Manual Merge with Mainline.
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% Title page
\title[]{Least Squares Fit\\Statistical Plotting}
\author[FOSSEE] {FOSSEE}
\institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
\date[] {31, October 2009\\Day 1, Session 3}
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\frametitle{Outline}
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% DOCUMENT STARTS
\begin{document}
\begin{frame}
\maketitle
\end{frame}
%% \begin{frame}
%% \frametitle{Outline}
%% \tableofcontents
%% % You might wish to add the option [pausesections]
%% \end{frame}
\begin{frame}
\frametitle{More on data processing}
\begin{block}{}
What do we do if we want to draw Pie charts for the data in a huge data file?
\end{block}
\end{frame}
\begin{frame}
\frametitle{Statistical Analysis and Parsing}
Read the data supplied in \emph{sslc1.txt} and obtain the following statistics:
\begin{itemize}
\item Draw a pie chart representing the number of students who scored more than 90\% in Science per region.
\item Draw a pie chart representing the number of students who scored more than 90\% per subject(All regions combined).
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{Statistical Analysis and Parsing \ldots}
Machinery Required -
\begin{itemize}
\item File reading and parsing
\item Dictionaries
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{File reading and parsing}
Understanding the structure of sslc1.txt
\begin{itemize}
\item Each line in the file, i.e each row of a file is a single record.
\item Each record corresponds to a record of a single student
\item Each record consists of several fields separated by a ';'
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{File reading and parsing \ldots}
Each record consists of:
\begin{itemize}
\item Region Code
\item Roll Number
\item Name
\item Marks of 5 subjects
\item Total marks
\item Pass (P)
\item Withdrawn (W)
\item Fail (F)
\end{itemize}
\end{frame}
\begin{frame}[fragile]
\frametitle{File reading and parsing \ldots}
\begin{lstlisting}
for record in open('sslc1.txt'):
fields = record.split(';')
\end{lstlisting}
\end{frame}
\begin{frame}[fragile]
\frametitle{Dictionary - Building parsed data}
\begin{itemize}
\item Let the parsed data be stored in list of dictionaries.
\item d = \{\} is an empty dictionary
\end{itemize}
\end{frame}
\begin{frame}[fragile]
\frametitle{Dictionary - Building parsed data}
\begin{lstlisting}
ninety_percents = [{}, {}, {}, {}, {}]
\end{lstlisting}
\end{frame}
\begin{frame}[fragile]
\frametitle{Dictionary - Building parsed data}
\begin{itemize}
\item Index of a dictionary is called a \emph{key}
\item \emph{Keys} of these dictionaries are strings - region codes
\end{itemize}
\end{frame}
\begin{frame}[fragile]
\frametitle{Dictionary - Building parsed data \ldots}
\begin{itemize}
\item Value of a \emph{key} can be any legal Python value
\item In this problem let the value of a \emph{key} be another an integer
\item This dictionary contains:
\end{itemize}
'region code': Number of students who scored more than 90\% in this region for this subject
\end{frame}
\begin{frame}[fragile]
\frametitle{Building parsed data \ldots}
\begin{lstlisting}
from pylab import *
ninety_percents = [{}, {}, {}, {}, {}]
for record in open('sslc1.txt'):
record = record.strip()
fields = record.split(';')
region_code = fields[0].strip()
\end{lstlisting}
\end{frame}
\begin{frame}[fragile]
\frametitle{Building parsed data \ldots}
\small
\begin{lstlisting}
for i, field in enumerate(fields[3:8]):
if region_code not in ninety_percents[i]:
ninety_percents[i][region_code] = 0
score_str = field.strip()
score = 0 if score_str == 'AA' else
int(score_str)
if score > 90:
ninety_percents[i][region_code] += 1
\end{lstlisting}
\end{frame}
\begin{frame}[fragile]
\frametitle{Consolidating data}
\begin{lstlisting}
subj_total = []
for subject in ninety_percents:
subj_total.append(sum(
subject.values()))
\end{lstlisting}
\end{frame}
\begin{frame}[fragile]
\frametitle{Pie charts}
\small
\begin{lstlisting}
figure(1)
pie(ninety_percents[4].values(),
labels=ninety_percents[1].keys())
title('Students scoring 90% and above
in science by region')
savefig('/tmp/science.png')
\end{lstlisting}
\begin{columns}
\column{5.25\textwidth}
\hspace*{1.1in}
\includegraphics[height=2in, interpolate=true]{data/science}
\column{0.8\textwidth}
\end{columns}
\end{frame}
\begin{frame}[fragile]
\frametitle{Pie charts}
\begin{lstlisting}
figure(2)
pie(subj_total, labels=['English',
'Hindi', 'Maths', 'Science',
'Social'])
title('Students scoring more than
90% by subject(All regions
combined).')
savefig('/tmp/all_regions.png')
\end{lstlisting}
\end{frame}
\begin{frame}[fragile]
\frametitle{Pie charts}
\includegraphics[height=3in, interpolate=true]{data/all_regions}
\end{frame}
\begin{frame}[fragile]
\frametitle{Dealing with data whole-sale}
\begin{lstlisting}
In []: for t in T:
....: TSq.append(t*t)
\end{lstlisting}
\begin{itemize}
\item This is not very efficient
\item We are squaring element after element
\item We use arrays to make this efficient
\end{itemize}
\begin{lstlisting}
In []: L = array(L)
In []: T = array(T)
In []: TSq = T*T
\end{lstlisting}
\end{frame}
\begin{frame}[fragile]
\frametitle{Arrays}
\begin{itemize}
\item \typ{T} and \typ{L} are now arrays
\item arrays are very efficient and powerful
\item Very easy to perform element-wise operations
\item \typ{+, -, *, /, \%}
\item More about arrays later
\end{itemize}
\end{frame}
\begin{frame}[fragile]
\frametitle{Least Squares Fit}
\vspace{-0.15in}
\begin{figure}
\includegraphics[width=4in]{data/L-Tsq-Line.png}
\end{figure}
\end{frame}
\begin{frame}[fragile]
\frametitle{Least Squares Fit}
\vspace{-0.15in}
\begin{figure}
\includegraphics[width=4in]{data/least-sq-fit.png}
\end{figure}
\end{frame}
\begin{frame}
\frametitle{Least Square Fit Curve}
\begin{itemize}
\item $T^2$ and $L$ have a linear relationship
\item Hence, Least Square Fit Curve is a line
\item we shall use the \typ{lstsq} function
\end{itemize}
\end{frame}
\begin{frame}[fragile]
\frametitle{\typ{lstsq}}
\begin{itemize}
\item We need to fit a line through points for the equation $T^2 = m \cdot L+c$
\item The equation can be re-written as $T^2 = A \cdot p$
\item where A is
$\begin{bmatrix}
L_1 & 1 \\
L_2 & 1 \\
\vdots & \vdots\\
L_N & 1 \\
\end{bmatrix}$
and p is
$\begin{bmatrix}
m\\
c\\
\end{bmatrix}$
\item We need to find $p$ to plot the line
\end{itemize}
\end{frame}
\begin{frame}[fragile]
\frametitle{Van der Monde Matrix}
\begin{itemize}
\item A is also called a Van der Monde matrix
\item It can be generated using \typ{vander}
\end{itemize}
Van der Monde matrix of order M
\begin{equation*}
\begin{bmatrix}
l_1^{M-1} & \ldots & l_1 & 1 \\
l_2^{M-1} & \ldots &l_2 & 1 \\
\vdots & \ldots & \vdots & \vdots\\
l_N^{M-1} & \ldots & l_N & 1 \\
\end{bmatrix}
\end{equation*}
\begin{lstlisting}
In []: A = vander(L,2)
\end{lstlisting}
\end{frame}
\begin{frame}[fragile]
\frametitle{\typ{lstsq} \ldots}
\begin{itemize}
\item Now use the \typ{lstsq} function
\item Along with a lot of things, it returns the least squares solution
\end{itemize}
\begin{lstlisting}
In []: coef, res, r, s = lstsq(A,TSq)
\end{lstlisting}
\end{frame}
\begin{frame}[fragile]
\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]
\end{lstlisting}
\begin{itemize}
\item Now plot Tline vs. L, to get the Least squares fit line.
\end{itemize}
\begin{lstlisting}
In []: plot(L, Tline)
\end{lstlisting}
\end{frame}
\begin{frame}[fragile]
\frametitle{What did we learn?}
\begin{itemize}
\item Dictionaries
\item Drawing pie charts
\item Arrays
\item Least Square fitting
\item Intro to Matrices
\end{itemize}
\end{frame}
\end{document}