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    15. 

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    16. 

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    17. 

  17. <main>
    18. 

  18. <article id="content">
    19. 

  19. <header>
    20. 

  20. <h1 class="title"><code>analysis.utils</code> module</h1>
    21. 

  21. </header>
    22. 

  22. <section id="section-intro">
    23. 

  23. <details class="source">
    24. 

  24. <summary>Source code</summary>
    25. 

  25. <pre><code class="python">import pickle
    26. 

  26. import numpy as np
    27. 

  27. 

  28. def loadData(fileName, timestep, absolute=False):
    29. 

  29.     &#34;&#34;&#34;Load the data in data/fileName/ at the given timestep.
    30. 

  30. 

  31.     Parameters:
    32. 

  32.         fileName (string): data is loaded from data/fileName/
    33. 

  33.         timestep (integer): timestep at which to load the data
    34. 

  34.         absolute (bool): true to load relative to parent folder.
    35. 

  35.             Used for interactive jupyter notebook.
    36. 

  36. 

  37.     Returns:
    38. 

  38.         data instance that was saved by Simulation.save
    39. 

  39.     &#34;&#34;&#34;
    40. 

  40.     prepend = &#39;./..&#39; if absolute else &#39;./&#39;
    41. 

  41.     return pickle.load(open(prepend+&#39;/data/{}/data{}.pickle&#39;.format(fileName, timestep), &#34;rb&#34; ))
    42. 

  42. 

  43. def calculateEccentricity(M, ref_r, ref_v, r, v):
    44. 

  44.     &#34;&#34;&#34;Calculates the orbital eccentricity of a list of particles.
    45. 

  45. 

  46.     Parameters:
    47. 

  47.         M (string): mass of the central object
    48. 

  48.         ref_r (array): reference position of the central object
    49. 

  49.         ref_v (array): reference velocity of the central object
    50. 

  50.         r (array): list of positions of all particles (n particles, 3)
    51. 

  51.         v (array): list of velocities of all particles (n particles, 3)
    52. 

  52. 

  53.     Returns:
    54. 

  54.         Array of shape (n particles, 3) with the eccentricities of the orbits
    55. 

  55.     &#34;&#34;&#34;
    56. 

  56.     v1 = v - ref_v
    57. 

  57.     r1 = r - ref_r
    58. 

  58.     h_vec = np.cross(r1, v1)
    59. 

  59.     h = np.linalg.norm(h_vec, axis=-1)
    60. 

  60.     # Make use of $\vec{e} = (v \times (r \times v)) / M$, and e = |\vec{e}|
    61. 

  61.     e_vec = np.cross(v1, h_vec)/M - r1/np.linalg.norm(r1, axis=-1, keepdims=True)
    62. 

  62.     e = np.linalg.norm(e_vec, axis=-1)
    63. 

  63.     return e
    64. 

  64. 

  65. #############################  PLOTTING UTILS ########################
    66. 

  66. # Matplotlib can be tedious at times. These short functions make the
    67. 

  67. # repetitive parts simpler and ensure consistency.
    68. 

  68. 

  69. def plotCOM(ax):
    70. 

  70.     &#34;&#34;&#34;Plots cross at (0,0)&#34;&#34;&#34;
    71. 

  71.     ax.scatter([0],[0],marker=&#39;+&#39;, c=&#39;black&#39;, s=500, 
    72. 

  72.                alpha=.5, linewidth=1, zorder=-1)
    73. 

  73. 

  74. def plotCenterMasses(ax, data):
    75. 

  75.     &#34;&#34;&#34;Plots stars at the position of the central masses&#34;&#34;&#34;
    76. 

  76.     ax.scatter(data[&#39;r_vec&#39;][data[&#39;type&#39;][:,0]==&#39;center&#39;][:,0], 
    77. 

  77.                data[&#39;r_vec&#39;][data[&#39;type&#39;][:,0]==&#39;center&#39;][:,1], 
    78. 

  78.                s=100, marker=&#34;*&#34;, c=&#39;black&#39;, alpha=.7)
    79. 

  79. 

  80. def plotTracks(ax, tracks):
    81. 

  81.     &#34;&#34;&#34;Plots the tracks of the central masses&#34;&#34;&#34;
    82. 

  82.     for track in tracks:
    83. 

  83.         ax.plot(track[:,0], track[:,1], 
    84. 

  84.                 c=&#39;black&#39;, alpha=1.0, linewidth=1)
    85. 

  85. 

  86. def setSize(ax, x=None, y=None, mode=None):
    87. 

  87.     &#34;&#34;&#34;Sets the size of the plot. If mode=&#39;square&#39;, the x and y axis
    88. 

  88.     will have the same scale.&#34;&#34;&#34;
    89. 

  89.     if mode==&#39;square&#39;: ax.axis(&#39;square&#39;)
    90. 

  90.     if x is not None: ax.set_xlim(x)
    91. 

  91.     if y is not None: ax.set_ylim(y)
    92. 

  92. 

  93. def setAxes(ax, x=None, y=None, xcoords=None, ycoords=None, mode=None):
    94. 

  94.     &#34;&#34;&#34;&#34;Sets the axis labels (x, y) and their position (None). The mode
    95. 

  95.     keyword can be used to hide all the axes (&#39;hide&#39;), only plot the bottom
    96. 

  96.     axis (&#39;bottom&#39;) or only plot the bottom and left axes (&#39;bottomleft&#39;)&#34;&#34;&#34;
    97. 

  97.     if x is not None: ax.set_xlabel(x)
    98. 

  98.     if y is not None: ax.set_ylabel(y)
    99. 

  99.     if mode==&#39;hide&#39;:
    100. 

  100.         ax.spines[&#39;right&#39;].set_visible(False)
    101. 

  101.         ax.spines[&#39;top&#39;].set_visible(False)
    102. 

  102.         ax.spines[&#39;left&#39;].set_visible(False)
    103. 

  103.         ax.spines[&#39;bottom&#39;].set_visible(False)
    104. 

  104.         ax.set_xticklabels([])
    105. 

  105.         ax.set_xticks([])
    106. 

  106.         ax.set_yticklabels([])
    107. 

  107.         ax.set_yticks([])
    108. 

  108.     elif mode==&#39;bottomleft&#39;:
    109. 

  109.         ax.spines[&#39;right&#39;].set_visible(False)
    110. 

  110.         ax.spines[&#39;top&#39;].set_visible(False)
    111. 

  111.     elif mode==&#39;bottom&#39;:
    112. 

  112.         ax.get_yaxis().set_ticks([])
    113. 

  113.         ax.set_ylabel(&#39;&#39;)   
    114. 

  114.         ax.spines[&#39;left&#39;].set_visible(False)
    115. 

  115.         ax.spines[&#39;right&#39;].set_visible(False)
    116. 

  116.         ax.spines[&#39;top&#39;].set_visible(False)
    117. 

  117.     if xcoords is not None: ax.xaxis.set_label_coords(*xcoords)
    118. 

  118.     if ycoords is not None: ax.yaxis.set_label_coords(*ycoords)
    119. 

  119. 

  120. def stylizePlot(axs):
    121. 

  121.     &#34;&#34;&#34;Adds ticks (a la root style) for prettier plots&#34;&#34;&#34;
    122. 

  122.     for ax in axs:
    123. 

  123.         ax.tick_params(axis=&#39;both&#39;, which=&#39;both&#39;, direction=&#39;in&#39;, top=True, right=True)
    124. 

  124.         ax.minorticks_on()</code></pre>
    125. 

  125. </details>
    126. 

  126. </section>
    127. 

  127. <section>
    128. 

  128. </section>
    129. 

  129. <section>
    130. 

  130. </section>
    131. 

  131. <section>
    132. 

  132. <h2 class="section-title" id="header-functions">Functions</h2>
    133. 

  133. <dl>
    134. 

  134. <dt id="analysis.utils.calculateEccentricity"><code class="name flex">
    135. 

  135. <span>def <span class="ident">calculateEccentricity</span></span>(<span>M, ref_r, ref_v, r, v)</span>
    136. 

  136. </code></dt>
    137. 

  137. <dd>
    138. 

  138. <section class="desc"><p>Calculates the orbital eccentricity of a list of particles.</p>
    139. 

  139. <h2 id="parameters">Parameters</h2>
    140. 

  140. <dl>
    141. 

  141. <dt><strong><code>M</code></strong> :&ensp;<code>string</code></dt>
    142. 

  142. <dd>mass of the central object</dd>
    143. 

  143. <dt><strong><code>ref_r</code></strong> :&ensp;<code>array</code></dt>
    144. 

  144. <dd>reference position of the central object</dd>
    145. 

  145. <dt><strong><code>ref_v</code></strong> :&ensp;<code>array</code></dt>
    146. 

  146. <dd>reference velocity of the central object</dd>
    147. 

  147. <dt><strong><code>r</code></strong> :&ensp;<code>array</code></dt>
    148. 

  148. <dd>list of positions of all particles (n particles, 3)</dd>
    149. 

  149. <dt><strong><code>v</code></strong> :&ensp;<code>array</code></dt>
    150. 

  150. <dd>list of velocities of all particles (n particles, 3)</dd>
    151. 

  151. </dl>
    152. 

  152. <h2 id="returns">Returns</h2>
    153. 

  153. <p>Array of shape (n particles, 3) with the eccentricities of the orbits</p></section>
    154. 

  154. <details class="source">
    155. 

  155. <summary>Source code</summary>
    156. 

  156. <pre><code class="python">def calculateEccentricity(M, ref_r, ref_v, r, v):
    157. 

  157.     &#34;&#34;&#34;Calculates the orbital eccentricity of a list of particles.
    158. 

  158. 

  159.     Parameters:
    160. 

  160.         M (string): mass of the central object
    161. 

  161.         ref_r (array): reference position of the central object
    162. 

  162.         ref_v (array): reference velocity of the central object
    163. 

  163.         r (array): list of positions of all particles (n particles, 3)
    164. 

  164.         v (array): list of velocities of all particles (n particles, 3)
    165. 

  165. 

  166.     Returns:
    167. 

  167.         Array of shape (n particles, 3) with the eccentricities of the orbits
    168. 

  168.     &#34;&#34;&#34;
    169. 

  169.     v1 = v - ref_v
    170. 

  170.     r1 = r - ref_r
    171. 

  171.     h_vec = np.cross(r1, v1)
    172. 

  172.     h = np.linalg.norm(h_vec, axis=-1)
    173. 

  173.     # Make use of $\vec{e} = (v \times (r \times v)) / M$, and e = |\vec{e}|
    174. 

  174.     e_vec = np.cross(v1, h_vec)/M - r1/np.linalg.norm(r1, axis=-1, keepdims=True)
    175. 

  175.     e = np.linalg.norm(e_vec, axis=-1)
    176. 

  176.     return e</code></pre>
    177. 

  177. </details>
    178. 

  178. </dd>
    179. 

  179. <dt id="analysis.utils.loadData"><code class="name flex">
    180. 

  180. <span>def <span class="ident">loadData</span></span>(<span>fileName, timestep, absolute=False)</span>
    181. 

  181. </code></dt>
    182. 

  182. <dd>
    183. 

  183. <section class="desc"><p>Load the data in data/fileName/ at the given timestep.</p>
    184. 

  184. <h2 id="parameters">Parameters</h2>
    185. 

  185. <dl>
    186. 

  186. <dt><strong><code>fileName</code></strong> :&ensp;<code>string</code></dt>
    187. 

  187. <dd>data is loaded from data/fileName/</dd>
    188. 

  188. <dt><strong><code>timestep</code></strong> :&ensp;<code>integer</code></dt>
    189. 

  189. <dd>timestep at which to load the data</dd>
    190. 

  190. <dt><strong><code>absolute</code></strong> :&ensp;<code>bool</code></dt>
    191. 

  191. <dd>true to load relative to parent folder.
    192. 

  192. Used for interactive jupyter notebook.</dd>
    193. 

  193. </dl>
    194. 

  194. <h2 id="returns">Returns</h2>
    195. 

  195. <p>data instance that was saved by Simulation.save</p></section>
    196. 

  196. <details class="source">
    197. 

  197. <summary>Source code</summary>
    198. 

  198. <pre><code class="python">def loadData(fileName, timestep, absolute=False):
    199. 

  199.     &#34;&#34;&#34;Load the data in data/fileName/ at the given timestep.
    200. 

  200. 

  201.     Parameters:
    202. 

  202.         fileName (string): data is loaded from data/fileName/
    203. 

  203.         timestep (integer): timestep at which to load the data
    204. 

  204.         absolute (bool): true to load relative to parent folder.
    205. 

  205.             Used for interactive jupyter notebook.
    206. 

  206. 

  207.     Returns:
    208. 

  208.         data instance that was saved by Simulation.save
    209. 

  209.     &#34;&#34;&#34;
    210. 

  210.     prepend = &#39;./..&#39; if absolute else &#39;./&#39;
    211. 

  211.     return pickle.load(open(prepend+&#39;/data/{}/data{}.pickle&#39;.format(fileName, timestep), &#34;rb&#34; ))</code></pre>
    212. 

  212. </details>
    213. 

  213. </dd>
    214. 

  214. <dt id="analysis.utils.plotCOM"><code class="name flex">
    215. 

  215. <span>def <span class="ident">plotCOM</span></span>(<span>ax)</span>
    216. 

  216. </code></dt>
    217. 

  217. <dd>
    218. 

  218. <section class="desc"><p>Plots cross at (0,0)</p></section>
    219. 

  219. <details class="source">
    220. 

  220. <summary>Source code</summary>
    221. 

  221. <pre><code class="python">def plotCOM(ax):
    222. 

  222.     &#34;&#34;&#34;Plots cross at (0,0)&#34;&#34;&#34;
    223. 

  223.     ax.scatter([0],[0],marker=&#39;+&#39;, c=&#39;black&#39;, s=500, 
    224. 

  224.                alpha=.5, linewidth=1, zorder=-1)</code></pre>
    225. 

  225. </details>
    226. 

  226. </dd>
    227. 

  227. <dt id="analysis.utils.plotCenterMasses"><code class="name flex">
    228. 

  228. <span>def <span class="ident">plotCenterMasses</span></span>(<span>ax, data)</span>
    229. 

  229. </code></dt>
    230. 

  230. <dd>
    231. 

  231. <section class="desc"><p>Plots stars at the position of the central masses</p></section>
    232. 

  232. <details class="source">
    233. 

  233. <summary>Source code</summary>
    234. 

  234. <pre><code class="python">def plotCenterMasses(ax, data):
    235. 

  235.     &#34;&#34;&#34;Plots stars at the position of the central masses&#34;&#34;&#34;
    236. 

  236.     ax.scatter(data[&#39;r_vec&#39;][data[&#39;type&#39;][:,0]==&#39;center&#39;][:,0], 
    237. 

  237.                data[&#39;r_vec&#39;][data[&#39;type&#39;][:,0]==&#39;center&#39;][:,1], 
    238. 

  238.                s=100, marker=&#34;*&#34;, c=&#39;black&#39;, alpha=.7)</code></pre>
    239. 

  239. </details>
    240. 

  240. </dd>
    241. 

  241. <dt id="analysis.utils.plotTracks"><code class="name flex">
    242. 

  242. <span>def <span class="ident">plotTracks</span></span>(<span>ax, tracks)</span>
    243. 

  243. </code></dt>
    244. 

  244. <dd>
    245. 

  245. <section class="desc"><p>Plots the tracks of the central masses</p></section>
    246. 

  246. <details class="source">
    247. 

  247. <summary>Source code</summary>
    248. 

  248. <pre><code class="python">def plotTracks(ax, tracks):
    249. 

  249.     &#34;&#34;&#34;Plots the tracks of the central masses&#34;&#34;&#34;
    250. 

  250.     for track in tracks:
    251. 

  251.         ax.plot(track[:,0], track[:,1], 
    252. 

  252.                 c=&#39;black&#39;, alpha=1.0, linewidth=1)</code></pre>
    253. 

  253. </details>
    254. 

  254. </dd>
    255. 

  255. <dt id="analysis.utils.setAxes"><code class="name flex">
    256. 

  256. <span>def <span class="ident">setAxes</span></span>(<span>ax, x=None, y=None, xcoords=None, ycoords=None, mode=None)</span>
    257. 

  257. </code></dt>
    258. 

  258. <dd>
    259. 

  259. <section class="desc"><p>"Sets the axis labels (x, y) and their position (None). The mode
    260. 

  260. keyword can be used to hide all the axes ('hide'), only plot the bottom
    261. 

  261. axis ('bottom') or only plot the bottom and left axes ('bottomleft')</p></section>
    262. 

  262. <details class="source">
    263. 

  263. <summary>Source code</summary>
    264. 

  264. <pre><code class="python">def setAxes(ax, x=None, y=None, xcoords=None, ycoords=None, mode=None):
    265. 

  265.     &#34;&#34;&#34;&#34;Sets the axis labels (x, y) and their position (None). The mode
    266. 

  266.     keyword can be used to hide all the axes (&#39;hide&#39;), only plot the bottom
    267. 

  267.     axis (&#39;bottom&#39;) or only plot the bottom and left axes (&#39;bottomleft&#39;)&#34;&#34;&#34;
    268. 

  268.     if x is not None: ax.set_xlabel(x)
    269. 

  269.     if y is not None: ax.set_ylabel(y)
    270. 

  270.     if mode==&#39;hide&#39;:
    271. 

  271.         ax.spines[&#39;right&#39;].set_visible(False)
    272. 

  272.         ax.spines[&#39;top&#39;].set_visible(False)
    273. 

  273.         ax.spines[&#39;left&#39;].set_visible(False)
    274. 

  274.         ax.spines[&#39;bottom&#39;].set_visible(False)
    275. 

  275.         ax.set_xticklabels([])
    276. 

  276.         ax.set_xticks([])
    277. 

  277.         ax.set_yticklabels([])
    278. 

  278.         ax.set_yticks([])
    279. 

  279.     elif mode==&#39;bottomleft&#39;:
    280. 

  280.         ax.spines[&#39;right&#39;].set_visible(False)
    281. 

  281.         ax.spines[&#39;top&#39;].set_visible(False)
    282. 

  282.     elif mode==&#39;bottom&#39;:
    283. 

  283.         ax.get_yaxis().set_ticks([])
    284. 

  284.         ax.set_ylabel(&#39;&#39;)   
    285. 

  285.         ax.spines[&#39;left&#39;].set_visible(False)
    286. 

  286.         ax.spines[&#39;right&#39;].set_visible(False)
    287. 

  287.         ax.spines[&#39;top&#39;].set_visible(False)
    288. 

  288.     if xcoords is not None: ax.xaxis.set_label_coords(*xcoords)
    289. 

  289.     if ycoords is not None: ax.yaxis.set_label_coords(*ycoords)</code></pre>
    290. 

  290. </details>
    291. 

  291. </dd>
    292. 

  292. <dt id="analysis.utils.setSize"><code class="name flex">
    293. 

  293. <span>def <span class="ident">setSize</span></span>(<span>ax, x=None, y=None, mode=None)</span>
    294. 

  294. </code></dt>
    295. 

  295. <dd>
    296. 

  296. <section class="desc"><p>Sets the size of the plot. If mode='square', the x and y axis
    297. 

  297. will have the same scale.</p></section>
    298. 

  298. <details class="source">
    299. 

  299. <summary>Source code</summary>
    300. 

  300. <pre><code class="python">def setSize(ax, x=None, y=None, mode=None):
    301. 

  301.     &#34;&#34;&#34;Sets the size of the plot. If mode=&#39;square&#39;, the x and y axis
    302. 

  302.     will have the same scale.&#34;&#34;&#34;
    303. 

  303.     if mode==&#39;square&#39;: ax.axis(&#39;square&#39;)
    304. 

  304.     if x is not None: ax.set_xlim(x)
    305. 

  305.     if y is not None: ax.set_ylim(y)</code></pre>
    306. 

  306. </details>
    307. 

  307. </dd>
    308. 

  308. <dt id="analysis.utils.stylizePlot"><code class="name flex">
    309. 

  309. <span>def <span class="ident">stylizePlot</span></span>(<span>axs)</span>
    310. 

  310. </code></dt>
    311. 

  311. <dd>
    312. 

  312. <section class="desc"><p>Adds ticks (a la root style) for prettier plots</p></section>
    313. 

  313. <details class="source">
    314. 

  314. <summary>Source code</summary>
    315. 

  315. <pre><code class="python">def stylizePlot(axs):
    316. 

  316.     &#34;&#34;&#34;Adds ticks (a la root style) for prettier plots&#34;&#34;&#34;
    317. 

  317.     for ax in axs:
    318. 

  318.         ax.tick_params(axis=&#39;both&#39;, which=&#39;both&#39;, direction=&#39;in&#39;, top=True, right=True)
    319. 

  319.         ax.minorticks_on()</code></pre>
    320. 

  320. </details>
    321. 

  321. </dd>
    322. 

  322. </dl>
    323. 

  323. </section>
    324. 

  324. <section>
    325. 

  325. </section>
    326. 

  326. </article>
    327. 

  327. <nav id="sidebar">
    328. 

  328. <h1>Index</h1>
    329. 

  329. <div class="toc">
    330. 

  330. <ul></ul>
    331. 

  331. </div>
    332. 

  332. <ul id="index">
    333. 

  333. <li><h3><a href="#header-functions">Functions</a></h3>
    334. 

  334. <ul class="">
    335. 

  335. <li><code><a title="analysis.utils.calculateEccentricity" href="#analysis.utils.calculateEccentricity">calculateEccentricity</a></code></li>
    336. 

  336. <li><code><a title="analysis.utils.loadData" href="#analysis.utils.loadData">loadData</a></code></li>
    337. 

  337. <li><code><a title="analysis.utils.plotCOM" href="#analysis.utils.plotCOM">plotCOM</a></code></li>
    338. 

  338. <li><code><a title="analysis.utils.plotCenterMasses" href="#analysis.utils.plotCenterMasses">plotCenterMasses</a></code></li>
    339. 

  339. <li><code><a title="analysis.utils.plotTracks" href="#analysis.utils.plotTracks">plotTracks</a></code></li>
    340. 

  340. <li><code><a title="analysis.utils.setAxes" href="#analysis.utils.setAxes">setAxes</a></code></li>
    341. 

  341. <li><code><a title="analysis.utils.setSize" href="#analysis.utils.setSize">setSize</a></code></li>
    342. 

  342. <li><code><a title="analysis.utils.stylizePlot" href="#analysis.utils.stylizePlot">stylizePlot</a></code></li>
    343. 

  343. </ul>
    344. 

  344. </li>
    345. 

  345. </ul>
    346. 

  346. </nav>
    347. 

  347. </main>
    348. 

  348. <footer id="footer">
    349. 

  349. <p>Generated by <a href="https://pdoc3.github.io/pdoc"><cite>pdoc</cite> 0.5.2</a>.</p>
    350. 

  350. </footer>
    351. 

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    352. 

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    353. 

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    354. 

  354. </html>
    355.