adv_py: Add notes, slides and a few exercises.

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+\section{Arrays}
+
+\begin{frame}[fragile]
+  \frametitle{Arrays: Introduction}
+  \begin{itemize}
+  \item Similar to lists, but homogeneous
+  \item Much faster than arrays
+  \end{itemize}
+  \begin{lstlisting}
+    a1 = array([1,2,3,4])
+    a1 # 1-D
+    a2 = array([[1,2,3,4],[5,6,7,8]])
+    a2 # 2-D
+  \end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{\texttt{arange} and \texttt{shape}}
+  \begin{lstlisting}
+    ar1 = arange(1, 5)
+
+    ar2 = arange(1, 9) 
+    print ar2
+    ar2.shape = 2, 4
+    print ar2
+  \end{lstlisting}
+  \begin{itemize}
+  \item \texttt{linspace} and \texttt{loadtxt} also returned arrays
+  \end{itemize}
+  \begin{lstlisting}
+    ar1.shape
+    ar2.shape
+  \end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Special methods}
+  \begin{lstlisting}
+    identity(3)
+  \end{lstlisting}
+  \begin{itemize}
+  \item array of shape (3, 3) with diagonals as 1s, rest 0s
+  \end{itemize}
+  \begin{lstlisting}
+    zeros((4,5))
+  \end{lstlisting}
+  \begin{itemize}
+  \item array of shape (4, 5) with all 0s
+  \end{itemize}
+  \begin{lstlisting}
+    a = zeros_like([1.5, 1, 2, 3]
+    print a, a.dtype
+  \end{lstlisting}
+  \begin{itemize}
+  \item An array with all 0s, with similar shape and dtype as argument
+  \item Homogeneity makes the dtype of a to be float
+  \item \texttt{ones, ones\_like, empty, empty\_like}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Operations on arrays}
+  \begin{lstlisting}
+    a1
+    a1 * 2
+    a1
+  \end{lstlisting}
+  \begin{itemize}
+  \item The array is not changed; New array is returned
+  \end{itemize}
+  \begin{lstlisting}
+    a1 + 3
+    a1 - 7
+    a1 / 2.0
+  \end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Operations on arrays \ldots}
+  \begin{itemize}
+  \item Like lists, we can assign the new array, the old name
+  \end{itemize}
+  \begin{lstlisting}
+    a1 = a1 + 2
+    a1
+  \end{lstlisting}
+  \begin{itemize}
+   \item \alert{Beware of Augmented assignment!}
+  \end{itemize}
+  \begin{lstlisting}
+    a, b = arange(1, 5), arange(1, 5)
+    print a, a.dtype, b, b.dtype
+    a = a/2.0
+    b /= 2.0
+    print a, a.dtype, b, b.dtype
+  \end{lstlisting}
+  \begin{itemize}
+  \item Operations on two arrays; element-wise
+  \end{itemize}
+  \begin{lstlisting}
+    a1 + a1
+    a1 * a2
+  \end{lstlisting}
+\end{frame}
+
+\section{Accessing pieces of arrays}
+
+\begin{frame}[fragile]
+  \frametitle{Accessing \& changing elements}
+  \begin{lstlisting}
+    A = array([12, 23, 34, 45, 56])
+
+    C = array([[11, 12, 13, 14, 15],
+               [21, 22, 23, 24, 25],
+               [31, 32, 33, 34, 35],
+               [41, 42, 43, 44, 45],
+               [51, 52, 53, 54, 55]])
+
+    A[2]
+    C[2, 3]
+  \end{lstlisting}
+  \begin{itemize}
+  \item Indexing starts from 0
+  \item Assign new values, to change elements
+  \end{itemize}
+  \begin{lstlisting}
+    A[2] = -34
+    C[2, 3] = -34
+  \end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Accessing rows}
+  \begin{itemize}
+  \item Indexing works just like with lists
+  \end{itemize}
+  \begin{lstlisting}
+    C[2]
+    C[4]
+    C[-1]
+  \end{lstlisting}
+  \begin{itemize}
+  \item Change the last row into all zeros
+  \end{itemize}
+  \begin{lstlisting}
+    C[-1] = [0, 0, 0, 0, 0]
+  \end{lstlisting}
+  OR
+  \begin{lstlisting}
+    C[-1] = 0
+  \end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Accessing columns}
+  \begin{lstlisting}
+    C[:, 2]
+    C[:, 4]
+    C[:, -1]
+  \end{lstlisting}
+  \begin{itemize}
+  \item The first parameter is replaced by a \texttt{:} to specify we
+    require all elements of that dimension
+  \end{itemize}
+  \begin{lstlisting}
+    C[:, -1] = 0
+  \end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Slicing}
+  \begin{lstlisting}
+    I = imread('squares.png')
+    imshow(I)
+  \end{lstlisting}
+  \begin{itemize}
+  \item The image is just an array
+  \end{itemize}
+  \begin{lstlisting}
+    print I, I.shape
+  \end{lstlisting}
+  \begin{enumerate}
+  \item Get the top left quadrant of the image
+  \item Obtain the square in the center of the image
+  \end{enumerate}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Slicing \ldots}
+  \begin{itemize}
+  \item Slicing works just like with lists
+  \end{itemize}
+  \begin{lstlisting}
+    C[0:3, 2]
+    C[2, 0:3]
+    C[2, :3]
+  \end{lstlisting}
+  \begin{lstlisting}
+    imshow(I[:150, :150])
+
+    imshow(I[75:225, 75:225])
+  \end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Striding}
+  \begin{itemize}
+  \item Compress the image to a fourth, by dropping alternate rows and
+    columns
+  \item We shall use striding
+  \item The idea is similar to striding in lists
+  \end{itemize}
+  \begin{lstlisting}
+    C[0:5:2, 0:5:2]
+    C[::2, ::2]
+    C[1::2, ::2]
+  \end{lstlisting}
+  \begin{itemize}
+  \item Now, the image can be shrunk by
+  \end{itemize}
+  \begin{lstlisting}
+    imshow(I[::2, ::2])
+  \end{lstlisting}
+\end{frame}
+
+\section{Matrix Operations}
+
+\begin{frame}[fragile]
+  \frametitle{Matrix Operations using \texttt{arrays}}
+  We can perform various matrix operations on \texttt{arrays}\\ 
+  A few are listed below.
+
+  \begin{center}
+    \begin{tabular}{lll}
+      Operation                    &  How?           &  Example           \\
+      \hline
+      Transpose                    &  \texttt{.T}       &  \texttt{A.T}         \\
+      Product                      &  \texttt{dot}      &  \texttt{dot(A, B)}   \\
+      Inverse                      &  \texttt{inv}      &  \texttt{inv(A)}      \\
+      Determinant                  &  \texttt{det}      &  \texttt{det(A)}      \\
+      Sum of all elements          &  \texttt{sum}      &  \texttt{sum(A)}      \\
+      Eigenvalues                  &  \texttt{eigvals}  &  \texttt{eigvals(A)}  \\
+      Eigenvalues \& Eigenvectors  &  \texttt{eig}      &  \texttt{eig(A)}      \\
+      Norms                        &  \texttt{norm}     &  \texttt{norm(A)}     \\
+      SVD                          &  \texttt{svd}      &  \texttt{svd(A)}      \\
+    \end{tabular}
+  \end{center}
+\end{frame}
+
+\section{Least square fit}
+
+\begin{frame}[fragile]
+  \frametitle{Least Square Fit}
+  \begin{lstlisting}
+    l, t = loadtxt("pendulum.txt", unpack=True)
+    l
+    t
+    tsq = t * t
+    plot(l, tsq, 'bo')
+    plot(l, tsq, 'r')
+  \end{lstlisting}
+  \begin{itemize}
+  \item Both the plots, aren't what we expect -- linear plot
+  \item Enter Least square fit!
+  \end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Matrix Formulation}
+  \begin{itemize}
+  \item We need to fit a line through points for the equation $T^2 = m \cdot L+c$
+  \item In matrix form, the equation can be represented as $T_{sq} = A \cdot p$, where $T_{sq}$ is
+    $\begin{bmatrix}
+    T^2_1 \\
+    T^2_2 \\
+    \vdots\\
+    T^2_N \\
+  \end{bmatrix}$
+    , A is   
+    $\begin{bmatrix}
+    L_1 & 1 \\
+    L_2 & 1 \\
+    \vdots & \vdots\\
+    L_N & 1 \\
+  \end{bmatrix}$
+    and p is 
+    $\begin{bmatrix}
+      m\\
+      c\\
+    \end{bmatrix}$
+  \item We need to find $p$ to plot the line
+  \end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Least Square Fit Line}
+  \begin{lstlisting}
+    A = array((l, ones_like(l)))
+    A.T
+    A
+  \end{lstlisting}
+  \begin{itemize}
+  \item We now have \texttt{A} and \texttt{tsq}
+  \end{itemize}
+  \begin{lstlisting}
+    result = lstsq(A, tsq)
+  \end{lstlisting}
+  \begin{itemize}
+  \item Result has a lot of values along with m and c, that we need
+  \end{itemize}
+  \begin{lstlisting}
+    m, c = result[0]
+    print m, c
+  \end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Least Square Fit Line}
+  \begin{itemize}
+  \item Now that we have m and c, we use them to generate line and plot
+  \end{itemize}
+  \begin{lstlisting}
+    tsq_fit = m * l + c
+    plot(l, tsq, 'bo')
+    plot(l, tsq_fit, 'r')
+  \end{lstlisting}
+\end{frame}
+