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%Tutorial slides on Python.

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% Author: FOSSEE 

% Copyright (c) 2009, FOSSEE, IIT Bombay

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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}

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    \frametitle{Outline}

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    \frametitle{Outline}

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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}