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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    22 \usepackage[english]{babel}

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    24 %\usepackage{times}

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    26 

    27 % Taken from Fernando's slides.

    28 \usepackage{ae,aecompl}

    29 \usepackage{mathpazo,courier,euler}

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

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    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,

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

    43 % Macros

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    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,

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    71 % }

    72 

    73 

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

    75 % Title page

    76 \title[]{Matrices and Arrays\\ \& \\2D Plotting}

    77 

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

    79 

    80 \institute[FOSSEE] {FOSSEE Team}

    81 \date[] {11, October 2009}

    82 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    83 

    84 %\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo}

    85 %\logo{\pgfuseimage{iitmlogo}}

    86 

    87 

    88 %% Delete this, if you do not want the table of contents to pop up at

    89 %% the beginning of each subsection:

    90 \AtBeginSubsection[]

    91 {

    92   \begin{frame}<beamer>

    93     \frametitle{Outline}

    94     \tableofcontents[currentsection,currentsubsection]

    95   \end{frame}

    96 }

    97 

    98 \AtBeginSection[]

    99 {

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   101     \frametitle{Outline}

   102     \tableofcontents[currentsection,currentsubsection]

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   104 }

   105 

   106 % If you wish to uncover everything in a step-wise fashion, uncomment

   107 % the following command: 

   108 %\beamerdefaultoverlayspecification{<+->}

   109 

   110 %\includeonlyframes{current,current1,current2,current3,current4,current5,current6}

   111 

   112 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   113 % DOCUMENT STARTS

   114 \begin{document}

   115 

   116 \begin{frame}

   117   \maketitle

   118 \end{frame}

   119 

   120 \begin{frame}

   121   \frametitle{Outline}

   122   \tableofcontents

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

   124 \end{frame}

   125 

   126 \section{Matrices and Arrays}

   127 

   128 \subsection{Basic \typ{numpy} }

   129 

   130 \newcommand{\num}{\texttt{numpy}}

   131 

   132 \begin{frame}

   133   \frametitle{The \num\ module}

   134   \begin{itemize}

   135       \item Why?

   136   \item What:

   137     \begin{itemize}

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

   139       types

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

   141       arrays

   142     \end{itemize}

   143   \end{itemize}

   144 \end{frame}

   145 

   146 \begin{frame}[fragile]

   147   \frametitle{Examples of \num}

   148 \begin{lstlisting}

   149 # Simple array math example

   150 >>> from numpy import *

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

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

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

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

   155 # Pi and e are defined.

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

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

   158 # apply functions to array.

   159 >>> y = sin(x)

   160 \end{lstlisting}

   161 \end{frame}

   162 

   163 \begin{frame}

   164   \frametitle{Basic concepts}

   165   \begin{itemize}

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

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

   168   \item arbitrary dimensionality

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

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

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

   172     \alert{elementwise}

   173   \item Indices, slicing: just like lists 

   174   \end{itemize}

   175 \end{frame}

   176 

   177 

   178 \begin{frame}[fragile]

   179   \frametitle{More examples of \num}

   180 \vspace*{-8pt}

   181 \begin{lstlisting}

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

   183 >>> size(x)

   184 4

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

   186 dtype('float64')

   187 >>> x.shape

   188 (4,)

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

   190 1 8

   191 >>> x[0] = 10

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

   193 10.0 4.0

   194 \end{lstlisting}

   195     

   196 \inctime{10}

   197 \end{frame}

   198 

   199 \begin{frame}

   200     {More Numpy}

   201 

   202     \begin{itemize}

   203         \item Multi-dimensional arrays

   204         \item Random number generation

   205     \end{itemize}

   206 

   207 \end{frame}

   208 

   209 \begin{frame}[fragile]

   210   \frametitle{Multi-dimensional arrays}

   211 \begin{lstlisting}

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

   213 ...            [10,11,12,13]])

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

   215 (2, 4)

   216 # Accessing and setting values

   217 >>> a[1,3] 

   218 13

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

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

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

   222 

   223 \end{lstlisting}

   224 \end{frame}

   225 

   226 \begin{frame}[fragile]

   227   \frametitle{Slicing arrays}

   228 \begin{lstlisting}

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

   230                [7,8,9]])

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

   232 array([2, 3])

   233 >>> a[1:,1:]

   234 array([[5, 6],

   235        [8, 9]])

   236 >>> a[:,2]

   237 array([3, 6, 9])

   238 \end{lstlisting}

   239 \end{frame}

   240 \begin{frame}[fragile]

   241   \frametitle{Striding arrays}

   242 \begin{lstlisting}

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

   244 array([[1, 3],

   245        [7, 9]])

   246 # Slices are references to the 

   247 # same memory!

   248 \end{lstlisting}

   249 \end{frame}

   250 

   251 \subsection{Array creation }

   252 \begin{frame}[fragile]

   253   \frametitle{Array creation functions}

   254   \begin{itemize}

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

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

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

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

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

   260   \item \typ{identity(n)}

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

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

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

   264   \end{itemize}

   265 \end{frame}

   266 

   267 \subsection{Array math}

   268 \begin{frame}[fragile]

   269   \frametitle{Array math}

   270   \begin{itemize}

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

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

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

   274       a)} etc.

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

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

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

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

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

   280   \item \typ{dot(a, bp)}

   281   \end{itemize}

   282 \end{frame}

   283 

   284 

   285 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   286 \section{2D Plotting}

   287 \subsection{Getting Started}

   288 

   289 \begin{frame}

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

   291 \begin{itemize}

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

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

   294     \item Imports all of pylab for you!

   295     \item Allows for interactive plotting

   296 \end{itemize}

   297 \end{frame}

   298 

   299 \begin{frame}[fragile]

   300     \frametitle{Basic 2D plotting}

   301 

   302 \begin{lstlisting}

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

   304 >>> plot(x, sin(x)) 

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

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

   307 # LaTeX markup!

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

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

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

   311 \end{lstlisting}

   312 \begin{itemize}

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

   314 \end{itemize}

   315 \end{frame}

   316        

   317 \subsection{Playing with lines}

   318 \begin{frame}[fragile]

   319   \frametitle{Basic plotting \ldots}

   320 \begin{lstlisting}

   321 # Set properties of objects:

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

   323 # Why "l,"?

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

   325 >>> l.set_linewidth(2.0)

   326 >>> draw() # Redraw.

   327 >>> setp(l) # Print properties

   328 >>> clf() # Clear figure.

   329 >>> close() # Close figure.

   330 \end{lstlisting}

   331 \end{frame}

   332 

   333 \begin{frame}[fragile]

   334     \frametitle{Multiple figures}

   335 

   336 \begin{lstlisting}

   337 >>> figure(1)

   338 >>> plot(x, sin(x))

   339 >>> figure(2)

   340 >>> plot(x, tanh(x))

   341 >>> figure(1)

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

   343 \end{lstlisting}

   344     

   345 \end{frame}

   346 

   347 \subsection{Handling Text}

   348 

   349 \begin{frame}[fragile]

   350   \frametitle{Legends and Annotation}

   351 \begin{lstlisting}

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

   353          label='cosine')

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

   355          label='sine')

   356 >>> legend() 

   357 # Or use:

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

   359 # Annotation:

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

   361 \end{lstlisting}

   362 \end{frame}

   363 

   364 \begin{frame}[fragile]

   365     \frametitle{More commands \ldots}

   366     \begin{lstlisting}

   367 # semilog, loglog 

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

   369 >>> semilogx(x, x)

   370 >>> semilogy(x, x)

   371 >>> loglog(x, x)

   372 >>> loglog(x, x*x)

   373     \end{lstlisting}

   374 \end{frame}

   375 

   376 \begin{frame}[fragile]

   377     \frametitle{More plots \ldots}

   378     \begin{lstlisting}

   379 >>> clf()

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

   381 >>> s = exp(-t)

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

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

   384 # Scatter plots

   385 >>> clf()

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

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

   388     \end{lstlisting}

   389 \end{frame}

   390 

   391 \begin{frame}[fragile]

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

   393 \begin{lstlisting}

   394 import pylab

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

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

   397 

   398 # Can also use:

   399 from pylab import linspace, sin, plot

   400 \end{lstlisting}

   401 \end{frame}

   402 

   403 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   404 \subsection{Types of Plots}

   405 \begin{frame}[fragile]

   406   \frametitle{X-Y plot}

   407   \begin{columns}

   408     \column{0.5\textwidth}

   409     \hspace*{-0.5in}

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

   411     \column{0.45\textwidth}

   412     \begin{block}{Example code}

   413     \tiny

   414 \begin{lstlisting}

   415 t1 = arange(0.0, 5.0, 0.1)

   416 t2 = arange(0.0, 5.0, 0.02)

   417 t3 = arange(0.0, 2.0, 0.01)

   418 subplot(211)

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

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

   421 grid(True)

   422 title('A tale of 2 subplots')

   423 ylabel('Damped')

   424 subplot(212)

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

   426 grid(True)

   427 xlabel('time (s)')

   428 ylabel('Undamped')

   429 \end{lstlisting}

   430     \end{block}

   431   \end{columns}

   432 \end{frame}

   433 

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

   435   \begin{columns}

   436     \column{0.5\textwidth}

   437     \hspace*{-0.5in}

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

   439     \column{0.45\textwidth}

   440     \begin{block}{Example code}

   441     \tiny

   442 \begin{lstlisting}

   443 dt = 0.01

   444 t = arange(dt, 20.0, dt)

   445 subplot(311)

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

   447 ylabel('semilogy')

   448 grid(True)

   449 subplot(312)

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

   451 ylabel('semilogx')

   452 grid(True)

   453 # minor grid on too

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

   455 subplot(313)

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

   457 grid(True)

   458 ylabel('loglog base 4 on x')

   459 \end{lstlisting}

   460   \end{block}

   461 \end{columns}

   462 \end{frame}

   463 

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

   465   \begin{columns}

   466     \column{0.5\textwidth}

   467     \hspace*{-0.5in}

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

   469     \column{0.45\textwidth}

   470     \begin{block}{Example code}

   471     \tiny

   472 \begin{lstlisting}

   473 t = arange(0.1, 4, 0.1)

   474 s = exp(-t)

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

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

   477 g = 2*e

   478 h = 2*f

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

   480 xlabel('Distance (m)')

   481 ylabel('Height (m)')

   482 title('Mean and standard error '\

   483       'as a function of distance')

   484 \end{lstlisting}

   485   \end{block}

   486 \end{columns}

   487 \end{frame}

   488 

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

   490   \begin{columns}

   491     \column{0.5\textwidth}

   492     \hspace*{-0.5in}

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

   494     \column{0.45\textwidth}

   495     \begin{block}{Example code}

   496     \tiny

   497 \begin{lstlisting}

   498 mu, sigma = 100, 15

   499 x = mu + sigma*randn(10000)

   500 # the histogram of the data

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

   502 # add a 'best fit' line

   503 y = normpdf( bins, mu, sigma)

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

   505 xlim(40, 160)

   506 xlabel('Smarts')

   507 ylabel('P')

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

   509 \end{lstlisting}

   510   \end{block}

   511 \end{columns}

   512 \end{frame}

   513 

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

   515   \begin{columns}

   516     \column{0.5\textwidth}

   517     \hspace*{-0.5in}

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

   519     \column{0.45\textwidth}

   520     \begin{block}{Example code}

   521     \tiny

   522 \begin{lstlisting}

   523 N = 5

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

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

   526 # the x locations for the groups

   527 ind = arange(N) 

   528 # the width of the bars

   529 width = 0.35       

   530 p1 = bar(ind, menMeans, width, 

   531          color='r', yerr=menStd)

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

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

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

   535          color='y', yerr=womenStd)

   536 ylabel('Scores')

   537 title('Scores by group and gender')

   538 xticks(ind+width, 

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

   540 xlim(-width,len(ind))

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

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

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

   544 \end{lstlisting}

   545   \end{block}

   546 \end{columns}

   547 \end{frame}

   548 

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

   550   \begin{columns}

   551     \column{0.5\textwidth}

   552     \hspace*{-0.4in}

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

   554     \column{0.45\textwidth}

   555     \begin{block}{Example code}

   556     \tiny

   557 \begin{lstlisting}

   558 # make a square figure and axes

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

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

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

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

   563 explode=(0, 0.05, 0, 0)

   564 pie(fracs, explode=explode, labels=labels, 

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

   566 title('Raining Hogs and Dogs', 

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

   568 \end{lstlisting}

   569   \end{block}

   570 \end{columns}

   571 \end{frame}

   572 

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

   574   \begin{columns}

   575     \column{0.5\textwidth}

   576     \hspace*{-0.4in}

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

   578     \column{0.45\textwidth}

   579     \begin{block}{Example code}

   580     \tiny

   581 \begin{lstlisting}

   582 N = 30

   583 x = 0.9*rand(N)

   584 y = 0.9*rand(N)

   585 # 0 to 10 point radiuses

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

   587 volume = 400 + rand(N)*450

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

   589         alpha=0.75)

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

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

   592 title(r'Volume and percent change')

   593 grid(True)

   594 colorbar()

   595 savefig('scatter')

   596 \end{lstlisting}

   597   \end{block}

   598 \end{columns}

   599 \end{frame}

   600 

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

   602   \begin{columns}

   603     \column{0.5\textwidth}

   604     \hspace*{-0.5in}

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

   606     \column{0.45\textwidth}

   607     \begin{block}{Example code}

   608     \tiny

   609 \begin{lstlisting}

   610 figure(figsize=(8,8))

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

   612           polar=True, 

   613           axisbg='#d5de9c')

   614 r = arange(0,1,0.001)

   615 theta = 2*2*pi*r

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

   617 # the radius of the grid labels

   618 setp(ax.thetagridlabels, y=1.075) 

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

   620 \end{lstlisting}

   621   \end{block}

   622 \end{columns}

   623 \end{frame}

   624 

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

   626   \begin{columns}

   627     \column{0.45\textwidth}

   628     \hspace*{-0.5in}

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

   630     \column{0.525\textwidth}

   631     \begin{block}{Example code}

   632     \tiny

   633 \begin{lstlisting}

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

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

   636 X, Y = meshgrid(x, y)

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

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

   639 # difference of Gaussians

   640 Z = 10.0 * (Z2 - Z1)

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

   642             origin='lower',

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

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

   645 # label every second level

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

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

   648 CS = contour(Z, levels,

   649              origin='lower',

   650              linewidths=2,

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

   652 # make a colorbar for the contour lines

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

   654 title('Lines with colorbar')

   655 hot(); flag()

   656 \end{lstlisting}

   657   \end{block}

   658 \end{columns}

   659 \end{frame}

   660 

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

   662   \begin{columns}

   663     \column{0.5\textwidth}

   664     \hspace*{-0.5in}

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

   666     \column{0.45\textwidth}

   667     \begin{block}{Example code}

   668     \tiny

   669 \begin{lstlisting}

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

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

   672 U = cos(X)

   673 V = sin(Y)

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

   675            U[::3, ::3], V[::3, ::3],

   676            color='r', units='x', 

   677            linewidths=(2,), 

   678            edgecolors=('k'), 

   679            headaxislength=5 )

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

   681                fontproperties=

   682                {'weight': 'bold'})

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

   684 title('triangular head; scale '\

   685       'with x view; black edges')

   686 \end{lstlisting}

   687   \end{block}

   688 \end{columns}

   689 \end{frame}

   690 

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

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

   693   \begin{center}

   694     \tiny

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

   696   \end{center}

   697 \end{frame}

   698 

   699 

   700 \begin{frame}

   701   \frametitle{More information}

   702   \begin{itemize}

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

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

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

   706   \end{itemize}

   707 

   708   \inctime{25}

   709 \end{frame}

   710 

   711 \begin{frame}

   712   \frametitle{Problem set 1.0}

   713   \begin{enumerate}

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

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

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

   717 \end{enumerate}

   718 \end{frame}

   719 

   720 \begin{frame}

   721   \frametitle{Problem set 1.1}

   722   \begin{enumerate}

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

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

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

   726           \begin{enumerate}

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

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

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

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

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

   732           \end{enumerate}

   733     \end{enumerate}

   734 \end{frame}

   735 

   736 \begin{frame}

   737   \frametitle{Problem set 1.2}

   738   \begin{enumerate}

   739 

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

   741           necessary points given the two points constituting a line.

   742           \pause

   743           \begin{enumerate}

   744               \item Split the line into 4 segments.

   745               \item The first and last segments are trivial.

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

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

   748                   by $\theta$.

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

   750                   done.

   751           \end{enumerate}

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

   753           difference of sin(x)

   754 \end{enumerate}

   755 \inctime{30}

   756 \end{frame}

   757 \end{document}