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author | Prabhu Ramachandran | 2016-12-09 18:13:35 +0530 |
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committer | Prabhu Ramachandran | 2016-12-09 18:13:35 +0530 |
commit | c64ef73e7d1f180a82bfde53b1891cbaa633932a (patch) | |
tree | 5c6946dfe4e97e6382110aaca9dc35b5caf4913b /scipy | |
download | python-workshops-c64ef73e7d1f180a82bfde53b1891cbaa633932a.tar.gz python-workshops-c64ef73e7d1f180a82bfde53b1891cbaa633932a.tar.bz2 python-workshops-c64ef73e7d1f180a82bfde53b1891cbaa633932a.zip |
Initial files for scipy india 2016 tutorial.
These are all from older material delivered at various places. The
material is from the PyConAPAC tutorial slides.
Diffstat (limited to 'scipy')
42 files changed, 9826 insertions, 0 deletions
diff --git a/scipy/basic/Makefile b/scipy/basic/Makefile new file mode 100644 index 0000000..ddcab0c --- /dev/null +++ b/scipy/basic/Makefile @@ -0,0 +1,21 @@ +.SUFFIXES: .tex .pdf + +.tex.pdf: + pdflatex $*.tex + pdflatex $*.tex + +SLIDES= session1.pdf \ + session2.pdf \ + session3.pdf \ + session4.pdf + +all: $(SLIDES) quickref.pdf + +cleanall: + rm -f *.dvi *.log *.bak *.aux *.bbl *.blg *.idx *.ps *.eps *.pdf *.toc *.out *~ *.vrb *.nav *.snm + +clean: + rm -f *.log *.bak *.aux *.bbl *.blg *.idx *.toc *.out *~ *.vrb *.nav *.snm + + + diff --git a/scipy/basic/README.txt b/scipy/basic/README.txt new file mode 100644 index 0000000..4cf4303 --- /dev/null +++ b/scipy/basic/README.txt @@ -0,0 +1,64 @@ +Basic Tutorial: + +* Tutorial title: Introductory Scientific Computing with Python + +* Intended audience (difficulty level, experience required): + + Beginning programmers who have experience with some programming + language. A knowledge of elementary programming concepts is essential. + Audience should know how to edit text files comfortably. We strongly + recommend that attendees go through at least 7 chapters of the online + tutorial on Python: http://docs.python.org/tutorial and ideally + complete it. It should take no more than one afternoon. + + Prior experience with Scilab/Matlab/octave or similar tools would be + useful but not necessary. + +* Prerequisites: What experience must attendees have in order to fully + benefit from this tutorial? + + Basic usage of a computer and elementary computer programming along + with experience with some form of numerical computing via + scilab/octave/matlab/mathematica. You should go through the official + Python tutorial (or be comfortable with the Python programming + language). You should definitely have the recommended packages + installed and your computer setup for this tutorial. + +* Promotional summary (max. 100 words). + + At the end of this tutorial, attendees should be able to use the basic + tools and libraries for Python-based scientific computing. We imagine + that an undergraduate/graduate engineering/science student would be + able to *start* doing most of their basic computing tasks using + Python. + +* Detailed tutorial outline + + The session is entirely hands-on. We focus on common tasks and + introduce the Python language in the context of these common tasks. + Here is a rough outline of what we propose to cover: + + - Introduction to IPython. + - Creating basic plots with matplotlib. + - NumPy array basics: 1D arrays. + - Reading data files. + - More on NumPy: multi-dimensional arrays, slicing, elementary image + processing. + - Some powertools: pandas dataframe basics. + - Using SciPy for Linear Algebra, FFT's, root finding and integrating + ODEs. + + +* Attendee Requirements: + + A laptop is definitely recommended since this will be a hands-on + session. You will need to have Python (2.7/3.x would work fine), + IPython (0.10.x), Numpy (1.x), SciPy (>0.5.x), matplotlib (any recent + version), Mayavi-3.x and above. + + On Windows and Mac OS X it is easiest to install these by installing + the Enthought Python Distribution. On GNU/Linux these are typically + available along with the distribution. The packages are all + available on Ubuntu. FOSSEE provides a live Ubuntu-based DVD with + all the necessary packages. It can be downloaded here: + http://fossee.in/download#DVDs diff --git a/scipy/basic/circulate/data.csv b/scipy/basic/circulate/data.csv new file mode 100644 index 0000000..ad9bc88 --- /dev/null +++ b/scipy/basic/circulate/data.csv @@ -0,0 +1,1001 @@ +x,y,temp +0.464692, 0.207857, 352.064934 +0.287122, 0.819894, 339.884474 +0.511280, 0.909909, 342.513659 +0.038794, 0.327338, 377.815108 +0.030478, 0.872233, 311.467743 +0.143192, 0.108978, 373.671751 +0.471574, 0.556972, 383.576433 +0.614923, 0.427789, 350.857724 +0.650243, 0.855297, 357.469773 +0.880238, 0.048500, 314.733263 +0.817662, 0.971383, 376.243349 +0.543586, 0.582363, 385.639913 +0.277319, 0.540493, 365.635426 +0.993291, 0.041490, 349.973442 +0.260272, 0.510142, 326.276592 +0.894163, 0.007942, 364.733654 +0.825232, 0.599491, 349.827958 +0.722885, 0.173658, 346.830978 +0.676946, 0.628864, 333.841118 +0.164791, 0.339059, 399.366832 +0.931913, 0.899820, 386.812020 +0.876083, 0.785217, 391.551388 +0.477106, 0.616531, 313.715544 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+\newcommand{\hr}{\centerline{\rule{3.5in}{1pt}}} +\newcommand{\skipin}{\hspace*{12pt}} +\newcommand{\typ}[1]{\lstinline{#1}} + +\usepackage{color} +\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} + +\begin{document} +\begin{multicols*}{3} +\begin{center} +\textbf{Scientific Computing with Python}\\ +\textbf{Quick Reference}\\ +\textbf{PyCon Asia-Pacific}\\ +\end{center} +\vspace{-2ex} + +%********************************************* + \hr\textbf{Starting up} + +To start \lstinline|ipython| with \lstinline|pylab|:\\ +\lstinline| $ ipython -pylab| %$ + +To exit: \lstinline|^D| (Ctrl-d) + +To break from loops: \lstinline|^C| (Ctrl-c) + +%********************************************* +\hr\textbf{Plotting} + +Creating a linear array:\\ +{\ex \lstinline| x = linspace(0, 2*pi, 50)|} + +Plotting two variables:\\ +{\ex \lstinline| plot(x, sin(x))|} + +Plotting two lists of equal length x, y:\\ +{\ex \lstinline| plot(x, y)|} + +Plots with colors:\\ +{\ex \lstinline| plot(x, sin(x), 'b')|} gives a blue line + +Line style and markers:\\ +{\ex \lstinline| plot(x, sin(x), '--')|} gives a dashed line\\ +{\ex \lstinline|'.'|} -- a point marker, {\ex \lstinline|'o'|} -- a circle marker + +Labels:\\ +{\ex \lstinline| xlabel('x')|} and {\ex \lstinline|ylabel('sin(x)')|} + +Title (\lstinline|pylab| accepts \TeX~in any text expression):\\ +{\ex \lstinline| title(r'$\sigma$ vs. $\sin(\sigma)$')|} + +Legend:\\ +{\ex \lstinline| legend(['sin(x)'], loc=center)|}\\ +{\ex \lstinline| legend(['sin(x)', 'cos(x)'])|}\\ +If \lstinline|loc| is not specified, \lstinline|best| is used + +Annotate:\\ +{\ex \lstinline| annotate('annotation string', xy=(1.5, 1))|} + +Saving figures:\\ +{\ex \lstinline| savefig('sinusoids.png')|} + +Axes lengths:\\ +Get the axes lengths:\\ +{\ex \lstinline| xmin, xmax = xlim()|}\\ +{\ex \lstinline| ymin, ymax = ylim()|}\\ +Set the axes lengths:\\ +{\ex \lstinline| xlim(-2*pi, 2*pi)|}\\ +{\ex \lstinline| ylim(-1.2, 1.2)|} + +Miscellaneous:\\ +{\ex \lstinline| clf()|} to clear the plot area\\ +{\ex \lstinline| close()|} to close the figure + +%********************************************* +\hr\textbf{IPython tips} + +\typ{TAB} completes commands\\ +History: Up, down arrows or (\typ{Ctrl-p}/\typ{Ctrl-n})\\ +Search: \typ{Ctrl-r} and start typing\\ +\typ{Ctrl-a}: go to start of line\\ +\typ{Ctrl-e}: go to end of line\\ +\typ{Ctrl-k}: kill to end of line\\ +Help: \typ{object?}\\ +Source Code: \typ{object??}\\ +Time execution of expression/statement: \typ{\%timeit} + +%********************************************* +\hr\textbf{Saving and Running scripts} + +{\ex \lstinline| %hist|} returns history of commands used. \\ +To save a set of lines, say 14-18, 20, 22, to \lstinline|sample.py| \\ +{\ex \lstinline| %save sample.py 14-18 20 22|}\\ +To run \lstinline|sample.py| \\ +{\ex \lstinline| %run -i sample.py|} + +%********************************************* + \hr\textbf{Reading from files} + +\lstinline|filename.txt| is a file with float data. +Using loadtxt: \\ +{\ex \lstinline|X = loadtxt('filename.txt')|} \\ +X is an array with all the data from \lstinline|filename.txt|\\ +{\ex \lstinline|X,Y = loadtxt('filename.txt', unpack=True)|} \\ +X,Y contain each column of the data\\ +{\ex \lstinline|X = loadtxt('filename.txt', delimiter=';')|} \\ +when ';' delmits the columns of data + +%********************************************* +\hr\textbf{Statistical operations} + +{\ex \lstinline|mean|, \lstinline|median|, \lstinline|std|} + +%********************************************* +\hr\textbf{NumPy Arrays} + +Fixed size: \typ{arr.size}\\ +Homogeneous: \typ{arr.dtype}\\ +Extent along each dimension: \typ{arr.shape}\\ +Bytes per element: \typ{arr.itemsize} + +%********************************************* +\hr\textbf{Array Creation} + +{\ex \lstinline|C = array([[11,12,13], [21,22,23], [31,32,33]])|}\\ +{\ex \lstinline|C.shape|} shape--- rows \& cols\\ +{\ex \lstinline|C.dtype|} data type\\ +{\ex \lstinline|B = ones_like(C)|} array of ones; same shape, dtype as C\\ +\skipin similarly \lstinline|zeros_like, empty_like| \\ +{\ex \lstinline|A = ones((3,2))|} array of ones of shape (3,2)\\ +\skipin similarly \lstinline|zeros, empty|\\ +{\ex \lstinline|I = identity(3)|} identity matrix of size 3x3\\ +{\ex \lstinline|x, y = mgrid[0:3, 0:5]|} mesh-grid of size 3x5\\ +{\ex \lstinline|x, y = ogrid[0:3, 0:5]|} open mesh-grid of size 3x5 + +%********************************************* +\hr\textbf{Accessing \& Changing elements} + +{\ex \lstinline|C[1, 2]|} gets third element of second row\\ +\skipin \textbf{Note:} Indexing starts from 0. \\ +{\ex \lstinline|C[1]|} gets the second row \\ +{\ex \lstinline|C[1,:]|} same as above (`:' implies all columns)\\ +{\ex \lstinline|C[:,1]|} gets the second column (`:' implies all rows)\\ +{\ex \lstinline|C[0:2,:]|} or {\ex \lstinline|C[:2,:]|} gets $1^{st}, 2^{nd}$ rows; all cols\\ +{\ex \lstinline|C[1:3,:]|} or {\ex \lstinline|C[1:,:]|} gets $2^{nd}, 3^{rd}$ +rows; all cols\\ +{\ex \lstinline|C[0:3:2,:]|} or {\ex \lstinline|C[::2,:]|} gets $1^{st}, 3^{rd}$ +rows; all cols + +%********************************************* +\hr\textbf{Matrix Operations} + +For matrices A and B of equal shapes:\\ +{\ex \lstinline|A.T|} transpose\\ +{\ex \lstinline|sum(A)|} sum of all elements\\ +{\ex \lstinline|A+B|} addition\\ +{\ex \lstinline|A*B|} element wise product\\ +{\ex \lstinline|dot(A, B)|} Matrix multiplication\\ +{\ex \lstinline|inv(A)|} inverse, {\ex \lstinline|det(A)|} determinant\\ +{\ex \lstinline|eig(A)|} eigen values and vectors\\ +{\ex \lstinline|norm(A)|} norm\\ +{\ex \lstinline|svd(A)|} singular value decomposition + +%********************************************* +\hr\textbf{Least Square Fit} + +To get the least square fit of $L$ vs. $tsq$:\\ +{\ex \lstinline|A = array([L, ones_like(L)])|}\\ +{\ex \lstinline|A = A.T|} vandermonde matrix\\ +{\ex \lstinline|result = lstsq(A, tsq)|}\\ +{\ex \lstinline|coef = result[0]|} coefficients +{\ex \lstinline|Tline = coef[0]*L + coef[1]|} + +%********************************************* +\hr\textbf{Solving Linear Equations} + +{\ex \lstinline|A = array([[3,2,-1], [2,-2,4], [-1, 0.5, -1]])|}\\ +\skipin coefficient array\\ +{\ex \lstinline|b = array([1, -2, 0])|} constant array\\ +{\ex \lstinline|x = solve(A, b)|} the required solution + +Checking the solution:\\ +{\ex \lstinline|Ax = dot(A,x)|} matrix multiplication of A and x\\ +{\ex \lstinline|allclose(Ax, b)|} check the closeness of Ax, b + +%********************************************* +\hr\textbf{Roots of Polynomials} + +{\ex \lstinline|coeffs = [1, 6, 13]|} coefficients in descending order\\ +{\ex \lstinline|roots(coeffs)|} returns complex roots of the polynomial + +%********************************************* +\hr\textbf{Roots of non-linear equations} + +{\ex \lstinline|from scipy.optimize import fsolve|}\\ +\skipin \lstinline|fsolve| is not in \lstinline|pylab|\\ +\skipin we import from \lstinline|scipy.optimize| \\ +We wish to find the roots of $f(x)=sin(x)+cos(x)^2$ +\vspace{-8pt} +\begin{lstlisting} +def f(x): + return sin(x)+cos(x)**2 +\end{lstlisting} +\vspace{-8pt} +{\ex \lstinline|fsolve(f, 0)|} \\ +\skipin arguments are function name and initial estimate + +%********************************************* +\hr\textbf{ODE} + +To solve the ODE below:\\ +$\frac{dy}{dt} = ky(L-y)$, L = 25000, k = 0.00003, y(0) = 250\\ +\vspace{-8pt} +\begin{lstlisting} +def f(y, t): + k, L = 0.00003, 25000 + return k*y*(L-y) +\end{lstlisting} +\vspace{-8pt} +{\ex \lstinline|t = linspace(0, 12, 60)|} time over which to solve ODE\\ +{\ex \lstinline|y0 = 250|} initial conditions\\ +{\ex \lstinline|from scipy.integrate import odeint|}\\ +{\ex \lstinline|y = odeint(f, y0, t)|} + +\hr\textbf{FFT} + +{\ex \lstinline|t = linspace(0, 2*pi, 500)|}\\ +{\ex \lstinline|y = sin(4*pi*t)|} a sinusoidal signal\\ +{\ex \lstinline|f = fft(y)|}\\ +{\ex \lstinline|freq = fftfreq(500, t[1] - t[0])|}\\ +{\ex \lstinline|plot(freq[:250], abs(f)[:250])|} + +\hr\textbf{Random Numbers} + +{\ex \typ{from numpy import random}}\\ +{\ex \typ{random.random}}: Uniform deviates in $[0, 1)$\\ +{\ex \typ{random.normal}}: Random samples -- Gaussian dist.\\ +{\ex \typ{random.normal}}: Random samples -- Gaussian dist.\\ +{\ex \typ{x = random.random(size=1000)}}\\ +{\ex \typ{x,y = random.normal(size=(2,1000))}} + +\hr\textbf{Record Arrays} + +{\ex \typ{typ = [('id', int), ('x', float)]}}\\ +{\ex \typ{rec = numpy.zeros(10, dtype=typ)}}\\ +{\ex \typ{rec['id'] = range(10)}}\\ +{\ex \typ{rec['x'] = random.random(size=10)}}\\ + +{\ex \typ{data = csv2rec('data.csv')}} from csv to record array + +\hr\textbf{\typ{mlab}} + +{\ex \typ{from enthought.mayavi import mlab}} Ready to Go!\\ +{\ex \typ{mlab.test_<TAB>}} Test Functions\\ +{\ex \typ{mlab.points3d(x, y, z)}} Plot points in 3D\\ +{\ex \typ{mlab.contour3d(x*x*0.5 + y*y + z*z*2)}} 3D contours\\ +{\ex \typ{gcf}} get current figure\\ +{\ex \typ{savefig}} save current figure\\ +{\ex \typ{figure}} switch figure or new figure\\ +{\ex \typ{axes}} create axes\\ +{\ex \typ{outline}} create outline\\ +{\ex \typ{title}} add title\\ +{\ex \typ{xlabel, ylabel, zlabel}} labels\\ +{\ex \typ{colorbar}} Add colorbar\\ +{\ex \typ{scalarbar}} Add colorbar for scalar color mapping\\ +{\ex \typ{vectorbar}} Add colorbar for vector color mapping\\ +{\ex \typ{show}} show figure (standalone scripts) + +\end{multicols*} + +\end{document} diff --git a/scipy/basic/session1.tex b/scipy/basic/session1.tex new file mode 100644 index 0000000..ac21d2a --- /dev/null +++ b/scipy/basic/session1.tex @@ -0,0 +1,904 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%Tutorial slides on Python. +% +% Author: FOSSEE +% Copyright (c) 2009-2016, FOSSEE, IIT Bombay +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\documentclass[14pt,compress]{beamer} + +% 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} + +% 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[Interactive Plotting]{Introductory Scientific Computing with +Python} +\subtitle{Introduction, IPython and Plotting} + +\author[FOSSEE] {FOSSEE} + +\institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay} +\date[] {SciPy India 2016,\\ +Mumbai +} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%\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} + \maketitle +\end{frame} + +%% \begin{frame} +%% \frametitle{Outline} +%% \tableofcontents +%% % You might wish to add the option [pausesections] +%% \end{frame} + +\begin{frame} + \frametitle{Acknowledgement} + \Large + \begin{center} + \alert{FOSSEE group (\url{fossee.in})} \\ + based at\\ + \alert{IIT Bombay}\\ + and funded by\\ + The National Mission on Education through ICT, \\ + \alert{Ministry of HRD, India} + \end{center} +\end{frame} + +\section{Checklist} +\begin{frame} +\frametitle{Checklist} + \begin{enumerate} + \item Editor - we recommend \alert{Canopy} + \item IPython + \item Data files: + \begin{itemize} + \item \typ{pendulum.txt} + \item \typ{data.csv} + \end{itemize} + \item Images + \begin{itemize} + \item \typ{lena.png} + \end{itemize} + \end{enumerate} +\end{frame} + +\begin{frame} + \frametitle{About the Tutorial} + \begin{block}{Intended Audience} + \begin{itemize} + \item Engg., Mathematics and Science researchers with a + reasonable programming background. + \end{itemize} + \end{block} + + \begin{block}{Goal: Successful participants will be able to} + \begin{itemize} + \item Start using Python as plotting, computational tool. + \item Use the basic libraries and tools for scientific computing + with Python. + \end{itemize} + \end{block} +\end{frame} + +%% \begin{frame}[fragile] +%% \frametitle{The Python interpreter \ldots} +%% \begin{block}{} +%% \begin{lstlisting} +%% $ python +%% \end{lstlisting} %$ +%% \end{block} +%% \begin{lstlisting} +%% >>> print "Hello, World!" +%% Hello, World! +%% \end{lstlisting} +%% Exiting +%% \begin{lstlisting} +%% >>> ^D(Ctrl-D) +%% $ +%% \end{lstlisting} %$ +%% \end{frame} + +\section{Starting up IPython} +\begin{frame}[fragile] +\frametitle{Starting up \ldots} +\begin{block}{Enthought Canopy menu} +\begin{itemize} + \item Canopy command prompt (Tools menu) + \item PyLab +\end{itemize} +\end{block} + +\begin{block}{Terminal} +\begin{lstlisting} + $ ipython --pylab +\end{lstlisting} %$ +\end{block} +\end{frame} + +% \section{Starting up IPython} +% \begin{frame}[fragile] +% \frametitle{Starting up \ldots} +% \begin{block}{Terminal Jupyter} +% \begin{lstlisting} +% $ jupyter console + +% In [1]: %pylab +% \end{lstlisting} %$ +% \end{block} +% \end{frame} + + +\begin{frame}[fragile] +\frametitle{Running IPython} +\begin{lstlisting} + In []: print("Hello, World!") + Hello, World! +\end{lstlisting} + +Exiting on the \textbf{terminal} +\begin{lstlisting} + In []: ^D(Ctrl-D) + Do you really want to exit([y]/n)? y +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Pressed Ctrl-D on Canopy? } + \begin{itemize} + \item Pressed \verb+Ctrl-D+ inside Canopy? + \item You suddenly lost the Python prompt? + \item Go to \verb+View->Python+ + \end{itemize} +\end{frame} + + +\section{Breaking out of loops} +\begin{frame}[fragile] +\frametitle{Breaking out of Loops} +Breaking out of loops +\begin{lstlisting} + In []: while True: + ...: print("Hello, World!") + ...: + Hello, World! + Hello, World!^C(Ctrl-C) + ------------------------------------ + KeyboardInterrupt +\end{lstlisting} + \inctime{10} +\end{frame} + +\section{Plotting} +\subsection{Drawing plots} +\begin{frame}[fragile] +\frametitle{First Plot} +\begin{columns} + \column{0.25\textwidth} + \hspace*{-0.25in} + \includegraphics[height=2in, interpolate=true]{data/firstplot} + \column{0.8\textwidth} + \begin{block}{} + \begin{small} +\begin{lstlisting} +In []: x = linspace(0, 2*pi, 50) +In []: plot(x, sin(x)) +\end{lstlisting} + \end{small} + \end{block} +\end{columns} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Walkthrough} +\begin{block}{\typ{x = linspace(start, stop, num)} } +returns \typ{num} evenly spaced points, in the interval [\typ{start}, \typ{stop}]. +\end{block} +\vspace*{.35in} +\begin{block}{} + \small +\begin{lstlisting} +In []: x[0] +Out[]: 0.0 + +In []: x[49] +Out[]: 6.2831853071795862 +\end{lstlisting} +\end{block} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Walkthrough \ldots} +\begin{block}{\typ{plot(x, y)}} +plots \typ{x} and \typ{y} using default line style and color +\end{block} +\inctime{5} +\end{frame} + +\begin{frame} + \frametitle{Important instructions} + \begin{itemize} + \item Please do not close the plot windows or IPython + \item For the first session, please do not experiment + \item Follow along and type everything! + \item Case matters + \item Every character you type matters! + \end{itemize} +\end{frame} + +\subsection{Decoration} +\begin{frame}[fragile] +\frametitle{Adding Labels} +\begin{columns} + \column{0.25\textwidth} + \hspace*{-0.45in} + \includegraphics[height=2in, interpolate=true]{data/label} + \hspace*{0.5in} + \column{0.55\textwidth} + \begin{block}{} + \small + \begin{lstlisting} +In []: xlabel('x') + +In []: ylabel('sin(x)') + \end{lstlisting} + \small +% \end{lstlisting} +%\typ{xlabel(s)} sets the label of the \typ{x}-axis to \typ{s} + +% \begin{lstlisting} + \end{block} +%\typ{ylabel(s)} sets the label of the \typ{y}-axis to \typ{s} +\end{columns} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Another example} + \begin{lstlisting} +In []: clf() + \end{lstlisting} +\emphbar{Clears the plot area.} + \begin{lstlisting} +In []: y = linspace(0, 2*pi, 50) +In []: plot(y, sin(2*y)) +In []: xlabel('y') +In []: ylabel('sin(2y)') + \end{lstlisting} +\end{frame} + +\begin{frame}[fragile] +\frametitle{IPython tips} + +\begin{itemize} +\item Use \typ{TAB} to complete command +\item Try: +\begin{lstlisting} +In []: pl<TAB> +\end{lstlisting} +\end{itemize} +\vspace*{0.5in} + +{\Large \structure{History}} +\begin{itemize} +\item Up arrow and down arrow + +\item Left / right to move and edit + +\item Type some text and press up arrow: +\begin{lstlisting} +In []: pl<Up Arrow> +\end{lstlisting} + +\end{itemize} + +\end{frame} + +\begin{frame}[fragile] + \frametitle{Advanced IPython tips \ldots} + \begin{itemize} +\item Search: \typ{Ctrl-r} and start typing + +\item \typ{Ctrl-a}: go to start of line + +\item \typ{Ctrl-e}: go to end of line + +\item \typ{Ctrl-k}: kill to end of line + \end{itemize} +\end{frame} + + +\subsection{More decoration} +\begin{frame}[fragile] +\frametitle{Title and Legends} +\vspace*{-0.15in} +% \begin{block}{} +% \small +\begin{lstlisting} +In []: title('Sinusoids') +In []: legend(['sin(2y)']) +\end{lstlisting} +% \small +% \end{block} + \vspace*{-0.1in} + \begin{center} + \includegraphics[height=2in, interpolate=true]{data/legend} + \end{center} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Legend Placement} +\begin{block}{} + \small +\begin{lstlisting} +In []: legend(['sin(2y)'], loc='center') +\end{lstlisting} +\end{block} + +\begin{columns} + \column{0.6\textwidth} + \includegraphics[height=2in, interpolate=true]{data/position} +\column{0.45\textwidth} +\vspace{-0.2in} +\begin{lstlisting} +'best' +'right' +'left' +'center' +\end{lstlisting} +\end{columns} +\inctime{15} +\end{frame} + +\begin{frame} + \frametitle{Important instructions} + \begin{itemize} + \item Please do not close the plot windows or IPython + \item For the first session, please do not experiment + \item Follow along and type everything! + \item Case matters + \item Every character you type matters! + \end{itemize} +\end{frame} + +%% \begin{frame}[fragile] +%% \frametitle{For arbitrary location} +%% \vspace*{-0.1in} +%% \begin{lstlisting} +%% In []: legend(['sin(2y)'], loc=(.8,.1)) +%% \end{lstlisting} +%% \emphbar{Specify south-east corner position} +%% %\vspace*{-0.2in} +%% \begin{center} +%% \includegraphics[height=2in, interpolate=true]{data/loc} +%% \end{center} +%% %\inctime{10} +%% \end{frame} + +\begin{frame}[fragile] +\frametitle{Showing it better} +\vspace{-0.15in} +\begin{lstlisting} +In []: plot(y, cos(y), 'r') +# See a red plot! + +In []: clf() +In []: plot(y, sin(y), 'g', linewidth=2) +\end{lstlisting} +\vspace*{-0.2in} +\begin{center} + \includegraphics[height=2.2in, interpolate=true]{data/green} +\end{center} +%\inctime{10} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Annotating} +\vspace*{-0.1in} +\begin{lstlisting} +In[]: annotate('local max', xy=(1.5, 1)) +\end{lstlisting} +\vspace*{-0.2in} +\begin{center} + \includegraphics[height=3in, interpolate=true]{data/annotate} +\end{center} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Saving \& Closing} +\begin{lstlisting} +In []: savefig('sin.png') + +In []: close() +\end{lstlisting} +Some supported formats: +\begin{itemize} +\item png +\item pdf +\item svg +\end{itemize} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Recap} + \begin{itemize} + \item \typ{linspace(start, end, num)} + \item \typ{plot(x, y)} + \item \typ{clf()} + \item \typ{xlabel, ylabel} + \item \typ{title, legend, annotate} + \item \typ{savefig} + \item \typ{close} + \end{itemize} + \inctime{10} +\end{frame} + +\section{Multiple plots} +\begin{frame}[fragile] + \frametitle{Overlaid Plots} +\begin{lstlisting} +In []: y = linspace(0, 2*pi, 50) +\end{lstlisting} + +\begin{lstlisting} +In []: clf() +In []: plot(y, sin(y)) +In []: plot(y, cos(y)) +In []: xlabel('y') +In []: ylabel('f(y)') +In []: legend(['sin(y)', 'cos(y)']) +# Note how we made two legends +\end{lstlisting} + + +\emphbar{By default plots would be overlaid!} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Plotting separate figures} +\begin{lstlisting} +In []: clf() +In []: figure(1) +In []: plot(y, sin(y)) +In []: figure(2) +In []: plot(y, cos(y)) +In []: savefig('cosine.png') +In []: figure(1) +In []: title('sin(y)') +In []: savefig('sine.png') +In []: close() +In []: close() +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Get Axes lengths} +\emphbar{Getting axes lengths} + \begin{lstlisting} +In []: xmin, xmax = xlim() +In []: ymin, ymax = ylim() +In []: print(xmin, xmax) +\end{lstlisting} +\pause +\emphbar{Set the axes limits} + \begin{lstlisting} +In []: xlim(xmin, 2*pi ) +In []: ylim(ymin-0.2, ymax+0.2) + \end{lstlisting} +\end{frame} + +\begin{frame}[plain,fragile] + \frametitle{Axes lengths} + \vspace*{-0.2in} + \begin{center} + \includegraphics[height=3.25in, interpolate=true]{data/limits} + \end{center} +\end{frame} + +\begin{frame}[fragile] +\frametitle{IPython tip: documentation} + +\begin{itemize} + + \item Try: +\begin{lstlisting} +In []: plot? +\end{lstlisting} + \vspace*{0.2in} + to get more information on \typ{plot} + + \item Use arrow keys to scroll docs + \item Note: exit help pager with ``q'' or ``ESC'' +\end{itemize} +\end{frame} + +\begin{frame}[fragile] +\frametitle{IPython tip: source} +\begin{itemize} + \item Try: +\begin{lstlisting} +In []: plot?? +\end{lstlisting} + to see the source code for \typ{plot} + +\end{itemize} +\inctime{10} +\end{frame} + + +\begin{frame}[plain,fragile] +\frametitle{Review Problem} +\begin{enumerate} +\item Plot $x, -x, \sin(x), x \sin(x)$ in range $-5\pi$ to $5\pi$ +\item Add a legend +\item Annotate the origin +\item Set axes limits to the range of x +\end{enumerate} +\vspace*{-0.15in} +\begin{center} + \includegraphics[height=2.6in, interpolate=true]{data/four_plot} +\end{center} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Review Problem \ldots} +\alert{Plotting \ldots} +\begin{lstlisting} +In []: x = linspace(-5*pi, 5*pi, 500) +In []: plot(x, x, 'b') +In []: plot(x, -x, 'b') +In []: plot(x, sin(x), 'g', linewidth=2) +In []: plot(x, x*sin(x), 'r', + linewidth=3) +\end{lstlisting} +$\vdots$ +\end{frame} + +\begin{frame}[fragile] +\frametitle{Review Problem \ldots} +\alert{Legend \& Annotation\ldots} +\begin{lstlisting} +In []: legend(['x', '-x', 'sin(x)', + 'xsin(x)']) +In []: annotate('origin', xy = (0, 0)) +\end{lstlisting} +\alert{Setting Axes limits\ldots} +\begin{lstlisting} +In []: xlim(-5*pi, 5*pi) +In []: ylim(-5*pi, 5*pi) +\end{lstlisting} +\inctime{5} +\end{frame} + +\section{Scripts -- Saving \& Running} +\begin{frame}[fragile] +\frametitle{Command History} +Use the \typ{\%hist} \alert{magic} command of IPython +\typ{In []: \%hist}\\ +This displays the ``Command History'' +\begin{block}{Careful about errors!} + \kwrd{\%hist} will contain the errors as well.\\ +\end{block} +\pause +\begin{block}{Magic Commands?} + Magic commands are commands provided by IPython to make our life easier. +\end{block} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Saving commands into a script} + \begin{itemize} + \item Create a new file on Canopy + \item Copy commands for assignment with your mouse + \item Save the script to \typ{four_plot.py} + \end{itemize} +\inctime{5} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Python Scripts\ldots} +Now, \typ{four_plot.py} is called a Python Script. + \begin{itemize} + \item run the script in IPython using \typ{\%run four_plot.py}\\ + \end{itemize} +\pause +\alert{\typ{NameError: name 'linspace' is not defined}} +\begin{block}{} +To avoid this, run using \alert{\typ{\%run -i four_plot.py}}\\ +\end{block} +\pause +Where is the plot? +\begin{lstlisting} +In []: show() +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Exercise} + \begin{itemize} + \item Add the \typ{show()} command to \typ{four_plot.py} + \item Test that it works + \end{itemize} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Result graph} + \begin{center} + \includegraphics[height=3in, interpolate=true]{data/four_plot} + \end{center} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Running with Python} + \begin{itemize} + \item Start a new Canopy terminal + \item Run the script as: + \end{itemize} +\begin{lstlisting} + $ python four_plot.py +\end{lstlisting} + \pause + Do you see: + \begin{small} +\begin{lstlisting} +NameError: name 'linspace' is not defined +\end{lstlisting} + \end{small} +\inctime{5} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Imports} + \begin{itemize} + \item \typ{ipython --pylab} does magic + \item Import libraries using \typ{import} + \end{itemize} +\begin{lstlisting} +In []: from pylab import linspace +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Exercise} + \begin{itemize} + \item Add \typ{from pylab import linspace} to top of \typ{four_plot.py} + \item Test that it works + \end{itemize} +\begin{lstlisting} +# four_plot.py +from pylab import linspace # <--- +x = linspace(-5*pi, 5*pi, 500) +plot(x, x, 'b') +... +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Try again} + \begin{itemize} + \item On Canopy terminal + \item Run the script as: + \end{itemize} +\begin{lstlisting} + $ python four_plot.py +\end{lstlisting} + \pause + \vspace*{0.15in} + Do you see: + \begin{small} +\begin{lstlisting} +NameError: name 'plot' is not defined +\end{lstlisting} + \end{small} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Exercise} + \begin{itemize} + \item Change line 1 to \typ{from pylab import *} + \item Test that it works + \end{itemize} +\begin{lstlisting} +# four_plot.py +from pylab import * # <--- +x = linspace(-5*pi, 5*pi, 500) +plot(x, x, 'b') +... +\end{lstlisting} +\inctime{5} +\end{frame} + + +\begin{frame}[fragile] + \frametitle{What did we learn?} + \begin{itemize} + \item Starting up IPython + \item Creating simple plots + \item Adding labels and legends + \item Annotating plots + \item Changing the looks: size, linewidth + \item Accessing history, documentation + \item \kwrd{\%hist} - History of commands + \item Creating a Python script on Canopy + \item Running a script using \kwrd{\%run -i} + \item Importing functionality + \item Running a script with\ \typ{python script.py} + \end{itemize} +\end{frame} + +\begin{frame} + \frametitle{Next: using Canopy} + \begin{itemize} + \item Much easier + \item Write code in the editor + \item Save (Ctrl-S or Cmd-S) + \item Run selection: Ctrl-Shift-R (Cmd-Shift-R on OS X) + \item Run code: Ctrl-R (Cmd-R on OS X) + \end{itemize} + \inctime{5} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Note on script file names} + \begin{itemize} + \item Should start with a letter + \item Can use \typ{_} (underscore) and numbers + \item No \typ{.} allowed + \item No spaces or special characters + \end{itemize} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Test} + \begin{itemize} + \item \typ{1_script.py} + \item \typ{script_1.py} + \item \typ{one11.py} + \item \typ{one script.py} + \item \typ{one,script;xxx.py} + \item \typ{one.two.py} + \end{itemize} +\end{frame} + +\end{document} + +%% Questions for Quiz %% +%% ------------------ %% + +\begin{frame}[fragile] +\frametitle{\incqno } +Draw (roughly) the plot obtained by the following: +\begin{lstlisting} +In []: x = linspace(0, pi, 3) +In []: plot(x, sin(x)) +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] +\frametitle{\incqno } +Describe the plot produced by the following: +\begin{lstlisting} +In []: x = linspace(0, 2*pi, 50) +In []: plot(x, cos(x), 'go') +\end{lstlisting} +\end{frame} + +\begin{frame} +\frametitle{\incqno } +How will you plot the previous graph with line width set to 3? How will +you set the $x$ and $y$ labels of the plot? +\end{frame} + +\begin{frame} +\frametitle{\incqno } +How will you set the x and y axis limits so that the region of interest +is in the rectangle $(0, -1.5)$ (left bottom coordinate) and $(2\pi, +1.5)$ (right top coordinate)? +\end{frame} + +\begin{frame} +\frametitle{\incqno } +What ipython magic command do you use to obtain the lines of code you have already typed in the interpreter? What command do you use to save them? +\end{frame} + +\begin{frame}[fragile] +\frametitle{\incqno } +The following code snippet has an error/bug: +\begin{lstlisting} +In []: y = linspace(0, 2*pi, 50) +In []: plot(y, sin(y)) +In []: clf() +In []: plot(y, cos(y)) +In []: legend(['sin(y)', 'cos(y)']) +\end{lstlisting} +What is the error? How do you fix it? +\end{frame} diff --git a/scipy/basic/session2.tex b/scipy/basic/session2.tex new file mode 100644 index 0000000..359d1c8 --- /dev/null +++ b/scipy/basic/session2.tex @@ -0,0 +1,902 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%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} + +% 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}}} } + +\newcommand{\num}{\texttt{numpy}} + +%%% 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[Interactive Plotting]{Introductory Scientific Computing with +Python} +\subtitle{More plotting, lists and numpy arrays} + +\author[Prabhu] {FOSSEE} + +\institute[FOSSEE -- IITB] {Department of Aerospace Engineering\\IIT Bombay} +\date[] {India\\ +2016 +} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%\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 + % You might wish to add the option [pausesections] +\end{frame} + +\section{Plotting Points} +\begin{frame}[fragile] +\frametitle{Why would I plot f(x)?} +Do we plot analytical functions or experimental data? +\begin{small} +\begin{lstlisting} +In []: time = [0., 1., 2, 3] + +In []: distance = [7., 11, 15, 19] + +In []: plot(time,distance) +Out[]: [<matplotlib.lines.Line2D object at 0xa73aa8c>] + +In []: xlabel('time') +Out[]: <matplotlib.text.Text object at 0x986e9ac> + +In []: ylabel('distance') +Out[]: <matplotlib.text.Text object at 0x98746ec> +\end{lstlisting} +\end{small} +\end{frame} + +\begin{frame}[fragile] +\begin{figure} +\includegraphics[width=3.5in]{data/straightline.png} +\end{figure} +\alert{Is this what you have?} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Plotting points} +\begin{itemize} +\item What if we want to plot the points? +\end{itemize} +\begin{lstlisting} + In []: clf() + + In []: plot(time, distance, 'o') + Out[]: [<matplotlib.lines.Line2D object at 0xac17e0c>] + + In []: clf() + In []: plot(time, distance, '.') + Out[]: [<matplotlib.lines.Line2D object at 0xac17e0c>] +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] +\begin{figure} +\includegraphics[interpolate=true,width=2.35in]{data/stline_dots.png} +\includegraphics[interpolate=true,width=2.35in]{data/stline_points.png} +\end{figure} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Additional Line Styles} +\begin{itemize} + \item \typ{'o'} - Filled circles + \item \typ{'.'} - Small Dots + \item \typ{'-'} - Lines + \item \typ{'--'} - Dashed lines +\end{itemize} +\end{frame} + +\section{Lists} +\begin{frame}[fragile] + \frametitle{Lists: Introduction} + \begin{lstlisting} + In []: time = [0, 1, 2, 3] + + In []: distance = [7, 11, 15, 19] + + \end{lstlisting} +What are \typ{x} and \typ{y}?\\ +\begin{center} +\alert{\typ{lists!!}} +\end{center} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Lists: Initializing \& accessing elements} +\begin{lstlisting} +In []: mtlist = [] +\end{lstlisting} +\emphbar{Empty List} +\begin{lstlisting} +In []: p = [ 2, 3, 5, 7] + +In []: p[1] +Out[]: 3 + +In []: p[0]+p[1]+p[-1] +Out[]: 12 +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] + \frametitle{List: Slicing} + \begin{block}{Remember\ldots} + \kwrd{In []: p = [ 2, 3, 5, 7]} + \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] +In []: p[1:] +Out[]: [3, 5, 7] +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] + \frametitle{List: Slicing \ldots} +\begin{lstlisting} +In []: p[0:4:2] +Out[]: [2, 5] +In []: p[0::2] +Out[]: [2, 5] +In []: p[::2] +Out[]: [2, 5] +In []: p[::3] +Out[]: [2, 7] +In []: p[::-1] +Out[]: [7, 5, 3, 2] +\end{lstlisting} +\alert{\typ{list[initial:final:step]}} +\end{frame} + +\begin{frame}[fragile] + \frametitle{List: Slicing} + What is the output of the following? +\begin{lstlisting} +In []: p[1::2] + +In []: p[1:-1:2] +\end{lstlisting} +\end{frame} + + +%% more on list slicing +\begin{frame}[fragile] +\frametitle{List operations} +\begin{lstlisting} +In []: b = [ 11, 13, 17] +In []: c = p + b + +In []: c +Out[]: [2, 3, 5, 7, 11, 13, 17] + +In []: p.append(11) +In []: p +Out[]: [ 2, 3, 5, 7, 11] +\end{lstlisting} +Question: Does \typ{c} change now that \typ{p} is changed? +\inctime{10} +\end{frame} + +\section{Simple Pendulum} +\begin{frame}[fragile] +\frametitle{Simple Pendulum - L and T} +Let us look at the Simple Pendulum experiment. +\begin{center} +\begin{small} +\begin{tabular}{| c | c | c |} +\hline +$L$ & $T$ & $T^2$ \\ \hline +0.1 & 0.69 & \\ \hline +0.2 & 0.90 & \\ \hline +0.3 & 1.19 & \\ \hline +0.4 & 1.30 & \\ \hline +0.5 & 1.47 & \\ \hline +0.6 & 1.58 & \\ \hline +0.7 & 1.77 & \\ \hline +0.8 & 1.83 & \\ \hline +0.9 & 1.94 & \\ \hline +\end{tabular} +\end{small}\\ +\alert{$L \alpha T^2$} +\end{center} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Lets use lists} +\begin{lstlisting} +In []: L = [0.1, 0.2, 0.3, 0.4, 0.5, + 0.6, 0.7, 0.8, 0.9] + +In []: t = [0.69, 0.90, 1.19, + 1.30, 1.47, 1.58, + 1.77, 1.83, 1.94] +\end{lstlisting} +\alert{Gotcha}: Make sure \typ{L} and \typ{t} have the same number +of elements + +\begin{lstlisting} +In []: print len(L), len(t) +\end{lstlisting} + +\end{frame} + +\begin{frame}[fragile] +\frametitle{Plotting $L$ vs $T^2$} +\begin{itemize} +\item We must square each of the values in \typ{t} +\item How do we do it? +\item We use a \kwrd{for} loop to iterate over \typ{t} +\end{itemize} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Plotting $L$ vs $T^2$} +\begin{lstlisting} +In []: tsq = [] + +In []: for time in t: + ....: tsq.append(time*time) + ....: + ....: + +\end{lstlisting} +This gives \typ{tsq} which is the list of squares of \typ{t} values. +\begin{lstlisting} +In []: print len(L), len(t), len(tsq) +Out[]: 9 9 9 + +In []: plot(L, tsq) +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] +\begin{figure} +\includegraphics[width=3.5in]{data/L-TSq-limited.png} +\end{figure} +\end{frame} + + +\begin{frame}[fragile] +\frametitle{This seems tedious} +\begin{itemize} + \item Lists +\begin{itemize} + \item Nice + \item Not too convenient + \item Slow +\end{itemize} +\item Enter NumPy arrays + \begin{itemize} + \item Fixed size, data type + \item Fast + \item Very convenient + \end{itemize} +\end{itemize} +\end{frame} + +\subsection{\num\ arrays} + +\begin{frame}[fragile] +\frametitle{NumPy arrays} +\begin{lstlisting} +In []: t = array(t) + +In []: tsq = t*t + +In []: print tsq + +In []: plot(L, tsq) # works! +\end{lstlisting} %$ +\end{frame} + + +\begin{frame}[fragile] +\frametitle{Speed?} + +\noindent Lets use range to create a large list. + +\begin{lstlisting} +In []: t = range(1000000) +In []: tsq = [] + +In []: for time in t: + ....: tsq.append(time*time) + ....: + ....: +\end{lstlisting} %$ + +\noindent Now try it with + +\begin{lstlisting} +In []: t = array(t) + +In []: tsq = t*t +\end{lstlisting} +\ldots +\end{frame} + +\begin{frame}[fragile] +\frametitle{How fast is this?} +\noindent Lets define a function for the list +\begin{lstlisting} +In []: def sqr(arr): + ...: result = [] + ...: for x in arr: + ...: result.append(x*x) + ...: return result + ...: + +In []: tsq = sqr(t) + +\end{lstlisting} %$ +\end{frame} + +\begin{frame}[fragile] + \frametitle{Aside: Defining functions} + \begin{itemize} + \item Consider the function \texttt{f(x) = x\textasciicircum{}2} + \item Let's write a Python function, equivalent to this + \end{itemize} + \begin{lstlisting} + In[]: def f(x): + ....: return x*x + ....: + + In[]: f(1) + In[]: f(2) + \end{lstlisting} + \begin{itemize} + \item \texttt{def} is a keyword + \item \texttt{f} is the name of the function + \item \texttt{x} the parameter of the function + \item \texttt{return} is a keyword + \end{itemize} +\end{frame} + +\begin{frame}[fragile] + \frametitle{IPython tip: Timing} + +Try the following: + \begin{lstlisting} +In []: %timeit sqr(t) + +In []: %timeit? + + \end{lstlisting} + + \begin{itemize} + \item \typ{\%timeit}: accurate, many measurements + \item Can also use \typ{\%time} + \item \typ{\%time}: less accurate, one measurement + \end{itemize} + +\inctime{15} +\end{frame} + + +\begin{frame}[fragile] +\frametitle{Exercise} +\begin{center} + Find out the speed difference between the \typ{sqr} function and + \typ{t*t} on the numpy array. +\end{center} + +\end{frame} + +\begin{frame}[fragile] + \frametitle{The \num\ module} + \begin{itemize} + \item Efficient, powerful array type + \item Abstracts out standard operations on arrays + \item Convenience functions + \item \typ{ipython -pylab} imports part of numpy + \item Without the Pylab mode do: + \end{itemize} + \begin{lstlisting} +In []: import numpy + +In []: from numpy import * + \end{lstlisting} +\end{frame} + +\begin{frame} + \frametitle{\num\ arrays} + \begin{itemize} + \item Fixed size (\typ{arr.size}) + \item Same type (\typ{arr.dtype}) + \item Arbitrary dimensionality: \typ{arr.shape} + \item \typ{shape}: extent (size) along each dimension + \item \typ{arr.itemsize}: number of bytes per element + \item \alert{Note:} \typ{shape} can change so long as the \typ{size} + is constant + \item Indices start from 0 + \item Negative indices work like lists + \end{itemize} +\end{frame} + +\begin{frame}[fragile] + \frametitle{\num\ arrays} +\begin{lstlisting} +In []: a = array([1,2,3,4]) +In []: b = array([2,3,4,5]) + +In []: print a[0], a[-1] +1, 4 + +In []: a[0] = -1 +In []: a[0] = 1 +\end{lstlisting} +Operations are elementwise +\end{frame} + +\begin{frame}[fragile] + \frametitle{Simple operations} +\begin{lstlisting} +In []: a + b +Out[]: array([3, 5, 7, 9]) +In []: a*b +Out[]: array([2, 6, 12, 20]) +In []: a/b +Out[]: array([0, 0, 0, 0]) +\end{lstlisting} +Operations are elementwise, types matter. +\end{frame} + +\begin{frame}[fragile] + \frametitle{Data type matters} + Try again with this: +\begin{lstlisting} +In []: a = array([1.,2,3,4]) +In []: a/b +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Examples} +\noindent \typ{pi} and \typ{e} are defined. +\begin{lstlisting} +In []: x = linspace(0.0, 10.0, 200) +In []: x *= 2*pi/10 +# apply functions to array. +In []: y = sin(x) +In []: y = cos(x) +In []: x[0] = -1 +In []: print x[0], x[-1] +-1.0 10.0 +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] + \frametitle{\typ{size, shape, rank} etc.} +\vspace*{-8pt} +\begin{lstlisting} +In []: x = array([1., 2, 3, 4]) +In []: size(x) +Out[]: 4 +In []: x.dtype +dtype('float64') +In []: x.shape +Out[] (4,) +In []: rank(x) +Out[]: 1 +In []: x.itemsize +Out[]: 8 +\end{lstlisting} +\end{frame} + + +\begin{frame}[fragile] + \frametitle{Multi-dimensional arrays} +\begin{lstlisting} +In []: a = array([[ 0, 1, 2, 3], + ...: [10,11,12,13]]) +In []: a.shape # (rows, columns) +Out[]: (2, 4) + +In []: a[1,3] +Out[]: 13 + +In []: a[1,3] = -1 +In []: a[1] # The second row +array([10,11,12,-1]) +In []: a[1] = 0 # Entire row to zero. +\end{lstlisting} + +\end{frame} + +\begin{frame}[fragile] + \frametitle{Slicing arrays} + \vspace*{-0.2in} +\begin{lstlisting} +In []: a = array([[1,2,3], [4,5,6], + ...: [7,8,9]]) +In []: a[0,1:3] +Out[]: array([2, 3]) +In []: a[1:,1:] +Out[]: array([[5, 6], + [8, 9]]) +In []: a[:,2] +Out[]: array([3, 6, 9]) +In []: a[0::2,0::2] # Striding... +Out[]: array([[1, 3], + [7, 9]]) +# Slices refer to the same memory! +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Array creation functions} + \begin{itemize} + \item \typ{array(object)} + \item \typ{linspace(start, stop, num=50)} + \item \typ{ones(shape)} + \item \typ{zeros((d1,...,dn))} + \item \typ{empty((d1,...,dn))} + \item \typ{identity(n)} + \item \typ{ones\_like(x)}, \typ{zeros\_like(x)}, \typ{empty\_like(x)} + \end{itemize} + May pass an optional \typ{dtype=} keyword argument + + For more dtypes see: \typ{numpy.typeDict} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Creation examples} + \vspace*{-0.25in} +\begin{lstlisting} +In []: a = array([1,2,3], dtype=float) +In []: ones( (2, 3) ) +Out[]: array([[ 1., 1., 1.], + [ 1., 1., 1.]]) +In []: identity(3) +Out[]: array([[ 1., 0., 0.], + [ 0., 1., 0.], + [ 0., 0., 1.]]) +In []: ones_like(a) +Out[]: array([ 1., 1., 1., 1.]) +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Array math} + \begin{itemize} + \item Basic \alert{elementwise} math (given two arrays \typ{a, b}): + \begin{itemize} + \item \typ{a + b} $\rightarrow$ \typ{add(a, b)} + \item \typ{a - b}, $\rightarrow$ \typ{subtract(a, b)} + \item \typ{a * b}, $\rightarrow$ \typ{multiply(a, b)} + \item \typ{a / b}, $\rightarrow$ \typ{divide(a, b)} + \item \typ{a \% b}, $\rightarrow$ \typ{remainder(a, b)} + \item \typ{a ** b}, $\rightarrow$ \typ{power(a, b)} + \end{itemize} + \item Inplace operators: \typ{a += b}, or \typ{add(a, b, + a)} + \alert{What happens if \typ{a} is \typ{int} and \typ{b} is \typ{float?}} + \item Logical operations: \typ{==, !=, <, >}, etc. + \item \typ{sin(x), arcsin(x), sinh(x)}, + \typ{exp(x), sqrt(x)} etc. + \item \typ{sum(x, axis=0), product(x, axis=0)} + \item \typ{dot(a, b)} + \end{itemize} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Convenience functions: \typ{loadtxt}} + \begin{itemize} + \item \typ{loadtxt(file_name)}: loads a text file + \item \typ{loadtxt(file_name, unpack=True)}: loads a text file and + unpacks columns + \end{itemize} + \begin{lstlisting} +In []: x = loadtxt('pendulum.txt') +In []: x.shape +Out[]: (90, 2) + +In []: x, y = loadtxt('pendulum.txt', + ...: unpack=True) +In []: x.shape +Out[]: (90,) + \end{lstlisting} + + \inctime{20} +\end{frame} + + +\begin{frame}[fragile] + \frametitle{Advanced} + \begin{itemize} + \item Only scratched the surface of \num + \item \typ{reduce, outer} + \item Typecasting + \item More functions: \typ{take, choose, where}, \typ{compress, + concatenate} + \item Array broadcasting and \typ{None} + \item Record arrays + \end{itemize} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Learn more} + \begin{itemize} + \item \url{http://wiki.scipy.org/Tentative_NumPy_Tutorial} + \item \url{http://numpy.org} + \end{itemize} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Recap} + \begin{itemize} + \item Basic concepts: creation, access, operations + \item 1D, multi-dimensional + \item Slicing + \item Array creation, dtypes + \item Math + \item \typ{loadtxt} + \end{itemize} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Example: plotting data from file} +\alert{Data is usually present in a file!} \\ +Lets look at the \typ{pendulum.txt} file. +\begin{lstlisting} +In []: cat pendulum.txt +1.0000e-01 6.9004e-01 +1.1000e-01 6.9497e-01 +1.2000e-01 7.4252e-01 +1.3000e-01 7.5360e-01 +\end{lstlisting} +\ldots +\end{frame} + +\begin{frame}[fragile] +\frametitle{Reading \typ{pendulum.txt}} +\begin{itemize} + \item File contains L vs.\ T values + \item First Column - L values + \item Second Column - T values + \item Let us generate a plot from the data file +\end{itemize} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Gotcha and an aside} + Ensure you are in the same directory as \typ{pendulum.txt}\\ + if not, do the following on IPython: + \begin{lstlisting} +In []: %cd directory_containing_file +# Check if pendulum.txt is there. +In []: ls +# Also try +In []: !ls + \end{lstlisting} + + \alert{Note:} \typ{\%cd} is an IPython magic command. For more information + do: + \begin{lstlisting} +In []: ? + \end{lstlisting} +\end{frame} + + +\begin{frame}[fragile] + \frametitle{Exercise} + \begin{itemize} + \item Plot L versus T square with dots + \item No line connecting points + \end{itemize} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Solution} +\begin{lstlisting} +In []: L, t = loadtxt('pendulum.txt', + ....: unpack=True) +In []: plot(L, t*t, '.') +\end{lstlisting} +or +\begin{lstlisting} +In []: x = loadtxt('pendulum.txt') +In []: L, t = x[:,0], x[:,1] +In []: plot(L, t*t, '.') +\end{lstlisting} + +\end{frame} + + +\begin{frame}[fragile] +\begin{figure} +\includegraphics[width=3.5in]{data/L-Tsq.png} +\end{figure} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Odds and ends} +\begin{lstlisting} +In []: mean(L) +Out[]: 0.54499999999999993 + +In []: std(L) +Out[]: 0.25979158313283879 +\end{lstlisting} +\end{frame} + +\section {Summary} +\begin{frame}[fragile] +\frametitle{What did we learn?} +\begin{itemize} + \item Plot attributes and plotting points + \item Lists + \item Introduction to \num\ arrays +\end{itemize} + +\inctime{10} +\end{frame} + +\end{document} + +%% Questions for Quiz %% +%% ------------------ %% + +\begin{frame}[fragile] +\frametitle{\incqno } + \begin{lstlisting} + In []: a = [1, 2, 5, 9] + In []: a[0:-1] + \end{lstlisting} + What is the output? +\end{frame} + +\begin{frame} +\frametitle{\incqno } + How do you combine two lists \emph{a} and \emph{b} to produce one list? +\end{frame} + +\begin{frame}[fragile] +\frametitle{\incqno } + \begin{lstlisting} + In []: a = [1, 2, 5, 9] + \end{lstlisting} + How do you add the value 10 to the end of this list? +\end{frame} + +\begin{frame} +\frametitle{\incqno } +Write the code to read a file \texttt{data.txt} and print each line of it? +\end{frame} + +\begin{frame}[fragile] +\frametitle{\incqno } +What would be the result of the following code snippet: +\begin{lstlisting} +In []: x = linspace(0, 10, 50) +In []: y = linspace(50, 100, 100) +In []: plot(x, y) +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] +\frametitle{\incqno } +The following code snippet has an error/bug: +\begin{lstlisting} +In []: l = [0.1, 0.2, 0.3, 0.4] +In []: t = [0.69, 0.90, 1.19, 1.30] +In []: tsq = [] +In []: for time in t: + ....: tsq.append(time*time) + ....: plot(l, tsq) +\end{lstlisting} +What is the error? How do you fix it? +\end{frame} diff --git a/scipy/basic/session3.tex b/scipy/basic/session3.tex new file mode 100644 index 0000000..6d603a5 --- /dev/null +++ b/scipy/basic/session3.tex @@ -0,0 +1,830 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%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[More on numpy arrays]{Introductory Scientific Computing with +Python} +\subtitle{More on numpy arrays} + +\author[Prabhu] {FOSSEE} + +\institute[FOSSEE -- IITB] {Department of Aerospace Engineering\\IIT Bombay} +\date[] {SciPy India, 2014\\ +December, 2014 +} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%\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} +\inctime{15} +\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} + \inctime{10} +\end{frame} + +\section{Least Squares Fit} +\begin{frame}[fragile] +\frametitle{$L$ vs. $T^2$ - Scatter} +Linear trend visible. +\vspace{-0.1in} +\begin{figure} +\includegraphics[width=4in]{data/L-Tsq-points} +\end{figure} +\end{frame} + +\begin{frame}[fragile] +\frametitle{$L$ vs. $T^2$ - Line} +This line does not make any mathematical sense. +\vspace{-0.1in} +\begin{figure} +\includegraphics[width=4in]{data/L-Tsq-Line} +\end{figure} +\end{frame} + +\begin{frame}[fragile] +\frametitle{$L$ vs. $T^2$ - Least Square Fit} +This is what our intention is. +\vspace{-0.1in} +\begin{figure} +\includegraphics[width=4in]{data/least-sq-fit} +\end{figure} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Matrix Formulation} +\begin{itemize} +\item We need to fit a line through points for the equation $T^2 = m \cdot L+c$ +\item In matrix form, the equation can be represented as $T_{sq} = A \cdot p$, where $T_{sq}$ is + $\begin{bmatrix} + T^2_1 \\ + T^2_2 \\ + \vdots\\ + T^2_N \\ + \end{bmatrix}$ +, A is + $\begin{bmatrix} + L_1 & 1 \\ + L_2 & 1 \\ + \vdots & \vdots\\ + L_N & 1 \\ + \end{bmatrix}$ + and p is + $\begin{bmatrix} + m\\ + c\\ + \end{bmatrix}$ +\item We need to find $p$ to plot the line +\end{itemize} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Getting $L$ and $T^2$} +%If you \alert{closed} IPython after session 2 +\begin{lstlisting} +In []: L, t = loadtxt('pendulum.txt', + ...: unpack=True) +In []: tsq = t*t +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Generating $A$} +\begin{lstlisting} +In []: A = array([L, ones_like(L)]) +In []: A = A.T +\end{lstlisting} +%% \begin{itemize} +%% \item A is also called a Van der Monde matrix +%% \item It can also be generated using \typ{vander} +%% \end{itemize} +%% \begin{lstlisting} +%% In []: A = vander(L, 2) +%% \end{lstlisting} +\end{frame} + +\begin{frame}[fragile] +\frametitle{\typ{lstsq} \ldots} +\begin{itemize} +\item Now use the \typ{lstsq} function +\item Along with a lot of things, it returns the least squares solution +\end{itemize} +\begin{lstlisting} +In []: result = lstsq(A,tsq) +In []: coef = result[0] +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Least Square Fit Line \ldots} +We get the points of the line from \typ{coef} +\begin{lstlisting} +In []: Tline = coef[0]*L + coef[1] + +In []: Tline.shape +\end{lstlisting} +\begin{itemize} +\item Now plot \typ{Tline} vs. \typ{L}, to get the least squares fit line. +\end{itemize} +\begin{lstlisting} +In []: plot(L, Tline, 'r') + +In []: plot(L, tsq, 'o') +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Least Squares Fit} +\vspace{-0.15in} +\begin{figure} +\includegraphics[width=4in]{data/least-sq-fit} +\end{figure} +\inctime{10} +\end{frame} + +\section{Random numbers} + +\begin{frame}[fragile] + \frametitle{\typ{numpy.random}} + \begin{itemize} + \item Easy random number generation + \end{itemize} + \begin{lstlisting} +In []: random? + \end{lstlisting} + Or: + \begin{lstlisting} +In []: import numpy +In []: numpy.random + \end{lstlisting} +\begin{itemize} + \item \typ{random.random}: produces uniform deviates in $[0, 1)$ + \item \typ{random.normal}: draws random samples from a Gaussian + distribution + \item Useful to create a random matrix of any shape +\end{itemize} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Using the \typ{random} module} +\begin{lstlisting} +In []: x = random.random(size=1000) +In []: y = random.random(size=1000) +In []: scatter(x, y) # Scatter plot it. + +In []: x,y = random.normal(size=(2,1000)) +In []: clf() +In []: scatter(x, y) +\end{lstlisting} +Note that \typ{size} can be a tuple. + +\end{frame} + +\begin{frame}[fragile] + \frametitle{Using the \typ{random} module} +\begin{lstlisting} +In []: img = random.random( + . size=(200, 200)) +In []: clf() +In []: imshow(img) +\end{lstlisting} +\inctime{5} +\end{frame} + + +\section{Record arrays} + +\begin{frame}[fragile] + \frametitle{Record arrays} + \begin{itemize} + \item Numpy arrays + \item Create custom data types + \item Consider: \\ + \typ{[ (id0, x0), (id1, x1), ...]} + \item \typ{id}: int + \item \typ{x}: float + + \end{itemize} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Record arrays} + \begin{lstlisting} +In []: typ = [('id', int), ('x', float)] +In []: rec = numpy.zeros(10, dtype=typ) +In []: rec['id'] = range(10) +In []: rec['x'] = random.random(size=10) + \end{lstlisting} + \begin{itemize} + \item Data type can be any valid numpy dtype + \item Very convenient + \end{itemize} +\end{frame} + +\begin{frame}[fragile] + \frametitle{\typ{csv2rec}} + \begin{itemize} + \item CSV file $\rightarrow$ Record array + \item Very convenient and powerful + \item Automatic naming + \item Handles missing data + \item Handles different delimiters + \end{itemize} + \begin{lstlisting} +In []: csv2rec? + \end{lstlisting} +\end{frame} + +\begin{frame}[fragile] + \frametitle{\typ{csv2rec} example data} + \begin{itemize} + \item \typ{data.csv} + \item First column ``x'' + \item Second column ``y'' + \item Third column ``temp'' + \end{itemize} +\end{frame} + +\begin{frame}[fragile] + \frametitle{\typ{csv2rec} example} + \begin{lstlisting} +In []: data = csv2rec('data.csv') +In []: scatter(data['x'], data['y'], + ...: c=data['temp']) +In []: colorbar() + \end{lstlisting} +\end{frame} + +\section{Summary} +\begin{frame} + \frametitle{What did we learn?} + \begin{itemize} + \item Matrices + \item Least Squares + \item Random numbers + \item Record arrays + \item \typ{csv2rec} + \end{itemize} + \inctime{5} +\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} + diff --git a/scipy/basic/session4.tex b/scipy/basic/session4.tex new file mode 100644 index 0000000..4c0cd5b --- /dev/null +++ b/scipy/basic/session4.tex @@ -0,0 +1,780 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%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{pgf} + +% Taken from Fernando's slides. +\usepackage{ae,aecompl} +\usepackage{mathpazo,courier,euler} +\usepackage[scaled=.95]{helvet} +\usepackage{amsmath} + +\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} +} + +\newcommand{\myemph}[1]{\structure{\emph{#1}}} +\newcommand{\PythonCode}[1]{\lstinline{#1}} + +\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[Basic SciPy and Mayavi]{Introductory Scientific Computing with +Python} +\subtitle{Basic SciPy and Mayavi} + +\author[Prabhu] {FOSSEE} + +\institute[FOSSEE -- IITB] {Department of Aerospace Engineering\\IIT Bombay} +\date[] {SciPy India, 2014\\ +December, 2014 +} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%\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} + \maketitle +\end{frame} + + +\section{Solving linear systems} + +\begin{frame}[fragile] +\frametitle{Solution of equations} +Consider, + \begin{align*} + 3x + 2y - z & = 1 \\ + 2x - 2y + 4z & = -2 \\ + -x + \frac{1}{2}y -z & = 0 + \end{align*} +Solution: + \begin{align*} + x & = 1 \\ + y & = -2 \\ + z & = -2 + \end{align*} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Solving using Matrices} +Let us now look at how to solve this using \kwrd{matrices} + \begin{lstlisting} +In []: A = array([[3,2,-1], + [2,-2,4], + [-1, 0.5, -1]]) +In []: b = array([1, -2, 0]) +In []: x = solve(A, b) + \end{lstlisting} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Solution:} +\begin{lstlisting} +In []: x +Out[]: array([ 1., -2., -2.]) +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Let's check!} +\begin{small} +\begin{lstlisting} +In []: Ax = dot(A, x) +In []: Ax +Out[]: array([ 1.00000000e+00, -2.00000000e+00, -1.11022302e-16]) +\end{lstlisting} +\end{small} +\begin{block}{} +The last term in the matrix is actually \alert{0}!\\ +We can use \kwrd{allclose()} to check. +\end{block} +\begin{lstlisting} +In []: allclose(Ax, b) +Out[]: True +\end{lstlisting} +\inctime{5} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Problem} +Solve the set of equations: +\begin{align*} + x + y + 2z -w & = 3\\ + 2x + 5y - z - 9w & = -3\\ + 2x + y -z + 3w & = -11 \\ + x - 3y + 2z + 7w & = -5\\ +\end{align*} +\inctime{5} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Solution} +Use \kwrd{solve()} +\begin{align*} + x & = -5\\ + y & = 2\\ + z & = 3\\ + w & = 0\\ +\end{align*} +\end{frame} + +\section{Finding Roots} + +\begin{frame}[fragile] +\frametitle{SciPy: \typ{roots}} +\begin{itemize} +\item Calculates the roots of polynomials +\item To calculate the roots of $x^2-5x+6$ +\end{itemize} +\begin{lstlisting} + In []: coeffs = [1, -5, 6] + In []: roots(coeffs) + Out[]: array([3., 2.]) +\end{lstlisting} +\vspace*{-.2in} +\begin{center} +\includegraphics[height=1.6in, interpolate=true]{data/roots} +\end{center} +\end{frame} + +\begin{frame}[fragile] +\frametitle{SciPy: \typ{fsolve}} +Find the root of $sin(z)+cos^2(z)$ nearest to $0$ +\vspace{-0.1in} +\begin{center} +\includegraphics[height=2.8in, interpolate=true]{data/fsolve} +\end{center} +\end{frame} + +\begin{frame}[fragile] +\frametitle{\typ{fsolve}} +\begin{small} +\begin{lstlisting} + In []: from scipy.optimize import fsolve +\end{lstlisting} +\end{small} +\begin{itemize} +\item Finds the roots of a system of non-linear equations +\item Input arguments - \alert{Function} and initial estimate +\item Returns the solution +\end{itemize} +\end{frame} + +\begin{frame}[fragile] +\frametitle{\typ{fsolve} \ldots} +\begin{lstlisting} +In []: def g(z): + ....: return sin(z)+cos(z)*cos(z) +In []: fsolve(g, 0) +Out[]: -0.66623943249251527 +\end{lstlisting} +\begin{center} +\includegraphics[height=2in, interpolate=true]{data/fsolve} +\end{center} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Exercise Problem} + Find the root of the equation $x^2 - sin(x) + cos^2(x) = tan(x)$ nearest to $0$ +\end{frame} + +\begin{frame}[fragile] + \frametitle{Solution} + \begin{small} + \begin{lstlisting} +def g(x): + return x**2 - sin(x) + cos(x)*cos(x) - tan(x) +fsolve(g, 0) + \end{lstlisting} + \end{small} + \begin{center} +\includegraphics[height=2in, interpolate=true]{data/fsolve_tanx} + \end{center} + \inctime{10} +\end{frame} + +%% \begin{frame}[fragile] +%% \frametitle{Scipy Methods \dots} +%% \begin{small} +%% \begin{lstlisting} +%% In []: from scipy.optimize import fixed_point + +%% In []: from scipy.optimize import bisect + +%% In []: from scipy.optimize import newton +%% \end{lstlisting} +%% \end{small} +%% \end{frame} + +\section{ODEs} + +\begin{frame}[fragile] +\frametitle{Solving ODEs using SciPy} +\begin{itemize} +\item Consider the spread of an epidemic in a population +\item $\frac{dy}{dt} = ky(L-y)$ gives the spread of the disease +\item $L$ is the total population. +\item Use $L = 2.5E5, k = 3E-5, y(0) = 250$ +\item Define a function as below +\end{itemize} +\begin{lstlisting} +In []: from scipy.integrate import odeint +In []: def epid(y, t): + .... k = 3.0e-5 + .... L = 2.5e5 + .... return k*y*(L-y) + .... +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Solving ODEs using SciPy \ldots} +\begin{lstlisting} +In []: t = linspace(0, 12, 61) + +In []: y = odeint(epid, 250, t) + +In []: plot(t, y) +\end{lstlisting} +%Insert Plot +\end{frame} + +\begin{frame}[fragile] +\frametitle{Result} +\begin{center} +\includegraphics[height=2in, interpolate=true]{data/image} +\end{center} +\end{frame} + + +\begin{frame}[fragile] +\frametitle{ODEs - Simple Pendulum} +We shall use the simple ODE of a simple pendulum. +\begin{equation*} +\ddot{\theta} = -\frac{g}{L}sin(\theta) +\end{equation*} +\begin{itemize} +\item This equation can be written as a system of two first order ODEs +\end{itemize} +\begin{align} +\dot{\theta} &= \omega \\ +\dot{\omega} &= -\frac{g}{L}sin(\theta) \\ + \text{At}\ t &= 0 : \nonumber \\ + \theta = \theta_0(10^o)\quad & \&\quad \omega = 0\ (Initial\ values)\nonumber +\end{align} +\end{frame} + +\begin{frame}[fragile] +\frametitle{ODEs - Simple Pendulum \ldots} +\begin{itemize} +\item Use \typ{odeint} to do the integration +\end{itemize} +\begin{lstlisting} +In []: def pend_int(initial, t): + .... theta = initial[0] + .... omega = initial[1] + .... g = 9.81 + .... L = 0.2 + .... F=[omega, -(g/L)*sin(theta)] + .... return F + .... +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] +\frametitle{ODEs - Simple Pendulum \ldots} +\begin{itemize} +\item \typ{t} is the time variable \\ +\item \typ{initial} has the initial values +\end{itemize} +\begin{lstlisting} +In []: t = linspace(0, 20, 101) +In []: initial = [10*2*pi/360, 0] +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] +\frametitle{ODEs - Simple Pendulum \ldots} +%%\begin{small} +\typ{In []: from scipy.integrate import odeint} +%%\end{small} +\begin{lstlisting} +In []: pend_sol = odeint(pend_int, + initial,t) +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Result} +\begin{center} +\includegraphics[height=2in, interpolate=true]{data/ode} +\end{center} + \inctime{10} +\end{frame} + +\section{FFTs} + +\begin{frame}[fragile] +\frametitle{The FFT} +\begin{itemize} + \item We have a simple signal $y(t)$ + \item Find the FFT and plot it +\end{itemize} +\begin{lstlisting} +In []: t = linspace(0, 2*pi, 500) +In []: y = sin(4*pi*t) + +In []: f = fft(y) +In []: freq = fftfreq(500, t[1] - t[0]) + +In []: plot(freq[:250], abs(f)[:250]) +In []: grid() +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] +\frametitle{FFTs cont\dots} +\begin{lstlisting} +In []: y1 = ifft(f) # inverse FFT +In []: allclose(y, y1) +Out[]: True +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] +\frametitle{FFTs cont\dots} +Let us add some noise to the signal +\begin{lstlisting} +In []: yr = y + random(size=500)*0.2 +In []: yn = y + normal(size=500)*0.2 + +In []: plot(t, yr) +In []: figure() +In []: plot(freq[:250], + ...: abs(fft(yn))[:250]) +\end{lstlisting} +\begin{itemize} + \item \typ{random}: produces uniform deviates in $[0, 1)$ + \item \typ{normal}: draws random samples from a Gaussian + distribution + \item Useful to create a random matrix of any shape +\end{itemize} +\end{frame} + +\begin{frame}[fragile] +\frametitle{FFTs cont\dots} +Filter the noisy signal: +\begin{lstlisting} +In []: from scipy import signal +In []: yc = signal.wiener(yn, 5) +In []: clf() +In []: plot(t, yc) +In []: figure() +In []: plot(freq[:250], + ...: abs(fft(yc))[:250]) +\end{lstlisting} +Only scratched the surface here \dots + \inctime{10} +\end{frame} + +\section{Basic Mayavi: \typ{mlab}} + +\begin{frame}[fragile] +\frametitle{Basic 3D visualization} +\begin{itemize} + \item Simple one liners for 3D visualization + \item Must import mlab. +\end{itemize} +\begin{lstlisting} +In []: from mayavi import mlab +\end{lstlisting} +Ready to go! +\end{frame} + +\begin{frame}[fragile] + \frametitle{Simple examples} + + \myemph{\Large Try these} + + \begin{lstlisting} +In []: mlab.test_<TAB> + +In []: mlab.test_points3d() +In []: mlab.clf() +In []: mlab.test_plot3d() +In []: mlab.clf() +In []: mlab.test_surf() +In []: mlab.test_surf?? + \end{lstlisting} +Explore the UI. +\end{frame} + + +\begin{frame}[fragile] + \frametitle{\typ{mlab} plotting functions} + \begin{columns} + \column{0.25\textwidth} + \myemph{\Large 0D data} + \column{0.5\textwidth} + \pgfimage[width=2in]{../MEDIA/m2/mlab/points3d_ex} + \end{columns} + + \begin{lstlisting} +In []: t = linspace(0, 2*pi, 50) +In []: u = cos(t) * pi +In []: x, y, z = sin(u), cos(u), sin(t) + \end{lstlisting} + \emphbar{\PythonCode{In []: mlab.points3d(x, y, z)}} +\end{frame} + +\begin{frame}[plain, fragile] + \frametitle{Changing how things look} + + \begin{block}{Clearing the view} + \PythonCode{>>> mlab.clf()} + \end{block} + + \pause + + \begin{block}{IPython is your friend!} + \PythonCode{>>> mlab.points3d?} + + \begin{itemize} + + \item Extra argument: Scalars + + \item Keyword arguments + + \item UI + \end{itemize} + \end{block} +\pause + \begin{lstlisting} +In []: mlab.points3d(x, y, z, t, + scale_mode='none') + \end{lstlisting} + +\end{frame} + + + +\begin{frame}[fragile] + \begin{columns} + \column{0.25\textwidth} + \myemph{\Large 1D data} + \column{0.5\textwidth} + \pgfimage[width=2.5in]{../MEDIA/m2/mlab/plot3d_ex} + \end{columns} + \emphbar{\PythonCode{In []: mlab.plot3d(x, y, z, t)}} + + Plots lines between the points + +\end{frame} + +\begin{frame}[fragile] + \begin{columns} + \column{0.25\textwidth} + \myemph{\Large 2D data} + \column{0.5\textwidth} + \pgfimage[width=2in]{../MEDIA/m2/mlab/surf_ex} + \end{columns} + \begin{lstlisting} +In []: x, y = mgrid[-3:3:100j,-3:3:100j] +In []: z = sin(x*x + y*y) + \end{lstlisting} + + \emphbar{\PythonCode{In []: mlab.surf(x, y, z)}} + + \alert{Assumes the points are rectilinear} + +\end{frame} + + +\begin{frame}[plain, fragile] + + \myemph{\Large 3D data} + \vspace*{0.25in} + + \pgfimage[width=1.5in]{../MEDIA/m2/mlab/contour3d}\\ + +\begin{lstlisting} +In []: x, y, z = ogrid[-5:5:64j, + ...: -5:5:64j, + ...: -5:5:64j] +In []: mlab.contour3d(x*x*0.5 + y*y + + z*z*2) +\end{lstlisting} +\end{frame} + +\begin{frame}[plain] + {Other utility functions} + \begin{itemize} + \item \PythonCode{gcf}: get current figure + \pause + \item \PythonCode{savefig}, \PythonCode{figure} + \pause + \item \PythonCode{axes}, \PythonCode{outline} + \pause + \item \PythonCode{title}, \PythonCode{xlabel, ylabel, zlabel} + \pause + \item \PythonCode{colorbar}, \PythonCode{scalarbar}, + \PythonCode{vectorbar} + \pause + \item \PythonCode{show}: Standalone mlab scripts + \pause + \item Others, see UG + \end{itemize} +\end{frame} + +\begin{frame} + {Exploring the documentation} + \begin{center} + \pgfimage[width=4in]{../MEDIA/m2/m2_ug_doc} + \end{center} + \inctime{20} +\end{frame} + + + +\begin{frame} + \frametitle{Things we have learned} + \begin{itemize} + \item Solving Linear Equations + \item Defining Functions + \item Finding Roots + \item Solving ODEs + \item FFTs and basic signal processing + \item Basic 3D visualization with Mayavi + \end{itemize} +\end{frame} + + +\begin{frame} + \frametitle{Further reading} + \begin{itemize} + \item \url{ipython.github.com/ipython-doc} + \item \url{matplotlib.sf.net/contents.html} + \item \url{scipy.org/Tentative_NumPy_Tutorial} + \item \url{docs.scipy.org/doc/scipy/reference/tutorial} + \item \url{github.enthought.com/mayavi/mayavi} + \end{itemize} +\end{frame} + +\end{document} + +%% Questions for Quiz %% +%% ------------------ %% + +\begin{frame} +\frametitle{\incqno } +Given a 4x4 matrix \texttt{A} and a 4-vector \texttt{b}, what command do +you use to solve for the equation \\ +\texttt{Ax = b}? +\end{frame} + +\begin{frame} +\frametitle{\incqno } +What command will you use if you wish to integrate a system of ODEs? +\end{frame} + +\begin{frame} +\frametitle{\incqno } +How do you calculate the roots of the polynomial, $y = 1 + 6x + 8x^2 + +x^3$? +\end{frame} + +\begin{frame} +\frametitle{\incqno } +Two arrays \lstinline+a+ and \lstinline+b+ are numerically almost equal, what command +do you use to check if this is true? +\end{frame} + +%% \begin{frame}[fragile] +%% \frametitle{\incqno } +%% \begin{lstlisting} +%% In []: x = arange(0, 1, 0.25) +%% In []: print x +%% \end{lstlisting} +%% What will be printed? +%% \end{frame} + + +%% \begin{frame}[fragile] +%% \frametitle{\incqno } +%% \begin{lstlisting} +%% from scipy.integrate import quad +%% def f(x): +%% res = x*cos(x) +%% quad(f, 0, 1) +%% \end{lstlisting} +%% What changes will you make to the above code to make it work? +%% \end{frame} + +%% \begin{frame} +%% \frametitle{\incqno } +%% What two commands will you use to create and evaluate a spline given +%% some data? +%% \end{frame} + +%% \begin{frame}[fragile] +%% \frametitle{\incqno } +%% What would be the result? +%% \begin{lstlisting} +%% In []: x +%% array([[0, 1, 2], +%% [3, 4, 5], +%% [6, 7, 8]]) +%% In []: x[::-1,:] +%% \end{lstlisting} +%% Hint: +%% \begin{lstlisting} +%% In []: x = arange(9) +%% In []: x[::-1] +%% array([8, 7, 6, 5, 4, 3, 2, 1, 0]) +%% \end{lstlisting} +%% \end{frame} + +%% \begin{frame}[fragile] +%% \frametitle{\incqno } +%% What would be the result? +%% \begin{lstlisting} +%% In []: y = arange(3) +%% In []: x = linspace(0,3,3) +%% In []: x-y +%% \end{lstlisting} +%% \end{frame} + +%% \begin{frame}[fragile] +%% \frametitle{\incqno } +%% \begin{lstlisting} +%% In []: x +%% array([[ 0, 1, 2, 3], +%% [ 4, 5, 6, 7], +%% [ 8, 9, 10, 11], +%% [12, 13, 14, 15]]) +%% \end{lstlisting} +%% How will you get the following \lstinline+x+? +%% \begin{lstlisting} +%% array([[ 5, 7], +%% [ 9, 11]]) +%% \end{lstlisting} +%% \end{frame} + +%% \begin{frame}[fragile] +%% \frametitle{\incqno } +%% What would be the output? +%% \begin{lstlisting} +%% In []: y = arange(4) +%% In []: x = array(([1,2,3,2],[1,3,6,0])) +%% In []: x + y +%% \end{lstlisting} +%% \end{frame} + +%% \begin{frame}[fragile] +%% \frametitle{\incqno } +%% \begin{lstlisting} +%% In []: line = plot(x, sin(x)) +%% \end{lstlisting} +%% Use the \lstinline+set_linewidth+ method to set width of \lstinline+line+ to 2. +%% \end{frame} + +%% \begin{frame}[fragile] +%% \frametitle{\incqno } +%% What would be the output? +%% \begin{lstlisting} +%% In []: x = arange(9) +%% In []: y = arange(9.) +%% In []: x == y +%% \end{lstlisting} +%% \end{frame} + |