# HG changeset patch # User Puneeth Chaganti # Date 1257307417 -19800 # Node ID ac31e2f3754e77a10d8619bf5cd50ddbfbdec0eb # Parent c3a1de5b8216f83d600179d5bd886a7e221ffb7b Changes to session1, 5 and 6 at Goa. diff -r c3a1de5b8216 -r ac31e2f3754e day1/session1.tex --- a/day1/session1.tex Sat Oct 31 01:23:23 2009 +0530 +++ b/day1/session1.tex Wed Nov 04 09:33:37 2009 +0530 @@ -181,6 +181,11 @@ \item \typ{points.txt} \item \typ{pos.txt} \end{itemize} + \item Python scripts: + \begin{itemize} + \item \typ{sslc_allreg.py} + \item \typ{sslc_science.py} + \end{itemize} \end{enumerate} \end{frame} diff -r c3a1de5b8216 -r ac31e2f3754e day1/session5.tex --- a/day1/session5.tex Sat Oct 31 01:23:23 2009 +0530 +++ b/day1/session5.tex Wed Nov 04 09:33:37 2009 +0530 @@ -124,8 +124,25 @@ %% % \pausesections %% \end{frame} +\section{\typ{loadtxt}} -\section{\typ{loadtxt}} +\begin{frame}[fragile] + \frametitle{Array slicing} + \begin{lstlisting} +In []: A = array([[ 1, 1, 2, -1], + [ 2, 5, -1, -9], + [ 2, 1, -1, 3], + [ 1, -3, 2, 7]]) + +In []: A[:,0] +Out[]: array([ 1, 2, 2, 1]) + +In []: A[1:3,1:3] +Out[]: +array([[ 5, -1], + [ 1, -1]]) +\end{lstlisting} +\end{frame} \begin{frame}[fragile] \frametitle{\typ{loadtxt}} @@ -134,8 +151,9 @@ \item Each row must have same number of values. \end{itemize} \begin{lstlisting} -In []: L, T = loadtxt('pendulum.txt', - unpack = True) +In []: data = loadtxt('pendulum.txt') +In []: x = data[:, 0] +In []: y = data[:, 1] \end{lstlisting} \end{frame} @@ -145,14 +163,13 @@ \section{Interpolation} \begin{frame}[fragile] -\frametitle{Interpolation} +\frametitle{Loading data (revisited)} \begin{itemize} \item Given data file \typ{points.txt}. \item It contains x,y position of particle. \item Plot the given points. %% \item Interpolate the missing region. \end{itemize} -\emphbar{Loading data (revisited)} \begin{lstlisting} In []: x, y = loadtxt('points.txt', unpack = True) @@ -160,6 +177,12 @@ \end{lstlisting} \end{frame} +\begin{frame} + \frametitle{Plot} + \begin{center} + \includegraphics[height=2in, interpolate=true]{data/missing_points} + \end{center} +\end{frame} %% \begin{frame}[fragile] %% \frametitle{Interpolation \ldots} %% \begin{small} @@ -218,7 +241,7 @@ \begin{frame}[fragile] \frametitle{\typ{splev}} -To Evaluate a B-spline and it's derivatives +To Evaluate a spline and it's derivatives \begin{lstlisting} In []: Xnew = arange(0.01,3,0.02) In []: Ynew = splev(Xnew, tck) @@ -241,6 +264,13 @@ %% \end{itemize} %% \end{frame} +\begin{frame} + \frametitle{Plot} + \begin{center} + \includegraphics[height=2in, interpolate=true]{data/interpolate} + \end{center} +\end{frame} + \section{Differentiation} \begin{frame}[fragile] @@ -252,8 +282,8 @@ \end{itemize} \begin{center} \begin{tabular}{l l} -$f(x+h)=f(x)+h.f^{'}(x)$ &Forward \\ -$f(x-h)=f(x)-h.f^{'}(x)$ &Backward +$f(x+h)=f(x)+hf^{'}(x)$ &Forward \\ +$f(x-h)=f(x)-hf^{'}(x)$ &Backward \end{tabular} \end{center} \end{frame} @@ -272,10 +302,14 @@ \frametitle{Forward Difference \ldots} \begin{lstlisting} In []: fD = (y[1:] - y[:-1]) / deltax -In []: plot(x, y, x[:-1], fD) +In []: print len(fD) +Out[]: 99 +In []: plot(x, y) +In []: plot(x[:-1], fD) \end{lstlisting} +\vspace{-.2in} \begin{center} - \includegraphics[height=2in, interpolate=true]{data/fwdDiff} + \includegraphics[height=1.8in, interpolate=true]{data/fwdDiff} \end{center} \end{frame} @@ -305,17 +339,13 @@ \frametitle{Example \ldots} \begin{itemize} \item Read the file -\item Obtain an array of x, y +\item Obtain an array of X, Y \item Obtain velocity and acceleration \item use \typ{deltaT = 0.05} \end{itemize} \begin{lstlisting} -In []: X = [] -In []: Y = [] -In []: for line in open('location.txt'): - .... points = line.split() - .... X.append(float(points[0])) - .... Y.append(float(points[1])) +In []: data = loadtxt('pos.txt') +In []: X,Y = data[:,0], data[:,1] In []: S = array([X, Y]) \end{lstlisting} \end{frame} @@ -323,9 +353,6 @@ \begin{frame}[fragile] \frametitle{Example \ldots} -\begin{itemize} -\item use \typ{deltaT = 0.05} -\end{itemize} \begin{lstlisting} In []: deltaT = 0.05 @@ -333,25 +360,36 @@ In []: a = (v[:,1:]-v[:,:-1])/deltaT \end{lstlisting} -Try Plotting the position, velocity \& acceleration. +\end{frame} + +\begin{frame}[fragile] +\frametitle{Example \ldots} +Plotting Y, $v_y$, $a_y$ +\begin{lstlisting} +In []: plot(Y) +In []: plot(v[1,:]) +In []: plot(a[1,:]) +\end{lstlisting} +\begin{center} + \includegraphics[height=1.8in, interpolate=true]{data/pos_vel_accel} +\end{center} \end{frame} \section{Quadrature} \begin{frame}[fragile] \frametitle{Quadrature} -\begin{itemize} -\item We wish to find area under a curve -\item Area under $(sin(x) + x^2)$ in $(0,1)$ -\item scipy has functions to do that -\end{itemize} -\begin{small} - \typ{In []: from scipy.integrate import quad} -\end{small} + +\emphbar{$\int_0^1(sin(x) + x^2)$} + +\typ{In []: from scipy.integrate import quad} + \begin{itemize} \item Inputs - function to integrate, limits \end{itemize} \begin{lstlisting} +In []: quad(sin(x)+x**2, 0, 1) +NameError: name 'x' is not defined In []: x = 0 In []: quad(sin(x)+x**2, 0, 1) \end{lstlisting} @@ -401,8 +439,7 @@ \end{lstlisting} Returns the integral and an estimate of the absolute error in the result. \begin{itemize} -\item Look at \typ{dblquad} for Double integrals -\item Use \typ{tplquad} for Triple integrals +\item \typ{dblquad}, \typ{tplquad} are available \end{itemize} \end{frame} diff -r c3a1de5b8216 -r ac31e2f3754e day1/session6.tex --- a/day1/session6.tex Sat Oct 31 01:23:23 2009 +0530 +++ b/day1/session6.tex Wed Nov 04 09:33:37 2009 +0530 @@ -138,7 +138,7 @@ \dot{\theta} &= \omega \\ \dot{\omega} &= -\frac{g}{L}sin(\theta) \\ \text{At}\ t &= 0 : \nonumber \\ - \theta = \theta_0\quad & \&\quad \omega = 0 \nonumber + \theta = \theta_0(10^o)\quad & \&\quad \omega = 0\ (Initial\ values)\nonumber \end{align} \end{frame} @@ -149,9 +149,9 @@ \item Define a function as below \end{itemize} \begin{lstlisting} -In []: def pend_int(unknown, t, p): - .... theta, omega = unknown - .... g, L = p +In []: def pend_int(initial, t): + .... theta, omega = initial + .... g, L = -9.81, 0.2 .... f=[omega, -(g/L)*sin(theta)] .... return f .... @@ -162,25 +162,22 @@ \frametitle{Solving ODEs using SciPy \ldots} \begin{itemize} \item \typ{t} is the time variable \\ -\item \typ{p} has the constants \\ \item \typ{initial} has the initial values \end{itemize} \begin{lstlisting} In []: t = linspace(0, 10, 101) -In []: p=(-9.81, 0.2) In []: initial = [10*2*pi/360, 0] -\end{lstlisting} +\end{lstlisting} \end{frame} \begin{frame}[fragile] \frametitle{Solving ODEs using SciPy \ldots} -\begin{small} - \typ{In []: from scipy.integrate import odeint} -\end{small} +%%\begin{small} +\typ{In []: from scipy.integrate import odeint} +%%\end{small} \begin{lstlisting} In []: pend_sol = odeint(pend_int, - initial,t, - args=(p,)) + initial,t) \end{lstlisting} \end{frame} @@ -308,14 +305,13 @@ \begin{frame}[fragile] \frametitle{Initial Estimates \ldots} \begin{lstlisting} - In []: def our_f(x): - ....: return cos(x)-x**2 - ....: - In []: x = linspace(-pi/2, pi/2, 11) +In []: def our_f(x): + ....: return cos(x) - x*x + ....: +In []: x = linspace(-pi/2, pi/2, 11) +In []: y = our_f(x) \end{lstlisting} -\begin{itemize} -\item Get the intervals of x, where sign changes occur -\end{itemize} +Get the intervals of x, where sign changes occur \end{frame} \begin{frame}[fragile] @@ -335,7 +331,6 @@ \frametitle{Scipy Methods - \typ{roots}} \begin{itemize} \item Calculates the roots of polynomials -\item Array of coefficients is the only parameter \end{itemize} \begin{lstlisting} In []: coeffs = [1, 6, 13]