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+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%Tutorial slides on Python.
+%
+% Author: FOSSEE
+% Copyright (c) 2009, FOSSEE, IIT Bombay
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\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{infolines}
+ \setbeamercovered{transparent}
+}
+
+\usepackage[english]{babel}
+\usepackage[latin1]{inputenc}
+%\usepackage{times}
+\usepackage[T1]{fontenc}
+\usepackage{amsmath}
+
+% 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]{\lstinline{#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[Arrays]{Python for Science and Engg: Arrays}
+
+\author[FOSSEE] {FOSSEE}
+
+\institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
+\date[] {SciPy 2010, Tutorials}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%\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}
+ \titlepage
+\end{frame}
+
+\begin{frame}
+ \frametitle{Outline}
+ \tableofcontents
+% \pausesections
+\end{frame}
+
+\section{Matrices}
+
+\begin{frame}
+\frametitle{Matrices: Introduction}
+\alert{All matrix operations are done using \kwrd{arrays}}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Matrices: 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{Initializing some special matrices}
+\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}
+\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}?
+\end{frame}
+
+\begin{frame}[fragile]
+ \frametitle{Slicing}
+\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 \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}
+ \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 a matrix}
+ \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 a matrix}
+\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}
+
+\begin{frame}[fragile]
+\frametitle{Transpose of a Matrix}
+\begin{lstlisting}
+In []: a = array([[ 1, 1, 2, -1],
+ ...: [ 2, 5, -1, -9],
+ ...: [ 2, 1, -1, 3],
+ ...: [ 1, -3, 2, 7]])
+
+In []: a.T
+Out[]:
+array([[ 1, 2, 2, 1],
+ [ 1, 5, 1, -3],
+ [ 2, -1, -1, 2],
+ [-1, -9, 3, 7]])
+\end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+ \frametitle{Matrix Addition}
+ \begin{lstlisting}
+In []: b = array([[3,2,-1,5],
+ [2,-2,4,9],
+ [-1,0.5,-1,-7],
+ [9,-5,7,3]])
+In []: a + b
+Out[]:
+array([[ 4. , 3. , 1. , 4. ],
+ [ 4. , 3. , 3. , 0. ],
+ [ 1. , 1.5, -2. , -4. ],
+ [ 10. , -8. , 9. , 10. ]])
+ \end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Elementwise Multiplication}
+\begin{lstlisting}
+In []: a*b
+Out[]:
+array([[ 3. , 2. , -2. , -5. ],
+ [ 4. , -10. , -4. , -81. ],
+ [ -2. , 0.5, 1. , -21. ],
+ [ 9. , 15. , 14. , 21. ]])
+
+\end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Matrix Multiplication}
+\begin{lstlisting}
+In []: dot(a, b)
+Out[]:
+array([[ -6. , 6. , -6. , -3. ],
+ [-64. , 38.5, -44. , 35. ],
+ [ 36. , -13.5, 24. , 35. ],
+ [ 58. , -26. , 34. , -15. ]])
+\end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Inverse of a Matrix}
+\begin{lstlisting}
+
+\end{lstlisting}
+\begin{small}
+\begin{lstlisting}
+In []: inv(a)
+Out[]:
+array([[-0.5 , 0.55, -0.15, 0.7 ],
+ [ 0.75, -0.5 , 0.5 , -0.75],
+ [ 0.5 , -0.15, -0.05, -0.1 ],
+ [ 0.25, -0.25, 0.25, -0.25]])
+\end{lstlisting}
+\end{small}
+\emphbar{Try this: \typ{I = dot(a, inv(a))}}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Determinant and sum of all elements}
+\begin{lstlisting}
+In []: det(a)
+Out[]: 80.0
+\end{lstlisting}
+ \begin{lstlisting}
+In []: sum(a)
+Out[]: 12
+ \end{lstlisting}
+
+\end{frame}
+
+%%use S=array(X,Y)
+\begin{frame}[fragile]
+\frametitle{Eigenvalues and Eigen Vectors}
+\begin{small}
+\begin{lstlisting}
+In []: e = array([[3,2,4],[2,0,2],[4,2,3]])
+
+In []: eig(e)
+Out[]:
+(array([-1., 8., -1.]),
+ array([[-0.74535599, 0.66666667, -0.1931126 ],
+ [ 0.2981424 , 0.33333333, -0.78664085],
+ [ 0.59628479, 0.66666667, 0.58643303]]))
+
+In []: eigvals(e)
+Out[]: array([-1., 8., -1.])
+\end{lstlisting}
+\end{small}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Computing Norms}
+\begin{lstlisting}
+In []: norm(e)
+Out[]: 8.1240384046359608
+\end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+ \frametitle{Singular Value Decomposition}
+ \begin{small}
+ \begin{lstlisting}
+In []: svd(e)
+Out[]:
+(array(
+[[ -6.66666667e-01, -1.23702565e-16, 7.45355992e-01],
+ [ -3.33333333e-01, -8.94427191e-01, -2.98142397e-01],
+ [ -6.66666667e-01, 4.47213595e-01, -5.96284794e-01]]),
+ array([ 8., 1., 1.]),
+ array([[-0.66666667, -0.33333333, -0.66666667],
+ [-0. , 0.89442719, -0.4472136 ],
+ [-0.74535599, 0.2981424 , 0.59628479]]))
+ \end{lstlisting}
+ \end{small}
+\end{frame}
+
+\section{Summary}
+\begin{frame}
+ \frametitle{What did we learn?}
+ \begin{itemize}
+ \item Matrices
+ \begin{itemize}
+ \item Initializing
+ \item Accessing elements
+ \item Slicing and Striding
+ \item Transpose
+ \item Addition
+ \item Multiplication
+ \item Inverse of a matrix
+ \item Determinant
+ \item Eigenvalues and Eigen vector
+ \item Singular Value Decomposition
+ \end{itemize}
+ \item Least Square Curve fitting
+ \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}
+