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    15. 

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    16. 

  16. <body>
    17. 

  17. <main>
    18. 

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

  19. <header>
    20. 

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

  21. </header>
    22. 

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

  23. <p>Plots the Antennae using Kernel Density Estimation to map the density</p>
    24. 

  24. <details class="source">
    25. 

  25. <summary>Source code</summary>
    26. 

  26. <pre><code class="python">&#34;&#34;&#34;Plots the Antennae using Kernel Density Estimation to map the density&#34;&#34;&#34;
    27. 

  27. 

  28. import matplotlib.pyplot as plt
    29. 

  29. import numpy as np
    30. 

  30. from scipy.stats import gaussian_kde
    31. 

  31. 

  32. from analysis.colormaps import red_map
    33. 

  33. from analysis import utils
    34. 

  34. 

  35. def plotKDE(i, theta, phi, view):
    36. 

  36.     &#34;&#34;&#34;Plot the Antennae galaxies using kernel density estimation
    37. 

  37. 

  38.     Parameters:
    39. 

  39.         i (int): Timestep at which to plot them
    40. 

  40.         theta (float): polar angle
    41. 

  41.         phi (float): azimuthal angle
    42. 

  42.         view (float): rotation along the line of sight
    43. 

  43.     &#34;&#34;&#34;
    44. 

  44.     data = utils.loadData(&#39;antennae&#39;, 13500)
    45. 

  45.     r_vec = data[&#39;r_vec&#39;][::]
    46. 

  46.     
    47. 

  47.     # Rotate to view from (theta, phi, view) viewpoint
    48. 

  48.     M1 = np.array([[1, 0, 0],
    49. 

  49.         [0, np.cos(theta), np.sin(theta)],
    50. 

  50.         [0, -np.sin(theta), np.cos(theta)]])
    51. 

  51.     M2 = np.array([[np.cos(phi), np.sin(phi), 0],
    52. 

  52.         [-np.sin(phi), np.cos(phi), 0],
    53. 

  53.         [0, 0, 1]])
    54. 

  54.     M3 = np.array([[np.cos(view), np.sin(view), 0],
    55. 

  55.         [-np.sin(view), np.cos(view), 0],
    56. 

  56.         [0, 0, 1]])
    57. 

  57.     M = np.matmul(M2, np.matmul(M1, M3))
    58. 

  58.     r_vec = np.tensordot(r_vec, M, axes=[1,0])
    59. 

  59.     
    60. 

  60.     # Plotting
    61. 

  61.     plt.figure(figsize=(4,5), dpi=400)
    62. 

  62.     # Perform Kernel Density Estimation to colour by density
    63. 

  63.     xy = np.vstack([r_vec[:,0],r_vec[:,1]])
    64. 

  64.     c = gaussian_kde(xy)(xy)
    65. 

  65.     # Densest points are plotted last
    66. 

  66.     idx = c.argsort()
    67. 

  67.     x, y, c = r_vec[:,0][idx], r_vec[:,1][idx], c[idx]
    68. 

  68. 

  69.     plt.scatter(x, y, c=c, s=3, edgecolor=&#39;&#39;, cmap=red_map)
    70. 

  70.     plt.axis(&#39;square&#39;)
    71. 

  71.     plt.show()
    72. 

  72.     
    73. 

  73. 

  74. plotKDE(135, 1.86, 4.10, 5.10)</code></pre>
    75. 

  75. </details>
    76. 

  76. </section>
    77. 

  77. <section>
    78. 

  78. </section>
    79. 

  79. <section>
    80. 

  80. </section>
    81. 

  81. <section>
    82. 

  82. <h2 class="section-title" id="header-functions">Functions</h2>
    83. 

  83. <dl>
    84. 

  84. <dt id="analysis.antennaeKDE.plotKDE"><code class="name flex">
    85. 

  85. <span>def <span class="ident">plotKDE</span></span>(<span>i, theta, phi, view)</span>
    86. 

  86. </code></dt>
    87. 

  87. <dd>
    88. 

  88. <section class="desc"><p>Plot the Antennae galaxies using kernel density estimation</p>
    89. 

  89. <h2 id="parameters">Parameters</h2>
    90. 

  90. <dl>
    91. 

  91. <dt><strong><code>i</code></strong> :&ensp;<code>int</code></dt>
    92. 

  92. <dd>Timestep at which to plot them</dd>
    93. 

  93. <dt><strong><code>theta</code></strong> :&ensp;<code>float</code></dt>
    94. 

  94. <dd>polar angle</dd>
    95. 

  95. <dt><strong><code>phi</code></strong> :&ensp;<code>float</code></dt>
    96. 

  96. <dd>azimuthal angle</dd>
    97. 

  97. <dt><strong><code>view</code></strong> :&ensp;<code>float</code></dt>
    98. 

  98. <dd>rotation along the line of sight</dd>
    99. 

  99. </dl></section>
    100. 

  100. <details class="source">
    101. 

  101. <summary>Source code</summary>
    102. 

  102. <pre><code class="python">def plotKDE(i, theta, phi, view):
    103. 

  103.     &#34;&#34;&#34;Plot the Antennae galaxies using kernel density estimation
    104. 

  104. 

  105.     Parameters:
    106. 

  106.         i (int): Timestep at which to plot them
    107. 

  107.         theta (float): polar angle
    108. 

  108.         phi (float): azimuthal angle
    109. 

  109.         view (float): rotation along the line of sight
    110. 

  110.     &#34;&#34;&#34;
    111. 

  111.     data = utils.loadData(&#39;antennae&#39;, 13500)
    112. 

  112.     r_vec = data[&#39;r_vec&#39;][::]
    113. 

  113.     
    114. 

  114.     # Rotate to view from (theta, phi, view) viewpoint
    115. 

  115.     M1 = np.array([[1, 0, 0],
    116. 

  116.         [0, np.cos(theta), np.sin(theta)],
    117. 

  117.         [0, -np.sin(theta), np.cos(theta)]])
    118. 

  118.     M2 = np.array([[np.cos(phi), np.sin(phi), 0],
    119. 

  119.         [-np.sin(phi), np.cos(phi), 0],
    120. 

  120.         [0, 0, 1]])
    121. 

  121.     M3 = np.array([[np.cos(view), np.sin(view), 0],
    122. 

  122.         [-np.sin(view), np.cos(view), 0],
    123. 

  123.         [0, 0, 1]])
    124. 

  124.     M = np.matmul(M2, np.matmul(M1, M3))
    125. 

  125.     r_vec = np.tensordot(r_vec, M, axes=[1,0])
    126. 

  126.     
    127. 

  127.     # Plotting
    128. 

  128.     plt.figure(figsize=(4,5), dpi=400)
    129. 

  129.     # Perform Kernel Density Estimation to colour by density
    130. 

  130.     xy = np.vstack([r_vec[:,0],r_vec[:,1]])
    131. 

  131.     c = gaussian_kde(xy)(xy)
    132. 

  132.     # Densest points are plotted last
    133. 

  133.     idx = c.argsort()
    134. 

  134.     x, y, c = r_vec[:,0][idx], r_vec[:,1][idx], c[idx]
    135. 

  135. 

  136.     plt.scatter(x, y, c=c, s=3, edgecolor=&#39;&#39;, cmap=red_map)
    137. 

  137.     plt.axis(&#39;square&#39;)
    138. 

  138.     plt.show()</code></pre>
    139. 

  139. </details>
    140. 

  140. </dd>
    141. 

  141. </dl>
    142. 

  142. </section>
    143. 

  143. <section>
    144. 

  144. </section>
    145. 

  145. </article>
    146. 

  146. <nav id="sidebar">
    147. 

  147. <h1>Index</h1>
    148. 

  148. <div class="toc">
    149. 

  149. <ul></ul>
    150. 

  150. </div>
    151. 

  151. <ul id="index">
    152. 

  152. <li><h3><a href="#header-functions">Functions</a></h3>
    153. 

  153. <ul class="">
    154. 

  154. <li><code><a title="analysis.antennaeKDE.plotKDE" href="#analysis.antennaeKDE.plotKDE">plotKDE</a></code></li>
    155. 

  155. </ul>
    156. 

  156. </li>
    157. 

  157. </ul>
    158. 

  158. </nav>
    159. 

  159. </main>
    160. 

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    161. 

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    167.