diff options
Diffstat (limited to 'advanced_python/slides/arrays.tex')
| -rw-r--r-- | advanced_python/slides/arrays.tex | 177 |
1 files changed, 105 insertions, 72 deletions
diff --git a/advanced_python/slides/arrays.tex b/advanced_python/slides/arrays.tex index 7b829f9..b565e72 100644 --- a/advanced_python/slides/arrays.tex +++ b/advanced_python/slides/arrays.tex @@ -7,9 +7,9 @@ \item Much faster than arrays \end{itemize} \begin{lstlisting} - a1 = array([1,2,3,4]) + In []: a1 = array([1,2,3,4]) a1 # 1-D - a2 = array([[1,2,3,4],[5,6,7,8]]) + In []: a2 = array([[1,2,3,4],[5,6,7,8]]) a2 # 2-D \end{lstlisting} \end{frame} @@ -17,39 +17,38 @@ \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 + 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} - ar1.shape - ar2.shape + In []: ar1.shape + In []: ar2.shape \end{lstlisting} \end{frame} \begin{frame}[fragile] \frametitle{Special methods} \begin{lstlisting} - identity(3) + In []: 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)) + In []: 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 + 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 @@ -61,17 +60,17 @@ \begin{frame}[fragile] \frametitle{Operations on arrays} \begin{lstlisting} - a1 - a1 * 2 - a1 + 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} - a1 + 3 - a1 - 7 - a1 / 2.0 + In []: a1 + 3 + In []: a1 - 7 + In []: a1 / 2.0 \end{lstlisting} \end{frame} @@ -81,25 +80,25 @@ \item Like lists, we can assign the new array, the old name \end{itemize} \begin{lstlisting} - a1 = a1 + 2 - a1 + In []: a1 = a1 + 2 + In []: 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 + 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} - a1 + a1 - a1 * a2 + In []: a1 + a1 + In []: a1 * a2 \end{lstlisting} \end{frame} @@ -108,24 +107,24 @@ \begin{frame}[fragile] \frametitle{Accessing \& changing elements} \begin{lstlisting} - A = array([12, 23, 34, 45, 56]) + In []: A = array([12, 23, 34, 45, 56]) - C = array([[11, 12, 13, 14, 15], + 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]]) - A[2] - C[2, 3] + 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} - A[2] = -34 - C[2, 3] = -34 + In []: A[2] = -34 + In []: C[2, 3] = -34 \end{lstlisting} \end{frame} @@ -135,49 +134,49 @@ \item Indexing works just like with lists \end{itemize} \begin{lstlisting} - C[2] - C[4] - C[-1] + 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} - C[-1] = [0, 0, 0, 0, 0] + In []: C[-1] = [0, 0, 0, 0, 0] \end{lstlisting} OR \begin{lstlisting} - C[-1] = 0 + In []: C[-1] = 0 \end{lstlisting} \end{frame} \begin{frame}[fragile] \frametitle{Accessing columns} \begin{lstlisting} - C[:, 2] - C[:, 4] - C[:, -1] + 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} - C[:, -1] = 0 + In []: C[:, -1] = 0 \end{lstlisting} \end{frame} \begin{frame}[fragile] \frametitle{Slicing} \begin{lstlisting} - I = imread('squares.png') - imshow(I) + In []: I = imread('squares.png') + In []: imshow(I) \end{lstlisting} \begin{itemize} \item The image is just an array \end{itemize} \begin{lstlisting} - print I, I.shape + In []: print I, I.shape \end{lstlisting} \begin{enumerate} \item Get the top left quadrant of the image @@ -191,14 +190,14 @@ \item Slicing works just like with lists \end{itemize} \begin{lstlisting} - C[0:3, 2] - C[2, 0:3] - C[2, :3] + In []:C[0:3, 2] + In []: C[2, 0:3] + In []:C[2, :3] \end{lstlisting} \begin{lstlisting} - imshow(I[:150, :150]) + In []: imshow(I[:150, :150]) - imshow(I[75:225, 75:225]) + In []: imshow(I[75:225, 75:225]) \end{lstlisting} \end{frame} @@ -211,15 +210,15 @@ \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] + 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} - imshow(I[::2, ::2]) + In []: imshow(I[::2, ::2]) \end{lstlisting} \end{frame} @@ -252,13 +251,28 @@ \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} + In []: L, t = loadtxt("pendulum.txt", + unpack=True) + In []: L + In []: t + In []: tsq = t * t + In []: plot(L, tsq, 'bo') +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] +\frametitle{$L$ vs. $T^2$ - Scatter} +Linear trend visible. +\begin{figure} +\includegraphics[width=4in]{data/L-Tsq-points} +\end{figure} +\end{frame} + +\begin{frame}[fragile] + \frametitle{Least Square Fit} +\begin{lstlisting} + 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! @@ -266,6 +280,23 @@ \end{frame} \begin{frame}[fragile] +\frametitle{$L$ vs. $T^2$ - Line} +This line does not make any mathematical sense. +\vspace{-0.1in} +\begin{figure} +\includegraphics[width=4in]{data/L-Tsq-Line} +\end{figure} +\end{frame} + +\begin{frame}[fragile] +\frametitle{$L$ vs. $T^2$ - Least Square Fit} +This is what our intention is. +\begin{figure} +\includegraphics[width=4in]{data/least-sq-fit} +\end{figure} +\end{frame} + +\begin{frame}[fragile] \frametitle{Matrix Formulation} \begin{itemize} \item We need to fit a line through points for the equation $T^2 = m \cdot L+c$ @@ -295,34 +326,36 @@ \begin{frame}[fragile] \frametitle{Least Square Fit Line} \begin{lstlisting} - A = array((l, ones_like(l))) - A.T - A + In []: A = array((L, ones_like(L))) + In []: A = A.T + In []: A \end{lstlisting} \begin{itemize} \item We now have \texttt{A} and \texttt{tsq} \end{itemize} \begin{lstlisting} - result = lstsq(A, tsq) + 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} - m, c = result[0] - print m, c + 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} - tsq_fit = m * l + c - plot(l, tsq, 'bo') - plot(l, tsq_fit, 'r') + In []: tsq_fit = m * L + c + In []: plot(L, tsq, 'bo') + In []:plot(L, tsq_fit, 'r') \end{lstlisting} \end{frame} |