diff options
Diffstat (limited to 'matrices/slides.tex')
| -rw-r--r-- | matrices/slides.tex | 280 |
1 files changed, 109 insertions, 171 deletions
diff --git a/matrices/slides.tex b/matrices/slides.tex index e0e8acd..47ab0ad 100644 --- a/matrices/slides.tex +++ b/matrices/slides.tex @@ -1,4 +1,4 @@ -% Created 2010-11-07 Sun 16:18 +% Created 2011-06-06 Mon 13:56 \documentclass[presentation]{beamer} \usepackage[latin1]{inputenc} \usepackage[T1]{fontenc} @@ -8,7 +8,6 @@ \usepackage{float} \usepackage{wrapfig} \usepackage{soul} -\usepackage{t1enc} \usepackage{textcomp} \usepackage{marvosym} \usepackage{wasysym} @@ -24,14 +23,14 @@ commentstyle=\color{red}\itshape, stringstyle=\color{darkgreen}, showstringspaces=false, keywordstyle=\color{blue}\bfseries} \providecommand{\alert}[1]{\textbf{#1}} -\title{Matrices} +\title{} \author{FOSSEE} \date{} \usetheme{Warsaw}\usecolortheme{default}\useoutertheme{infolines}\setbeamercovered{transparent} \begin{document} -\maketitle + @@ -42,41 +41,71 @@ showstringspaces=false, keywordstyle=\color{blue}\bfseries} \begin{frame} -\frametitle{Outline} -\label{sec-1} -\begin{itemize} -\item Creating Matrices +\begin{center} +\vspace{12pt} +\textcolor{blue}{\huge Matrices} +\end{center} +\vspace{18pt} +\begin{center} +\vspace{10pt} +\includegraphics[scale=0.95]{../images/fossee-logo.png}\\ +\vspace{5pt} +\scriptsize Developed by FOSSEE Team, IIT-Bombay. \\ +\scriptsize Funded by National Mission on Education through ICT\\ +\scriptsize MHRD,Govt. of India\\ +\includegraphics[scale=0.30]{../images/iitb-logo.png}\\ +\end{center} +\end{frame} +\begin{frame} +\frametitle{Objectives} +\label{sec-2} + + At the end of this tutorial, you will be able to, + +\begin{itemize} +\item Create matrices using data. +\item Create matrices from lists. +\item Do basic matrix operations like addition,multiplication. +\item Perform operations to find out the -- \begin{itemize} -\item using direct data -\item converting a list +\item inverse of a matrix +\item determinant of a matrix +\item eigen values and eigen vectors of a matrix +\item norm of a matrix +\item singular value decomposition of a matrix. \end{itemize} +\end{itemize} +\end{frame} +\begin{frame} +\frametitle{Pre-requisite} +\label{sec-3} -\item Matrix operations -\item Inverse of matrix -\item Determinant of matrix -\item Eigen values and Eigen vectors of matrices -\item Norm of matrix -\item Singular Value Decomposition of matrices + Spoken tutorial on - + +\begin{itemize} +\item Getting started with Lists. +\item Getting started with Arrays. +\item Accessing parts of Arrays. \end{itemize} \end{frame} \begin{frame}[fragile] \frametitle{Creating a matrix} -\label{sec-2} +\label{sec-4} + \begin{itemize} \item Creating a matrix using direct data \end{itemize} - \begin{verbatim} In []: m1 = array([1, 2, 3, 4]) \end{verbatim} + \begin{itemize} \item Creating a matrix using lists \end{itemize} - \begin{verbatim} In []: l1 = [[1,2,3,4],[5,6,7,8]] In []: m2 = array(l1) @@ -84,126 +113,59 @@ showstringspaces=false, keywordstyle=\color{blue}\bfseries} \end{frame} \begin{frame}[fragile] \frametitle{Exercise 1} -\label{sec-3} +\label{sec-5} - Create a (2, 4) matrix \texttt{m3} + Create a (2, 4) matrix \verb~m3~ \begin{verbatim} m3 = [[5, 6, 7, 8], - [9, 10, 11, 12]] -\end{verbatim} -\end{frame} -\begin{frame}[fragile] -\frametitle{Solution 1} -\label{sec-4} - -\begin{itemize} -\item m3 can be created as, -\end{itemize} - -\begin{verbatim} - In []: m3 = array([[5,6,7,8],[9,10,11,12]]) + [9, 10, 11, 12 \end{verbatim} \end{frame} \begin{frame}[fragile] \frametitle{Matrix operations} -\label{sec-5} +\label{sec-6} + \begin{itemize} -\item Element-wise addition (both matrix should be of order \texttt{mXn}) +\item Element-wise addition (both matrix should be of order \verb~mXn~) \begin{verbatim} In []: m3 + m2 \end{verbatim} -\item Element-wise subtraction (both matrix should be of order \texttt{mXn}) +\item Element-wise subtraction (both matrix should be of order \verb~mXn~) \begin{verbatim} In []: m3 - m2 \end{verbatim} \end{itemize} \end{frame} -\begin{frame}[fragile] -\frametitle{Matrix Multiplication} -\label{sec-6} - -\begin{itemize} -\item Element-wise multiplication using \texttt{m3 * m2} -\begin{verbatim} - In []: m3 * m2 -\end{verbatim} - -\item Matrix Multiplication using \texttt{dot(m3, m2)} -\begin{verbatim} - In []: dot(m3, m2) - Out []: ValueError: objects are not aligned -\end{verbatim} - -\end{itemize} -\end{frame} -\begin{frame}[fragile] -\frametitle{Matrix Multiplication (cont'd)} +\begin{frame} +\frametitle{Recall from \verb~array~} \label{sec-7} -\begin{itemize} -\item Create two compatible matrices of order \texttt{nXm} and \texttt{mXr} -\begin{verbatim} - In []: m1.shape -\end{verbatim} - - -\begin{itemize} -\item matrix m1 is of order \texttt{1 X 4} -\end{itemize} - -\item Creating another matrix of order \texttt{4 X 2} -\begin{verbatim} - In []: m4 = array([[1,2],[3,4],[5,6],[7,8]]) -\end{verbatim} - -\item Matrix multiplication -\begin{verbatim} - In []: dot(m1, m4) -\end{verbatim} - -\end{itemize} -\end{frame} -\begin{frame} -\frametitle{Recall from \texttt{array}} -\label{sec-8} \begin{itemize} \item The functions - \begin{itemize} -\item \texttt{identity(n)} - - creates an identity matrix of order \texttt{nXn} -\item \texttt{zeros((m,n))} - - creates a matrix of order \texttt{mXn} with 0's -\item \texttt{zeros\_like(A)} - - creates a matrix with 0's similar to the shape of matrix \texttt{A} -\item \texttt{ones((m,n))} - creates a matrix of order \texttt{mXn} with 1's -\item \texttt{ones\_like(A)} - creates a matrix with 1's similar to the shape of matrix \texttt{A} +\item \verb~identity(n)~ - + creates an identity matrix of order \verb~nXn~ +\item \verb~zeros((m,n))~ - + creates a matrix of order \verb~mXn~ with 0's +\item \verb~zeros_like(A)~ - + creates a matrix with 0's similar to the shape of matrix \verb~A~ +\item \verb~ones((m,n))~ + creates a matrix of order \verb~mXn~ with 1's +\item \verb~ones_like(A)~ + creates a matrix with 1's similar to the shape of matrix \verb~A~ \end{itemize} - \end{itemize} - Can also be used with matrices \end{frame} \begin{frame}[fragile] -\frametitle{More matrix operations} -\label{sec-9} - - Transpose of a matrix -\begin{verbatim} - In []: m4.T -\end{verbatim} -\end{frame} -\begin{frame}[fragile] \frametitle{Exercise 2 : Frobenius norm \& inverse} -\label{sec-10} +\label{sec-8} - Find out the Frobenius norm of inverse of a \texttt{4 X 4} matrix. + Find out the Frobenius norm of inverse of a \verb~4 X 4~ matrix. \begin{verbatim} \end{verbatim} @@ -213,38 +175,37 @@ showstringspaces=false, keywordstyle=\color{blue}\bfseries} m5 = arange(1,17).reshape(4,4) \end{verbatim} + \begin{itemize} \item Inverse of A, - \begin{itemize} \item $A^{-1} = inv(A)$ \end{itemize} - \item Frobenius norm is defined as, - \begin{itemize} \item $||A||_F = [\sum_{i,j} abs(a_{i,j})^2]^{1/2}$ \end{itemize} - \end{itemize} \end{frame} \begin{frame}[fragile] \frametitle{Exercise 3 : Infinity norm} -\label{sec-11} +\label{sec-9} - Find the infinity norm of the matrix \texttt{im5} + Find the infinity norm of the matrix \verb~im5~ \begin{verbatim} \end{verbatim} + \begin{itemize} \item Infinity norm is defined as, $max([\sum_{i} abs(a_{i})^2])$ \end{itemize} \end{frame} \begin{frame}[fragile] -\frametitle{\texttt{norm()} method} -\label{sec-12} +\frametitle{\verb~norm()~ method} +\label{sec-10} + \begin{itemize} \item Frobenius norm @@ -260,32 +221,15 @@ showstringspaces=false, keywordstyle=\color{blue}\bfseries} \end{itemize} \end{frame} \begin{frame}[fragile] -\frametitle{Determinant} -\label{sec-13} - - Find out the determinant of the matrix m5 -\begin{verbatim} - -\end{verbatim} - -\begin{itemize} -\item determinant can be found out using - -\begin{itemize} -\item \texttt{det(A)} - returns the determinant of matrix \texttt{A} -\end{itemize} - -\end{itemize} -\end{frame} -\begin{frame}[fragile] \frametitle{eigen values \& eigen vectors} -\label{sec-14} +\label{sec-11} - Find out the eigen values and eigen vectors of the matrix \texttt{m5}. + Find out the eigen values and eigen vectors of the matrix \verb~m5~. \begin{verbatim} \end{verbatim} + \begin{itemize} \item eigen values and vectors can be found out using \begin{verbatim} @@ -294,18 +238,14 @@ showstringspaces=false, keywordstyle=\color{blue}\bfseries} returns a tuple of \emph{eigen values} and \emph{eigen vectors} \item \emph{eigen values} in tuple - \begin{itemize} -\item \texttt{In []: eig(m5)[0]} +\item \verb~In []: eig(m5)[0]~ \end{itemize} - \item \emph{eigen vectors} in tuple - \begin{itemize} -\item \texttt{In []: eig(m5)[1]} +\item \verb~In []: eig(m5)[1]~ \end{itemize} - -\item Computing \emph{eigen values} using \texttt{eigvals()} +\item Computing \emph{eigen values} using \verb~eigvals()~ \begin{verbatim} In []: eigvals(m5) \end{verbatim} @@ -313,59 +253,57 @@ showstringspaces=false, keywordstyle=\color{blue}\bfseries} \end{itemize} \end{frame} \begin{frame}[fragile] -\frametitle{Singular Value Decomposition (\texttt{svd})} -\label{sec-15} +\frametitle{Singular Value Decomposition (\verb~svd~)} +\label{sec-12} $M = U \Sigma V^*$ + \begin{itemize} -\item U, an \texttt{mXm} unitary matrix over K. +\item U, an \verb~mXm~ unitary matrix over K. \item $\Sigma$ - , an \texttt{mXn} diagonal matrix with non-negative real numbers on diagonal. + , an \verb~mXn~ diagonal matrix with non-negative real numbers on diagonal. \item $V^*$ - , an \texttt{nXn} unitary matrix over K, denotes the conjugate transpose of V. -\item SVD of matrix \texttt{m5} can be found out as, + , an \verb~nXn~ unitary matrix over K, denotes the conjugate transpose of V. +\item SVD of matrix \verb~m5~ can be found out as, \end{itemize} - \begin{verbatim} In []: svd(m5) \end{verbatim} \end{frame} \begin{frame} \frametitle{Summary} -\label{sec-16} +\label{sec-13} -\begin{itemize} -\item Matrices + In this tutorial, we have learnt to, -\begin{itemize} -\item creating matrices -\end{itemize} -\item Matrix operations -\item Inverse (\texttt{inv()}) -\item Determinant (\texttt{det()}) -\item Norm (\texttt{norm()}) -\item Eigen values \& vectors (\texttt{eig(), eigvals()}) -\item Singular Value Decomposition (\texttt{svd()}) +\begin{itemize} +\item Create matrices using arrays. +\item Add and multiply the elements of matrix. +\item Find out the inverse of a matrix,using the function ``inv()``. +\item Use the function ``det()`` to find the determinant of a matrix. +\item Calculate the norm of a matrix using the for loop and also using + the function ``norm()``. +\item Find out the eigen vectors and eigen values of a matrix, using + functions ``eig()`` and ``eigvals()``. +\item Calculate singular value decomposition(SVD) of a matrix using the + function ``svd()``. \end{itemize} + \end{frame} \begin{frame} -\frametitle{Thank you!} -\label{sec-17} \begin{block}{} \begin{center} - This spoken tutorial has been produced by the - \textcolor{blue}{FOSSEE} team, which is funded by the + \textcolor{blue}{\Large THANK YOU!} \end{center} + \end{block} +\begin{block}{} \begin{center} - \textcolor{blue}{National Mission on Education through \\ - Information \& Communication Technology \\ - MHRD, Govt. of India}. + For more Information, visit our website\\ + \url{http://fossee.in/} \end{center} \end{block} - - \end{frame} -\end{document} +\end{document}
\ No newline at end of file |