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% Tutorial slides on Python.

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

% Copyright (c) 2005-2008, Prabhu Ramachandran

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% Title page

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

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

\institute[FOSSEE] {FOSSEE Team}

\date[] {11, October 2009}

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%% the beginning of each subsection:

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    \frametitle{Outline}

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% 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}

\inctime{5}

\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}

  \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}

\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{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), dot(a, bp)}   \inctime{10}

  \end{itemize}

  \inctime{10}

\end{frame}

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

\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}

\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])

>>> 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}

\begin{frame}[fragile]

\frametitle{Random Numbers}

\begin{lstlisting}

>>> np.random.rand(3,2)

array([[ 0.96276665,  0.77174861],

       [ 0.35138557,  0.61462271],

       [ 0.16789255,  0.43848811]])

>>> np.random.randint(1,100)

42

\end{lstlisting}

\inctime{15}

\end{frame}

\begin{frame}[fragile]

  \frametitle{Problem Set}

  \begin{lstlisting}

    >>> from scipy import misc

    >>> A=misc.imread(name)

    >>> misc.imshow(A)

  \end{lstlisting}

    \begin{enumerate}

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

    \item Scale the image to 50\%

    \item Introduce some random noise?

    \end{enumerate}

\inctime{15}

\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{Plots - Lines, Labels and Legends}

\begin{frame}[fragile]

  \frametitle{Basic plotting}

\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]

%\begin{itemize}

%  \item We already saw LaTeX markup support!

%\end{itemize}

\begin{lstlisting}

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

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

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

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

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

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

>>> annotate('maxima',xy=(0, 1), 

             xytext=(1, 0.8), 

             arrowprops=dict(

             facecolor='black', 

             shrink=0.05))

\end{lstlisting}

\end{frame}

\begin{frame}[fragile]

  \frametitle{Legends}

\begin{lstlisting}

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

         label='cosine')

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

         label='sine')

>>> legend() 

# Or use:

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

\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}

\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}