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diff --git a/advanced_python/slides/arrays.tex b/advanced_python/slides/arrays.tex deleted file mode 100644 index e4501c8..0000000 --- a/advanced_python/slides/arrays.tex +++ /dev/null @@ -1,341 +0,0 @@ -\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} - 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