Changed date format in day1/session{3,4,5}.tex.
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%Tutorial slides on Python.
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% Author: FOSSEE
% Copyright (c) 2009, FOSSEE, IIT Bombay
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% Taken from Fernando's slides.
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% Title page
\title[Arrays]{Python for Science and Engg: \\Arrays}
\author[FOSSEE] {FOSSEE}
\institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
\date[] {SciPy.in 2010, Tutorials}
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%% 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}
}
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{
\begin{frame}<beamer>
\frametitle{Outline}
\tableofcontents[currentsection,currentsubsection]
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% DOCUMENT STARTS
\begin{document}
\begin{frame}
\titlepage
\end{frame}
\begin{frame}
\frametitle{Outline}
\tableofcontents
% \pausesections
\end{frame}
\section{Motivation}
\begin{frame}[fragile]
\frametitle{Why arrays?}
\begin{itemize}
\item Speed!
\item Convenience
\item Easier to handle multi-dimensional data
\end{itemize}
\end{frame}
\begin{frame}[fragile]
\frametitle{Speed}
\begin{lstlisting}
In []: a = linspace(0, 100*pi, 1000000)
# array with a million elements
In []: b = []
In []: for each in a:
...: b.append(sin(each))
...:
...:
In []: sin(a)
\end{lstlisting}
\end{frame}
\begin{frame}[fragile]
\frametitle{Convenience}
The pendulum problem could've been solved as below::
\begin{lstlisting}
In []: L, T = loadtxt('pendulum.txt',
unpack=True)
In []: tsq = T*T
In []: plot (L, tsq, '.')
\end{lstlisting}
\end{frame}
\section{Initializing}
\begin{frame}[fragile]
\frametitle{Initializing}
\begin{lstlisting}
In []: c = array([[11,12,13],
[21,22,23],
[31,32,33]])
In []: c
Out[]:
array([[11, 12, 13],
[21, 22, 23],
[31, 32, 33]])
\end{lstlisting}
\end{frame}
\begin{frame}[fragile]
\frametitle{Some special arrays}
\begin{small}
\begin{lstlisting}
In []: ones((3,5))
Out[]:
array([[ 1., 1., 1., 1., 1.],
[ 1., 1., 1., 1., 1.],
[ 1., 1., 1., 1., 1.]])
In []: ones_like([1, 2, 3, 4])
Out[]: array([1, 1, 1, 1])
In []: identity(2)
Out[]:
array([[ 1., 0.],
[ 0., 1.]])
\end{lstlisting}
Also available \alert{\typ{zeros, zeros_like, empty, empty_like}}
\end{small}
\end{frame}
\begin{frame}[fragile]
\frametitle{Accessing elements}
\begin{small}
\begin{lstlisting}
In []: c
Out[]:
array([[11, 12, 13],
[21, 22, 23],
[31, 32, 33]])
In []: c[1][2]
Out[]: 23
In []: c[1,2]
Out[]: 23
In []: c[1]
Out[]: array([21, 22, 23])
\end{lstlisting}
\end{small}
Similar to \kwrd{lists} but improved!
\end{frame}
\begin{frame}[fragile]
\frametitle{Changing elements}
\begin{small}
\begin{lstlisting}
In []: c[1,1] = -22
In []: c
Out[]:
array([[ 11, 12, 13],
[ 21, -22, 23],
[ 31, 32, 33]])
In []: c[1] = 0
In []: c
Out[]:
array([[11, 12, 13],
[ 0, 0, 0],
[31, 32, 33]])
\end{lstlisting}
\end{small}
How do you access one \alert{column}? -- Enter Slicing!
\end{frame}
\section{Slicing \& Striding}
\begin{frame}[fragile]
\frametitle{Slicing: Lists}
\begin{block}{Define a list}
\kwrd{In []: p = [ 2, 3, 5, 7, 11, 13]}
\end{block}
\begin{lstlisting}
In []: p[1:3]
Out[]: [3, 5]
\end{lstlisting}
\emphbar{A slice}
\begin{lstlisting}
In []: p[0:-1]
Out[]: [2, 3, 5, 7, 11]
In []: p[:]
Out[]: [2, 3, 5, 7, 11, 13]
\end{lstlisting}
\end{frame}
\begin{frame}[fragile]
\frametitle{Striding: Lists}
\emphbar{Striding over \typ{p}}
\begin{lstlisting}
In []: p[::2]
Out[]: [2, 5, 11]
In []: p[1::2]
Out[]: [3, 7, 13]
In []: p[1:-1:2]
Out[]: [3, 7]
In []: p[::3]
Out[]: [2, 7]
\end{lstlisting}
\alert{\typ{list[initial:final:step]}}
\end{frame}
\begin{frame}[fragile]
\frametitle{Slicing \& Striding: Lists}
What is the output of the following?
\begin{lstlisting}
In []: p[1::4]
In []: p[1:-1:3]
\end{lstlisting}
\end{frame}
\begin{frame}[fragile]
\frametitle{Slicing: \typ{arrays}}
\begin{small}
\begin{lstlisting}
In []: c[:,1]
Out[]: array([12, 0, 32])
In []: c[1,:]
Out[]: array([0, 0, 0])
In []: c[0:2,:]
Out[]:
array([[11, 12, 13],
[ 0, 0, 0]])
In []: c[1:3,:]
Out[]:
array([[ 0, 0, 0],
[31, 32, 33]])
\end{lstlisting}
\end{small}
\end{frame}
\begin{frame}[fragile]
\frametitle{Slicing: \typ{arrays} \ldots}
\begin{small}
\begin{lstlisting}
In []: c[:2,:]
Out[]:
array([[11, 12, 13],
[ 0, 0, 0]])
In []: c[1:,:]
Out[]:
array([[ 0, 0, 0],
[31, 32, 33]])
In []: c[1:,:2]
Out[]:
array([[ 0, 0],
[31, 32]])
\end{lstlisting}
\end{small}
\end{frame}
\begin{frame}[fragile]
\frametitle{Striding: \typ{arrays}}
\begin{small}
\begin{lstlisting}
In []: c[::2,:]
Out[]:
array([[11, 12, 13],
[31, 32, 33]])
In []: c[:,::2]
Out[]:
array([[11, 13],
[ 0, 0],
[31, 33]])
In []: c[::2,::2]
Out[]:
array([[11, 13],
[31, 33]])
\end{lstlisting}
\end{small}
\end{frame}
\begin{frame}[fragile]
\frametitle{Shape of an \typ{array}}
\begin{lstlisting}
In []: c
Out[]:
array([[11, 12, 13],
[ 0, 0, 0],
[31, 32, 33]])
In []: c.shape
Out[]: (3, 3)
\end{lstlisting}
\emphbar{Shape specifies shape or dimensions of an array}
\end{frame}
\begin{frame}[fragile]
\frametitle{Elementary image processing}
\begin{small}
\begin{lstlisting}
In []: a = imread('lena.png')
In []: imshow(a)
Out[]: <matplotlib.image.AxesImage object at 0xa0384cc>
\end{lstlisting}
\end{small}
\typ{imread} returns an array of shape (512, 512, 4) which represents an image of 512x512 pixels and 4 shades.\\
\typ{imshow} renders the array as an image.
\end{frame}
\begin{frame}[fragile]
\frametitle{Slicing \& Striding Exercises}
\begin{itemize}
\item Crop the image to get the top-left quarter
\item Crop the image to get only the face
\item Resize image to half by dropping alternate pixels
\end{itemize}
\end{frame}
\begin{frame}[fragile]
\frametitle{Solutions}
\begin{small}
\begin{lstlisting}
In []: imshow(a[:256,:256])
Out[]: <matplotlib.image.AxesImage object at 0xb6f658c>
In []: imshow(a[200:400,200:400])
Out[]: <matplotlib.image.AxesImage object at 0xb757c2c>
In []: imshow(a[::2,::2])
Out[]: <matplotlib.image.AxesImage object at 0xb765c8c>
\end{lstlisting}
\end{small}
\end{frame}
\section{Operations on \typ{arrays}}
\begin{frame}[fragile]
\frametitle{Operations: Addition}
Operations on arrays, as already mentioned, are \alert{element-wise}
\begin{lstlisting}
In []: a = array([[-3,2.5],
[2.5,2]])
In []: b = array([[3,2],
[2,-2]])
In []: a + b
Out[]:
array([[ 0. , 4.5],
[ 4.5, 0. ]])
\end{lstlisting}
\end{frame}
\begin{frame}[fragile]
\frametitle{Elementwise Multiplication}
\begin{lstlisting}
In []: a*b
Out[]:
array([[-9., 5.],
[ 5., -4.]])
\end{lstlisting}
\end{frame}
\begin{frame}[fragile]
\frametitle{Matrix Operations using \typ{arrays}}
We can perform various matrix operations on \kwrd{arrays}\\
A few are listed below.
\vspace{-0.2in}
\begin{center}
\begin{tabular}{lll}
Operation & How? & Example \\
\hline
Transpose & \typ{.T} & \typ{A.T} \\
Product & \typ{dot} & \typ{dot(A, B)} \\
Inverse & \typ{inv} & \typ{inv(A)} \\
Determinant & \typ{det} & \typ{det(A)} \\
Sum of all elements & \typ{sum} & \typ{sum(A)} \\
Eigenvalues & \typ{eigvals} & \typ{eigvals(A)} \\
Eigenvalues \& Eigenvectors & \typ{eig} & \typ{eig(A)} \\
Norms & \typ{norm} & \typ{norm(A)} \\
SVD & \typ{svd} & \typ{svd(A)} \\
\end{tabular}
\end{center}
\end{frame}
\section{Summary}
\begin{frame}
\frametitle{What did we learn?}
\begin{itemize}
\item Arrays
\begin{itemize}
\item Initializing
\item Accessing elements
\item Slicing \& Striding
\item Element-wise Operations
\item Matrix Operations
\end{itemize}
\end{itemize}
\end{frame}
\end{document}
%% Questions for Quiz %%
%% ------------------ %%
\begin{frame}[fragile]
\frametitle{\incqno }
\begin{lstlisting}
In []: a = array([[1, 2],
[3, 4]])
In []: a[1,0] = 0
\end{lstlisting}
What is the resulting array?
\end{frame}
\begin{frame}[fragile]
\frametitle{\incqno }
\begin{lstlisting}
In []: x = array(([1,2,3,4],
[2,3,4,5]))
In []: x[-2][-3] = 4
In []: print x
\end{lstlisting}
What will be printed?
\end{frame}
%% \begin{frame}[fragile]
%% \frametitle{\incqno }
%% \begin{lstlisting}
%% In []: x = array([[1,2,3,4],
%% [3,4,2,5]])
%% \end{lstlisting}
%% What is the \lstinline+shape+ of this array?
%% \end{frame}
\begin{frame}[fragile]
\frametitle{\incqno }
\begin{lstlisting}
In []: x = array([[1,2,3,4]])
\end{lstlisting}
How to change \lstinline+x+ to \lstinline+array([[1,2,0,4]])+?
\end{frame}
\begin{frame}[fragile]
\frametitle{\incqno }
\begin{lstlisting}
In []: x = array([[1,2,3,4],
[3,4,2,5]])
\end{lstlisting}
How do you get the following slice of \lstinline+x+?
\begin{lstlisting}
array([[2,3],
[4,2]])
\end{lstlisting}
\end{frame}
\begin{frame}[fragile]
\frametitle{\incqno }
\begin{lstlisting}
In []: x = array([[9,18,27],
[30,60,90],
[14,7,1]])
\end{lstlisting}
What is the output of \lstinline+x[::3,::3]+
\end{frame}
\begin{frame}[fragile]
\frametitle{\incqno }
\begin{lstlisting}
In []: a = array([[1, 2],
[3, 4]])
\end{lstlisting}
How do you get the transpose of this array?
\end{frame}
\begin{frame}[fragile]
\frametitle{\incqno }
\begin{lstlisting}
In []: a = array([[1, 2],
[3, 4]])
In []: b = array([[1, 1],
[2, 2]])
In []: a*b
\end{lstlisting}
What does this produce?
\end{frame}
\begin{frame}
\frametitle{\incqno }
What command do you use to find the inverse of a matrix and its
eigenvalues?
\end{frame}
%% \begin{frame}
%% \frametitle{\incqno }
%% The file \lstinline+datafile.txt+ contains 3 columns of data. What
%% command will you use to read the entire data file into an array?
%% \end{frame}
%% \begin{frame}
%% \frametitle{\incqno }
%% If the contents of the file \lstinline+datafile.txt+ is read into an
%% $N\times3$ array called \lstinline+data+, how would you obtain the third
%% column of this data?
%% \end{frame}