diff options
Diffstat (limited to 'day1/session4.tex')
| -rw-r--r-- | day1/session4.tex | 79 |
1 files changed, 36 insertions, 43 deletions
diff --git a/day1/session4.tex b/day1/session4.tex index 99ca05b..42227f1 100644 --- a/day1/session4.tex +++ b/day1/session4.tex @@ -164,7 +164,7 @@ Out[]: array([[ 1., 0.], [ 0., 1.]]) \end{lstlisting} -Also available \alert{\typ{zeros, zeros_like, empty, empty_like}} +Also available \alert{\typ{zeros, zeros_like}} \end{small} \end{frame} @@ -182,8 +182,6 @@ In []: c[1][2] Out[]: 23 In []: c[1,2] Out[]: 23 -In []: c[1] -Out[]: array([21, 22, 23]) \end{lstlisting} \end{frame} @@ -191,6 +189,9 @@ Out[]: array([21, 22, 23]) \frametitle{Changing elements} \begin{small} \begin{lstlisting} +In []: c[1] +Out[]: array([21, 22, 23]) + In []: c[1,1] = -22 In []: c Out[]: @@ -206,7 +207,7 @@ array([[11, 12, 13], [31, 32, 33]]) \end{lstlisting} \end{small} -How to change one \alert{column}? +How to access one \alert{column}? \end{frame} \begin{frame}[fragile] @@ -294,23 +295,28 @@ Out[]: (3, 3) \end{frame} \begin{frame}[fragile] - \frametitle{Slicing \& Striding Exercises} + \frametitle{Elementary image processing} \begin{small} \begin{lstlisting} In []: a = imread('lena.png') In []: imshow(a) Out[]: <matplotlib.image.AxesImage object at 0xa0384cc> - \end{lstlisting} -\end{small} + \end{small} +\typ{imread} returns an array of shape (512, 512, 4) which represents an image of 512x512 pixels and 4 shades.\\ +\typ{imshow} renders the array as an image. +\end{frame} + +\begin{frame}[fragile] +\frametitle{Slicing \& Striding Exercises} \begin{itemize} \item Crop the image to get the top-left quarter \item Crop the image to get only the face \item Resize image to half by dropping alternate pixels \end{itemize} -\end{frame} +\end{frame} \begin{frame}[fragile] \frametitle{Solutions} \begin{small} @@ -345,14 +351,6 @@ array([[ 1, 2, 2, 1], \end{frame} \begin{frame}[fragile] - \frametitle{Sum of all elements} - \begin{lstlisting} -In []: sum(a) -Out[]: 12 - \end{lstlisting} -\end{frame} - -\begin{frame}[fragile] \frametitle{Matrix Addition} \begin{lstlisting} In []: b = array([[3,2,-1,5], @@ -410,11 +408,16 @@ array([[-0.5 , 0.55, -0.15, 0.7 ], \end{frame} \begin{frame}[fragile] -\frametitle{Determinant} +\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} + \end{frame} %%use S=array(X,Y) @@ -467,7 +470,8 @@ Out[]: array([-1., 8., -1.]) \section{Least Squares Fit} \begin{frame}[fragile] \frametitle{$L$ vs. $T^2$ - Scatter} -\vspace{-0.15in} +Linear trend visible. +\vspace{-0.1in} \begin{figure} \includegraphics[width=4in]{data/L-Tsq-points} \end{figure} @@ -475,37 +479,24 @@ Out[]: array([-1., 8., -1.]) \begin{frame}[fragile] \frametitle{$L$ vs. $T^2$ - Line} -\vspace{-0.15in} +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. $T^2$ } \frametitle{$L$ vs. $T^2$ - Least Square Fit} -\vspace{-0.15in} +This is what our intention is. +\vspace{-0.1in} \begin{figure} \includegraphics[width=4in]{data/least-sq-fit} \end{figure} \end{frame} -\begin{frame} -\frametitle{Least Square Fit Curve} -\begin{center} -\begin{itemize} -\item $L \alpha T^2$ -\item Best Fit Curve $\rightarrow$ Linear - \begin{itemize} - \item Least Square Fit - \end{itemize} -\item \typ{lstsq()} -\end{itemize} -\end{center} -\end{frame} - \begin{frame}[fragile] -\frametitle{\typ{lstsq}} +\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 @@ -535,11 +526,11 @@ Out[]: array([-1., 8., -1.]) \frametitle{Getting $L$ and $T^2$} %If you \alert{closed} IPython after session 2 \begin{lstlisting} -In []: l = [] +In []: L = [] In []: t = [] In []: for line in open('pendulum.txt'): .... point = line.split() - .... l.append(float(point[0])) + .... L.append(float(point[0])) .... t.append(float(point[1])) .... .... @@ -549,7 +540,7 @@ In []: for line in open('pendulum.txt'): \begin{frame}[fragile] \frametitle{Getting $L$ and $T^2$ \dots} \begin{lstlisting} -In []: l = array(l) +In []: L = array(L) In []: t = array(t) \end{lstlisting} \alert{\typ{In []: tsq = t*t}} @@ -558,7 +549,7 @@ In []: t = array(t) \begin{frame}[fragile] \frametitle{Generating $A$} \begin{lstlisting} -In []: A = array([l, ones_like(l)]) +In []: A = array([L, ones_like(L)]) In []: A = A.T \end{lstlisting} %% \begin{itemize} @@ -586,13 +577,15 @@ In []: coef = result[0] \frametitle{Least Square Fit Line \ldots} We get the points of the line from \typ{coef} \begin{lstlisting} -In []: Tline = coef[0]*l + coef[1] +In []: Tline = coef[0]*L + coef[1] + +In []: Tline.shape \end{lstlisting} \begin{itemize} -\item Now plot \typ{Tline} vs. \typ{l}, to get the Least squares fit line. +\item Now plot \typ{Tline} vs. \typ{L}, to get the Least squares fit line. \end{itemize} \begin{lstlisting} -In []: plot(l, Tline) +In []: plot(L, Tline) \end{lstlisting} \end{frame} |