author | Puneeth Chaganti <punchagan@fossee.in> |
Wed, 14 Oct 2009 16:34:30 +0530 | |
changeset 116 | cb91f43d2cbb |
parent 115 | 66709e58f765 |
child 117 | 958e3e090c6b |
permissions | -rw-r--r-- |
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% Tutorial slides on Python. |
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% Author: Prabhu Ramachandran <prabhu at aero.iitb.ac.in> |
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% Copyright (c) 2005-2009, Prabhu Ramachandran |
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\documentclass[14pt,compress]{beamer} |
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% Modified from: generic-ornate-15min-45min.de.tex |
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\usepackage{mathpazo,courier,euler} |
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\usepackage[scaled=.95]{helvet} |
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\usepackage{amsmath} |
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\definecolor{darkgreen}{rgb}{0,0.5,0} |
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\usepackage{listings} |
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% Macros |
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%%% This is from Fernando's setup. |
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% \usepackage{color} |
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% \definecolor{orange}{cmyk}{0,0.4,0.8,0.2} |
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% % Use and configure listings package for nicely formatted code |
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% \usepackage{listings} |
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% \lstset{ |
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% language=Python, |
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% } |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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% Title page |
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\title[]{Arrays \& Least Squares Fit} |
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\author[FOSSEE] {FOSSEE} |
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\institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay} |
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\date[] {31, October 2009} |
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%\includeonlyframes{current,current1,current2,current3,current4,current5,current6} |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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% DOCUMENT STARTS |
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\begin{document} |
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\begin{frame} |
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\maketitle |
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\end{frame} |
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%% \begin{frame} |
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%% \frametitle{Outline} |
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%% \tableofcontents |
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%% % You might wish to add the option [pausesections] |
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%% \end{frame} |
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\begin{frame} |
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\frametitle{Least Squares Fit} |
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In this session - |
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\begin{itemize} |
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\item We shall plot a least squares fit curve for time-period(T) squared vs. length(L) plot of a Simple Pendulum. |
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\item Given a file containing L and T values |
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\end{itemize} |
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\end{frame} |
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\begin{frame} |
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\frametitle{Least Squares Fit \ldots} |
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Machinery Required - |
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\begin{itemize} |
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\item Reading files and parsing data |
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\item Plotting points, lines |
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\item Calculating the Coefficients of the Least Squares Fit curve |
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\begin{itemize} |
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\item Arrays |
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\end{itemize} |
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\end{itemize} |
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\end{frame} |
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\begin{frame}[fragile] |
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\frametitle{Reading pendulum.txt} |
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\begin{itemize} |
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\item The file has two columns |
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\item Column1 - L; Column2 - T |
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\end{itemize} |
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\begin{lstlisting} |
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In []: L = [] |
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In []: T = [] |
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In []: for line in open('pendulum.txt'): |
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.... len, t = line.split() |
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.... L.append(float(len)) |
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.... T.append(float(t)) |
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\end{lstlisting} |
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We now have two lists L and T |
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\end{frame} |
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\begin{frame}[fragile] |
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\frametitle{Calculating T^2} |
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\begin{itemize} |
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\item Each element of the list T must be squared |
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\item Iterating over each element of the list works |
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\item But very slow \ldots |
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\item Instead, we use arrays |
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\end{itemize} |
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\begin{lstlisting} |
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In []: array(L) |
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In []: T = array(T) |
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In []: Tsq = T*T |
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In []: plot(L, Tsq, 'o') |
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\end{lstlisting} |
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\end{frame} |
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|
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\begin{frame}[fragile] |
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\frametitle{Arrays} |
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\begin{itemize} |
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\item T is now a \typ{numpy array} |
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\item \typ{numpy} arrays are very efficient and powerful |
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\item Very easy to perform element-wise operations |
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\item \typ{+, -, *, /, \%} |
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\item More about arrays later |
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\end{itemize} |
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\end{frame} |
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\begin{frame}[fragile] |
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\frametitle{Least Square Polynomial} |
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\begin{enumerate} |
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\item $T^2 = \frac{4\pi^2}{g}L$ |
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\item $T^2$ and $L$ have a linear relationship |
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\item We find an approximate solution to $Ax = y$, where A is the Van der Monde matrix to get coefficients of the least squares fit line. |
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\end{enumerate} |
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\end{frame} |
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|
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\begin{frame}[fragile] |
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\frametitle{Van der Monde Matrix} |
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Van der Monde matrix of order M |
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\begin{equation*} |
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\begin{bmatrix} |
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l_1^{M-1} & \ldots & l_1 & 1 \\ |
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l_2^{M-1} & \ldots &l_2 & 1 \\ |
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\vdots & \ldots & \vdots & \vdots\\ |
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l_N^{M-1} & \ldots & l_N & 1 \\ |
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\end{bmatrix} |
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\end{equation*} |
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\begin{lstlisting} |
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In []: A=vander(L,2) |
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\end{lstlisting} |
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\end{frame} |
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|
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\begin{frame}[fragile] |
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\frametitle{Least Square Fit Line} |
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\begin{itemize} |
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\item We use the \typ{lstsq} function of pylab |
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\item It returns the |
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\begin{enumerate} |
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\item Least squares solution |
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\item Sum of residues |
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\item Rank of matrix A |
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\item Singular values of A |
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\end{enumerate} |
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\end{itemize} |
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\begin{lstlisting} |
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coeffs, res, rank, sing = lstsq(A,Tsq) |
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\end{lstlisting} |
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\end{frame} |
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|
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\begin{frame}[fragile] |
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\frametitle{Least Square Fit Line \ldots} |
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\begin{itemize} |
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\item Use the poly1d function of pylab, to create a function for the line equation using the coefficients obtained |
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\begin{lstlisting} |
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p=poly1d(coeffs) |
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\end{lstlisting} |
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\item Get new T^2 values using the function \typ{p} obtained |
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\begin{lstlisting} |
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Tline = p(L) |
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\end{lstlisting} |
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\item Now plot Tline vs. L, to get the Least squares fit line. |
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\begin{lstlisting} |
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plot(L, Tline) |
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\end{lstlisting} |
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\end{frame} |
253 |
||
254 |
\end{document} |
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255 |
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256 |
Least squares: Smooth curve fit. |
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257 |
Array Operations: Mean, average (etc region wise like district wise and state wise from SSLC.txt) |
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258 |
Subject wise average. Introduce idea of dictionary. |
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259 |
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260 |
Session 3 |
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261 |
||
262 |
import scipy |
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263 |
from scipy import linalg. |
|
264 |
||
265 |
choose some meaningful plot. ?? |
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266 |
Newton's law of cooling. |
|
267 |
u, v, f - optics |
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268 |
hooke's law |
|
269 |
Least fit curves. |
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270 |
||
271 |
||
272 |
Choose a named problem. |
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ODE - first order. Whatever. |
|
274 |
||
275 |
||
276 |
arrays, etc etc. |
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277 |
sum, average, mean. whatever. statistical |
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278 |
sslc data |
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279 |
numpy load text?? |