diff options
Diffstat (limited to 'day1/session4.tex')
| -rw-r--r-- | day1/session4.tex | 144 |
1 files changed, 85 insertions, 59 deletions
diff --git a/day1/session4.tex b/day1/session4.tex index 79da193..33f1f68 100644 --- a/day1/session4.tex +++ b/day1/session4.tex @@ -79,7 +79,7 @@ \author[FOSSEE] {FOSSEE} \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay} -\date[] {7 November, 2009\\Day 1, Session 4} +\date[] {14 December, 2009\\Day 1, Session 4} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo} @@ -134,16 +134,15 @@ \begin{frame}[fragile] \frametitle{Matrices: Initializing} \begin{lstlisting} -In []: A = array([[ 1, 1, 2, -1], - [ 2, 5, -1, -9], - [ 2, 1, -1, 3], - [ 1, -3, 2, 7]]) -In []: A +In []: c = array([[1,1,2], + [2,4,1], + [-1,3,7]]) + +In []: c Out[]: -array([[ 1, 1, 2, -1], - [ 2, 5, -1, -9], - [ 2, 1, -1, 3], - [ 1, -3, 2, 7]]) +array([[1,1,2], + [2,4,1], + [-1,3,7]]) \end{lstlisting} \end{frame} @@ -157,8 +156,8 @@ array([[ 1., 1., 1., 1., 1.], [ 1., 1., 1., 1., 1.], [ 1., 1., 1., 1., 1.]]) -In []: ones_like([1, 2, 3, 4, 5]) -Out[]: array([1, 1, 1, 1, 1]) +In []: ones_like([1, 2, 3, 4]) +Out[]: array([1, 1, 1, 1]) In []: identity(2) Out[]: @@ -173,17 +172,17 @@ Also available \alert{\typ{zeros, zeros_like, empty, empty_like}} \begin{frame}[fragile] \frametitle{Accessing elements} \begin{lstlisting} -In []: C = array([[1,1,2], - [2,4,1], - [-1,3,7]]) +In []: c +Out[]: +array([[1,1,2], + [2,4,1], + [-1,3,7]]) -In []: C[1][2] +In []: c[1][2] Out[]: 1 - -In []: C[1,2] +In []: c[1,2] Out[]: 1 - -In []: C[1] +In []: c[1] Out[]: array([2, 4, 1]) \end{lstlisting} \end{frame} @@ -192,15 +191,15 @@ Out[]: array([2, 4, 1]) \frametitle{Changing elements} \begin{small} \begin{lstlisting} -In []: C[1,1] = -2 -In []: C +In []: c[1,1] = -2 +In []: c Out[]: array([[ 1, 1, 2], [ 2, -2, 1], [-1, 3, 7]]) -In []: C[1] = [0,0,0] -In []: C +In []: c[1] = [0,0,0] +In []: c Out[]: array([[ 1, 1, 2], [ 0, 0, 0], @@ -214,18 +213,18 @@ How to change one \alert{column}? \frametitle{Slicing} \begin{small} \begin{lstlisting} -In []: C[:,1] +In []: c[:,1] Out[]: array([1, 0, 3]) -In []: C[1,:] +In []: c[1,:] Out[]: array([0, 0, 0]) -In []: C[0:2,:] +In []: c[0:2,:] Out[]: array([[1, 1, 2], [0, 0, 0]]) -In []: C[1:3,:] +In []: c[1:3,:] Out[]: array([[ 0, 0, 0], [-1, 3, 7]]) @@ -237,17 +236,17 @@ array([[ 0, 0, 0], \frametitle{Slicing \ldots} \begin{small} \begin{lstlisting} -In []: C[:2,:] +In []: c[:2,:] Out[]: array([[1, 1, 2], [0, 0, 0]]) -In []: C[1:,:] +In []: c[1:,:] Out[]: array([[ 0, 0, 0], [-1, 3, 7]]) -In []: C[1:,:2] +In []: c[1:,:2] Out[]: array([[ 0, 0], [-1, 3]]) @@ -260,18 +259,18 @@ array([[ 0, 0], \frametitle{Striding} \begin{small} \begin{lstlisting} -In []: C[::2,:] +In []: c[::2,:] Out[]: array([[ 1, 1, 2], [-1, 3, 7]]) -In []: C[:,::2] +In []: c[:,::2] Out[]: xarray([[ 1, 2], [ 0, 0], [-1, 7]]) -In []: C[::2,::2] +In []: c[::2,::2] Out[]: array([[ 1, 2], [-1, 7]]) @@ -283,13 +282,11 @@ array([[ 1, 2], \frametitle{Slicing \& Striding Exercises} \begin{small} \begin{lstlisting} -In []: A = imread('lena.png') +In []: a = imread('lena.png') -In []: imshow(A) +In []: imshow(a) Out[]: <matplotlib.image.AxesImage object at 0xa0384cc> -In []: A.shape -Out[]: (512, 512, 4) \end{lstlisting} \end{small} \begin{itemize} @@ -303,13 +300,13 @@ Out[]: (512, 512, 4) \frametitle{Solutions} \begin{small} \begin{lstlisting} -In []: imshow(A[:256,:256]) +In []: imshow(a[:256,:256]) Out[]: <matplotlib.image.AxesImage object at 0xb6f658c> -In []: imshow(A[200:400,200:400]) +In []: imshow(a[200:400,200:400]) Out[]: <matplotlib.image.AxesImage object at 0xb757c2c> -In []: imshow(A[::2,::2]) +In []: imshow(a[::2,::2]) Out[]: <matplotlib.image.AxesImage object at 0xb765c8c> \end{lstlisting} \end{small} @@ -318,7 +315,12 @@ Out[]: <matplotlib.image.AxesImage object at 0xb765c8c> \begin{frame}[fragile] \frametitle{Transpose of a Matrix} \begin{lstlisting} -In []: A.T +In []: a = array([[ 1, 1, 2, -1], + ...: [ 2, 5, -1, -9], + ...: [ 2, 1, -1, 3], + ...: [ 1, -3, 2, 7]]) + +In []: a.T Out[]: array([[ 1, 2, 2, 1], [ 1, 5, 1, -3], @@ -330,7 +332,7 @@ array([[ 1, 2, 2, 1], \begin{frame}[fragile] \frametitle{Sum of all elements} \begin{lstlisting} -In []: sum(A) +In []: sum(a) Out[]: 12 \end{lstlisting} \end{frame} @@ -338,11 +340,11 @@ Out[]: 12 \begin{frame}[fragile] \frametitle{Matrix Addition} \begin{lstlisting} -In []: B = array([[3,2,-1,5], +In []: b = array([[3,2,-1,5], [2,-2,4,9], [-1,0.5,-1,-7], [9,-5,7,3]]) -In []: A + B +In []: a + b Out[]: array([[ 4. , 3. , 1. , 4. ], [ 4. , 3. , 3. , 0. ], @@ -354,7 +356,7 @@ array([[ 4. , 3. , 1. , 4. ], \begin{frame}[fragile] \frametitle{Elementwise Multiplication} \begin{lstlisting} -In []: A*B +In []: a*b Out[]: array([[ 3. , 2. , -2. , -5. ], [ 4. , -10. , -4. , -81. ], @@ -367,7 +369,7 @@ array([[ 3. , 2. , -2. , -5. ], \begin{frame}[fragile] \frametitle{Matrix Multiplication} \begin{lstlisting} -In []: dot(A,B) +In []: dot(a, b) Out[]: array([[ -6. , 6. , -6. , -3. ], [-64. , 38.5, -44. , 35. ], @@ -379,7 +381,7 @@ array([[ -6. , 6. , -6. , -3. ], \begin{frame}[fragile] \frametitle{Inverse of a Matrix} \begin{lstlisting} -In []: inv(A) +In []: inv(a) \end{lstlisting} \begin{small} \begin{lstlisting} @@ -395,7 +397,7 @@ array([[-0.5 , 0.55, -0.15, 0.7 ], \begin{frame}[fragile] \frametitle{Determinant} \begin{lstlisting} -In []: det(A) +In []: det(a) Out[]: 80.0 \end{lstlisting} \end{frame} @@ -405,16 +407,16 @@ Out[]: 80.0 \frametitle{Eigenvalues and Eigen Vectors} \begin{small} \begin{lstlisting} -In []: E = array([[3,2,4],[2,0,2],[4,2,3]]) +In []: e = array([[3,2,4],[2,0,2],[4,2,3]]) -In []: eig(E) +In []: eig(e) Out[]: (array([-1., 8., -1.]), array([[-0.74535599, 0.66666667, -0.1931126 ], [ 0.2981424 , 0.33333333, -0.78664085], [ 0.59628479, 0.66666667, 0.58643303]])) -In []: eigvals(E) +In []: eigvals(e) Out[]: array([-1., 8., -1.]) \end{lstlisting} \end{small} @@ -423,7 +425,7 @@ Out[]: array([-1., 8., -1.]) %% \begin{frame}[fragile] %% \frametitle{Computing Norms} %% \begin{lstlisting} -%% In []: norm(E) +%% In []: norm(e) %% Out[]: 8.1240384046359608 %% \end{lstlisting} %% \end{frame} @@ -432,7 +434,7 @@ Out[]: array([-1., 8., -1.]) %% \frametitle{Singular Value Decomposition} %% \begin{small} %% \begin{lstlisting} -%% In []: svd(E) +%% In []: svd(e) %% Out[]: %% (array( %% [[ -6.66666667e-01, -1.23702565e-16, 7.45355992e-01], @@ -503,9 +505,33 @@ Out[]: array([-1., 8., -1.]) \end{frame} \begin{frame}[fragile] +\frametitle{Getting $L$ and $T^2$} +If you \alert{closed} IPython after session 2 +\begin{lstlisting} +In []: l = [] +In []: t = [] +In []: for line in open('pendulum.txt'): + .... point = line.split() + .... l.append(float(point[0])) + .... t.append(float(point[1])) + .... + .... +\end{lstlisting} +\end{frame} + +\begin{frame}[fragile] +\frametitle{Getting $L$ and $T^2$ \dots} +\begin{lstlisting} +In []: l = array(l) +In []: t = array(t) +\end{lstlisting} +\alert{\typ{In []: tsq = t*t}} +\end{frame} + +\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} @@ -524,7 +550,7 @@ In []: A = A.T \item Along with a lot of things, it returns the least squares solution \end{itemize} \begin{lstlisting} -In []: result = lstsq(A,TSq) +In []: result = lstsq(A,tsq) In []: coef = result[0] \end{lstlisting} \end{frame} @@ -533,13 +559,13 @@ 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] \end{lstlisting} \begin{itemize} -\item Now plot Tline vs. 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} |