--- a/day1/session3.tex Thu Dec 09 18:46:09 2010 +0530
+++ b/day1/session3.tex Thu Dec 09 22:35:05 2010 +0530
@@ -74,7 +74,7 @@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Title page
-\title[Arrays]{Python for Science and Engg: Arrays}
+\title[Arrays]{Python for Science and Engg: \\Arrays}
\author[FOSSEE] {FOSSEE}
@@ -123,16 +123,45 @@
\tableofcontents
% \pausesections
\end{frame}
-
-\section{Matrices}
+\section{Motivation}
-\begin{frame}
-\frametitle{Matrices: Introduction}
-\alert{All matrix operations are done using \kwrd{arrays}}
+\begin{frame}[fragile]
+ \frametitle{Why arrays?}
+ \begin{itemize}
+ \item Speed!
+ \item Convenience
+ \item Easier to handle multi-dimensional data
+ \end{itemize}
\end{frame}
\begin{frame}[fragile]
-\frametitle{Matrices: Initializing}
+ \frametitle{Speed}
+ \begin{lstlisting}
+In []: a = random(1000000)
+# array with a million random elements
+In []: b = []
+In []: for each in a:
+ ...: b.append(sin(each))
+ ...:
+ ...:
+In []: sin(a)
+ \end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+ \frametitle{Convenience}
+The pendulum problem could've been solved as below::
+ \begin{lstlisting}
+In []: L, T = loadtxt('pendulum.txt',
+ unpack=True)
+In []: tsq = T*T
+In []: plot (L, tsq, '.')
+ \end{lstlisting}
+\end{frame}
+
+\section{Initializing}
+\begin{frame}[fragile]
+\frametitle{Initializing}
\begin{lstlisting}
In []: c = array([[11,12,13],
[21,22,23],
@@ -147,7 +176,7 @@
\end{frame}
\begin{frame}[fragile]
-\frametitle{Initializing some special matrices}
+\frametitle{Some special arrays}
\begin{small}
\begin{lstlisting}
In []: ones((3,5))
@@ -188,6 +217,7 @@
Out[]: array([21, 22, 23])
\end{lstlisting}
\end{small}
+Similar to \kwrd{lists} but improved!
\end{frame}
\begin{frame}[fragile]
@@ -209,11 +239,58 @@
[31, 32, 33]])
\end{lstlisting}
\end{small}
-How do you access one \alert{column}?
+How do you access one \alert{column}? -- Enter Slicing!
+\end{frame}
+
+\section{Slicing \& Striding}
+
+\begin{frame}[fragile]
+ \frametitle{Slicing: Lists}
+ \begin{block}{Define a list}
+ \kwrd{In []: p = [ 2, 3, 5, 7, 11, 13]}
+ \end{block}
+\begin{lstlisting}
+In []: p[1:3]
+Out[]: [3, 5]
+\end{lstlisting}
+\emphbar{A slice}
+\begin{lstlisting}
+In []: p[0:-1]
+Out[]: [2, 3, 5, 7, 11]
+In []: p[:]
+Out[]: [2, 3, 5, 7, 11, 13]
+\end{lstlisting}
\end{frame}
\begin{frame}[fragile]
- \frametitle{Slicing}
+ \frametitle{Striding: Lists}
+\emphbar{Striding over \typ{p}}
+\begin{lstlisting}
+In []: p[::2]
+Out[]: [2, 5, 11]
+In []: p[1::2]
+Out[]: [3, 7, 13]
+In []: p[1:-1:2]
+Out[]: [3, 7]
+In []: p[::3]
+Out[]: [2, 7]
+\end{lstlisting}
+\alert{\typ{list[initial:final:step]}}
+\end{frame}
+
+\begin{frame}[fragile]
+ \frametitle{Slicing \& Striding: Lists}
+ What is the output of the following?
+\begin{lstlisting}
+In []: p[1::4]
+
+In []: p[1:-1:3]
+\end{lstlisting}
+\end{frame}
+
+
+\begin{frame}[fragile]
+ \frametitle{Slicing: \typ{arrays}}
\begin{small}
\begin{lstlisting}
In []: c[:,1]
@@ -236,7 +313,7 @@
\end{frame}
\begin{frame}[fragile]
- \frametitle{Slicing \ldots}
+ \frametitle{Slicing: \typ{arrays} \ldots}
\begin{small}
\begin{lstlisting}
In []: c[:2,:]
@@ -259,7 +336,7 @@
\end{frame}
\begin{frame}[fragile]
- \frametitle{Striding}
+ \frametitle{Striding: \typ{arrays}}
\begin{small}
\begin{lstlisting}
In []: c[::2,:]
@@ -282,7 +359,7 @@
\end{frame}
\begin{frame}[fragile]
- \frametitle{Shape of a matrix}
+ \frametitle{Shape of an \typ{array}}
\begin{lstlisting}
In []: c
Out[]:
@@ -293,7 +370,7 @@
In []: c.shape
Out[]: (3, 3)
\end{lstlisting}
-\emphbar{Shape specifies shape or dimensions of a matrix}
+\emphbar{Shape specifies shape or dimensions of an array}
\end{frame}
\begin{frame}[fragile]
@@ -335,36 +412,21 @@
\end{small}
\end{frame}
+\section{Operations on \typ{arrays}}
\begin{frame}[fragile]
-\frametitle{Transpose of a Matrix}
-\begin{lstlisting}
-In []: a = array([[ 1, 1, 2, -1],
- ...: [ 2, 5, -1, -9],
- ...: [ 2, 1, -1, 3],
- ...: [ 1, -3, 2, 7]])
+ \frametitle{Operations: Addition}
+ Operations on arrays, as already mentioned, are \alert{element-wise}
+ \begin{lstlisting}
+In []: a = array([[-3,2.5],
+ [2.5,2]])
-In []: a.T
-Out[]:
-array([[ 1, 2, 2, 1],
- [ 1, 5, 1, -3],
- [ 2, -1, -1, 2],
- [-1, -9, 3, 7]])
-\end{lstlisting}
-\end{frame}
+In []: b = array([[3,2],
+ [2,-2]])
-\begin{frame}[fragile]
- \frametitle{Matrix Addition}
- \begin{lstlisting}
-In []: b = array([[3,2,-1,5],
- [2,-2,4,9],
- [-1,0.5,-1,-7],
- [9,-5,7,3]])
In []: a + b
Out[]:
-array([[ 4. , 3. , 1. , 4. ],
- [ 4. , 3. , 3. , 0. ],
- [ 1. , 1.5, -2. , -4. ],
- [ 10. , -8. , 9. , 10. ]])
+array([[ 0. , 4.5],
+ [ 4.5, 0. ]])
\end{lstlisting}
\end{frame}
@@ -373,121 +435,49 @@
\begin{lstlisting}
In []: a*b
Out[]:
-array([[ 3. , 2. , -2. , -5. ],
- [ 4. , -10. , -4. , -81. ],
- [ -2. , 0.5, 1. , -21. ],
- [ 9. , 15. , 14. , 21. ]])
-
-\end{lstlisting}
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Matrix Multiplication}
-\begin{lstlisting}
-In []: dot(a, b)
-Out[]:
-array([[ -6. , 6. , -6. , -3. ],
- [-64. , 38.5, -44. , 35. ],
- [ 36. , -13.5, 24. , 35. ],
- [ 58. , -26. , 34. , -15. ]])
+array([[-9., 5.],
+ [ 5., -4.]])
\end{lstlisting}
\end{frame}
\begin{frame}[fragile]
-\frametitle{Inverse of a Matrix}
-\begin{lstlisting}
-
-\end{lstlisting}
-\begin{small}
-\begin{lstlisting}
-In []: inv(a)
-Out[]:
-array([[-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}
-\emphbar{Try this: \typ{I = dot(a, inv(a))}}
-\end{frame}
+\frametitle{Matrix Operations using \typ{arrays}}
-\begin{frame}[fragile]
-\frametitle{Determinant and sum of all elements}
-\begin{lstlisting}
-In []: det(a)
-Out[]: 80.0
-\end{lstlisting}
- \begin{lstlisting}
-In []: sum(a)
-Out[]: 12
- \end{lstlisting}
+We can perform various matrix operations on \kwrd{arrays}\\
+A few are listed below.
-\end{frame}
-
-%%use S=array(X,Y)
-\begin{frame}[fragile]
-\frametitle{Eigenvalues and Eigen Vectors}
-\begin{small}
-\begin{lstlisting}
-In []: e = array([[3,2,4],[2,0,2],[4,2,3]])
+\vspace{-0.2in}
-In []: eig(e)
-Out[]:
-(array([-1., 8., -1.]),
- array([[-0.74535599, 0.66666667, -0.1931126 ],
- [ 0.2981424 , 0.33333333, -0.78664085],
- [ 0.59628479, 0.66666667, 0.58643303]]))
-
-In []: eigvals(e)
-Out[]: array([-1., 8., -1.])
-\end{lstlisting}
-\end{small}
-\end{frame}
+\begin{center}
+\begin{tabular}{lll}
+ Operation & How? & Example \\
+\hline
+ Transpose & \typ{.T} & \typ{A.T} \\
+ Product & \typ{dot} & \typ{dot(A, B)} \\
+ Inverse & \typ{inv} & \typ{inv(A)} \\
+ Determinant & \typ{det} & \typ{det(A)} \\
+ Sum of all elements & \typ{sum} & \typ{sum(A)} \\
+ Eigenvalues & \typ{eigvals} & \typ{eigvals(A)} \\
+ Eigenvalues \& Eigenvectors & \typ{eig} & \typ{eig(A)} \\
+ Norms & \typ{norm} & \typ{norm(A)} \\
+ SVD & \typ{svd} & \typ{svd(A)} \\
+\end{tabular}
+\end{center}
-\begin{frame}[fragile]
-\frametitle{Computing Norms}
-\begin{lstlisting}
-In []: norm(e)
-Out[]: 8.1240384046359608
-\end{lstlisting}
-\end{frame}
-
-\begin{frame}[fragile]
- \frametitle{Singular Value Decomposition}
- \begin{small}
- \begin{lstlisting}
-In []: svd(e)
-Out[]:
-(array(
-[[ -6.66666667e-01, -1.23702565e-16, 7.45355992e-01],
- [ -3.33333333e-01, -8.94427191e-01, -2.98142397e-01],
- [ -6.66666667e-01, 4.47213595e-01, -5.96284794e-01]]),
- array([ 8., 1., 1.]),
- array([[-0.66666667, -0.33333333, -0.66666667],
- [-0. , 0.89442719, -0.4472136 ],
- [-0.74535599, 0.2981424 , 0.59628479]]))
- \end{lstlisting}
- \end{small}
\end{frame}
\section{Summary}
\begin{frame}
\frametitle{What did we learn?}
\begin{itemize}
- \item Matrices
+ \item Arrays
\begin{itemize}
- \item Initializing
- \item Accessing elements
- \item Slicing and Striding
- \item Transpose
- \item Addition
- \item Multiplication
- \item Inverse of a matrix
- \item Determinant
- \item Eigenvalues and Eigen vector
- \item Singular Value Decomposition
+ \item Initializing
+ \item Accessing elements
+ \item Slicing \& Striding
+ \item Element-wise Operations
+ \item Matrix Operations
\end{itemize}
- \item Least Square Curve fitting
\end{itemize}
\end{frame}