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}

     9 %\documentclass[draft]{beamer}

    10 %\documentclass[compress,handout]{beamer}

    11 %\usepackage{pgfpages} 

    12 %\pgfpagesuselayout{2 on 1}[a4paper,border shrink=5mm]

    13 

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

    15 \mode<presentation>

    16 {

    17   \usetheme{Warsaw}

    18   \useoutertheme{split}

    19   \setbeamercovered{transparent}

    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

    44 \setbeamercolor{emphbar}{bg=blue!20, fg=black}

    45 \newcommand{\emphbar}[1]

    46 {\begin{beamercolorbox}[rounded=true]{emphbar} 

    47       {#1}

    48  \end{beamercolorbox}

    49 }

    50 \newcounter{time}

    51 \setcounter{time}{0}

    52 \newcommand{\inctime}[1]{\addtocounter{time}{#1}{\tiny \thetime\ m}}

    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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    75 % Title page

    76 \title[]{Numerical Computing with Numpy \& Scipy}

    77 

    78 \author[FOSSEE Team] {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 {

   100   \begin{frame}<beamer>

   101     \frametitle{Outline}

   102     \tableofcontents[currentsection,currentsubsection]

   103   \end{frame}

   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}[fragile]

   121   \frametitle{Broadcasting}

   122   \begin{itemize}

   123     \item Used so that functions can take inputs that are not of the same shape.

   124     \item 2 rules -

   125       \begin{enumerate}

   126       \item 1 (repeatedly) pre-pended to shapes of smaller arrays

   127       \item Size 1 in a dimension -> Largest size in that dimension

   128       \end{enumerate}

   129   \end{itemize}

   130   \begin{columns}

   131     \column{0.65\textwidth}

   132     \hspace*{-1.5in}

   133     \begin{lstlisting}

   134       >>> x = np.arange(4)

   135       >>> x+3

   136       array([3, 4, 5, 6])

   137     \end{lstlisting}

   138     \column{0.35\textwidth}

   139     \includegraphics[height=0.7in, interpolate=true]{data/broadcast_scalar}

   140   \end{columns}

   141 \end{frame}

   142 

   143 \begin{frame}[fragile]

   144   \frametitle{Broadcasting in 3D}

   145     \begin{lstlisting}

   146       >>> x = np.zeros((3, 5))

   147       >>> y = np.zeros(8)

   148       >>> (x[..., None] + y).shape

   149       (3, 5, 8)

   150     \end{lstlisting}

   151     \begin{figure}

   152       \begin{center}

   153       \includegraphics[height=1.5in, interpolate=true]{data/array_3x5x8}        

   154       \end{center}

   155     \end{figure}

   156 \end{frame}

   157 

   158 \begin{frame}[fragile]

   159   \frametitle{Copies \& Views}

   160   \begin{lstlisting}

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

   162                    [7,8,9]])

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

   164     array([2, 3])

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

   166     array([[1, 3],

   167           [7, 9]])

   168   \end{lstlisting}

   169   \begin{itemize}

   170   \item Slicing and Striding just reference the same memory

   171   \item They produce views of the data, not copies

   172   \end{itemize}

   173 \end{frame}

   174 

   175 \begin{frame}[fragile]

   176   \frametitle{Copies contd \ldots}

   177   \begin{lstlisting}

   178     >>> a[np.array([0,1,2])]

   179     array([[1, 2, 3],

   180            [4, 5, 6],

   181            [7, 8, 9]])

   182   \end{lstlisting}

   183   \begin{itemize}

   184   \item Index arrays or Boolean arrays produce copies

   185   \end{itemize}

   186 \inctime{15}

   187 \end{frame}

   188 

   189 \begin{frame}

   190   \frametitle{More Numpy Functions \& Methods}

   191   More functions

   192   \begin{itemize}

   193     \item \typ{take}

   194     \item \typ{choose}

   195     \item \typ{where}

   196     \item \typ{compress}

   197     \item \typ{concatenate}

   198   \end{itemize}

   199   Ufunc methods 

   200   \begin{itemize}

   201     \item \typ{reduce}

   202     \item \typ{accumulate}

   203     \item \typ{outer}

   204     \item \typ{reduceat}

   205   \end{itemize}

   206 \inctime{5}

   207 \end{frame}

   208 

   209 \begin{frame}

   210     {Intro to SciPy}

   211   \begin{itemize}

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

   213   \item Open source scientific libraries for Python

   214   \item Based on NumPy

   215     \end{itemize}

   216 \end{frame}

   217 

   218 \begin{frame}

   219   \frametitle{SciPy}

   220   \begin{itemize}

   221   \item Provides:

   222     \begin{itemize}

   223     \item Linear algebra

   224     \item Numerical integration

   225     \item Fourier transforms

   226     \item Signal processing

   227     \item Special functions

   228     \item Statistics

   229     \item Optimization

   230     \item Image processing

   231     \item ODE solvers

   232     \end{itemize}

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

   234   \end{itemize}

   235 \end{frame}

   236 

   237 \begin{frame}[fragile]

   238   \frametitle{Linear Algebra}

   239   \typ{>>> from scipy import linalg}

   240   \begin{itemize}

   241     \item \typ{linalg.det, linalg.norm}

   242     \item \typ{linalg.eig, linalg.lu}

   243     \item \typ{linalg.expm, linalg.logm}

   244     \item \typ{linalg.sinm, linalg.sinhm}

   245   \end{itemize}

   246 \end{frame}

   247 

   248 \begin{frame}[fragile]

   249   \frametitle{Linear Algebra \ldots}

   250   \begin{align*}

   251     3x + 2y - z  & = 1 \\

   252     2x - 2y + 4z  & = -2 \\

   253     -x + \frac{1}{2}y -z & = 0

   254   \end{align*}

   255   \begin{lstlisting}

   256     >>> linalg.solve(A,B)

   257   \end{lstlisting}

   258 \inctime{15}

   259 \end{frame}

   260 

   261 \begin{frame}[fragile]

   262   \begin{itemize}

   263     \item Integrating Functions given function object

   264     \item Integrating Functions given fixed samples

   265     \item Numerical integrators of ODE systems

   266   \end{itemize}

   267   \frametitle{Integrate}

   268   Calculate $\int^1_0sin(x) + x^2$

   269   \begin{lstlisting}

   270     >>> def f(x):

   271             return np.sin(x)+x**2

   272     >>> integrate.quad(f, 0, 1)

   273   \end{lstlisting}

   274 \end{frame}

   275 

   276 \begin{frame}[fragile]

   277   \frametitle{Integrate \ldots}

   278   Numerically solve ODEs\\

   279   \begin{align*}

   280   \frac{dx}{dt}&=-e^{(-t)}x^2(t)\\ 

   281            x(0)&=2    

   282   \end{align*}

   283   \begin{lstlisting}

   284     def dx_dt(x,t):

   285         return -np.exp(-t)*x**2

   286 

   287     x=integrate.odeint(dx_dt, 2, t)

   288     plt.plot(x,t)

   289   \end{lstlisting}

   290 \inctime{10}

   291 \end{frame}

   292 

   293 \begin{frame}[fragile]

   294   \frametitle{Interpolation}

   295   \begin{itemize}

   296     \item \typ{interpolate.interp1d, ...}

   297     \item \typ{interpolate.splrep, splev}

   298   \end{itemize}

   299   Cubic Spline of $sin(x)$

   300   \begin{lstlisting}

   301     x = np.arange(0,2*np.pi,np.pi/8)

   302     y = np.sin(x)

   303     t = interpolate.splrep(x,y,s=0)

   304     X = np.arange(0,2*np.pi,np.pi/50)

   305     Y = interpolate.splev(X,t,der=0)

   306 

   307     plt.plot(x,y,'o',x,y,X,Y)

   308     plt.show()

   309   \end{lstlisting}

   310 \inctime{10}

   311 \end{frame}

   312 

   313 \begin{frame}[fragile]

   314   \frametitle{Signal \& Image Processing}

   315     \begin{itemize}

   316      \item Convolution

   317      \item B-splines

   318      \item Filtering

   319      \item Filter design

   320      \item IIR filter design

   321      \item Linear Systems

   322      \item LTI Reresentations

   323      \item Waveforms

   324      \item Window functions

   325      \item Wavelets

   326     \end{itemize}

   327 \end{frame}

   328 

   329 \begin{frame}[fragile]

   330   \frametitle{Signal \& Image Processing}

   331   Applying a simple median filter

   332   \begin{lstlisting}

   333     from scipy import signal, ndimage

   334     from scipy import lena

   335     A=lena().astype('float32')

   336     B=signal.medfilt2d(A)

   337     imshow(B)

   338   \end{lstlisting}

   339   Zooming an array - uses spline interpolation

   340   \begin{lstlisting}

   341     b=ndimage.zoom(A,0.5)

   342     imshow(b)

   343     \inctime{5}

   344   \end{lstlisting}

   345 

   346 \end{frame}

   347 

   348 \begin{frame}[fragile]

   349   \frametitle{Problems}

   350   The Van der Pol oscillator is a type of nonconservative oscillator with nonlinear damping. It evolves in time according to the second order differential equation:

   351   \begin{equation*}

   352   \frac{d^2x}{dt^2}+\mu(x^2-1)\frac{dx}{dt}+x= 0

   353   \end{equation*}

   354 \inctime{25}

   355 \end{frame}

   356 

   357 

   358 \end{document}

   359 

   360 - Numpy arrays (30 mins)

   361     - Matrices

   362     - random number generation.

   363     - Image manipulation: jigsaw puzzle.

   364     - Monte-carlo integration.

   365 

   366