diff options
Diffstat (limited to 'day1')
| -rw-r--r-- | day1/session3.tex | 31 | ||||
| -rw-r--r-- | day1/session4.tex | 124 |
2 files changed, 101 insertions, 54 deletions
diff --git a/day1/session3.tex b/day1/session3.tex index ae0eea2..69f28d5 100644 --- a/day1/session3.tex +++ b/day1/session3.tex @@ -126,6 +126,7 @@ %% % You might wish to add the option [pausesections] %% \end{frame} +\section{Statistics} \begin{frame} \frametitle{More on data processing} \begin{block}{} @@ -178,8 +179,10 @@ \item Pass/Fail (P/F) \item Withdrawn (W) \end{itemize} + \inctime{5} \end{frame} +\subsection{Data processing} \begin{frame}[fragile] \frametitle{File reading and parsing \ldots} \begin{lstlisting} @@ -188,22 +191,23 @@ for record in open('sslc1.txt'): \end{lstlisting} \end{frame} +\subsection{Dictionary} \begin{frame}[fragile] \frametitle{Dictionary: Introduction} \begin{itemize} \item lists index: 0 \ldots n \item dictionaries index using strings \end{itemize} -\begin{block}{Example} + \begin{block}{Example} d = \{ ``Hitchhiker's guide'' : 42, ``Terminator'' : ``I'll be back''\}\\ d[``Terminator''] => ``I'll be back'' -\end{block} + \end{block} \end{frame} \begin{frame}[fragile] \frametitle{Dictionary: Introduction} -\begin{lstlisting} + \begin{lstlisting} In [1]: d = {"Hitchhiker's guide" : 42, "Terminator" : "I'll be back"} @@ -215,24 +219,24 @@ Out[3]: True In [4]: "Guido" in d Out[4]: False -\end{lstlisting} + \end{lstlisting} \end{frame} \begin{frame}[fragile] \frametitle{Dictionary: Introduction} -\begin{lstlisting} + \begin{lstlisting} In [5]: d.keys() Out[5]: ['Terminator', "Hitchhiker's guide"] In [6]: d.values() Out[6]: ["I'll be back", 42] -\end{lstlisting} + \end{lstlisting} \end{frame} \begin{frame}[fragile] \frametitle{enumerate: Iterating through list indices} -\begin{lstlisting} + \begin{lstlisting} In [1]: names = ["Guido","Alex", "Tim"] In [2]: for i, name in enumerate(names): @@ -241,15 +245,16 @@ In [2]: for i, name in enumerate(names): 0 Guido 1 Alex 2 Tim -\end{lstlisting} + \end{lstlisting} + \inctime{5} \end{frame} \begin{frame}[fragile] \frametitle{Dictionary: Building parsed data} - Let our dictionary be: - \begin{lstlisting} + Let our dictionary be: + \begin{lstlisting} science = {} # is an empty dictionary - \end{lstlisting} + \end{lstlisting} \end{frame} \begin{frame}[fragile] @@ -291,6 +296,7 @@ if score > 90: \end{lstlisting} \end{frame} +\subsection{Visualizing the data} \begin{frame}[fragile] \frametitle{Pie charts} \small @@ -308,6 +314,7 @@ savefig('/tmp/science.png') \includegraphics[height=2in, interpolate=true]{data/science} \column{0.8\textwidth} \end{columns} + \inctime{5} \end{frame} \begin{frame}[fragile] @@ -381,6 +388,7 @@ savefig('/tmp/all_regions.png') \includegraphics[height=3in, interpolate=true]{data/all_regions} \end{frame} +\subsection{Obtaining stastics} \begin{frame}[fragile] \frametitle{Obtaining statistics} \begin{lstlisting} @@ -395,6 +403,7 @@ print "Mode: ", stats.mode(math_scores) print "Standard Deviation: ", std(math_scores) \end{lstlisting} + \inctime{15} \end{frame} \begin{frame}[fragile] diff --git a/day1/session4.tex b/day1/session4.tex index f6351a6..1a38a2d 100644 --- a/day1/session4.tex +++ b/day1/session4.tex @@ -136,14 +136,16 @@ let us now look at matrices in a little more detail. \begin{frame}[fragile] \frametitle{Matrices: Initializing} \begin{lstlisting} -In []: A = ([[5, 2, 4], - [-3, 6, 2], - [3, -3, 1]]) - +In []: A = matrix([[ 1, 1, 2, -1], + [ 2, 5, -1, -9], + [ 2, 1, -1, 3], + [ 1, -3, 2, 7]]) In []: A -Out[]: [[5, 2, 4], - [-3, 6, 2], - [3, -3, 1]] +Out[]: +matrix([[ 1, 1, 2, -1], + [ 2, 5, -1, -9], + [ 2, 1, -1, 3], + [ 1, -3, 2, 7]]) \end{lstlisting} \end{frame} @@ -153,10 +155,11 @@ Out[]: [[5, 2, 4], \frametitle{Transpose of a Matrix} \begin{lstlisting} In []: linalg.transpose(A) -Out[]: -matrix([[ 5, -3, 3], - [ 2, 6, -3], - [ 4, 2, 1]]) +Out[]: +matrix([[ 1, 2, 2, 1], + [ 1, 5, 1, -3], + [ 2, -1, -1, 2], + [-1, -9, 3, 7]]) \end{lstlisting} \end{frame} @@ -164,22 +167,23 @@ matrix([[ 5, -3, 3], \frametitle{Sum of all elements} \begin{lstlisting} In []: linalg.sum(A) -Out[]: 17 +Out[]: 12 \end{lstlisting} \end{frame} \begin{frame}[fragile] \frametitle{Matrix Addition} \begin{lstlisting} -In []: B = matrix([[3,2,-1], - [2,-2,4], - [-1, 0.5, -1]]) - -In []: linalg.add(A, B) +In []: B = matrix([[3,2,-1,5], + [2,-2,4,9], + [-1,0.5,-1,-7], + [9,-5,7,3]]) +In []: linalg.add(A,B) Out[]: -matrix([[ 8. , 4. , 3. ], - [-1. , 4. , 6. ], - [ 2. , -2.5, 0. ]]) +matrix([[ 4. , 3. , 1. , 4. ], + [ 4. , 3. , 3. , 0. ], + [ 1. , 1.5, -2. , -4. ], + [ 10. , -8. , 9. , 10. ]]) \end{lstlisting} \end{frame} @@ -188,9 +192,10 @@ matrix([[ 8. , 4. , 3. ], \begin{lstlisting} In []: linalg.multiply(A, B) Out[]: -matrix([[ 15. , 4. , -4. ], - [ -6. , -12. , 8. ], - [ -3. , -1.5, -1. ]]) +matrix([[ 3. , 2. , -2. , -5. ], + [ 4. , -10. , -4. , -81. ], + [ -2. , 0.5, 1. , -21. ], + [ 9. , 15. , 14. , 21. ]]) \end{lstlisting} \end{frame} @@ -200,9 +205,10 @@ matrix([[ 15. , 4. , -4. ], \begin{lstlisting} In []: linalg.inv(A) Out[]: -array([[ 0.28571429, -0.33333333, -0.47619048], - [ 0.21428571, -0.16666667, -0.52380952], - [-0.21428571, 0.5 , 0.85714286]]) +matrix([[-0.5 , 0.55, -0.15, 0.7 ], + [ 0.75, -0.5 , 0.5 , -0.75], + [ 0.5 , -0.15, -0.05, -0.1 ], + [ 0.25, -0.25, 0.25, -0.25]]) \end{lstlisting} \end{small} \end{frame} @@ -211,7 +217,7 @@ array([[ 0.28571429, -0.33333333, -0.47619048], \frametitle{Determinant} \begin{lstlisting} In []: det(A) -Out[]: 42.0 +Out[66]: 80.0 \end{lstlisting} \end{frame} @@ -221,10 +227,11 @@ Out[]: 42.0 \begin{lstlisting} In []: linalg.eig(A) Out[]: -(array([ 7., 2., 3.]), - matrix([[-0.57735027, 0.42640143, 0.37139068], - [ 0.57735027, 0.63960215, 0.74278135], - [-0.57735027, -0.63960215, -0.55708601]])) +(array([ 11.41026155, 3.71581643, -0.81723144, -2.30884654]), + matrix([[ 0.12300187, -0.53899627, 0.63269982, 0.56024583], + [ 0.8225266 , -0.67562403, -0.63919634, -0.20747251], + [-0.04763219, -0.47575453, -0.3709497 , -0.80066041], + [-0.55321941, -0.16331814, -0.23133374, 0.04497415]])) \end{lstlisting} \end{small} \end{frame} @@ -232,8 +239,8 @@ Out[]: \begin{frame}[fragile] \frametitle{Computing Norms} \begin{lstlisting} - In []: linalg.norm(A) - Out[]: 10.63014581273465 +In []: linalg.norm(A) +Out[]: 14.0 \end{lstlisting} \end{frame} @@ -243,14 +250,16 @@ Out[]: \begin{lstlisting} In []: linalg.svd(A) Out[]: -(matrix([[-0.13391246, -0.94558684, -0.29653495], - [ 0.84641267, -0.26476432, 0.46204486], - [-0.51541542, -0.18911737, 0.83581192]]), - array([ 7.96445022, 7. , 0.75334767]), - matrix([[-0.59703387, 0.79815896, 0.08057807], - [-0.64299905, -0.41605821, -0.64299905], - [-0.47969029, -0.43570384, 0.7616163 ]])) - \end{lstlisting} +(matrix([[-0.08588113, 0.29164297, -0.74892678, 0.58879325], + [-0.79093255, 0.39530483, -0.11188116, -0.45347812], + [ 0.1523891 , 0.78799358, 0.51966138, 0.29290907], + [ 0.58636823, 0.37113957, -0.39565558, -0.60156827]]), + array([ 13.17656506, 3.76954116, 2.79959047, 0.57531379]), + matrix([[-0.05893795, -0.42858358, 0.12442679, 0.89295039], + [ 0.80364672, 0.51537891, 0.03774111, 0.29514767], + [-0.11752501, 0.14226922, -0.96333552, 0.19476145], + [-0.58040171, 0.72832696, 0.23468759, 0.27855956]])) +\end{lstlisting} \end{small} \end{frame} @@ -282,8 +291,6 @@ Let us now look at how to solve this using \kwrd{matrices} In []: b = matrix([[1], [-2], [0]]) In []: x = linalg.solve(A, b) In []: Ax = dot(A, x) - In []: allclose(Ax, b) - Out[]: True \end{lstlisting} \end{frame} @@ -295,13 +302,44 @@ Out[]: array([[ 1.], [-2.], [-2.]]) +\end{lstlisting} +\end{frame} +\begin{frame}[fragile] +\frametitle{Let's check!} +\begin{lstlisting} In []: Ax Out[]: matrix([[ 1.00000000e+00], [ -2.00000000e+00], [ 2.22044605e-16]]) \end{lstlisting} +\begin{block}{} +The last term in the matrix is actually \alert{0}!\\ +We can use \kwrd{allclose()} to check. +\end{block} +\begin{lstlisting} +In []: allclose(Ax, b) +Out[]: True +\end{lstlisting} +\end{frame} + +\subsection{Exercises} + +\begin{frame}[fragile] +\frametitle{Problem} + +\end{frame} + +\begin{frame}[fragile] +\frametitle{Problem} +Solve the set of equations: +\begin{align*} + x + y + 2z -w & = 3\\ + 2x + 5y - z - 9w & = -3\\ + 2x + y -z + 3w & = -11 \\ + x - 3y + 2z + 7w & = -5\\ +\end{align*} \end{frame} \section{Summary} |