotlib.sf.net}

   670   \item \url{http://matplotlib.sf.net/tutorial.html}

   671   \item \url{http://matplotlib.sf.net/screenshots.html}

   672   \end{itemize}

   673 

   674   \inctime{25}

   675 \end{frame}

   676 

   677 \begin{frame}

   678   \frametitle{Problem set 1.0}

   679   \begin{enumerate}

   680       \item Write a function that plots any n-gon given \typ{n}.

   681       \item Consider the logistic map, $f(x) = kx(1-x)$, plot it for

   682           $k=2.5, 3.5$ and $4$

   683 \end{enumerate}

   684 \end{frame}

   685 

   686 \begin{frame}

   687   \frametitle{Problem set 1.1}

   688   \begin{enumerate}

   689       \item Consider the iteration $x_{n+1} = f(x_n)$ where $f(x) =

   690           kx(1-x)$.  Plot the successive iterates of this process.

   691       \item Plot this using a cobweb plot as follows:

   692           \begin{enumerate}

   693               \item Start at $(x_0, 0)$

   694               \item Draw line to $(x_i, f(x_i))$; 

   695               \item Set $x_{i+1} = f(x_i)$

   696               \item Draw line to $(x_i, x_i)$

   697               \item Repeat from 2 for as long as you want 

   698           \end{enumerate}

   699     \end{enumerate}

   700 \end{frame}

   701 

   702 \begin{frame}

   703   \frametitle{Problem set 1.2}

   704   \begin{enumerate}

   705 

   706       \item Plot the Koch snowflake.  Write a function to generate the

   707           necessary points given the two points constituting a line.

   708           \pause

   709           \begin{enumerate}

   710               \item Split the line into 4 segments.

   711               \item The first and last segments are trivial.

   712               \item To rotate the point you can use complex numbers,

   713                   recall that $z e^{j \theta}$ rotates a point $z$ in 2D

   714                   by $\theta$.

   715               \item Do this for all line segments till everything is

   716                   done.

   717           \end{enumerate}

   718       \item Show rate of convergence for a first and second order finite

   719           difference of sin(x)

   720 \end{enumerate}

   721 \inctime{30}

   722 \end{frame}

   723 

   724 

   725 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   726 

   727 \begin{frame}[fragile]

   728   \frametitle{More IPython features}

   729   \begin{itemize}

   730   \item Input and output caching:

   731     \begin{itemize}

   732     \item \verb+In+: a list of all entered input

   733     \item \verb+Out+: a dict of all output

   734     \item \verb+%hist [-n]+ macro shows previous history, \verb+-n+

   735       suppresses line number information

   736     \end{itemize}

   737   \item Log the session using \verb+%logstart+, \verb+%logon+ and

   738     \verb+%logoff+

   739   \item Use \verb+;+ to suppress printing output

   740   \item \verb+%time statement+

   741   \item \verb+%timeit [-n<N> -r<R> [-t|-c]] statement+

   742 

   743   \end{itemize}

   744 \end{frame}

   745 

   746 \begin{frame}[fragile]

   747   \frametitle{More IPython features}

   748   \begin{itemize}

   749   \item \verb+%run [options] file[.py]+ -- running Python code

   750   \item \verb+%prun+ runs a statement/expression under the profiler

   751   \item \verb+%debug+: Helps with debugging after a crash

   752   \end{itemize}

   753 \end{frame}

   754 

   755 \begin{frame}[fragile]

   756   \frametitle{More IPython features \ldots}

   757   \begin{itemize}

   758   \item \verb+%edit [options] [args]+: edit lines of code or file

   759     specified in editor (configure editor via \verb+$EDITOR+)

   760   \item \verb+%cd+ changes directory, see also \verb+%pushd, %popd, %dhist+

   761   \item Shell access

   762     \begin{itemize}

   763     \item \verb+!command+ runs a shell command and returns its output

   764     \item \verb+files = !ls+ sets

   765       \verb+files+ to all result of the \verb+ls+ command

   766     \item \verb+!ls $files+ passes the \verb+files+ variable to the

   767       shell command

   768   \end{itemize}

   769     \end{itemize}

   770 \end{frame}

   771 

   772 \begin{frame}[fragile]

   773   \frametitle{More IPython features \ldots}

   774   \begin{itemize}

   775   \item \verb+%bookmark+: store a bookmarked location, for use with \verb+%cd+

   776   \item \verb+%save [options] filename n1-n2 n3-n4+: save lines to a

   777     file

   778   \item Can define and use profiles to setup IPython differently:

   779     \verb+math, scipy, numeric, pysh+ etc.

   780   \item \verb+%magic+: \alert{Show help on all magics}

   781   \item Check out the \verb+%macro+ magic

   782   \end{itemize}

   783 \end{frame}

   784 

   785 \begin{frame}

   786   \frametitle{Problem set 2}

   787   \begin{itemize}

   788     \item Compare your linspace with that of numpy for 1 million

   789         elements in terms of speed.

   790 \end{itemize}

   791 \inctime{10}

   792 \end{frame}

   793 

   794 

   795 \begin{frame}[fragile]

   796     \frametitle{Debugging effectively}

   797 

   798     \begin{itemize}

   799         \item  \kwrd{print} based strategy

   800         \item Process: Hypothesis, test, refine, rinse-repeat

   801         \item Using \typ{\%debug} and \typ{\%pdb} in IPython

   802     \end{itemize}

   803 

   804     \inctime{10} 

   805 \end{frame}

   806 

   807 \section{Debugging and testing}

   808 

   809 \begin{frame}[fragile]

   810     \frametitle{Testing code with \typ{nosetests}}

   811    

   812     \begin{itemize}

   813         \item Writing tests is really simple!

   814 

   815         \item Using nose

   816 

   817         \item Example!

   818     \end{itemize}

   819 \end{frame}

   820 

   821 \begin{frame}[fragile]

   822     \frametitle{Nosetest}

   823 \begin{lstlisting}

   824 def gcd(a, b):

   825     """Returns gcd of a and b, 

   826      handles only positive numbers."""

   827     if a%b == 0: return b

   828     return gcd(b, a%b)

   829 def lcm(a, b):

   830     return a*b/gcd(a, b)

   831 

   832 if __name__ == '__main__':

   833     import nose

   834     nose.main()

   835 \end{lstlisting}

   836 

   837     \inctime{10} 

   838 \end{frame}

   839 

   840 \section{NumPy and SciPy}

   841 

   842 \begin{frame}

   843     {More Numpy}

   844 

   845     \begin{itemize}

   846         \item Multi-dimensional arrays

   847         \item Random number generation

   848     \end{itemize}

   849 

   850 \end{frame}

   851 

   852 \begin{frame}[fragile]

   853   \frametitle{Multi-dimensional arrays}

   854 \begin{lstlisting}

   855 >>> a = array([[ 0, 1, 2, 3],

   856 ...            [10,11,12,13]])

   857 >>> a.shape # (rows, columns)

   858 (2, 4)

   859 # Accessing and setting values

   860 >>> a[1,3] 

   861 13

   862 >>> a[1,3] = -1

   863 >>> a[1] # The second row

   864 array([10,11,12,-1])

   865 

   866 \end{lstlisting}

   867 \end{frame}

   868 

   869 \begin{frame}[fragile]

   870   \frametitle{Slicing arrays}

   871 \begin{lstlisting}

   872 >>> a = array([[1,2,3], [4,5,6], 

   873                [7,8,9]])

   874 >>> a[0,1:3]

   875 array([2, 3])

   876 >>> a[1:,1:]

   877 array([[5, 6],

   878        [8, 9]])

   879 >>> a[:,2]

   880 array([3, 6, 9])

   881 \end{lstlisting}

   882 \end{frame}

   883 \begin{frame}[fragile]

   884   \frametitle{Striding arrays}

   885 \begin{lstlisting}

   886 >>> a[0::2,0::2]

   887 array([[1, 3],

   888        [7, 9]])

   889 # Slices are references to the 

   890 # same memory!

   891 \end{lstlisting}

   892 \end{frame}

   893 

   894 \begin{frame}[fragile]

   895   \frametitle{Array creation functions}

   896   \begin{itemize}

   897   \item \typ{array(object, dtype=None, \ldots)}

   898   \item \typ{arange(start, stop=None, step=1 \ldots)}

   899   \item \typ{linspace(start, stop, num=50, \ldots)}

   900   \item \typ{ones(shape, dtype=None, \ldots)}

   901   \item \typ{zeros(shape, dtype=float,\ldots)}

   902   \item \typ{identity(n)}

   903   \item \typ{empty(shape, dtype=float,\ldots)}

   904   \item \typ{ones\_like(x)}, 

   905   \item \typ{zeros\_like(x)}, \typ{empty\_like(x)}

   906   \end{itemize}

   907 \end{frame}

   908 

   909 \begin{frame}[fragile]

   910   \frametitle{Array math}

   911   \begin{itemize}

   912   \item Basic \alert{elementwise} math (given two arrays \typ{a, b}):

   913       \typ{+, -, *, /, \%}

   914   \item Inplace operators: \typ{a += b}, or \typ{add(a, b,

   915       a)} etc.

   916   \item Logical operations: \typ{equal (==)}, \typ{not\_equal (!=)},

   917     \typ{less (<)}, \typ{greater (>)} etc.

   918   \item Trig and other functions: \typ{sin(x), arcsin(x), sinh(x),

   919       exp(x), sqrt(x)} etc.

   920   \item \typ{sum(x, axis=0), product(x, axis=0)} 

   921   \item \typ{dot(a, b)}

   922   \end{itemize}

   923 \end{frame}

   924 

   925 \begin{frame}[fragile]

   926   \frametitle{Advanced}

   927   \begin{itemize}

   928   \item Only scratched the surface of \num

   929   \item Ufunc methods: \typ{reduce, accumulate, outer, reduceat}

   930   \item Typecasting

   931   \item More functions: \typ{take, choose, where, compress,

   932       concatenate}

   933   \item Array broadcasting and \typ{None}

   934   \end{itemize}

   935   \inctime{15}

   936 \end{frame}

   937 

   938 \begin{frame}

   939     {Intro to SciPy}

   940   \begin{itemize}

   941   \item \url{http://www.scipy.org}

   942   \item Open source scientific libraries for Python

   943   \item Based on NumPy

   944     \end{itemize}

   945 

   946     \inctime{25}

   947 \end{frame}

   948 

   949 \begin{frame}

   950   \frametitle{SciPy}

   951   \begin{itemize}

   952   \item Provides:

   953     \begin{itemize}

   954     \item Linear algebra

   955     \item Numerical integration

   956     \item Fourier transforms

   957     \item Signal processing

   958     \item Special functions

   959     \item Statistics

   960     \item Optimization

   961     \item Image processing

   962     \item ODE solvers

   963     \end{itemize}

   964   \item Uses LAPACK, QUADPACK, ODEPACK, FFTPACK etc. from netlib

   965   \end{itemize}

   966 \end{frame}

   967 

   968 

   969 \section{3D Plotting}

   970 

   971 \begin{frame}

   972   \frametitle{Introduction to Mayavi}

   973   \begin{itemize}

   974   \item Most scientists not interested in details of visualization

   975   \item Visualization of data files with a nice UI

   976   \item Interactive visualization of data (think Matlab)

   977   \item Embedding visualizations in applications

   978   \item Customization

   979   \end{itemize}

   980   \pause

   981   \begin{block}{The Goal}

   982       Provide a \alert{flexible} library/app for every one of these needs!

   983   \end{block}

   984 \end{frame}

   985 

   986 \begin{frame}[fragile]

   987     \frametitle{\typ{mlab}}

   988   \begin{columns}

   989     \column{0.62\textwidth}

   990     \hspace*{-0.45in}

   991       \footnotesize

   992 \begin{lstlisting}

   993 from enthought.mayavi import mlab

   994 from numpy import ogrid, sin

   995 

   996 x, y, z = ogrid[-10:10:100j, 

   997                 -10:10:100j, 

   998                 -10:10:100j]

   999 

  1000 mlab.contour3d(sin(x*y*z)/(x*y*z))

  1001 mlab.show()

  1002 \end{lstlisting}

  1003     \column{0.4\textwidth}

  1004     \hspace*{-0.1\linewidth}

  1005     \includegraphics[width=1.18\linewidth]{data/mlab.png}

  1006   \end{columns}

  1007 \end{frame}

  1008 

  1009 \begin{frame}

  1010     {A Look at the docs }

  1011 

  1012     \inctime{20}

  1013 \end{frame}

  1014 

  1015 

  1016 \section{Integration demo: Lorenz equations}

  1017 

  1018 \begin{frame}

  1019     \frametitle{Lorenz equation example}

  1020     \begin{eqnarray*}

  1021         \frac{d x}{dt} &=& s (y-x)\\

  1022         \frac{d y}{d t} &=& rx -y -xz\\

  1023         \frac{d z}{d t} &=& xy - bz\\

  1024     \end{eqnarray*}

  1025     \begin{itemize}

  1026         \item Specifies the evolution of the system

  1027         \item Think: Velocity of a particle in 3D

  1028         \item Lets trace its path

  1029     \end{itemize}

  1030 \end{frame}

  1031 

  1032 \begin{frame}

  1033     {Interactive exploration}

  1034 

  1035     \inctime{25}

  1036 \end{frame}

  1037 

  1038 

  1039 \end{document}

  1040 

  1041 - Numpy arrays (30 mins)

  1042     - Matrices

  1043     - random number generation.

  1044     - Image manipulation: jigsaw puzzle.

  1045     - Monte-carlo integration.

  1046 

  1047 

  1048 

  1049 

  1050 

  1051 \begin{frame}[fragile]

  1052   \frametitle{More on functions}

  1053   \begin{itemize}

  1054   \item Support default and keyword arguments

  1055   \item Scope of variables in the function is local

  1056   \item Mutable items are \alert{passed by reference}

  1057   \item First line after definition may be a documentation string

  1058     (\alert{recommended!})

  1059   \item Function definition and execution defines a name bound to the

  1060     function

  1061   \item You \emph{can} assign a variable to a function!

  1062   \end{itemize}

  1063 \end{frame}

  1064 

  1065 

  1066 \begin{frame}[fragile]

  1067   \frametitle{Functions: default arguments}

  1068   \begin{lstlisting}

  1069 def ask_ok(prompt, retries=4, complaint='Yes or no!'):

  1070     while True:

  1071         ok = raw_input(prompt)

  1072         if ok in ('y', 'ye', 'yes'): 

  1073             return True

  1074         if ok in ('n', 'no', 'nop', 'nope'): 

  1075             return False

  1076         retries = retries - 1

  1077         if retries < 0: 

  1078             raise IOError, 'bad user'

  1079         print complaint

  1080   \end{lstlisting}

  1081 \end{frame}

  1082 

  1083 \begin{frame}[fragile]

  1084   \frametitle{Functions: keyword arguments}

  1085   \begin{lstlisting}

  1086 def parrot(voltage, state='a stiff', 

  1087            action='voom', type='Norwegian Blue'):

  1088     print "-- This parrot wouldn't", action,

  1089     print "if you put", voltage, "Volts through it."

  1090     print "-- Lovely plumage, the", type

  1091     print "-- It's", state, "!"

  1092 

  1093 parrot(1000)

  1094 parrot(action = 'VOOOOOM', voltage = 1000000)

  1095 parrot('a thousand', state = 'pushing up the daisies')

  1096 parrot('a million', 'bereft of life', 'jump')

  1097 \end{lstlisting}

  1098 \end{frame}

  1099 

  1100 \begin{frame}[fragile]

  1101   \frametitle{Functions: arbitrary argument lists}

  1102   \begin{itemize}

  1103   \item Arbitrary number of arguments using \verb+*args+ or

  1104     \verb+*whatever+

  1105   \item Keyword arguments using \verb+**kw+

  1106   \item Given a tuple/dict how do you call a function?

  1107     \begin{itemize}

  1108     \item Using argument unpacking

  1109     \item For positional arguments: \verb+foo(*[5, 10])+

  1110     \item For keyword args: \verb+foo(**{'a':5, 'b':10})+

  1111     \end{itemize}

  1112   \end{itemize}

  1113 \begin{lstlisting}

  1114 def foo(a=10, b=100):

  1115     print a, b

  1116 def func(*args, **keyword):

  1117     print args, keyword

  1118 # Unpacking:

  1119 args = [5, 10]

  1120 foo(*args)

  1121 kw = {'a':5, 'b':10}

  1122 foo(**kw)

  1123 \end{lstlisting}

  1124 \end{frame}

  1125 

  1126 \subsection{Modules, exceptions, classes}

  1127 

  1128 \begin{frame}

  1129   \frametitle{Modules}

  1130   \begin{itemize}

  1131   \item Define variables, functions and classes in a file with a

  1132     \typ{.py} extension

  1133   \item This file becomes a module!

  1134   \item Modules are searched in the following:

  1135     \begin{itemize}

  1136     \item Current directory