Workshop materials: comparison day2/session1.tex

equal deleted inserted replaced

-:a749db24e73b
+:555237dbce44
 %    postbreak = \space\dots
 % }
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % Title page
-\title[]{Matrices and Arrays\\ \& \\2D Plotting}
+\title[]{Arrays\\ \& \\2D Plotting}
-\author[FOSSEE Team] {Asokan Pichai\\Prabhu Ramachandran}
+\author[FOSSEE Team] {FOSSEE}
 \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
 \date[] {11, October 2009}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \frametitle{Outline}
 \tableofcontents
 % You might wish to add the option [pausesections]
 \end{frame}
-\section{Matrices and Arrays}
+\section{Arrays}
 \subsection{Basic \typ{numpy}}
 \begin{frame}
-\frametitle{The \num module}
+\frametitle{The \num\  module}
 \begin{itemize}
 \item Why?
 \item What:
 \begin{itemize}
 \item An efficient and powerful array type for various common data types
 \begin{frame}[fragile]
 \frametitle{Examples of \num}
 \begin{lstlisting}
 # Simple array math example
->>> import numpy as np
+>>> from numpy import *
->>> a = np.array([1,2,3,4])
+>>> a = array([1,2,3,4])
->>> b = np.arange(2,6)
+>>> b = arange(2,6)
 >>> b
 array([2,3,4,5])
 >>> a*2 + b + 1 # Basic math!
 array([5, 8, 11, 14])
 \end{lstlisting}
 \begin{frame}[fragile]
 \frametitle{Examples of \num}
 \begin{lstlisting}
 # Pi and e are defined.
->>> x = np.linspace(0.0, 10.0, 1000)
+>>> x = linspace(0.0, 10.0, 1000)
->>> x *= 2*np.pi/10 # inplace.
+>>> x *= 2*pi/10 # inplace.
 # apply functions to array.
->>> y = np.sin(x)
+>>> y = sin(x)
->>> z = np.exp(y)
+>>> z = exp(y)
 \end{lstlisting}
 \inctime{5}
 \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 x.itemsize
+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)
+>>> a.shape=4,2
+# Accessing and setting values
+>>> a[1][3]
+>>> a[1,3]
+>>> a[1,3] = -1
+>>> a[1] # The second row
+\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}
+\item \typ{sum(x, axis=0)},
+\typ{product(x, axis=0)},
+\typ{dot(a, bp)}
+\end{itemize}
+\begin{lstlisting}
+>>> x = array([[0,2,4,2],[1,2,3,4]])
+>>> sum(x)
+>>> sum(x,axis=1)
+\end{lstlisting}
+\end{frame}
+\begin{frame}[fragile]
+\frametitle{Array math cont.}
+\begin{itemize}
+\item Logical operations: \typ{==}, \typ{!=},
+\typ{<}, \typ{>} etc.
+\item Trig and other functions: \typ{sin(x),}
+\typ{arcsin(x), sinh(x),}
+\typ{exp(x), sqrt(x)} etc.
+\end{itemize}
+\begin{lstlisting}
+>>> a<4, a!=3
+>>> sqrt(a)
+\end{lstlisting}
+\inctime{10}
+\end{frame}
 \begin{frame}
-\frametitle{Basic concepts}
+\frametitle{Summary of 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:} 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 = np.array([1., 2, 3, 4])
->>> np.size(x)
-4
->>> x.dtype # What is a.dtype?
-dtype('float64')
->>> x.shape
-(4,)
->>> print np.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 = np.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{np.add(a, b, a)} etc.
-\item \typ{np.sum(x, axis=0)},
-\typ{np.product(x, axis=0)},
-\typ{np.dot(a, bp)}
-\end{itemize}
-\begin{lstlisting}
->>> b=np.array([[0,2,4,2],[1,2,3,4]])
->>> np.add(a,b,a)
->>> np.sum(x,axis=1)
-\end{lstlisting}
-\end{frame}
-\begin{frame}[fragile]
-\frametitle{Array math cont.}
-\begin{itemize}
-\item Logical operations: \typ{==}, \typ{!=},
-\typ{<}, \typ{>} etc.
-\item Trig and other functions: \typ{np.sin(x),}
-\typ{np.arcsin(x), np.sinh(x),}
-\typ{np.exp(x), np.sqrt(x)} etc.
-\end{itemize}
-\begin{lstlisting}
->>> a<4, a!=3
->>> np.sqrt(a)
-\end{lstlisting}
-\inctime{10}
-\end{frame}
 \subsection{Array Creation \& Slicing, Striding Arrays}
 \begin{frame}[fragile]
 \frametitle{Array creation functions}
 \begin{itemize}
-\item \typ{np.array(object,dtype=None,...)}
+\item \typ{array?} \alert{\#Doc string reading}
+\item \typ{array(object,dtype=None,...)}
 \begin{lstlisting}
->>> np.array([2,3,4])
+>>> array([2,3,4])
 array([2, 3, 4])
 \end{lstlisting}
-\item \typ{np.linspace(start,stop,num)}
+\item \typ{linspace(start,stop,num)}
 \begin{lstlisting}
->>> np.linspace(0, 2, 4)
+>>> linspace(0, 2, 4)
 array([0.,0.6666667,1.3333333,2.])
 \end{lstlisting}
-\item Also try \typ{np.arange}
+\item \typ{arange?}
+\alert{\# float version of range}
 \end{itemize}
 \end{frame}
 \begin{frame}[fragile]
 \frametitle{Array creation functions cont.}
 \begin{itemize}
-\item \typ{np.ones(shape, dtype=None, ...)}
+\item \typ{ones(shape, dtype=None, ...)}
 \begin{lstlisting}
->>>np.ones((2,2))
+>>> ones((2,2))
 array([[ 1.,  1.],
 [ 1.,  1.]])
 \end{lstlisting}
-\item \typ{np.identity(n)}
+\item \typ{identity(n)}
-\item \typ{np.ones\_like(x)}
+\item \typ{ones\_like(x)}
 \begin{lstlisting}
->>>a = np.array([[1,2,3],[4,5,6]])
+>>> a = array([[1,2,3],[4,5,6]])
->>>np.ones_like(a)
+>>> ones_like(a)
 array([[1, 1, 1],
 [1, 1, 1]])
 \end{lstlisting}
 \item Also try \typ{zeros, zeros\_like, empty}
 \end{itemize}
 \end{frame}
 \begin{frame}[fragile]
 \frametitle{Slicing arrays}
 \begin{lstlisting}
->>> a = np.array([[1,2,3], [4,5,6],
+>>> 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}
 \end{frame}
 \begin{frame}[fragile]
 \frametitle{Random Numbers}
 \begin{lstlisting}
->>> np.random.rand(3,2)
+>>> random.random()
+0.94134734326214331
+>>> random.random(2)
+array([ 0.73955352,  0.49463645])
+>>> random.random(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}
+\frametitle{Problem}
+Finite difference
+\begin{equation*}
+\frac{sin(x+h)-sin(x)}{h}
+\end{equation*}
+\begin{lstlisting}
+>>> x = linspace(0,2*pi,100)
+>>> y = sin(x)
+>>> deltax = x[1]-x[0]
+\end{lstlisting}
+\pause
+\begin{enumerate}
+\item Given this, get the finite difference of sin in the range 0 to 2*pi
+\end{enumerate}
+\end{frame}
+\begin{frame}[fragile]
+\frametitle{Advanced Problem}
 \begin{lstlisting}
 >>> from scipy import misc
->>> A=misc.imread(name)
+>>> A=misc.imread('filename')
 >>> 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\%
 \section{2D Plotting}
 \subsection{Getting Started}
 \begin{frame}
 {IPython's \typ{pylab} mode}
-\begin{block}{Immediate use:}
+\begin{block}{Immediate use -}
 \typ{\$ ipython -pylab}
 \end{block}
 \begin{itemize}
 \item \typ{pylab}: convenient 2D plotting interface to MPL
 \item Imports all of pylab for you!
 >>> ylabel(r'sin($\chi$)', color='r')
 >>> title('Simple figure', fontsize=20)
 >>> savefig('/tmp/test.png')
 \end{lstlisting}
 \begin{itemize}
-\item Also: PDF, PS, EPS, SVG, PDF
+\item Also: PS, EPS, SVG, PDF
 \end{itemize}
 \inctime{5}
 \end{frame}
 \subsection{Plots - Lines, Labels and Legends}
 >>> 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}
->>> x = linspace(0, 2*np.pi, 1000)
+>>> x = linspace(0, 2*pi, 1000)
 >>> plot(x, cos(5*x), 'r--',
 label='cosine')
 >>> plot(x, sin(5*x), 'g--',
 label='sine')
 >>> legend()
 \inctime{5}
 \end{frame}
 \begin{frame}
 \frametitle{Problem Set}
-\begin{enumerate}
+\begin{itemize}
-\item Write a function that plots any regular n-gon given \typ{n}.
+\item[1] Write a function that plots any regular n-gon given \typ{n}.
-\item Consider the logistic map, $f(x) = kx(1-x)$, plot it for
+\item[2] Consider the logistic map, $f(x) = kx(1-x)$, plot it for
 $k=2.5, 3.5$ and $4$ in the same plot.
-\end{enumerate}
+\end{itemize}
 \end{frame}
 \begin{frame}[fragile]
 \frametitle{Problem Set}
 \begin{columns}
 \column{0.6\textwidth}
 \small{
-\begin{enumerate}
+\begin{itemize}
-\item Consider the iteration $x_{n+1} = f(x_n)$ where $f(x) = kx(1-x)$.  Plot the successive iterates of this process.
+\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.
-\item Plot this using a cobweb plot as follows:
+\end{itemize}}
-\begin{enumerate}
-\item Start at $(x_0, 0)$
-\item Draw line to $(x_i, f(x_i))$;
-\item Set $x_i = f(x_i)$
-\item Draw line to $(x_i, x_i)$
-\item Repeat from 2 for as long as you want
-\end{enumerate}
-\end{enumerate}}
 \column{0.35\textwidth}
 \hspace*{-0.5in}
 \includegraphics[height=1.6in, interpolate=true]{data/cobweb}
 \end{columns}
+\end{frame}
+\begin{frame}
+Plot the cobweb plot as follows:
+\begin{enumerate}
+\item Start at $(x_0, 0)$ ($\implies$ i=0)
+\item Draw a line to $(x_i, f(x_i))$
+\item Set $x_{i+1} = f(x_i)$
+\item Draw a line to $(x_{i+1}, x_{i+1})$
+\item $(i\implies i+1)$
+\item Repeat from 2 for as long as you want
+\end{enumerate}
 \inctime{20}
 \end{frame}
 \begin{frame}{Summary}
 \begin{itemize}
 \item Basics of Numpy.
 \item Array operations.
 \item Plotting in 2D.

changeset 97	555237dbce44
parent 96	a749db24e73b