
diff -r 7c5431fa2d46 -r ca37cf69cd18 day1/session3.tex
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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}
+




