restructring repo

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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}
-   In[]: a1 = array([1,2,3,4])
-   In[]: a1 # 1-D
-   In[]: a2 = array([[1,2,3,4],[5,6,7,8]])
-   In[]: a2 # 2-D
-  \end{lstlisting}
-\end{frame}
-
-\begin{frame}[fragile]
-  \frametitle{\texttt{arange} and \texttt{shape}}
-  \begin{lstlisting}
-   In[]: ar1 = arange(1, 5)
-   In[]: ar2 = arange(1, 9) 
-   In[]: print ar2
-   In[]: ar2.shape = 2, 4
-   In[]: print ar2
-  \end{lstlisting}
-  \begin{itemize}
-  \item \texttt{linspace} and \texttt{loadtxt} also returned arrays
-  \end{itemize}
-  \begin{lstlisting}
-   In[]: ar1.shape
-   In[]: ar2.shape
-  \end{lstlisting}
-\end{frame}
-
-\begin{frame}[fragile]
-  \frametitle{Special methods}
-  \begin{lstlisting}
-   In[]: identity(3)
-  \end{lstlisting}
-  \begin{itemize}
-  \item array of shape (3, 3) with diagonals as 1s, rest 0s
-  \end{itemize}
-  \begin{lstlisting}
-   In[]: zeros((4,5))
-  \end{lstlisting}
-  \begin{itemize}
-  \item array of shape (4, 5) with all 0s
-  \end{itemize}
-  \begin{lstlisting}
-   In[]: a = zeros_like([1.5, 1, 2, 3])
-   In[]: 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}
-  In[]:  a1
-  In[]:  a1 * 2
-  In[]:  a1
-  \end{lstlisting}
-  \begin{itemize}
-  \item The array is not changed; New array is returned
-  \end{itemize}
-  \begin{lstlisting}
-   In[]: a1 + 3
-   In[]: a1 - 7
-   In[]: 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}
-   In[]: a1 = a1 + 2
-   In[]: a1
-  \end{lstlisting}
-  \begin{itemize}
-   \item \alert{Beware of Augmented assignment!}
-  \end{itemize}
-  \begin{lstlisting}
-   In[]: a, b = arange(1, 5), arange(1, 5)
-   In[]: print a, a.dtype, b, b.dtype
-   In[]: a = a/2.0
-   In[]: b /= 2.0
-   In[]: print a, a.dtype, b, b.dtype
-  \end{lstlisting}
-  \begin{itemize}
-  \item Operations on two arrays; element-wise
-  \end{itemize}
-  \begin{lstlisting}
-   In[]: a1 + a1
-   In[]: a1 * a2
-  \end{lstlisting}
-\end{frame}
-
-\section{Accessing pieces of arrays}
-
-\begin{frame}[fragile]
-  \frametitle{Accessing \& changing elements}
-  \begin{lstlisting}
-  In[]:  A = array([12, 23, 34, 45, 56])
-
-  In[]:  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]])
-
-   In[]: A[2]
-   In[]: C[2, 3]
-  \end{lstlisting}
-  \begin{itemize}
-  \item Indexing starts from 0
-  \item Assign new values, to change elements
-  \end{itemize}
-  \begin{lstlisting}
-   In[]: A[2] = -34
-   In[]: 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}
-   In[]: C[2]
-   In[]: C[4]
-   In[]: C[-1]
-  \end{lstlisting}
-  \begin{itemize}
-  \item Change the last row into all zeros
-  \end{itemize}
-  \begin{lstlisting}
-   In[]:  C[-1] = [0, 0, 0, 0, 0]
-  \end{lstlisting}
-  OR
-  \begin{lstlisting}
-   In[]: C[-1] = 0
-  \end{lstlisting}
-\end{frame}
-
-\begin{frame}[fragile]
-  \frametitle{Accessing columns}
-  \begin{lstlisting}
-  In[]:  C[:, 2]
-  In[]:  C[:, 4]
-  In[]:  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}
-  In[]: C[:, -1] = 0
-  \end{lstlisting}
-\end{frame}
-
-\begin{frame}[fragile]
-  \frametitle{Slicing}
-  \begin{lstlisting}
-   In[]: I = imread('squares.png')
-   In[]: imshow(I)
-  \end{lstlisting}
-  \begin{itemize}
-  \item The image is just an array
-  \end{itemize}
-  \begin{lstlisting}
-   In[]: 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}
-  In[]: C[0:3, 2]
-  In[]: C[2, 0:3]
-  In[]: C[2, :3]
-  \end{lstlisting}
-  \begin{lstlisting}
-  In[]: imshow(I[:150, :150])
-
-  In[]: imshow(I[75:225, 75:225])
-  \end{lstlisting}
-\end{frame}
-
-\begin{frame}
-\frametitle{Image after slicing}
-\includegraphics[scale=0.45]{../advanced_python/images/slice.png}\\
-\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}
-  In[]: C[0:5:2, 0:5:2]
-  In[]: C[::2, ::2]
-  In[]: C[1::2, ::2]
-  \end{lstlisting}
-  \begin{itemize}
-  \item Now, the image can be shrunk by
-  \end{itemize}
-  \begin{lstlisting}
-  In[]: 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}
-  In[]:  L, t = loadtxt("pendulum.txt", 
-                unpack=True)
-  In[]:  L
-  In[]:  t
-  In[]:  tsq = t * t
-  In[]:  plot(L, tsq, 'bo')
-  In[]:  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}
-  In[]:  A = array((L, ones_like(L)))
-  In[]:  A.T
-  In[]:  A
-  \end{lstlisting}
-  \begin{itemize}
-  \item We now have \texttt{A} and \texttt{tsq}
-  \end{itemize}
-  \begin{lstlisting}
-  In[]: 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}
-  In[]: m, c = result[0]
-  In[]: 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}
-  In[]:  tsq_fit = m * L + c
-  In[]:  plot(L, tsq, 'bo')
-  In[]:  plot(L, tsq_fit, 'r')
-  \end{lstlisting}
-\end{frame}
-
-\begin{frame}
-\frametitle{Least Square Fit Line}
-\includegraphics[scale=0.45]{../advanced_python/images/lst-sq-fit.png}\\
-\end{frame}
-
-