Workshop materials: comparison day2/session2.tex

equal deleted inserted replaced

-:d0679d2f9339
+:1c1d6aaa2be3
 \begin{itemize}
 \item Integrating Functions given function object
 \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
 >>> integrate.quad(f, 0, 1)
 \end{lstlisting}
 \begin{align*}
 \frac{dx}{dt}&=-e^{-t}x^2\\
 x(0)&=2
 \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)
+>>> x=integrate.odeint(dx_dt, 2, t)
-plt.plot(x,t)
+>>> plt.plot(x,t)
 \end{lstlisting}
 \inctime{10}
 \end{frame}
 \subsection{Interpolation}
 \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)
+>>> x = np.arange(0,2*np.pi,np.pi/4)
-y = np.sin(x)
+>>> y = np.sin(x)
-tck = interpolate.splrep(x,y)
+>>> tck = interpolate.splrep(x,y)
-X = np.arange(0,2*np.pi,np.pi/50)
+>>> X = np.arange(0,2*np.pi,np.pi/50)
-Y = interpolate.splev(X,tck,der=0)
+>>> Y = interpolate.splev(X,tck,der=0)
-plt.plot(x,y,'o',x,y,X,Y)
+>>> plt.plot(x,y,'o',x,y,X,Y)
-plt.show()
+>>> plt.show()
 \end{lstlisting}
 \inctime{10}
 \end{frame}
 \subsection{Signal Processing}
 \begin{frame}[fragile]
 \frametitle{Signal \& Image Processing}
 Applying a simple median filter
 \begin{lstlisting}
-from scipy import signal, ndimage
+>>> from scipy import signal, ndimage
-from scipy import lena
+>>> from scipy import lena
-A=lena().astype('float32')
+>>> A=lena().astype('float32')
-B=signal.medfilt2d(A)
+>>> B=signal.medfilt2d(A)
-imshow(B)
+>>> 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)
+>>> imshow(b)
 \end{lstlisting}
 \inctime{5}
 \end{frame}
 \begin{frame}[fragile]

changeset 72	1c1d6aaa2be3
parent 71	d0679d2f9339
child 76	b24c2560f626