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<main>
<article id="content">
<header>
<h1 class="title"><code>analysis.antennaeKDE</code> module</h1>
</header>
<section id="section-intro">
<p>Plots the Antennae using Kernel Density Estimation to map the density</p>
<details class="source">
<summary>Source code</summary>
<pre><code class="python">&#34;&#34;&#34;Plots the Antennae using Kernel Density Estimation to map the density&#34;&#34;&#34;

import matplotlib.pyplot as plt
import numpy as np
from scipy.stats import gaussian_kde

from analysis.colormaps import red_map
from analysis import utils

def plotKDE(i, theta, phi, view):
    &#34;&#34;&#34;Plot the Antennae galaxies using kernel density estimation

    Parameters:
        i (int): Timestep at which to plot them
        theta (float): polar angle
        phi (float): azimuthal angle
        view (float): rotation along the line of sight
    &#34;&#34;&#34;
    data = utils.loadData(&#39;antennae&#39;, 13500)
    r_vec = data[&#39;r_vec&#39;][::]
    
    # Rotate to view from (theta, phi, view) viewpoint
    M1 = np.array([[1, 0, 0],
        [0, np.cos(theta), np.sin(theta)],
        [0, -np.sin(theta), np.cos(theta)]])
    M2 = np.array([[np.cos(phi), np.sin(phi), 0],
        [-np.sin(phi), np.cos(phi), 0],
        [0, 0, 1]])
    M3 = np.array([[np.cos(view), np.sin(view), 0],
        [-np.sin(view), np.cos(view), 0],
        [0, 0, 1]])
    M = np.matmul(M2, np.matmul(M1, M3))
    r_vec = np.tensordot(r_vec, M, axes=[1,0])
    
    # Plotting
    plt.figure(figsize=(4,5), dpi=400)
    # Perform Kernel Density Estimation to colour by density
    xy = np.vstack([r_vec[:,0],r_vec[:,1]])
    c = gaussian_kde(xy)(xy)
    # Densest points are plotted last
    idx = c.argsort()
    x, y, c = r_vec[:,0][idx], r_vec[:,1][idx], c[idx]

    plt.scatter(x, y, c=c, s=3, edgecolor=&#39;&#39;, cmap=red_map)
    plt.axis(&#39;square&#39;)
    plt.show()
    

plotKDE(135, 1.86, 4.10, 5.10)</code></pre>
</details>
</section>
<section>
</section>
<section>
</section>
<section>
<h2 class="section-title" id="header-functions">Functions</h2>
<dl>
<dt id="analysis.antennaeKDE.plotKDE"><code class="name flex">
<span>def <span class="ident">plotKDE</span></span>(<span>i, theta, phi, view)</span>
</code></dt>
<dd>
<section class="desc"><p>Plot the Antennae galaxies using kernel density estimation</p>
<h2 id="parameters">Parameters</h2>
<dl>
<dt><strong><code>i</code></strong> :&ensp;<code>int</code></dt>
<dd>Timestep at which to plot them</dd>
<dt><strong><code>theta</code></strong> :&ensp;<code>float</code></dt>
<dd>polar angle</dd>
<dt><strong><code>phi</code></strong> :&ensp;<code>float</code></dt>
<dd>azimuthal angle</dd>
<dt><strong><code>view</code></strong> :&ensp;<code>float</code></dt>
<dd>rotation along the line of sight</dd>
</dl></section>
<details class="source">
<summary>Source code</summary>
<pre><code class="python">def plotKDE(i, theta, phi, view):
    &#34;&#34;&#34;Plot the Antennae galaxies using kernel density estimation

    Parameters:
        i (int): Timestep at which to plot them
        theta (float): polar angle
        phi (float): azimuthal angle
        view (float): rotation along the line of sight
    &#34;&#34;&#34;
    data = utils.loadData(&#39;antennae&#39;, 13500)
    r_vec = data[&#39;r_vec&#39;][::]
    
    # Rotate to view from (theta, phi, view) viewpoint
    M1 = np.array([[1, 0, 0],
        [0, np.cos(theta), np.sin(theta)],
        [0, -np.sin(theta), np.cos(theta)]])
    M2 = np.array([[np.cos(phi), np.sin(phi), 0],
        [-np.sin(phi), np.cos(phi), 0],
        [0, 0, 1]])
    M3 = np.array([[np.cos(view), np.sin(view), 0],
        [-np.sin(view), np.cos(view), 0],
        [0, 0, 1]])
    M = np.matmul(M2, np.matmul(M1, M3))
    r_vec = np.tensordot(r_vec, M, axes=[1,0])
    
    # Plotting
    plt.figure(figsize=(4,5), dpi=400)
    # Perform Kernel Density Estimation to colour by density
    xy = np.vstack([r_vec[:,0],r_vec[:,1]])
    c = gaussian_kde(xy)(xy)
    # Densest points are plotted last
    idx = c.argsort()
    x, y, c = r_vec[:,0][idx], r_vec[:,1][idx], c[idx]

    plt.scatter(x, y, c=c, s=3, edgecolor=&#39;&#39;, cmap=red_map)
    plt.axis(&#39;square&#39;)
    plt.show()</code></pre>
</details>
</dd>
</dl>
</section>
<section>
</section>
</article>
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<h1>Index</h1>
<div class="toc">
<ul></ul>
</div>
<ul id="index">
<li><h3><a href="#header-functions">Functions</a></h3>
<ul class="">
<li><code><a title="analysis.antennaeKDE.plotKDE" href="#analysis.antennaeKDE.plotKDE">plotKDE</a></code></li>
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