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<header> | ||
<h1 class="title">Module <code>traceon.focus</code></h1> | ||
</header> | ||
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<section id="section-intro"> | ||
<p>Module containing a single function to find the focus of a beam of electron trajecories.</p> | ||
</section> | ||
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<section> | ||
</section> | ||
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<section> | ||
</section> | ||
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<section> | ||
<h2 class="section-title" id="header-functions">Functions</h2> | ||
<dl> | ||
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<dt id="traceon.focus.focus_position"><code class="name flex"> | ||
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<span>def <span class="ident">focus_position</span></span>(<span>positions)</span> | ||
</code></dt> | ||
<dd> | ||
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<details class="source"> | ||
<summary> | ||
<span>Expand source code</span> | ||
</summary> | ||
<pre><code class="python">def focus_position(positions): | ||
""" | ||
Find the focus of the given trajectories (which are returned from `traceon.tracing.Tracer.__call__`). | ||
The focus is found using a least square method by considering the final positions and velocities of | ||
the given trajectories and linearly extending the trajectories backwards. | ||
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Parameters | ||
------------ | ||
positions: iterable of (N,6) np.ndarray float64 | ||
Trajectories of electrons, as returned by `traceon.tracing.Tracer.__call__` | ||
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Returns | ||
-------------- | ||
(3,) np.ndarray of float64, representing the position of the focus | ||
""" | ||
assert all(p.shape == (len(p), 6) for p in positions) | ||
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angles_x = np.array([p[-1, 3]/p[-1, 5] for p in positions]) | ||
angles_y = np.array([p[-1, 4]/p[-1, 5] for p in positions]) | ||
x, y, z = [np.array([p[-1, i] for p in positions]) for i in [0, 1, 2]] | ||
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N = len(positions) | ||
first_column = np.concatenate( (-angles_x, -angles_y) ) | ||
second_column = np.concatenate( (np.ones(N), np.zeros(N)) ) | ||
third_column = np.concatenate( (np.zeros(N), np.ones(N)) ) | ||
right_hand_side = np.concatenate( (x - z*angles_x, y - z*angles_y) ) | ||
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(z, x, y) = np.linalg.lstsq( | ||
np.array([first_column, second_column, third_column]).T, | ||
right_hand_side, rcond=None)[0] | ||
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return np.array([x, y, z])</code></pre> | ||
</details> | ||
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<div class="desc"><p>Find the focus of the given trajectories (which are returned from <code><a title="traceon.tracing.Tracer.__call__" href="tracing.html#traceon.tracing.Tracer.__call__">Tracer.__call__()</a></code>). | ||
The focus is found using a least square method by considering the final positions and velocities of | ||
the given trajectories and linearly extending the trajectories backwards.</p> | ||
<h2 id="parameters">Parameters</h2> | ||
<dl> | ||
<dt><strong><code>positions</code></strong> : <code>iterable</code> of <code>(N,6) np.ndarray float64</code></dt> | ||
<dd>Trajectories of electrons, as returned by <code><a title="traceon.tracing.Tracer.__call__" href="tracing.html#traceon.tracing.Tracer.__call__">Tracer.__call__()</a></code></dd> | ||
</dl> | ||
<h2 id="returns">Returns</h2> | ||
<p>(3,) np.ndarray of float64, representing the position of the focus</p></div> | ||
</dd> | ||
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<li><code><a title="traceon.focus.focus_position" href="#traceon.focus.focus_position">focus_position</a></code></li> | ||
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