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Diffstat (limited to 'day2/session2.tex')
| -rw-r--r-- | day2/session2.tex | 100 |
1 files changed, 59 insertions, 41 deletions
diff --git a/day2/session2.tex b/day2/session2.tex index 07514f7..0f471f5 100644 --- a/day2/session2.tex +++ b/day2/session2.tex @@ -116,17 +116,20 @@ \begin{frame} \maketitle \end{frame} + +\section{Advanced Numpy} \begin{frame}[fragile] \frametitle{Broadcasting} Try it! \begin{lstlisting} >>> a = np.arange(4) >>> b = np.arange(5) - >>> a+b + >>> a+b #Does this work? >>> a+3 >>> c=np.array([3]) - >>> a+c - >>> b+c + >>> a+c #Works! + >>> b+c #But how? + >>> a.shape, b.shape, c.shape \end{lstlisting} \begin{itemize} \item Enter Broadcasting! @@ -147,7 +150,7 @@ \includegraphics[height=0.7in, interpolate=true]{data/broadcast_scalar} \end{columns} \begin{itemize} - \item Allows functions to take inputs not of the same shape + \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 @@ -174,8 +177,9 @@ \begin{frame}[fragile] \frametitle{Copies \& Views} Try it! + \vspace{-0.1in} \begin{lstlisting} - >>> a = np.array([[1,2,3],[4,5,6]]) + >>> a = np.arange(1,9); a.shape=3,3 >>> b = a >>> b is a >>> b[0,0]=0; print a @@ -192,9 +196,8 @@ \begin{frame}[fragile] \frametitle{Copies \& Views} Try it! + \vspace{-0.1in} \begin{lstlisting} - >>> a = np.arange(1,9) - >>> a.shape=3,3 >>> b = a[0,1:3] >>> c = a[0::2,0::2] >>> a.flags.owndata @@ -226,6 +229,8 @@ \inctime{15} \end{frame} +\section{SciPy} +\subsection{Introduction} \begin{frame} {Intro to SciPy} \begin{itemize} @@ -266,6 +271,7 @@ \end{lstlisting} \end{frame} +\subsection{Linear Algebra} \begin{frame}[fragile] \frametitle{Linear Algebra} Try it! @@ -311,6 +317,7 @@ \inctime{15} \end{frame} +\subsection{Integration} \begin{frame}[fragile] \frametitle{Integrate} \begin{itemize} @@ -318,7 +325,7 @@ \item Integrating Functions given fixed samples \item Numerical integrators of ODE systems \end{itemize} - Calculate $\int^1_0(sin(x) + x^2)dx$ + Calculate the area under $(sin(x) + x^2)$ in the range $(0,1)$ \begin{lstlisting} >>> def f(x): return np.sin(x)+x**2 @@ -331,48 +338,50 @@ Numerically solve ODEs\\ \begin{align*} \frac{dx}{dt}&=-e^{-t}x^2\\ - x(0)&=2 + x&=2 \quad at \ t=0 \end{align*} \begin{lstlisting} - def dx_dt(x,t): +>>> def dx_dt(x,t): return -np.exp(-t)*x**2 - - x=integrate.odeint(dx_dt, 2, t) - plt.plot(x,t) +>>> t=np.linspace(0,2,100) +>>> 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) - >>> y = np.sin(x) - >>> fl = interpolate.interp1d(x,y,kind='linear') - >>> fc = interpolate.interp1d(x,y,kind='cubic') - >>> fl(np.pi/3) - >>> fc(np.pi/3) +>>> from scipy import interpolate +>>> interpolate.interp1d? +>>> x = np.arange(0,2*np.pi,np.pi/4) +>>> y = np.sin(x) +>>> fl = interpolate.interp1d( + x,y,kind='linear') +>>> fc = interpolate.interp1d( + x,y,kind='cubic') +>>> fl(np.pi/3) +>>> fc(np.pi/3) \end{lstlisting} \end{frame} \begin{frame}[fragile] \frametitle{Interpolation - Splines} - Cubic Spline of $sin(x)$ + Plot the Cubic Spline of $sin(x)$ \begin{lstlisting} - x = np.arange(0,2*np.pi,np.pi/4) - y = np.sin(x) - 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) - plt.show() +>>> 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) +>>> plt.show() \end{lstlisting} \inctime{10} \end{frame} +\subsection{Signal Processing} \begin{frame}[fragile] \frametitle{Signal \& Image Processing} \begin{itemize} @@ -393,16 +402,16 @@ \frametitle{Signal \& Image Processing} Applying a simple median filter \begin{lstlisting} - from scipy import signal, ndimage - from scipy import lena - A=lena().astype('float32') - B=signal.medfilt2d(A) - imshow(B) +>>> from scipy import signal, ndimage +>>> from scipy import lena +>>> 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) - imshow(b) +>>> b=ndimage.zoom(A,0.5) +>>> imshow(b) \end{lstlisting} \inctime{5} \end{frame} @@ -413,10 +422,21 @@ \begin{equation*} \frac{d^2x}{dt^2}+\mu(x^2-1)\frac{dx}{dt}+x= 0 \end{equation*} -\inctime{25} + Make a plot of $\frac{dx}{dt}$ vs. $x$. +\inctime{30} +\end{frame} +\begin{frame}{Summary} + \begin{itemize} + \item Advanced NumPy + \item SciPy + \begin{itemize} + \item Linear Algebra + \item Integration + \item Interpolation + \item Signal and Image processing + \end{itemize} + \end{itemize} \end{frame} - - \end{document} - Numpy arrays (30 mins) @@ -424,5 +444,3 @@ - random number generation. - Image manipulation: jigsaw puzzle. - Monte-carlo integration. - - |