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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[Statistics]{Python for Science and Engg: Statistics}

\author[FOSSEE] {FOSSEE}

\institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}

\date[] {31, October 2009\\Day 1, Session 3}

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\begin{document}

\begin{frame}

  \maketitle

\end{frame}

%% \begin{frame}

%%   \frametitle{Outline}

%%   \tableofcontents

%%   % You might wish to add the option [pausesections]

%% \end{frame}

\section{Statistics}

\begin{frame}

  \frametitle{More on data processing}

  \begin{block}{}

    We have a huge--1m records--data file.\\How do we do \emph{efficient} statistical computations, that is find mean, median, mode, standard deveiation etc; draw pie charts?

  \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).

    \item Print mean, median, mode and standard deviation of math scores for all regions combined.

  \end{itemize}

\end{frame}

\begin{frame}

  \frametitle{Statistical Analysis and Parsing \ldots}

  Machinery Required -

  \begin{itemize}

    \item File reading

    \item Parsing

    \item Dictionaries

    \item NumPy arrays

    \item Statistical operations

  \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 corresponds to one student's details

    \item aka record

    \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: English, Hindi, Maths, Science, Social

    \item Total marks

    \item Pass/Fail (P/F)

    \item Withdrawn (W)

  \end{itemize}

  \inctime{5}

\end{frame}

\subsection{Data processing}

\begin{frame}[fragile]

  \frametitle{File reading and parsing \ldots}

  \begin{lstlisting}

for record in open('sslc1.txt'):

    fields = record.split(';')

  \end{lstlisting}

\end{frame}

\subsection{Dictionary}

\begin{frame}[fragile]

  \frametitle{Dictionary: Introduction}

  \begin{itemize}

    \item lists index: 0 \ldots n

    \item dictionaries index using strings

  \end{itemize}

  \begin{block}{Example}

d = \{ ``Hitchhiker's guide'' : 42,

     ``Terminator'' : ``I'll be back''\}\\

d[``Terminator''] => ``I'll be back''

  \end{block}

\end{frame}

\begin{frame}[fragile]

  \frametitle{Dictionary: Introduction}

  \begin{lstlisting}

In [1]: d = {"Hitchhiker's guide" : 42,

      "Terminator" : "I'll be back"}

In [2]: d["Hitchhiker's guide"]

Out[2]: 42

In [3]: "Hitchhiker's guide" in d

Out[3]: True

In [4]: "Guido" in d

Out[4]: False

  \end{lstlisting}

\end{frame}

\begin{frame}[fragile]

  \frametitle{Dictionary: Introduction}

  \begin{lstlisting}

In [5]: d.keys()

Out[5]: ['Terminator', "Hitchhiker's 

                              guide"]

In [6]: d.values()

Out[6]: ["I'll be back", 42]

  \end{lstlisting}

\end{frame}

\begin{frame}[fragile]

  \frametitle{enumerate: Iterating through list indices}

  \begin{lstlisting}

In [1]: names = ["Guido","Alex", "Tim"]

In [2]: for i, name in enumerate(names):

   ...:     print i, name

   ...: 

0 Guido

1 Alex

2 Tim

  \end{lstlisting}

  \inctime{5}

\end{frame}

\begin{frame}[fragile]

  \frametitle{Dictionary: Building parsed data}

  Let our dictionary be:

  \begin{lstlisting}

science = {} # is an empty dictionary

  \end{lstlisting}

\end{frame}

\begin{frame}[fragile]

  \frametitle{Dictionary - Building parsed data}

  \begin{itemize}

    \item \emph{Keys} of \emph{science} will be region codes

    \item Value of a \emph{science} will be the number students who scored more than 90\% in that region

  \end{itemize}

\end{frame}

\begin{frame}[fragile]

  \frametitle{Building parsed data \ldots}

  \begin{lstlisting}

from pylab import pie

science = {}

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}

  \begin{lstlisting}

if region_code not in science:

    science[region_code] = 0

score_str = fields[4].strip()

score = int(score_str) if

    score_str != 'AA' else 0

if score > 90:

    science[region_code] += 1

  \end{lstlisting}

\end{frame}

\subsection{Visualizing the data}

\begin{frame}[fragile]

  \frametitle{Pie charts}

  \small

  \begin{lstlisting}

figure(1)

pie(science.values(), 

    labels=science.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}

  \inctime{5}

\end{frame}

\begin{frame}[fragile]

  \frametitle{Building data for all subjects \ldots}

  \begin{lstlisting}

from pylab import pie

from scipy import mean, median, std

from scipy import stats

scores = [[], [], [], [], []]

ninety_percents = [{}, {}, {}, {}, {}]

  \end{lstlisting}

\end{frame}

\begin{frame}[fragile]

  \frametitle{Building data for all subjects \ldots}

  \begin{lstlisting}

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 data for all subjects \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 = int(score_str) if

      score_str != 'AA' else 0

    scores[i].append(score)

    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}

  \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}

\subsection{Obtaining stastics}

\begin{frame}[fragile]

  \frametitle{Obtaining statistics}

  \begin{lstlisting}

math_scores = array(scores[2])

print "Mean: ", mean(math_scores)

print "Median: ", median(math_scores)

print "Mode: ", stats.mode(math_scores)

print "Standard Deviation: ",

              std(math_scores)

  \end{lstlisting}

  \inctime{15}

\end{frame}

\begin{frame}[fragile]

  \frametitle{What tools did we use?}

  \begin{itemize}

   \item Dictionaries for storing data

   \item Facilities for drawing pie charts

   \item NumPy arrays for efficient array manipulations

   \item Functions for statistical computations - mean, median, mode, standard deviation

  \end{itemize}

\end{frame}

\begin{frame}

\frametitle{L vs $T^2$ \ldots}

Let's go back to the L vs $T^2$ plot

\begin{itemize}

\item We first look at obtaining $T^2$ from T

\item Then, we look at plotting a Least Squares fit

\end{itemize}

\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/L-Tsq-points.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