76 \title[Exercises]{Exercises} |
76 \title[Exercises]{Exercises} |
77 |
77 |
78 \author[FOSSEE] {FOSSEE} |
78 \author[FOSSEE] {FOSSEE} |
79 |
79 |
80 \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay} |
80 \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay} |
81 \date[] {14 December, 2009\\Day 1, Session 5} |
81 \date[] {11 January, 2010\\Day 1, Session 5} |
82 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
82 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
83 |
83 |
84 %\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo} |
84 %\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo} |
85 %\logo{\pgfuseimage{iitmlogo}} |
85 %\logo{\pgfuseimage{iitmlogo}} |
86 |
86 |
109 \begin{frame} |
109 \begin{frame} |
110 \titlepage |
110 \titlepage |
111 \end{frame} |
111 \end{frame} |
112 |
112 |
113 |
113 |
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114 \begin{frame}[fragile] |
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115 \frametitle{Problem 1} |
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116 \begin{columns} |
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117 \column{0.5\textwidth} |
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118 \hspace*{-0.5in} |
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119 \includegraphics[height=2in, interpolate=true]{data/L-Tsq.png} |
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120 \column{0.45\textwidth} |
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121 \begin{block}{Example code} |
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122 \tiny |
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123 \begin{lstlisting} |
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124 l = [] |
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125 t = [] |
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126 for line in open('pendulum.txt'): |
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127 point = line.split() |
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128 l.append(float(point[0])) |
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129 t.append(float(point[1])) |
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130 tsq = [] |
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131 for time in t: |
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132 tsq.append(time*time) |
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133 plot(l, tsq, '.') |
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134 \end{lstlisting} |
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135 \end{block} |
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136 \end{columns} |
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137 \begin{block}{Problem Statement} |
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138 Tweak above code to plot data in file 'location.txt'. |
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139 \end{block} |
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140 \end{frame} |
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141 |
114 \begin{frame} |
142 \begin{frame} |
115 \frametitle{Problem 1} |
143 \frametitle{Problem 1 cont...} |
116 \begin{itemize} |
144 \begin{itemize} |
117 \item Open file 'pos.txt', it has X and Y Coordinate of a particle under motion |
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118 \item Plot X vs Y Graph. |
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119 \item Label both the axes. |
145 \item Label both the axes. |
120 \item What kind of motion is this? |
146 \item What kind of motion is this? |
121 \item Title the graph accordingly. |
147 \item Title the graph accordingly. |
122 \item Annotate the position where vertical velocity is zero. |
148 \item Annotate the position where vertical velocity is zero. |
123 \end{itemize} |
149 \end{itemize} |
124 \end{frame} |
150 \end{frame} |
125 |
151 |
126 \begin{frame} |
152 \begin{frame}[fragile] |
127 \frametitle{Problem 2} |
153 \frametitle{Problem 2} |
128 Write a Program that plots a regular n-gon(Let n = 5). |
154 \begin{columns} |
129 \end{frame} |
155 \column{0.5\textwidth} |
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156 \hspace*{-0.5in} |
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157 \includegraphics[height=2in, interpolate=true]{data/points} |
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158 \column{0.45\textwidth} |
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159 \begin{block}{Line between two points} |
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160 \tiny |
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161 \begin{lstlisting} |
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162 In []: x = [1, 5] |
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163 In []: y = [1, 4] |
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164 In []: plot(x, y) |
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165 \end{lstlisting} |
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166 \end{block} |
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167 \end{columns} |
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168 Line can be plotted using arrays of coordinates. |
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169 \pause |
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170 \begin{block}{Problem statement} |
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171 Write a Program that plots a regular n-gon(Let n = 5). |
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172 \end{block} |
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173 \end{frame} |
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174 |
130 |
175 |
131 \begin{frame}[fragile] |
176 \begin{frame}[fragile] |
132 \frametitle{Problem 3} |
177 \frametitle{Problem 3} |
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178 \begin{columns} |
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179 \column{0.5\textwidth} |
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180 \hspace*{-0.5in} |
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181 \includegraphics[height=2in, interpolate=true]{data/damp} |
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182 \column{0.45\textwidth} |
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183 \begin{block}{Damped Oscillation} |
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184 \tiny |
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185 \begin{lstlisting} |
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186 In []: x = linspace(0, 4*pi) |
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187 In []: plot(x, exp(x/10)*sin(x)) |
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188 \end{lstlisting} |
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189 \end{block} |
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190 \end{columns} |
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191 \end{frame} |
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192 |
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193 \begin{frame}[fragile] |
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194 \frametitle{Problem 3 cont...} |
133 Create a sequence of images in which the damped oscillator($e^{x/10}sin(x)$) slowly evolves over time. |
195 Create a sequence of images in which the damped oscillator($e^{x/10}sin(x)$) slowly evolves over time. |
134 \begin{columns} |
196 \begin{columns} |
135 \column{0.35\textwidth} |
197 \column{0.35\textwidth} |
136 \includegraphics[width=1.5in,height=1.5in, interpolate=true]{data/plot2} |
198 \includegraphics[width=1.5in,height=1.5in, interpolate=true]{data/plot2} |
137 \column{0.35\textwidth} |
199 \column{0.35\textwidth} |
145 savefig('plot'+str(i)+'.png') #i is int variable |
207 savefig('plot'+str(i)+'.png') #i is int variable |
146 \end{lstlisting} |
208 \end{lstlisting} |
147 \end{block} |
209 \end{block} |
148 \end{frame} |
210 \end{frame} |
149 |
211 |
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212 \begin{frame}[fragile] |
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213 \frametitle{Problem 4} |
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214 \begin{lstlisting} |
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215 In []: x = imread('smoothing.png') |
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216 In []: x.shape |
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217 Out[]: (256, 256) |
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218 In []: imshow(x,cmap=cm.gray) |
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219 \end{lstlisting} |
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220 \emphbar{Replace each pixel with mean of neighboring pixels} |
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221 \begin{center} |
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222 \includegraphics[height=1in, interpolate=true]{data/neighbour} |
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223 \end{center} |
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224 \end{frame} |
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225 |
150 \begin{frame} |
226 \begin{frame} |
151 \frametitle{Problem 4} |
227 \begin{center} |
152 Legendre polynomials $P_n(x)$ are defined by the following recurrence relation |
228 \includegraphics[height=3in, interpolate=true]{data/smoothing} |
153 |
229 \end{center} |
154 \center{$(n+1)P_{n+1}(x) - (2n+1)xP_n(x) + nP_{n-1}(x) = 0$}\\ |
230 \end{frame} |
155 |
231 |
156 with $P_0(x) = 1$, $P_1(x) = x$ and $P_2(x) = (3x^2 - 1)/2$. Compute the next three |
232 \begin{frame}[fragile] |
157 Legendre polynomials and plot all 6 over the interval [-1,1]. |
233 \frametitle{Problem 4: Approach} |
158 \end{frame} |
234 For \typ{y} being resultant image: |
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235 \begin{lstlisting} |
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236 y[1, 1] = x[0, 1]/4 + x[1, 0]/4 |
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237 + x[2, 1]/4 + x[1, 2]/4 |
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238 \end{lstlisting} |
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239 \begin{columns} |
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240 \column{0.45\textwidth} |
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241 \hspace*{-0.5in} |
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242 \includegraphics[height=1.5in, interpolate=true]{data/smoothing} |
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243 \column{0.45\textwidth} |
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244 \hspace*{-0.5in} |
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245 \includegraphics[height=1.5in, interpolate=true]{data/after-filter} |
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246 \end{columns} |
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247 \begin{block}{Hint:} |
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248 Use array Slicing. |
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249 \end{block} |
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250 \end{frame} |
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251 |
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252 \begin{frame}[fragile] |
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253 \frametitle{Solution} |
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254 \begin{lstlisting} |
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255 In []: y = zeros_like(x) |
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256 In []: y[1:-1,1:-1] = x[:-2,1:-1]/4+ |
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257 x[2:,1:-1]/4+ |
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258 x[1:-1,2:]/4+ |
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259 x[1:-1,:-2]/4 |
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260 In []: imshow(y,cmap=cm.gray) |
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261 \end{lstlisting} |
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262 \end{frame} |
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263 |
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264 |
159 \end{document} |
265 \end{document} |
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266 |
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267 %% \begin{frame} |
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268 %% \frametitle{Problem 4} |
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269 %% Legendre polynomials $P_n(x)$ are defined by the following recurrence relation |
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270 |
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271 %% \center{$(n+1)P_{n+1}(x) - (2n+1)xP_n(x) + nP_{n-1}(x) = 0$}\\ |
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272 |
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273 %% with $P_0(x) = 1$, $P_1(x) = x$ and $P_2(x) = (3x^2 - 1)/2$. Compute the next three |
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274 %% Legendre polynomials and plot all 6 over the interval [-1,1]. |
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275 %% \end{frame} |
160 |
276 |
161 %% \begin{frame}[fragile] |
277 %% \begin{frame}[fragile] |
162 %% \frametitle{Problem Set 5} |
278 %% \frametitle{Problem Set 5} |
163 %% \begin{columns} |
279 %% \begin{columns} |
164 %% \column{0.6\textwidth} |
280 %% \column{0.6\textwidth} |