diff options
Diffstat (limited to 'day1')
| -rw-r--r-- | day1/session1.tex | 8 | ||||
| -rw-r--r-- | day1/session2.tex | 25 | ||||
| -rw-r--r-- | day1/session4.tex | 47 | ||||
| -rwxr-xr-x | day1/session6.tex | 110 |
4 files changed, 73 insertions, 117 deletions
diff --git a/day1/session1.tex b/day1/session1.tex index c4d33e5..125f823 100644 --- a/day1/session1.tex +++ b/day1/session1.tex @@ -488,6 +488,14 @@ Save commands of review problem into file \end{frame} \begin{frame} +\frametitle{Python Scripts\ldots} + This is called a Python Script. + \begin{itemize} + \item run the script in IPython using \typ{\%run -i sine_plot.py}\\ + \end{itemize} +\end{frame} + +\begin{frame} \frametitle{What did we learn?} \begin{itemize} \item Creating simple plots. diff --git a/day1/session2.tex b/day1/session2.tex index 361b9b3..6df6649 100644 --- a/day1/session2.tex +++ b/day1/session2.tex @@ -123,28 +123,7 @@ % You might wish to add the option [pausesections] \end{frame} -%\begin{frame} -%\frametitle{Python Scripts\ldots} -% \begin{itemize} -% \item Open a new file in an \alert{editor} -% \item Copy and paste from the output of \typ{\%hist -n} -% \item Save the file as \typ{sine_plot.py} -% \end{itemize} -% \begin{itemize} -% \item run the file in IPython using \typ{\%run -i sine_plot.py}\\ -% \end{itemize} -%\end{frame} - -\section{Scripts} - -\begin{frame}[fragile] -\frametitle{Python Scripts} - \begin{itemize} - \item four\_plot.py is called a Python Script - \item run the file in IPython using \typ{\%run -i four_plot.py} - \end{itemize} -\end{frame} - +\section{Plotting Points} \begin{frame}[fragile] \frametitle{Why would I plot f(x)?} How often do we plot analytical functions?\\We plot experimental data more. @@ -483,8 +462,6 @@ plot(l, tsq, '.') \begin{frame}[fragile] \frametitle{What did we learn?} \begin{itemize} - \item Python scripts - \item \kwrd{\%run -i} \item Plotting points \item Plot attributes \item Lists diff --git a/day1/session4.tex b/day1/session4.tex index fd8a088..79da193 100644 --- a/day1/session4.tex +++ b/day1/session4.tex @@ -148,6 +148,29 @@ array([[ 1, 1, 2, -1], \end{frame} \begin{frame}[fragile] +\frametitle{Initializing some special matrices} +\begin{small} + \begin{lstlisting} +In []: ones((3,5)) +Out[]: +array([[ 1., 1., 1., 1., 1.], + [ 1., 1., 1., 1., 1.], + [ 1., 1., 1., 1., 1.]]) + +In []: ones_like([1, 2, 3, 4, 5]) +Out[]: array([1, 1, 1, 1, 1]) + +In []: identity(2) +Out[]: +array([[ 1., 0.], + [ 0., 1.]]) + \end{lstlisting} +Also available \alert{\typ{zeros, zeros_like, empty, empty_like}} +\end{small} +\end{frame} + + +\begin{frame}[fragile] \frametitle{Accessing elements} \begin{lstlisting} In []: C = array([[1,1,2], @@ -426,7 +449,7 @@ Out[]: array([-1., 8., -1.]) \section{Least Squares Fit} \begin{frame}[fragile] -\frametitle{$L$ vs. $T^2$} +\frametitle{$L$ vs. $T^2$ - Scatter} \vspace{-0.15in} \begin{figure} \includegraphics[width=4in]{data/L-Tsq-points} @@ -434,7 +457,7 @@ Out[]: array([-1., 8., -1.]) \end{frame} \begin{frame}[fragile] -\frametitle{$L$ vs. $T^2$} +\frametitle{$L$ vs. $T^2$ - Line} \vspace{-0.15in} \begin{figure} \includegraphics[width=4in]{data/L-Tsq-Line} @@ -442,7 +465,8 @@ Out[]: array([-1., 8., -1.]) \end{frame} \begin{frame}[fragile] -\frametitle{Least Squares Fit} +\frametitle{$L$ vs. $T^2$ } +\frametitle{$L$ vs. $T^2$ - Least Square Fit} \vspace{-0.15in} \begin{figure} \includegraphics[width=4in]{data/least-sq-fit} @@ -484,22 +508,6 @@ Out[]: array([-1., 8., -1.]) In []: A = array([L, ones_like(L)]) In []: A = A.T \end{lstlisting} -\begin{small} -\begin{block}{} - \begin{lstlisting} -In []: ones((3,5)) -Out[]: -array([[ 1., 1., 1., 1., 1.], - [ 1., 1., 1., 1., 1.], - [ 1., 1., 1., 1., 1.]]) - -In []: ones_like([1, 2, 3, 4, 5]) -Out[]: array([1, 1, 1, 1, 1]) - \end{lstlisting} -Also available \alert{\typ{zeros, zeros_like, empty, empty_like}} -\end{block} -\end{small} - %% \begin{itemize} %% \item A is also called a Van der Monde matrix %% \item It can also be generated using \typ{vander} @@ -549,6 +557,7 @@ In []: plot(L, Tline) \begin{itemize} \item Matrices \begin{itemize} + \item Initializing \item Accessing elements \item Slicing and Striding \item Transpose diff --git a/day1/session6.tex b/day1/session6.tex index a647eb1..acfc687 100755 --- a/day1/session6.tex +++ b/day1/session6.tex @@ -188,74 +188,7 @@ Out[]: True \subsection{Exercises} \begin{frame}[fragile] -\frametitle{Problem 1} -Given the matrix:\\ -\begin{center} -$\begin{bmatrix} --2 & 2 & 3\\ - 2 & 1 & 6\\ --1 &-2 & 0\\ -\end{bmatrix}$ -\end{center} -Find: -\begin{itemize} - \item[i] Transpose - \item[ii]Inverse - \item[iii]Determinant - \item[iv] Eigenvalues and Eigen vectors - \item[v] Singular Value decomposition -\end{itemize} -\end{frame} - -\begin{frame}[fragile] -\frametitle{Problem 2} -Given -\begin{center} -A = -$\begin{bmatrix} --3 & 1 & 5 \\ -1 & 0 & -2 \\ -5 & -2 & 4 \\ -\end{bmatrix}$ -, B = -$\begin{bmatrix} -0 & 9 & -12 \\ --9 & 0 & 20 \\ -12 & -20 & 0 \\ -\end{bmatrix}$ -\end{center} -Find: -\begin{itemize} - \item[i] Sum of A and B - \item[ii]Elementwise Product of A and B - \item[iii] Matrix product of A and B -\end{itemize} -\end{frame} - -\begin{frame}[fragile] -\frametitle{Solution} -Sum: -$\begin{bmatrix} --3 & 10 & 7 \\ --8 & 0 & 18 \\ -17 & -22 & 4 \\ -\end{bmatrix}$ -,\\ Elementwise Product: -$\begin{bmatrix} -0 & 9 & -60 \\ --9 & 0 & -40 \\ -60 & 40 & 0 \\ -\end{bmatrix}$ -,\\ Matrix product: -$\begin{bmatrix} -51 & -127 & 56 \\ --24 & 49 & -12 \\ -66 & -35 & -100 \\ -\end{bmatrix}$ -\end{frame} - -\begin{frame}[fragile] -\frametitle{Problem 3} +\frametitle{Problem} Solve the set of equations: \begin{align*} x + y + 2z -w & = 3\\ @@ -374,8 +307,38 @@ Out[]: -0.66623943249251527 %% \end{frame} \section{ODEs} + \begin{frame}[fragile] -\frametitle{ODE Integration} +\frametitle{Solving ODEs using SciPy} +\begin{itemize} +\item Let's consider the spread of an epidemic in a population +\item $\frac{dy}{dt} = ky(L-y)$ gives the spread of the disease +\item L is the total population. +\item Use L = 25000, k = 0.00003, y(0) = 250 +\item Define a function as below +\end{itemize} +\begin{lstlisting} +In []: def epid(y, t): + .... k, L = 0.00003, 25000 + .... return k*y*(L-y) + .... +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Solving ODEs using SciPy \ldots} +\begin{lstlisting} +In []: t = arange(0, 12, 0.2) + +In []: y = odeint(epid, 250, t) + +In []: plot(t, y) +\end{lstlisting} +%Insert Plot +\end{frame} + +\begin{frame}[fragile] +\frametitle{ODEs - Simple Pendulum} We shall use the simple ODE of a simple pendulum. \begin{equation*} \ddot{\theta} = -\frac{g}{L}sin(\theta) @@ -392,10 +355,9 @@ We shall use the simple ODE of a simple pendulum. \end{frame} \begin{frame}[fragile] -\frametitle{Solving ODEs using SciPy} +\frametitle{ODEs - Simple Pendulum \ldots} \begin{itemize} -\item We use the \typ{odeint} function from scipy to do the integration -\item Define a function as below +\item Use \typ{odeint} to do the integration \end{itemize} \begin{lstlisting} In []: def pend_int(initial, t): @@ -408,7 +370,7 @@ In []: def pend_int(initial, t): \end{frame} \begin{frame}[fragile] -\frametitle{Solving ODEs using SciPy \ldots} +\frametitle{ODEs - Simple Pendulum \ldots} \begin{itemize} \item \typ{t} is the time variable \\ \item \typ{initial} has the initial values @@ -420,7 +382,7 @@ In []: initial = [10*2*pi/360, 0] \end{frame} \begin{frame}[fragile] -\frametitle{Solving ODEs using SciPy \ldots} +\frametitle{ODEs - Simple Pendulum \ldots} %%\begin{small} \typ{In []: from scipy.integrate import odeint} %%\end{small} |