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

     2 % Tutorial slides on Python.

     3 %

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

     5 % Copyright (c) 2005-2009, Prabhu Ramachandran

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

     7 

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

     9 %\documentclass[draft]{beamer}

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

    15 \mode<presentation>

    16 {

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    20 }

    21 

    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,

    40   keywordstyle=\color{blue}\bfseries}

    41 

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

    43 % Macros

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    53 

    54 \newcommand{\typ}[1]{\lstinline{#1}}

    55 

    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},

    67 %    stringstyle=\ttfamily\color{orange},

    68 %    showstringspaces=false,

    69 %    breaklines=true,

    70 %    postbreak = \space\dots

    71 % }

    72 

    73 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    74 % Title page

    75 \title[]{Arrays\\ \& \\2D Plotting}

    76 

    77 \author[FOSSEE Team] {FOSSEE}

    78 

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

    80 \date[] {11, October 2009}

    81 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    82 

    83 %\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo}

    84 %\logo{\pgfuseimage{iitmlogo}}

    85 

    86 

    87 %% Delete this, if you do not want the table of contents to pop up at

    88 %% the beginning of each subsection:

    89 \AtBeginSubsection[]

    90 {

    91   \begin{frame}<beamer>

    92     \frametitle{Outline}

    93     \tableofcontents[currentsection,currentsubsection]

    94   \end{frame}

    95 }

    96 

    97 \AtBeginSection[]

    98 {

    99   \begin{frame}<beamer>

   100     \frametitle{Outline}

   101     \tableofcontents[currentsection,currentsubsection]

   102   \end{frame}

   103 }

   104 

   105 \newcommand{\num}{\texttt{numpy}}

   106 

   107 

   108 % If you wish to uncover everything in a step-wise fashion, uncomment

   109 % the following command: 

   110 %\beamerdefaultoverlayspecification{<+->}

   111 

   112 %\includeonlyframes{current,current1,current2,current3,current4,current5,current6}

   113 

   114 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   115 % DOCUMENT STARTS

   116 \begin{document}

   117 

   118 \begin{frame}

   119   \maketitle

   120 \end{frame}

   121 

   122 \begin{frame}

   123   \frametitle{Outline}

   124   \tableofcontents

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

   126 \end{frame}

   127 

   128 \section{Arrays}

   129 

   130 \subsection{Basic \typ{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 types

   139     \item Abstracts out the most commonly used standard operations on arrays

   140     \end{itemize}

   141   \end{itemize}

   142 \end{frame}

   143 

   144 \begin{frame}[fragile]

   145   \frametitle{Examples of \num}

   146 \begin{lstlisting}

   147 # Simple array math example

   148 >>> from numpy import *

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

   150 >>> b = arange(2,6)

   151 >>> b

   152 array([2,3,4,5])

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

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

   155 \end{lstlisting}

   156 \end{frame}

   157 

   158 \begin{frame}[fragile]

   159   \frametitle{Examples of \num}

   160 \begin{lstlisting}

   161 # Pi and e are defined.

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

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

   164 # apply functions to array.

   165 >>> y = sin(x)

   166 >>> z = exp(y)

   167 \end{lstlisting}

   168 \inctime{5}

   169 \end{frame}

   170 

   171 \begin{frame}[fragile]

   172   \frametitle{More examples of \num}

   173 \vspace*{-8pt}

   174 \begin{lstlisting}

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

   176 >>> size(x)

   177 4

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

   179 dtype('float64')

   180 >>> x.shape

   181 (4,)

   182 >>> print x.itemsize

   183 8

   184 >>> x[0] = 10

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

   186 10.0 4.0

   187 \end{lstlisting}

   188 \end{frame}

   189 

   190 \begin{frame}[fragile]

   191   \frametitle{Multi-dimensional arrays}

   192 \begin{lstlisting}

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

   194 ...            [10,11,12,13]])

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

   196 (2, 4)

   197 >>> a.shape=4,2

   198 # Accessing and setting values

   199 >>> a[1][3] 

   200 >>> a[1,3] 

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

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

   203 \end{lstlisting}

   204 \end{frame}

   205 

   206 \begin{frame}[fragile]

   207   \frametitle{Array math}

   208   \begin{itemize}

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

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

   211   \item Inplace operators: \typ{a += b}

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

   213         \typ{product(x, axis=0)},

   214         \typ{dot(a, bp)}   

   215   \end{itemize}

   216 \begin{lstlisting}

   217 >>> x = array([[0,2,4,2],[1,2,3,4]])

   218 >>> sum(x)

   219 >>> sum(x,axis=1)

   220 \end{lstlisting}

   221 \end{frame}

   222 

   223 \begin{frame}[fragile]

   224   \frametitle{Array math cont.}

   225   \begin{itemize}

   226   \item Logical operations: \typ{==}, \typ{!=},

   227     \typ{<}, \typ{>} etc.

   228   \item Trig and other functions: \typ{sin(x),}

   229         \typ{arcsin(x), sinh(x),}

   230       \typ{exp(x), sqrt(x)} etc.

   231   \end{itemize}

   232 \begin{lstlisting}

   233 >>> a<4, a!=3

   234 >>> sqrt(a)

   235 \end{lstlisting}

   236 \inctime{10}

   237 \end{frame}

   238 

   239 \begin{frame}

   240   \frametitle{Summary of Concepts}

   241   \begin{itemize}

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

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

   244   \item arbitrary dimensionality

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

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

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

   248     \alert{elementwise}

   249   \end{itemize}

   250 \end{frame}

   251 

   252 \subsection{Array Creation \& Slicing, Striding Arrays}

   253 

   254 \begin{frame}[fragile]

   255   \frametitle{Array creation functions}

   256   \begin{itemize}

   257     \item \typ{array?} \alert{\#Doc string reading}

   258     \item \typ{array(object,dtype=None,...)}

   259     \begin{lstlisting}

   260 >>> array([2,3,4])  

   261 array([2, 3, 4])

   262     \end{lstlisting}

   263     \item \typ{linspace(start,stop,num)}

   264     \begin{lstlisting}

   265 >>> linspace(0, 2, 4)   

   266 array([0.,0.6666667,1.3333333,2.])

   267     \end{lstlisting}

   268     \item \typ{arange?}

   269       \alert{\# float version of range}

   270   \end{itemize}

   271 \end{frame}

   272 

   273 \begin{frame}[fragile]

   274   \frametitle{Array creation functions cont.}

   275   \begin{itemize}  

   276   \item \typ{ones(shape, dtype=None, ...)}  

   277   \begin{lstlisting} 

   278 >>> ones((2,2))

   279 array([[ 1.,  1.],

   280      [ 1.,  1.]])

   281   \end{lstlisting}  

   282   \item \typ{identity(n)} 

   283   \item \typ{ones\_like(x)}  

   284   \begin{lstlisting} 

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

   286 >>> ones_like(a)

   287 array([[1, 1, 1],

   288        [1, 1, 1]])

   289   \end{lstlisting}

   290   \item Also try \typ{zeros, zeros\_like, empty}

   291   \end{itemize}

   292 \end{frame}

   293 

   294 \begin{frame}[fragile]

   295   \frametitle{Slicing arrays}

   296 \begin{lstlisting}

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

   298                [7,8,9]])

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

   300 array([2, 3])

   301 >>> a[1:,1:]

   302 array([[5, 6],

   303        [8, 9]])

   304 >>> a[:,2]

   305 array([3, 6, 9])

   306 \end{lstlisting}

   307 \end{frame}

   308 

   309 \begin{frame}[fragile]

   310   \frametitle{Striding arrays}

   311 \begin{lstlisting}

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

   313 array([[1, 3],

   314        [7, 9]])

   315 # Slices are references to the 

   316 # same memory!

   317 \end{lstlisting}

   318 \end{frame}

   319 

   320 \begin{frame}[fragile]

   321 \frametitle{Random Numbers}

   322 \begin{lstlisting}

   323 >>> random.random()

   324 0.94134734326214331

   325 >>> random.random(2)

   326 array([ 0.73955352,  0.49463645])

   327 >>> random.random(3,2)

   328 array([[ 0.96276665,  0.77174861],

   329        [ 0.35138557,  0.61462271],

   330        [ 0.16789255,  0.43848811]])

   331 \end{lstlisting}

   332 \inctime{15}

   333 \end{frame}

   334 

   335 \begin{frame}[fragile]

   336   \frametitle{Problem}

   337   Finite difference

   338   \begin{equation*}

   339   \frac{sin(x+h)-sin(x)}{h}

   340   \end{equation*}

   341   \begin{lstlisting}

   342   >>> x = linspace(0,2*pi,100)

   343   >>> y = sin(x)

   344   >>> deltax = x[1]-x[0]

   345   \end{lstlisting}

   346   \pause

   347     \begin{enumerate}

   348       \item Given this, get the finite difference of sin in the range 0 to 2*pi

   349     \end{enumerate}

   350 \end{frame}

   351 

   352 

   353 \begin{frame}[fragile]

   354   \frametitle{Advanced Problem}

   355   \begin{lstlisting}

   356     >>> from scipy import misc

   357     >>> A=misc.imread('filename')

   358     >>> misc.imshow(A)

   359   \end{lstlisting}

   360     \begin{enumerate}

   361     \item Convert an RGB image to Grayscale. $ Y = 0.5R + 0.25G + 0.25B $

   362     \item Scale the image to 50\%

   363     \item Introduce some random noise

   364     \item Smooth the image using a mean filter

   365       \\\small{Each element in the array is replaced by mean of all the neighbouring elements}

   366       \\\small{How fast does your code run?}

   367     \end{enumerate}

   368 \inctime{15}

   369 \end{frame}

   370 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   371 

   372 \section{2D Plotting}

   373 \subsection{Getting Started}

   374 

   375 \begin{frame}

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

   377 \begin{block}{Immediate use -}

   378  \typ{\$ ipython -pylab}

   379 \end{block}

   380 \begin{itemize}

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

   382     \item Imports all of pylab for you!

   383     \item Allows for interactive plotting

   384 \end{itemize}

   385 \end{frame}

   386 

   387 \begin{frame}[fragile]

   388     \frametitle{Basic 2D plotting}

   389 

   390 \begin{lstlisting}

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

   392 >>> plot(x, sin(x)) 

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

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

   395 # LaTeX markup!

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

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

   398 >>> savefig('/tmp/test.png')

   399 \end{lstlisting}

   400 \begin{itemize}

   401   \item Also: PS, EPS, SVG, PDF

   402 \end{itemize}

   403 \inctime{5}

   404 \end{frame}

   405        

   406 \subsection{Plots - Lines, Labels and Legends}

   407 \begin{frame}[fragile]

   408   \frametitle{Tweaking plots}

   409 \begin{lstlisting}

   410 # Set properties of objects:

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

   412 # Why "l,"?

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

   414 >>> l.set_linewidth(2.0)

   415 >>> draw() # Redraw.

   416 >>> setp(l) # Print properties.

   417 >>> clf() # Clear figure.

   418 >>> close() # Close figure.

   419 \end{lstlisting}

   420 \end{frame}

   421 

   422 \begin{frame}[fragile]

   423    \frametitle{Working with text \ldots}

   424 %\begin{itemize}

   425 %  \item We already saw LaTeX markup support!

   426 %\end{itemize}

   427 \begin{lstlisting}

   428 >>> w = arange(-2,2,.1)

   429 >>> plot(w,exp(-(w*w))*cos)

   430 >>> ylabel('$f(\omega)$')

   431 >>> xlabel('$\omega$')

   432 >>> title(r"$f(\omega)=e^{-\omega^2}

   433             cos({\omega^2})$")

   434 \end{lstlisting}

   435     

   436 \end{frame}

   437 

   438 \begin{frame}[fragile]

   439   \frametitle{Legends}

   440 \begin{lstlisting}

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

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

   443          label='cosine')

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

   445          label='sine')

   446 >>> legend() 

   447 # Or use:

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

   449 \end{lstlisting}

   450 \end{frame}

   451 

   452 \begin{frame}[fragile]

   453     \frametitle{Multiple figures}

   454 

   455 \begin{lstlisting}

   456 >>> figure(1)

   457 >>> plot(x, sin(x))

   458 >>> figure(2)

   459 >>> plot(x, tanh(x))

   460 >>> figure(1)

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

   462 \end{lstlisting}

   463     

   464 

   465 \end{frame}

   466 

   467 \begin{frame}[fragile]

   468     \frametitle{\typ{pylab} in Python scripts}

   469 \begin{lstlisting}

   470 import pylab

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

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

   473 

   474 # Can also use:

   475 from pylab import linspace, sin, plot

   476 \end{lstlisting}

   477 \inctime{10}

   478 \end{frame}

   479 

   480 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   481 \subsection{Types of Plots}

   482 \begin{frame}[fragile]

   483   \frametitle{X-Y plot}

   484   \begin{columns}

   485     \column{0.5\textwidth}

   486     \hspace*{-0.5in}

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

   488     \column{0.45\textwidth}

   489     \begin{block}{Example code}

   490     \tiny

   491 \begin{lstlisting}

   492 t1 = arange(0.0, 5.0, 0.1)

   493 t2 = arange(0.0, 5.0, 0.02)

   494 t3 = arange(0.0, 2.0, 0.01)

   495 subplot(211)

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

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

   498 grid(True)

   499 title('A tale of 2 subplots')

   500 ylabel('Damped')

   501 subplot(212)

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

   503 grid(True)

   504 xlabel('time (s)')

   505 ylabel('Undamped')

   506 \end{lstlisting}

   507     \end{block}

   508   \end{columns}

   509 \end{frame}

   510 

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

   512   \begin{columns}

   513     \column{0.5\textwidth}

   514     \hspace*{-0.5in}

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

   516     \column{0.45\textwidth}

   517     \begin{block}{Example code}

   518     \tiny

   519 \begin{lstlisting}

   520 dt = 0.01

   521 t = arange(dt, 20.0, dt)

   522 subplot(311)

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

   524 ylabel('semilogy')

   525 grid(True)

   526 subplot(312)

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

   528 ylabel('semilogx')

   529 grid(True)

   530 # minor grid on too

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

   532 subplot(313)

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

   534 grid(True)

   535 ylabel('loglog base 4 on x')

   536 \end{lstlisting}

   537   \end{block}

   538 \end{columns}

   539 \end{frame}

   540 

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

   542   \begin{columns}

   543     \column{0.5\textwidth}

   544     \hspace*{-0.5in}

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

   546     \column{0.45\textwidth}

   547     \begin{block}{Example code}

   548     \tiny

   549 \begin{lstlisting}

   550 t = arange(0.1, 4, 0.1)

   551 s = exp(-t)

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

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

   554 g = 2*e

   555 h = 2*f

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

   557 xlabel('Distance (m)')

   558 ylabel('Height (m)')

   559 title('Mean and standard error '\

   560       'as a function of distance')

   561 \end{lstlisting}

   562   \end{block}

   563 \end{columns}

   564 \end{frame}

   565 

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

   567   \begin{columns}

   568     \column{0.5\textwidth}

   569     \hspace*{-0.5in}

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

   571     \column{0.45\textwidth}

   572     \begin{block}{Example code}

   573     \tiny

   574 \begin{lstlisting}

   575 mu, sigma = 100, 15

   576 x = mu + sigma*randn(10000)

   577 # the histogram of the data

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

   579 # add a 'best fit' line

   580 y = normpdf( bins, mu, sigma)

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

   582 xlim(40, 160)

   583 xlabel('Smarts')

   584 ylabel('P')

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

   586 \end{lstlisting}

   587   \end{block}

   588 \end{columns}

   589 \end{frame}

   590 

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

   592   \begin{columns}

   593     \column{0.5\textwidth}

   594     \hspace*{-0.5in}

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

   596     \column{0.45\textwidth}

   597     \begin{block}{Example code}

   598     \tiny

   599 \begin{lstlisting}

   600 N = 5

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

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

   603 # the x locations for the groups

   604 ind = arange(N) 

   605 # the width of the bars

   606 width = 0.35       

   607 p1 = bar(ind, menMeans, width, 

   608          color='r', yerr=menStd)

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

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

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

   612          color='y', yerr=womenStd)

   613 ylabel('Scores')

   614 title('Scores by group and gender')

   615 xticks(ind+width, 

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

   617 xlim(-width,len(ind))

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

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

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

   621 \end{lstlisting}

   622   \end{block}

   623 \end{columns}

   624 \end{frame}

   625 

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

   627   \begin{columns}

   628     \column{0.5\textwidth}

   629     \hspace*{-0.4in}

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

   631     \column{0.45\textwidth}

   632     \begin{block}{Example code}

   633     \tiny

   634 \begin{lstlisting}

   635 # make a square figure and axes

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

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

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

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

   640 explode=(0, 0.05, 0, 0)

   641 pie(fracs, explode=explode, labels=labels, 

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

   643 title('Raining Hogs and Dogs', 

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

   645 \end{lstlisting}

   646   \end{block}

   647 \end{columns}

   648 \end{frame}

   649 

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

   651   \begin{columns}

   652     \column{0.5\textwidth}

   653     \hspace*{-0.4in}

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

   655     \column{0.45\textwidth}

   656     \begin{block}{Example code}

   657     \tiny

   658 \begin{lstlisting}

   659 N = 30

   660 x = 0.9*rand(N)

   661 y = 0.9*rand(N)

   662 # 0 to 10 point radiuses

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

   664 volume = 400 + rand(N)*450

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

   666         alpha=0.75)

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

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

   669 title(r'Volume and percent change')

   670 grid(True)

   671 colorbar()

   672 savefig('scatter')

   673 \end{lstlisting}

   674   \end{block}

   675 \end{columns}

   676 \end{frame}

   677 

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

   679   \begin{columns}

   680     \column{0.5\textwidth}

   681     \hspace*{-0.5in}

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

   683     \column{0.45\textwidth}

   684     \begin{block}{Example code}

   685     \tiny

   686 \begin{lstlisting}

   687 figure(figsize=(8,8))

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

   689           polar=True, 

   690           axisbg='#d5de9c')

   691 r = arange(0,1,0.001)

   692 theta = 2*2*pi*r

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

   694 # the radius of the grid labels

   695 setp(ax.thetagridlabels, y=1.075) 

   696 title(r'$\theta=4\pi r$', fontsize=20)

   697 \end{lstlisting}

   698 

   699   \end{block}

   700 \end{columns}

   701 \end{frame}

   702 

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

   704   \begin{columns}

   705     \column{0.45\textwidth}

   706     \hspace*{-0.5in}

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

   708     \column{0.525\textwidth}

   709     \begin{block}{Example code}

   710     \tiny

   711 \begin{lstlisting}

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

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

   714 X, Y = meshgrid(x, y)

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

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

   717 # difference of Gaussians

   718 Z = 10.0 * (Z2 - Z1)

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

   720             origin='lower',

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

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

   723 # label every second level

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

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

   726 CS = contour(Z, levels,

   727              origin='lower',

   728              linewidths=2,

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

   730 # make a colorbar for the contour lines

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

   732 title('Lines with colorbar')

   733 hot(); flag()

   734 \end{lstlisting}

   735   \end{block}

   736 \end{columns}

   737 \end{frame}

   738 

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

   740   \begin{columns}

   741     \column{0.5\textwidth}

   742     \hspace*{-0.5in}

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

   744     \column{0.45\textwidth}

   745     \begin{block}{Example code}

   746     \tiny

   747 \begin{lstlisting}

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

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

   750 U = cos(X)

   751 V = sin(Y)

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

   753            U[::3, ::3], V[::3, ::3],

   754            color='r', units='x', 

   755            linewidths=(2,), 

   756            edgecolors=('k'), 

   757            headaxislength=5 )

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

   759                fontproperties=

   760                {'weight': 'bold'})

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

   762 title('triangular head; scale '\

   763       'with x view; black edges')

   764 \end{lstlisting}

   765   \end{block}

   766 \end{columns}

   767 \end{frame}

   768 

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

   770   \includegraphics[height=2.3in, interpolate=true]{data/plotmap}  

   771   \begin{center}

   772     \tiny

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

   774   \end{center}

   775 \end{frame}

   776 

   777 

   778 \begin{frame}

   779   \frametitle{More information}

   780   \begin{itemize}

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

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

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

   784   \end{itemize}

   785 \inctime{5}

   786 \end{frame}

   787 

   788 \begin{frame}

   789   \frametitle{Problem Set}

   790   \begin{itemize}

   791       \item[1] Write a function that plots any regular n-gon given \typ{n}.

   792       \item[2] Consider the logistic map, $f(x) = kx(1-x)$, plot it for

   793           $k=2.5, 3.5$ and $4$ in the same plot.

   794 \end{itemize}

   795 \end{frame}

   796 

   797 \begin{frame}[fragile] 

   798 \frametitle{Problem Set}

   799   \begin{columns}

   800     \column{0.6\textwidth}

   801     \small{

   802     \begin{itemize}

   803       \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. 

   804     \end{itemize}}

   805     \column{0.35\textwidth}

   806     \hspace*{-0.5in}

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

   808 \end{columns}

   809 \end{frame}

   810 

   811 \begin{frame}

   812   

   813   Plot the cobweb plot as follows:

   814   \begin{enumerate}

   815     \item Start at $(x_0, 0)$ ($\implies$ i=0)

   816     \item Draw a line to $(x_i, f(x_i))$

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

   818     \item Draw a line to $(x_{i+1}, x_{i+1})$

   819     \item $(i\implies i+1)$ 

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

   821   \end{enumerate}

   822 \inctime{20}

   823 \end{frame}

   824 

   825 \begin{frame}{Summary}

   826   \begin{itemize}

   827   \item Basics of Numpy.

   828   \item Array operations.

   829   \item Plotting in 2D.

   830   \end{itemize}

   831 \end{frame}

   832 \end{document}