--- a/day2/session2.tex Mon Oct 12 16:26:02 2009 +0530
+++ b/day2/session2.tex Mon Oct 12 16:29:11 2009 +0530
@@ -75,7 +75,7 @@
% 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}
@@ -120,13 +120,12 @@
\section{Advanced Numpy}
\begin{frame}[fragile]
\frametitle{Broadcasting}
- Try it!
\begin{lstlisting}
- >>> a = np.arange(4)
- >>> b = np.arange(5)
+ >>> a = arange(4)
+ >>> b = 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
@@ -142,29 +141,21 @@
\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))
- >>> y = np.ones(8)
- >>> (x[..., None] + y).shape
+ >>> x = ones((3, 5, 1))
+ >>> y = ones(8)
+ >>> (x + y).shape
(3, 5, 8)
\end{lstlisting}
\begin{figure}
@@ -176,10 +167,9 @@
\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
@@ -195,7 +185,6 @@
\begin{frame}[fragile]
\frametitle{Copies \& Views}
- Try it!
\vspace{-0.1in}
\begin{lstlisting}
>>> b = a[0,1:3]
@@ -214,12 +203,10 @@
\begin{frame}[fragile]
\frametitle{Copies contd \ldots}
\begin{lstlisting}
- >>> b = a[np.array([0,1,2])]
- array([[1, 2, 3],
- [4, 5, 6],
- [7, 8, 9]])
+ >>> a = arange(1, 10, 2)
+ >>> b = a[array([0,2,3])]
>>> b.flags.owndata
- >>> abool=np.greater(a,2)
+ >>> abool=a>5
>>> c = a[abool]
>>> c.flags.owndata
\end{lstlisting}
@@ -274,12 +261,11 @@
\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.shape=3,3
+ >>> A = sp.array(sp.arange(1,10))
+ >>> A.shape = 3,3
>>> linalg.inv(A)
>>> linalg.det(A)
>>> linalg.norm(A)
@@ -290,10 +276,9 @@
\begin{frame}[fragile]
\frametitle{Linear Algebra ...}
- Try it!
\begin{lstlisting}
- >>> A = sp.mat(np.arange(1,10))
- >>> A.shape=3,3
+ >>> A = sp.array(sp.arange(1,10))
+ >>> A.shape = 3,3
>>> linalg.lu(A)
>>> linalg.eig(A)
>>> linalg.eigvals(A)
@@ -302,6 +287,7 @@
\begin{frame}[fragile]
\frametitle{Solving Linear Equations}
+ \vspace{-0.2in}
\begin{align*}
3x + 2y - z & = 1 \\
2x - 2y + 4z & = -2 \\
@@ -309,10 +295,12 @@
\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]])
- >>> linalg.solve(A,B)
+ >>> b = sp.array([1,-2,0])
+ >>> x = linalg.solve(A,b)
+ >>> Ax = sp.dot(A,x)
+ >>> sp.allclose(Ax, b)
\end{lstlisting}
\inctime{15}
\end{frame}
@@ -328,7 +316,7 @@
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}
@@ -342,9 +330,9 @@
\end{align*}
\begin{lstlisting}
>>> def dx_dt(x,t):
- return -np.exp(-t)*x**2
->>> t=np.linspace(0,2,100)
->>> x=integrate.odeint(dx_dt, 2, t)
+ return -exp(-t)*x**2
+>>> t = linspace(0,2,100)
+>>> x = integrate.odeint(dx_dt, 2, t)
>>> plt.plot(x,t)
\end{lstlisting}
\inctime{10}
@@ -353,18 +341,17 @@
\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)
->>> y = np.sin(x)
+>>> x = arange(0,2*pi,pi/4)
+>>> y = sin(x)
>>> fl = interpolate.interp1d(
x,y,kind='linear')
>>> fc = interpolate.interp1d(
x,y,kind='cubic')
->>> fl(np.pi/3)
->>> fc(np.pi/3)
+>>> fl(pi/3)
+>>> fc(pi/3)
\end{lstlisting}
\end{frame}
@@ -373,9 +360,9 @@
Plot the Cubic Spline of $sin(x)$
\begin{lstlisting}
>>> tck = interpolate.splrep(x,y)
->>> X = np.arange(0,2*np.pi,np.pi/50)
->>> Y = interpolate.splev(X,tck,der=0)
->>> plt.plot(x,y,'o',x,y,X,Y)
+>>> xs = arange(0,2*pi,pi/50)
+>>> ys = interpolate.splev(X,tck,der=0)
+>>> plt.plot(x,y,'o',x,y,xs,ys)
>>> plt.show()
\end{lstlisting}
\inctime{10}
@@ -386,15 +373,12 @@
\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 Waveforms
+ \item LTI Representations
\item Window functions
- \item Wavelets
\end{itemize}
\end{frame}
@@ -404,14 +388,15 @@
\begin{lstlisting}
>>> from scipy import signal, ndimage
>>> from scipy import lena
->>> A=lena().astype('float32')
->>> B=signal.medfilt2d(A)
+>>> A = lena().astype('float32')
+>>> 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}