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%Tutorial slides on Python.

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% Author: FOSSEE

% Copyright (c) 2009, FOSSEE, IIT Bombay

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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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% 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    \item Withdrawn (W)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}