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+\documentclass{article}
+\usepackage{graphicx}  
+\usepackage[landscape]{geometry}
+\usepackage[pdftex]{color}
+\usepackage{url}
+\usepackage{multicol}
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\newcommand{\ex}{\color{blue}}
+\pagestyle{empty}
+\advance\topmargin-.9in
+\advance\textheight2in
+\advance\textwidth3.0in
+\advance\oddsidemargin-1.45in
+\advance\evensidemargin-1.45in
+\parindent0pt
+\parskip2pt
+
+\newcommand{\hr}{\centerline{\rule{3.5in}{1pt}}}
+\newcommand{\skipin}{\hspace*{12pt}}
+
+\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{Python for Scientific Computing}\\
+\textbf{Quick Reference}\\
+FOSSEE -- Dec 1, 2010\\
+\end{center}
+\vspace{-2ex}
+
+%*********************************************
+ \hr\textbf{Starting up}
+
+To start \lstinline|ipython| with \lstinline|pylab|:\\
+\lstinline|    $ ipython -pylab| %$
+
+To exit: \lstinline|^D| (Ctrl-D)
+
+%*********************************************
+\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:\\
+Use standard placement:\\
+{\ex \lstinline|    legend('sin(x)', loc=center)|}\\
+Or explicitly specify location:\\
+{\ex \lstinline|    legend(['sin(x)'], loc=(.8,.1))|}
+
+Annotate:\\
+{\ex \lstinline|    legend('annotation string', xy=(1.5, 1))|}
+
+Saving figures:\\
+{\ex \lstinline|    savefig('sinusoids.png')|}
+
+Miscellaneous:\\
+{\ex \lstinline|    clf()|} to clear the plot area\\
+{\ex \lstinline|    close()|} to close the figure
+
+%*********************************************
+\textbf{Other plots}
+
+Pie Charts:\\
+{\ex \lstinline|    pie(science.values(), labels=science.keys())|},
+where {\ex \lstinline|science|} is a dictionary.
+
+%*********************************************
+\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 a for loop: (reading line by line)
+\vspace{-8pt}
+\begin{lstlisting}
+for line in open('filename.txt'):
+    # some processing
+\end{lstlisting}
+\vspace{-8pt}
+Using loadtxt: (reading all the data at once)\\
+{\ex \lstinline|X = loadtxt('filename.txt')|} \\
+X is an array with all the data from \lstinline|filename.txt|\\
+{\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{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
+
+%*********************************************
+\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 a Matrix 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{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])|}\\
+
+\end{multicols*}
+
+\end{document}