Workshop materials: comparison day2/session2.tex

equal deleted inserted replaced

-:e0610b591526
+:919c93e5aa71
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % Title page
 \title[]{Numerical Computing with Numpy \& Scipy}
-\author[FOSSEE Team] {Asokan Pichai\\Prabhu Ramachandran}
+\author[FOSSEE Team] {FOSSEE}
 \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
 \date[] {11, October 2009}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \end{frame}
 \section{Advanced Numpy}
 \begin{frame}[fragile]
 \frametitle{Broadcasting}
-Try it!
+\begin{lstlisting}
-\begin{lstlisting}
+>>> a = arange(4)
->>> a = np.arange(4)
+>>> b = arange(5)
->>> b = np.arange(5)
 >>> a+b #Does this work?
 >>> a+3
->>> c=np.array([3])
+>>> c = array([3])
 >>> a+c #Works!
 >>> b+c #But how?
 >>> a.shape, b.shape, c.shape
 \end{lstlisting}
 \begin{itemize}
 \frametitle{Broadcasting}
 \begin{columns}
 \column{0.65\textwidth}
 \hspace*{-1.5in}
 \begin{lstlisting}
->>> a = np.arange(4)
+>>> a = arange(4)
 >>> a+3
 array([3, 4, 5, 6])
 \end{lstlisting}
 \column{0.35\textwidth}
 \includegraphics[height=0.7in, interpolate=true]{data/broadcast_scalar}
 \end{columns}
-\begin{itemize}
-\item Allows functions to take inputs that are not of the same shape
-\item 2 rules -
-\begin{enumerate}
-\item 1 is (repeatedly) prepended to shapes of smaller arrays
-\item Size 1 in a dimension changed to Largest size in that dimension
-\end{enumerate}
-\end{itemize}
 \end{frame}
 \begin{frame}[fragile]
 \frametitle{Broadcasting in 3D}
 \begin{lstlisting}
->>> x = np.ones((3, 5))
+>>> x = ones((3, 5, 1))
->>> y = np.ones(8)
+>>> y = ones(8)
->>> (x[..., None] + y).shape
+>>> (x + y).shape
 (3, 5, 8)
 \end{lstlisting}
 \begin{figure}
 \begin{center}
 \includegraphics[height=1.5in, interpolate=true]{data/array_3x5x8}
 \end{figure}
 \end{frame}
 \begin{frame}[fragile]
 \frametitle{Copies \& Views}
-Try it!
 \vspace{-0.1in}
 \begin{lstlisting}
->>> a = np.arange(1,9); a.shape=3,3
+>>> a = arange(1,9); a.shape=3,3
 >>> b = a
 >>> b is a
 >>> b[0,0]=0; print a
 >>> c = a.view()
 >>> c is a
 \end{lstlisting}
 \end{frame}
 \begin{frame}[fragile]
 \frametitle{Copies \& Views}
-Try it!
 \vspace{-0.1in}
 \begin{lstlisting}
 >>> b = a[0,1:3]
 >>> c = a[0::2,0::2]
 >>> a.flags.owndata
 \end{frame}
 \begin{frame}[fragile]
 \frametitle{Copies contd \ldots}
 \begin{lstlisting}
->>> b = a[np.array([0,1,2])]
+>>> a = arange(1, 10, 2)
-array([[1, 2, 3],
+>>> b = a[array([0,2,3])]
-[4, 5, 6],
-[7, 8, 9]])
 >>> b.flags.owndata
->>> abool=np.greater(a,2)
+>>> abool=a>5
 >>> c = a[abool]
 >>> c.flags.owndata
 \end{lstlisting}
 \begin{itemize}
 \item Indexing arrays or Boolean arrays produce copies
 \end{frame}
 \subsection{Linear Algebra}
 \begin{frame}[fragile]
 \frametitle{Linear Algebra}
-Try it!
 \begin{lstlisting}
 >>> import scipy as sp
 >>> from scipy import linalg
->>> A=sp.mat(np.arange(1,10))
+>>> A = sp.array(sp.arange(1,10))
->>> A.shape=3,3
+>>> A.shape = 3,3
 >>> linalg.inv(A)
 >>> linalg.det(A)
 >>> linalg.norm(A)
 >>> linalg.expm(A) #logm
 >>> linalg.sinm(A) #cosm, tanm, ...
 \end{lstlisting}
 \end{frame}
 \begin{frame}[fragile]
 \frametitle{Linear Algebra ...}
-Try it!
+\begin{lstlisting}
-\begin{lstlisting}
+>>> A = sp.array(sp.arange(1,10))
->>> A = sp.mat(np.arange(1,10))
+>>> A.shape = 3,3
->>> A.shape=3,3
 >>> linalg.lu(A)
 >>> linalg.eig(A)
 >>> linalg.eigvals(A)
 \end{lstlisting}
 \end{frame}
 \begin{frame}[fragile]
 \frametitle{Solving Linear Equations}
+\vspace{-0.2in}
 \begin{align*}
 3x + 2y - z  & = 1 \\
 2x - 2y + 4z  & = -2 \\
 -x + \frac{1}{2}y -z & = 0
 \end{align*}
 To Solve this,
 \begin{lstlisting}
->>> A = sp.mat([[3,2,-1],[2,-2,4]
+>>> A = sp.array([[3,2,-1],[2,-2,4]
 ,[-1,1/2,-1]])
->>> B = sp.mat([[1],[-2],[0]])
+>>> b = sp.array([1,-2,0])
->>> linalg.solve(A,B)
+>>> x = linalg.solve(A,b)
+>>> Ax = sp.dot(A,x)
+>>> sp.allclose(Ax, b)
 \end{lstlisting}
 \inctime{15}
 \end{frame}
 \subsection{Integration}
 \item Numerical integrators of ODE systems
 \end{itemize}
 Calculate the area under $(sin(x) + x^2)$ in the range $(0,1)$
 \begin{lstlisting}
 >>> def f(x):
-return np.sin(x)+x**2
+return sin(x)+x**2
 >>> integrate.quad(f, 0, 1)
 \end{lstlisting}
 \end{frame}
 \begin{frame}[fragile]
 \frac{dx}{dt}&=-e^{-t}x^2\\
 x&=2 \quad at \ t=0
 \end{align*}
 \begin{lstlisting}
 >>> def dx_dt(x,t):
-return -np.exp(-t)*x**2
+return -exp(-t)*x**2
->>> t=np.linspace(0,2,100)
+>>> t = linspace(0,2,100)
->>> x=integrate.odeint(dx_dt, 2, t)
+>>> x = integrate.odeint(dx_dt, 2, t)
 >>> plt.plot(x,t)
 \end{lstlisting}
 \inctime{10}
 \end{frame}
 \subsection{Interpolation}
 \begin{frame}[fragile]
 \frametitle{Interpolation}
-Try it!
 \begin{lstlisting}
 >>> from scipy import interpolate
 >>> interpolate.interp1d?
->>> x = np.arange(0,2*np.pi,np.pi/4)
+>>> x = arange(0,2*pi,pi/4)
->>> y = np.sin(x)
+>>> y = sin(x)
 >>> fl = interpolate.interp1d(
 x,y,kind='linear')
 >>> fc = interpolate.interp1d(
 x,y,kind='cubic')
->>> fl(np.pi/3)
+>>> fl(pi/3)
->>> fc(np.pi/3)
+>>> fc(pi/3)
 \end{lstlisting}
 \end{frame}
 \begin{frame}[fragile]
 \frametitle{Interpolation - Splines}
 Plot the Cubic Spline of $sin(x)$
 \begin{lstlisting}
 >>> tck = interpolate.splrep(x,y)
->>> X = np.arange(0,2*np.pi,np.pi/50)
+>>> xs = arange(0,2*pi,pi/50)
->>> Y = interpolate.splev(X,tck,der=0)
+>>> ys = interpolate.splev(X,tck,der=0)
->>> plt.plot(x,y,'o',x,y,X,Y)
+>>> plt.plot(x,y,'o',x,y,xs,ys)
 >>> plt.show()
 \end{lstlisting}
 \inctime{10}
 \end{frame}
 \subsection{Signal Processing}
 \begin{frame}[fragile]
 \frametitle{Signal \& Image Processing}
 \begin{itemize}
 \item Convolution
-\item B-splines
 \item Filtering
 \item Filter design
 \item IIR filter design
 \item Linear Systems
-\item LTI Reresentations
+\item LTI Representations
-\item Waveforms
 \item Window functions
-\item Wavelets
 \end{itemize}
 \end{frame}
 \begin{frame}[fragile]
 \frametitle{Signal \& Image Processing}
 Applying a simple median filter
 \begin{lstlisting}
 >>> from scipy import signal, ndimage
 >>> from scipy import lena
->>> A=lena().astype('float32')
+>>> A = lena().astype('float32')
->>> B=signal.medfilt2d(A)
+>>> B = signal.medfilt2d(A)
 >>> imshow(B)
 \end{lstlisting}
 Zooming an array - uses spline interpolation
 \begin{lstlisting}
->>> b=ndimage.zoom(A,0.5)
+>>> b = ndimage.zoom(A,0.5)
 >>> imshow(b)
+>>> b = ndimage.zoom(A,2)
 \end{lstlisting}
 \inctime{5}
 \end{frame}
 \begin{frame}[fragile]

changeset 101	919c93e5aa71
parent 97	555237dbce44