--- a/day1/session4.tex Tue Dec 29 19:02:01 2009 +0530
+++ b/day1/session4.tex Tue Dec 29 19:25:11 2009 +0530
@@ -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 @@
[ 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 @@
\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 @@
\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 @@
\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 @@
\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 @@
\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 @@
\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 @@
\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 @@
\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 @@
\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 @@
\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 @@
\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 @@
\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 @@
\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 @@
\begin{frame}[fragile]
\frametitle{Determinant}
\begin{lstlisting}
-In []: det(A)
+In []: det(a)
Out[]: 80.0
\end{lstlisting}
\end{frame}
@@ -405,16 +407,16 @@
\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 @@
%% \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 @@
%% \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 @@
\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 @@
\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 @@
\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}