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1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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2 %Tutorial slides on Python. |
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3 % |
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4 % Author: FOSSEE |
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5 % Copyright (c) 2009, FOSSEE, IIT Bombay |
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6 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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7 |
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8 \documentclass[14pt,compress]{beamer} |
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9 %\documentclass[draft]{beamer} |
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10 %\documentclass[compress,handout]{beamer} |
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11 %\usepackage{pgfpages} |
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12 %\pgfpagesuselayout{2 on 1}[a4paper,border shrink=5mm] |
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13 |
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14 % Modified from: generic-ornate-15min-45min.de.tex |
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15 \mode<presentation> |
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16 { |
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17 \usetheme{Warsaw} |
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18 \useoutertheme{infolines} |
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19 \setbeamercovered{transparent} |
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20 } |
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21 |
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22 \usepackage[english]{babel} |
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23 \usepackage[latin1]{inputenc} |
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24 %\usepackage{times} |
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25 \usepackage[T1]{fontenc} |
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26 |
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27 % Taken from Fernando's slides. |
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28 \usepackage{ae,aecompl} |
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29 \usepackage{mathpazo,courier,euler} |
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30 \usepackage[scaled=.95]{helvet} |
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31 |
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32 \definecolor{darkgreen}{rgb}{0,0.5,0} |
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33 |
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34 \usepackage{listings} |
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35 \lstset{language=Python, |
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36 basicstyle=\ttfamily\bfseries, |
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37 commentstyle=\color{red}\itshape, |
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38 stringstyle=\color{darkgreen}, |
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39 showstringspaces=false, |
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40 keywordstyle=\color{blue}\bfseries} |
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41 |
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42 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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43 % Macros |
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44 \setbeamercolor{emphbar}{bg=blue!20, fg=black} |
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45 \newcommand{\emphbar}[1] |
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46 {\begin{beamercolorbox}[rounded=true]{emphbar} |
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47 {#1} |
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48 \end{beamercolorbox} |
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49 } |
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50 \newcounter{time} |
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51 \setcounter{time}{0} |
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52 \newcommand{\inctime}[1]{\addtocounter{time}{#1}{\tiny \thetime\ m}} |
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53 |
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54 \newcommand{\typ}[1]{\lstinline{#1}} |
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55 |
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56 \newcommand{\kwrd}[1]{ \texttt{\textbf{\color{blue}{#1}}} } |
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57 |
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58 % Title page |
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59 \title{Python for Scientific Computing : Least Square Fit} |
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60 |
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61 \author[FOSSEE] {FOSSEE} |
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62 |
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63 \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay} |
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64 \date{} |
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65 |
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66 % DOCUMENT STARTS |
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67 \begin{document} |
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68 |
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69 \begin{frame} |
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70 \maketitle |
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71 \end{frame} |
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72 |
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73 \begin{frame} |
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74 \frametitle{About the Session} |
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75 \begin{block}{Goal} |
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76 Finding least square fit of given data-set |
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77 \end{block} |
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78 \begin{block}{Checklist} |
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79 \begin{itemize} |
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80 \item pendulum.txt |
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81 \end{itemize} |
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82 \end{block} |
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83 \end{frame} |
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84 |
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85 \begin{frame}[fragile] |
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86 \frametitle{$L$ vs. $T^2$ - Scatter} |
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87 \vspace{-0.15in} |
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88 \begin{figure} |
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89 \includegraphics[width=4in]{data/L-Tsq-points} |
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90 \end{figure} |
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91 \end{frame} |
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92 |
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93 \begin{frame}[fragile] |
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94 \frametitle{$L$ vs. $T^2$ - Line} |
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95 \vspace{-0.15in} |
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96 \begin{figure} |
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97 \includegraphics[width=4in]{data/L-Tsq-Line} |
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98 \end{figure} |
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99 \end{frame} |
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100 |
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101 \begin{frame}[fragile] |
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102 \frametitle{$L$ vs. $T^2$ } |
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103 \frametitle{$L$ vs. $T^2$ - Least Square Fit} |
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104 \vspace{-0.15in} |
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105 \begin{figure} |
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106 \includegraphics[width=4in]{data/least-sq-fit} |
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107 \end{figure} |
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108 \end{frame} |
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109 |
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110 \begin{frame} |
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111 \frametitle{Least Square Fit Curve} |
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112 \begin{center} |
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113 \begin{itemize} |
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114 \item $L \alpha T^2$ |
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115 \item Best Fit Curve $\rightarrow$ Linear |
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116 \begin{itemize} |
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117 \item Least Square Fit |
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118 \end{itemize} |
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119 \item \typ{lstsq()} |
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120 \end{itemize} |
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121 \end{center} |
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122 \end{frame} |
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123 |
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124 \begin{frame}[fragile] |
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125 \frametitle{\typ{lstsq}} |
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126 \begin{itemize} |
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127 \item We need to fit a line through points for the equation $T^2 = m \cdot L+c$ |
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128 \item In matrix form, the equation can be represented as $T_{sq} = A \cdot p$, where $T_{sq}$ is |
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129 $\begin{bmatrix} |
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130 T^2_1 \\ |
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131 T^2_2 \\ |
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132 \vdots\\ |
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133 T^2_N \\ |
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134 \end{bmatrix}$ |
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135 , A is |
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136 $\begin{bmatrix} |
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137 L_1 & 1 \\ |
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138 L_2 & 1 \\ |
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139 \vdots & \vdots\\ |
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140 L_N & 1 \\ |
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141 \end{bmatrix}$ |
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142 and p is |
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143 $\begin{bmatrix} |
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144 m\\ |
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145 c\\ |
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146 \end{bmatrix}$ |
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147 \item We need to find $p$ to plot the line |
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148 \end{itemize} |
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149 \end{frame} |
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150 |
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151 \begin{frame}[fragile] |
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152 \frametitle{Summary} |
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153 \begin{block}{} |
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154 |
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155 \end{block} |
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156 \end{frame} |
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157 |
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158 \begin{frame} |
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159 \frametitle{Thank you!} |
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160 \begin{block}{} |
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161 This session is part of \textcolor{blue}{FOSSEE} project funded by: |
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162 \begin{center} |
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163 \textcolor{blue}{NME through ICT from MHRD, Govt. of India}. |
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164 \end{center} |
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165 \end{block} |
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166 \end{frame} |
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167 |
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168 \end{document} |