--- a/day1/session4.tex Tue Oct 27 10:59:11 2009 +0530
+++ b/day1/session4.tex Tue Oct 27 11:51:21 2009 +0530
@@ -124,6 +124,53 @@
% \pausesections
\end{frame}
+\section{Solving linear equations}
+\begin{frame}[fragile]
+\frametitle{Solution of equations}
+Consider,
+ \begin{align*}
+ 3x + 2y - z & = 1 \\
+ 2x - 2y + 4z & = -2 \\
+ -x + \frac{1}{2}y -z & = 0
+ \end{align*}
+Solution:
+ \begin{align*}
+ x & = 1 \\
+ y & = -2 \\
+ z & = -2
+ \end{align*}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Solving using Matrices}
+Let us now look at how to solve this using \kwrd{matrices}
+ \begin{lstlisting}
+ In []: A = matrix([[3,2,-1],[2,-2,4],[-1, 0.5, -1]])
+ In []: b = matrix([[1], [-2], [0]])
+ In []: x = linalg.solve(A, b)
+ In []: Ax = dot(A, x)
+ In []: allclose(Ax, b)
+ Out[]: True
+ \end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Solution:}
+\begin{lstlisting}
+In []: x
+Out[]:
+array([[ 1.],
+ [-2.],
+ [-2.]])
+
+In []: Ax
+Out[]:
+matrix([[ 1.00000000e+00],
+ [ -2.00000000e+00],
+ [ 2.22044605e-16]])
+\end{lstlisting}
+\end{frame}
+
\section{Matrices}
\subsection{Initializing}
\begin{frame}[fragile]
@@ -144,13 +191,15 @@
\subsection{Basic Operations}
\begin{frame}[fragile]
\frametitle{Inverse of a Matrix}
+
\begin{small}
\begin{lstlisting}
- In []: linalg.inv(a)
- Out[]:
- matrix([[ 3.15221191e+15, -6.30442381e+15, 3.15221191e+15],
- [ -6.30442381e+15, 1.26088476e+16, -6.30442381e+15],
- [ 3.15221191e+15, -6.30442381e+15, 3.15221191e+15]])
+In []: linalg.inv(A)
+Out[]:
+matrix([[ 0.07734807, 0.01657459, 0.32044199],
+ [ 0.09944751, -0.12154696, -0.01657459],
+ [-0.02762431, -0.07734807, 0.17127072]])
+
\end{lstlisting}
\end{small}
\end{frame}
@@ -176,11 +225,11 @@
\begin{small}
\begin{lstlisting}
In []: linalg.eigvals(a)
- Out[]: array([ 1.61168440e+01, -1.11684397e+00, -1.22196337e-15])
+ Out[]: array([1.61168440e+01, -1.11684397e+00, -1.22196337e-15])
In []: linalg.eig(a)
Out[]:
- (array([ 1.61168440e+01, -1.11684397e+00, -1.22196337e-15]),
+ (array([ 1.61168440e+01, -1.11684397e+00, -1.22196337e-15]),
matrix([[-0.23197069, -0.78583024, 0.40824829],
[-0.52532209, -0.08675134, -0.81649658],
[-0.8186735 , 0.61232756, 0.40824829]]))
@@ -188,28 +237,6 @@
\end{small}
\end{frame}
-\section{Solving linear equations}
-\begin{frame}[fragile]
-\frametitle{Solution of equations}
-Example problem: Consider the set of equations
-\vspace{-0.1in}
- \begin{align*}
- 3x + 2y - z & = 1 \\
- 2x - 2y + 4z & = -2 \\
- -x + \frac{1}{2}y -z & = 0
- \end{align*}
-\vspace{-0.08in}
- To Solve this,
- \begin{lstlisting}
- In []: A = array([[3,2,-1],[2,-2,4],[-1, 0.5, -1]])
- In []: b = array([1, -2, 0])
- In []: x = linalg.solve(A, b)
- In []: Ax = dot(A, x)
- In []: allclose(Ax, b)
- Out[]: True
- \end{lstlisting}
-\end{frame}
-
\section{Integration}