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diff --git a/day2/session1.tex b/day2/session1.tex new file mode 100644 index 0000000..d8bbecc --- /dev/null +++ b/day2/session1.tex @@ -0,0 +1,757 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Tutorial slides on Python. +% +% Author: Prabhu Ramachandran <prabhu at aero.iitb.ac.in> +% Copyright (c) 2005-2008, Prabhu Ramachandran +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\documentclass[14pt,compress]{beamer} +%\documentclass[draft]{beamer} +%\documentclass[compress,handout]{beamer} +%\usepackage{pgfpages} +%\pgfpagesuselayout{2 on 1}[a4paper,border shrink=5mm] + +% Modified from: generic-ornate-15min-45min.de.tex +\mode<presentation> +{ + \usetheme{Warsaw} + \useoutertheme{split} + \setbeamercovered{transparent} +} + +\usepackage[english]{babel} +\usepackage[latin1]{inputenc} +%\usepackage{times} +\usepackage[T1]{fontenc} + +% Taken from Fernando's slides. +\usepackage{ae,aecompl} +\usepackage{mathpazo,courier,euler} +\usepackage[scaled=.95]{helvet} + +\definecolor{darkgreen}{rgb}{0,0.5,0} + +\usepackage{listings} +\lstset{language=Python, + basicstyle=\ttfamily\bfseries, + commentstyle=\color{red}\itshape, + stringstyle=\color{darkgreen}, + showstringspaces=false, + keywordstyle=\color{blue}\bfseries} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Macros +\setbeamercolor{emphbar}{bg=blue!20, fg=black} +\newcommand{\emphbar}[1] +{\begin{beamercolorbox}[rounded=true]{emphbar} + {#1} + \end{beamercolorbox} +} +\newcounter{time} +\setcounter{time}{0} +\newcommand{\inctime}[1]{\addtocounter{time}{#1}{\tiny \thetime\ m}} + +\newcommand{\typ}[1]{\texttt{#1}} + +\newcommand{\kwrd}[1]{ \texttt{\textbf{\color{blue}{#1}}} } + +%%% This is from Fernando's setup. +% \usepackage{color} +% \definecolor{orange}{cmyk}{0,0.4,0.8,0.2} +% % Use and configure listings package for nicely formatted code +% \usepackage{listings} +% \lstset{ +% language=Python, +% basicstyle=\small\ttfamily, +% commentstyle=\ttfamily\color{blue}, +% stringstyle=\ttfamily\color{orange}, +% showstringspaces=false, +% breaklines=true, +% postbreak = \space\dots +% } + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Title page +\title[]{Matrices and Arrays\\ \& \\2D Plotting} + +\author[Asokan \& Prabhu] {Asokan Pichai\\Prabhu Ramachandran} + +\institute[FOSSEE] {FOSSEE Team} +\date[] {11, October 2009} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo} +%\logo{\pgfuseimage{iitmlogo}} + + +%% Delete this, if you do not want the table of contents to pop up at +%% the beginning of each subsection: +\AtBeginSubsection[] +{ + \begin{frame}<beamer> + \frametitle{Outline} + \tableofcontents[currentsection,currentsubsection] + \end{frame} +} + +\AtBeginSection[] +{ + \begin{frame}<beamer> + \frametitle{Outline} + \tableofcontents[currentsection,currentsubsection] + \end{frame} +} + +% If you wish to uncover everything in a step-wise fashion, uncomment +% the following command: +%\beamerdefaultoverlayspecification{<+->} + +%\includeonlyframes{current,current1,current2,current3,current4,current5,current6} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% DOCUMENT STARTS +\begin{document} + +\begin{frame} + \maketitle +\end{frame} + +\begin{frame} + \frametitle{Outline} + \tableofcontents + % You might wish to add the option [pausesections] +\end{frame} + +\section{Matrices and Arrays} + +\subsection{Basic \typ{numpy} } + +\newcommand{\num}{\texttt{numpy}} + +\begin{frame} + \frametitle{The \num\ module} + \begin{itemize} + \item Why? + \item What: + \begin{itemize} + \item An efficient and powerful array type for various common data + types + \item Abstracts out the most commonly used standard operations on + arrays + \end{itemize} + \end{itemize} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Examples of \num} +\begin{lstlisting} +# Simple array math example +>>> from numpy import * +>>> a = array([1,2,3,4]) +>>> b = array([2,3,4,5]) +>>> a*2 + b + 1 # Basic math! +array([5, 8, 11, 14]) +# Pi and e are defined. +>>> x = linspace(0.0, 10.0, 1000) +>>> x *= 2*pi/10 # inplace. +# apply functions to array. +>>> y = sin(x) +\end{lstlisting} +\end{frame} + +\begin{frame} + \frametitle{Basic concepts} + \begin{itemize} + \item fixed size (\typ{arr.size}); + \item Same type (\typ{arr.dtype}) of data + \item arbitrary dimensionality + \item \typ{arr.shape}: size in each dimension + \item \alert{Note:} \typ{len(arr) != arr.size} in general + \item \alert{Note:} By default array operations are performed + \alert{elementwise} + \item Indices, slicing: just like lists + \end{itemize} +\end{frame} + + +\begin{frame}[fragile] + \frametitle{More examples of \num} +\vspace*{-8pt} +\begin{lstlisting} +>>> x = array([1., 2, 3, 4]) +>>> size(x) +4 +>>> x.dtype # What is a.dtype? +dtype('float64') +>>> x.shape +(4,) +>>> print rank(x), x.itemsize +1 8 +>>> x[0] = 10 +>>> print x[0], x[-1] +10.0 4.0 +\end{lstlisting} + +\inctime{10} +\end{frame} + +\begin{frame} + {More Numpy} + + \begin{itemize} + \item Multi-dimensional arrays + \item Random number generation + \end{itemize} + +\end{frame} + +\begin{frame}[fragile] + \frametitle{Multi-dimensional arrays} +\begin{lstlisting} +>>> a = array([[ 0, 1, 2, 3], +... [10,11,12,13]]) +>>> a.shape # (rows, columns) +(2, 4) +# Accessing and setting values +>>> a[1,3] +13 +>>> a[1,3] = -1 +>>> a[1] # The second row +array([10,11,12,-1]) + +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Slicing arrays} +\begin{lstlisting} +>>> a = array([[1,2,3], [4,5,6], + [7,8,9]]) +>>> a[0,1:3] +array([2, 3]) +>>> a[1:,1:] +array([[5, 6], + [8, 9]]) +>>> a[:,2] +array([3, 6, 9]) +\end{lstlisting} +\end{frame} +\begin{frame}[fragile] + \frametitle{Striding arrays} +\begin{lstlisting} +>>> a[0::2,0::2] +array([[1, 3], + [7, 9]]) +# Slices are references to the +# same memory! +\end{lstlisting} +\end{frame} + +\subsection{Array creation } +\begin{frame}[fragile] + \frametitle{Array creation functions} + \begin{itemize} + \item \typ{array(object, dtype=None, \ldots)} + \item \typ{arange(start, stop=None, step=1 \ldots)} + \item \typ{linspace(start, stop, num=50, \ldots)} + \item \typ{ones(shape, dtype=None, \ldots)} + \item \typ{zeros(shape, dtype=float,\ldots)} + \item \typ{identity(n)} + \item \typ{empty(shape, dtype=float,\ldots)} + \item \typ{ones\_like(x)}, + \item \typ{zeros\_like(x)}, \typ{empty\_like(x)} + \end{itemize} +\end{frame} + +\subsection{Array math} +\begin{frame}[fragile] + \frametitle{Array math} + \begin{itemize} + \item Basic \alert{elementwise} math (given two arrays \typ{a, b}): + \typ{+, -, *, /, \%} + \item Inplace operators: \typ{a += b}, or \typ{add(a, b, + a)} etc. + \item Logical operations: \typ{equal (==)}, \typ{not\_equal (!=)}, + \typ{less (<)}, \typ{greater (>)} etc. + \item Trig and other functions: \typ{sin(x), arcsin(x), sinh(x), + exp(x), sqrt(x)} etc. + \item \typ{sum(x, axis=0), product(x, axis=0)} + \item \typ{dot(a, bp)} + \end{itemize} +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{2D Plotting} +\subsection{Getting Started} + +\begin{frame} + {IPython's \typ{pylab} mode} +\begin{itemize} + \item \typ{pylab}: convenient 2D plotting interface to MPL + \item Immediate use: \typ{ipython -pylab} + \item Imports all of pylab for you! + \item Allows for interactive plotting +\end{itemize} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Basic 2D plotting} + +\begin{lstlisting} +>>> x = linspace(0, 2*pi, 1000) +>>> plot(x, sin(x)) +>>> plot(x, sin(x), 'ro') +>>> xlabel(r'$\chi$', color='g') +# LaTeX markup! +>>> ylabel(r'sin($\chi$)', color='r') +>>> title('Simple figure', fontsize=20) +>>> savefig('/tmp/test.eps') +\end{lstlisting} +\begin{itemize} + \item Also: PNG, PDF, PS, EPS, SVG, PDF +\end{itemize} +\end{frame} + +\subsection{Playing with lines} +\begin{frame}[fragile] + \frametitle{Basic plotting \ldots} +\begin{lstlisting} +# Set properties of objects: +>>> l, = plot(x, sin(x)) +# Why "l,"? +>>> setp(l, linewidth=2.0, color='r') +>>> l.set_linewidth(2.0) +>>> draw() # Redraw. +>>> setp(l) # Print properties +>>> clf() # Clear figure. +>>> close() # Close figure. +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Multiple figures} + +\begin{lstlisting} +>>> figure(1) +>>> plot(x, sin(x)) +>>> figure(2) +>>> plot(x, tanh(x)) +>>> figure(1) +>>> title('Easy as 1,2,3') +\end{lstlisting} + +\end{frame} + +\subsection{Handling Text} + +\begin{frame}[fragile] + \frametitle{Legends and Annotation} +\begin{lstlisting} +>>> plot(x, cos(5*x), 'r--', + label='cosine') +>>> plot(x, sin(5*x), 'g--', + label='sine') +>>> legend() +# Or use: +>>> legend(['cosine', 'sine']) +# Annotation: +>>> text(1,0, '(1,0)') +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] + \frametitle{More commands \ldots} + \begin{lstlisting} +# semilog, loglog +>>> x = 10.**(-arange(100)*0.1) +>>> semilogx(x, x) +>>> semilogy(x, x) +>>> loglog(x, x) +>>> loglog(x, x*x) + \end{lstlisting} +\end{frame} + +\begin{frame}[fragile] + \frametitle{More plots \ldots} + \begin{lstlisting} +>>> clf() +>>> t = arange(0.1, 4, 0.1) +>>> s = exp(-t) +>>> e = 0.1*abs(randn(len(s))) +>>> errorbar(t, s, e) +# Scatter plots +>>> clf() +>>> t = randn(len(e)) +>>> scatter(t, e, c=s) + \end{lstlisting} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Note: \typ{pylab} in Python scripts} +\begin{lstlisting} +import pylab +x = pylab.linspace(0, 20, 1000) +pylab.plot(x, pylab.sin(x)) + +# Can also use: +from pylab import linspace, sin, plot +\end{lstlisting} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Types of Plots} +\begin{frame}[fragile] + \frametitle{X-Y plot} + \begin{columns} + \column{0.5\textwidth} + \hspace*{-0.5in} + \includegraphics[height=2in, interpolate=true]{data/xyplot} + \column{0.45\textwidth} + \begin{block}{Example code} + \tiny +\begin{lstlisting} +t1 = arange(0.0, 5.0, 0.1) +t2 = arange(0.0, 5.0, 0.02) +t3 = arange(0.0, 2.0, 0.01) +subplot(211) +plot(t1, cos(2*pi*t1)*exp(-t1), 'bo', + t2, cos(2*pi*t2)*exp(-t2), 'k') +grid(True) +title('A tale of 2 subplots') +ylabel('Damped') +subplot(212) +plot(t3, cos(2*pi*t3), 'r--') +grid(True) +xlabel('time (s)') +ylabel('Undamped') +\end{lstlisting} + \end{block} + \end{columns} +\end{frame} + +\begin{frame}[fragile] \frametitle{Semi-log and log-log plots} + \begin{columns} + \column{0.5\textwidth} + \hspace*{-0.5in} + \includegraphics[height=2in, interpolate=true]{data/log} + \column{0.45\textwidth} + \begin{block}{Example code} + \tiny +\begin{lstlisting} +dt = 0.01 +t = arange(dt, 20.0, dt) +subplot(311) +semilogy(t, exp(-t/5.0)) +ylabel('semilogy') +grid(True) +subplot(312) +semilogx(t, sin(2*pi*t)) +ylabel('semilogx') +grid(True) +# minor grid on too +gca().xaxis.grid(True, which='minor') +subplot(313) +loglog(t, 20*exp(-t/10.0), basex=4) +grid(True) +ylabel('loglog base 4 on x') +\end{lstlisting} + \end{block} +\end{columns} +\end{frame} + +\begin{frame}[fragile] \frametitle{Errorbar} + \begin{columns} + \column{0.5\textwidth} + \hspace*{-0.5in} + \includegraphics[height=2in, interpolate=true]{data/errorbar} + \column{0.45\textwidth} + \begin{block}{Example code} + \tiny +\begin{lstlisting} +t = arange(0.1, 4, 0.1) +s = exp(-t) +e = 0.1*abs(randn(len(s))) +f = 0.1*abs(randn(len(s))) +g = 2*e +h = 2*f +errorbar(t, s, [e,g], f, fmt='o') +xlabel('Distance (m)') +ylabel('Height (m)') +title('Mean and standard error '\ + 'as a function of distance') +\end{lstlisting} + \end{block} +\end{columns} +\end{frame} + +\begin{frame}[fragile] \frametitle{Histogram} + \begin{columns} + \column{0.5\textwidth} + \hspace*{-0.5in} + \includegraphics[height=2in, interpolate=true]{data/histogram} + \column{0.45\textwidth} + \begin{block}{Example code} + \tiny +\begin{lstlisting} +mu, sigma = 100, 15 +x = mu + sigma*randn(10000) +# the histogram of the data +n, bins, patches = hist(x, 100, normed=1) +# add a 'best fit' line +y = normpdf( bins, mu, sigma) +l = plot(bins, y, 'r--', linewidth=2) +xlim(40, 160) +xlabel('Smarts') +ylabel('P') +title(r'$\rm{IQ:}\/ \mu=100,\/ \sigma=15$') +\end{lstlisting} + \end{block} +\end{columns} +\end{frame} + +\begin{frame}[fragile] \frametitle{Bar charts} + \begin{columns} + \column{0.5\textwidth} + \hspace*{-0.5in} + \includegraphics[height=2in, interpolate=true]{data/barchart} + \column{0.45\textwidth} + \begin{block}{Example code} + \tiny +\begin{lstlisting} +N = 5 +menMeans = (20, 35, 30, 35, 27) +menStd = ( 2, 3, 4, 1, 2) +# the x locations for the groups +ind = arange(N) +# the width of the bars +width = 0.35 +p1 = bar(ind, menMeans, width, + color='r', yerr=menStd) +womenMeans = (25, 32, 34, 20, 25) +womenStd = ( 3, 5, 2, 3, 3) +p2 = bar(ind+width, womenMeans, width, + color='y', yerr=womenStd) +ylabel('Scores') +title('Scores by group and gender') +xticks(ind+width, + ('G1', 'G2', 'G3', 'G4', 'G5')) +xlim(-width,len(ind)) +yticks(arange(0,41,10)) +legend((p1[0], p2[0]), + ('Men', 'Women'), shadow=True) +\end{lstlisting} + \end{block} +\end{columns} +\end{frame} + +\begin{frame}[fragile] \frametitle{Pie charts} + \begin{columns} + \column{0.5\textwidth} + \hspace*{-0.4in} + \includegraphics[height=2.0in, interpolate=true]{data/piechart} + \column{0.45\textwidth} + \begin{block}{Example code} + \tiny +\begin{lstlisting} +# make a square figure and axes +figure(1, figsize=(8,8)) +ax = axes([0.1, 0.1, 0.8, 0.8]) +labels = 'Frogs', 'Hogs', 'Dogs', 'Logs' +fracs = [15,30,45, 10] +explode=(0, 0.05, 0, 0) +pie(fracs, explode=explode, labels=labels, + autopct='%1.1f%%', shadow=True) +title('Raining Hogs and Dogs', + bbox={'facecolor':'0.8', 'pad':5}) +\end{lstlisting} + \end{block} +\end{columns} +\end{frame} + +\begin{frame}[fragile] \frametitle{Scatter plots} + \begin{columns} + \column{0.5\textwidth} + \hspace*{-0.4in} + \includegraphics[height=2in, interpolate=true]{data/scatter} + \column{0.45\textwidth} + \begin{block}{Example code} + \tiny +\begin{lstlisting} +N = 30 +x = 0.9*rand(N) +y = 0.9*rand(N) +# 0 to 10 point radiuses +area = pi*(10 * rand(N))**2 +volume = 400 + rand(N)*450 +scatter(x,y,s=area, marker='o', c=volume, + alpha=0.75) +xlabel(r'$\Delta_i$', size='x-large') +ylabel(r'$\Delta_{i+1}$', size='x-large') +title(r'Volume and percent change') +grid(True) +colorbar() +savefig('scatter') +\end{lstlisting} + \end{block} +\end{columns} +\end{frame} + +\begin{frame}[fragile] \frametitle{Polar} + \begin{columns} + \column{0.5\textwidth} + \hspace*{-0.5in} + \includegraphics[height=2in, interpolate=true]{data/polar} + \column{0.45\textwidth} + \begin{block}{Example code} + \tiny +\begin{lstlisting} +figure(figsize=(8,8)) +ax = axes([0.1, 0.1, 0.8, 0.8], + polar=True, + axisbg='#d5de9c') +r = arange(0,1,0.001) +theta = 2*2*pi*r +polar(theta, r, color='#ee8d18', lw=3) +# the radius of the grid labels +setp(ax.thetagridlabels, y=1.075) +title(r"$\theta=4\pi r", fontsize=20) +\end{lstlisting} + \end{block} +\end{columns} +\end{frame} + +\begin{frame}[fragile] \frametitle{Contours} + \begin{columns} + \column{0.45\textwidth} + \hspace*{-0.5in} + \includegraphics[height=2in, interpolate=true]{data/contour} + \column{0.525\textwidth} + \begin{block}{Example code} + \tiny +\begin{lstlisting} +x = arange(-3.0, 3.0, 0.025) +y = arange(-2.0, 2.0, 0.025) +X, Y = meshgrid(x, y) +Z1 = bivariate_normal(X, Y, 1.0, 1.0, 0.0, 0.0) +Z2 = bivariate_normal(X, Y, 1.5, 0.5, 1, 1) +# difference of Gaussians +Z = 10.0 * (Z2 - Z1) +im = imshow(Z, interpolation='bilinear', + origin='lower', + cmap=cm.gray, extent=(-3,3,-2,2)) +levels = arange(-1.2, 1.6, 0.2) +# label every second level +clabel(CS, levels[1::2], inline=1, + fmt='%1.1f', fontsize=14) +CS = contour(Z, levels, + origin='lower', + linewidths=2, + extent=(-3,3,-2,2)) +# make a colorbar for the contour lines +CB = colorbar(CS, shrink=0.8, extend='both') +title('Lines with colorbar') +hot(); flag() +\end{lstlisting} + \end{block} +\end{columns} +\end{frame} + +\begin{frame}[fragile] \frametitle{Velocity vectors} + \begin{columns} + \column{0.5\textwidth} + \hspace*{-0.5in} + \includegraphics[height=2in, interpolate=true]{data/quiver} + \column{0.45\textwidth} + \begin{block}{Example code} + \tiny +\begin{lstlisting} +X,Y = meshgrid(arange(0,2*pi,.2), + arange(0,2*pi,.2) ) +U = cos(X) +V = sin(Y) +Q = quiver(X[::3, ::3], Y[::3, ::3], + U[::3, ::3], V[::3, ::3], + color='r', units='x', + linewidths=(2,), + edgecolors=('k'), + headaxislength=5 ) +qk = quiverkey(Q, 0.5, 0.03, 1, '1 m/s', + fontproperties= + {'weight': 'bold'}) +axis([-1, 7, -1, 7]) +title('triangular head; scale '\ + 'with x view; black edges') +\end{lstlisting} + \end{block} +\end{columns} +\end{frame} + +\begin{frame}[fragile] \frametitle{Maps} + \includegraphics[height=2.5in, interpolate=true]{data/plotmap} + \begin{center} + \tiny + For details see \url{http://matplotlib.sourceforge.net/screenshots/plotmap.py} + \end{center} +\end{frame} + + +\begin{frame} + \frametitle{More information} + \begin{itemize} + \item More information here: \url{http://matplotlib.sf.net} + \item \url{http://matplotlib.sf.net/tutorial.html} + \item \url{http://matplotlib.sf.net/screenshots.html} + \end{itemize} + + \inctime{25} +\end{frame} + +\begin{frame} + \frametitle{Problem set 1.0} + \begin{enumerate} + \item Write a function that plots any n-gon given \typ{n}. + \item Consider the logistic map, $f(x) = kx(1-x)$, plot it for + $k=2.5, 3.5$ and $4$ +\end{enumerate} +\end{frame} + +\begin{frame} + \frametitle{Problem set 1.1} + \begin{enumerate} + \item Consider the iteration $x_{n+1} = f(x_n)$ where $f(x) = + kx(1-x)$. Plot the successive iterates of this process. + \item Plot this using a cobweb plot as follows: + \begin{enumerate} + \item Start at $(x_0, 0)$ + \item Draw line to $(x_i, f(x_i))$; + \item Set $x_{i+1} = f(x_i)$ + \item Draw line to $(x_i, x_i)$ + \item Repeat from 2 for as long as you want + \end{enumerate} + \end{enumerate} +\end{frame} + +\begin{frame} + \frametitle{Problem set 1.2} + \begin{enumerate} + + \item Plot the Koch snowflake. Write a function to generate the + necessary points given the two points constituting a line. + \pause + \begin{enumerate} + \item Split the line into 4 segments. + \item The first and last segments are trivial. + \item To rotate the point you can use complex numbers, + recall that $z e^{j \theta}$ rotates a point $z$ in 2D + by $\theta$. + \item Do this for all line segments till everything is + done. + \end{enumerate} + \item Show rate of convergence for a first and second order finite + difference of sin(x) +\end{enumerate} +\inctime{30} +\end{frame} +\end{document} |