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<div class="section" id="Playing-Darts-and-Estimating-Pi">
<h1>Playing Darts and Estimating Pi<a class="headerlink" href="#Playing-Darts-and-Estimating-Pi" title="Permalink to this headline">¶</a></h1>
<p>You and some friends are playing darts. You all are <strong>very</strong> bad at darts. Each throw is guaranteed to hit the square board depicted below, but otherwise each throw will land in a completely random position within the square. To entertain yourself during this pathetic display, you decide to use this as an opportunity to estimate the irrational number <span class="math notranslate nohighlight">\(\pi \approx 3.14159\)</span>.</p>
<p><img alt="A dart board" src="../../_images/circle_square_small.png" /></p>
<p>Because each throw falls randomly within the square, you realize that the probability of a dart landing within the circle is given by the ratio of the circle’s area to the square’s area:</p>
<div class="math notranslate nohighlight">
\begin{equation}
P_{circle} = \frac{Area_{circle}}{Area_{square}} = \frac{\pi r^2}{(2r)^2}
\end{equation}</div><p>Furthermore, we can interpret <span class="math notranslate nohighlight">\(P_{circle}\)</span> as being approximated by the fraction of darts thrown that land in the circle. Thus, we find:</p>
<div class="math notranslate nohighlight">
\begin{equation}
\frac{N_{circle}}{N_{total}} \approx \frac{\pi r^2}{(2r)^2} = \frac{\pi}{4}
\end{equation}</div><p>where <span class="math notranslate nohighlight">\(N_{total}\)</span> is the total number of darts thrown, and <span class="math notranslate nohighlight">\(N_{circle}\)</span> is the number of darts that land within the circle. Thus simply by keeping tally of where the darts land, you can begin to estimate the value of <span class="math notranslate nohighlight">\(\pi\)</span>!</p>
<div class="section" id="Problem-1">
<h2>Problem 1<a class="headerlink" href="#Problem-1" title="Permalink to this headline">¶</a></h2>
<p>Write code that simulates the dart throwing and tallying process, and keep a running estimate of <span class="math notranslate nohighlight">\(\pi\)</span> as “darts are being thrown”. For simplicity, you can assume that the board is centered at <span class="math notranslate nohighlight">\((0, 0)\)</span>, and that <span class="math notranslate nohighlight">\(r = 1\)</span> (the radius of the circle). Use <code class="docutils literal notranslate"><span class="pre">numpy.random.rand</span></code> (<a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.random.rand.html">link to docs</a>) to randomly generate the positions on the board where the darts land. Do this for <span class="math notranslate nohighlight">\(N = 10,000\)</span> darts in
total. For each dart thrown determine whether or not it landed within the circle, and update your estimate of <span class="math notranslate nohighlight">\(\pi\)</span> according to the formula: <span class="math notranslate nohighlight">\(N_{circle} / N_{total} \approx \pi / 4\)</span></p>
<p>Keep in mind that each dart can land in <span class="math notranslate nohighlight">\((x \in [-1, 1], y \in [-1, 1])\)</span> and that a dart that lands at <span class="math notranslate nohighlight">\((x, y)\)</span> falls within the circle if</p>
<div class="math notranslate nohighlight">
\begin{equation}
\sqrt{x^2 + y^2} < 1
\end{equation}</div><p>You can start this problem by writing a solution that uses explicit for-loops to help make clear the solution. That being said, you should strive to write a fully-vectorized solution (i.e. compute the running estimation of <span class="math notranslate nohighlight">\(\pi\)</span> during <span class="math notranslate nohighlight">\(10,000\)</span> dart throws without any explicit for-loops).</p>
</div>
<div class="section" id="Relevant-Reading">
<h2>Relevant Reading<a class="headerlink" href="#Relevant-Reading" title="Permalink to this headline">¶</a></h2>
<p>You will need to be familiar with NumPy’s <a class="reference external" href="http://www.pythonlikeyoumeanit.com/Module3_IntroducingNumpy/VectorizedOperations.html">vectorized operations</a> and with <a class="reference external" href="http://www.pythonlikeyoumeanit.com/Module3_IntroducingNumpy/VectorizedOperations.html#Specifying-the-axis-Keyword-Argument-in-Sequential-NumPy-Functions">summing over axes</a>. It will also likely be useful to leverage <a class="reference external" href="http://www.pythonlikeyoumeanit.com/Module3_IntroducingNumpy/AdvancedIndexing.html#Boolean-Array-Indexing">boolean
indexing</a>.</p>
<p>It is strongly recommended that you use matplotlib to visualize your running estimate of <span class="math notranslate nohighlight">\(\pi\)</span>. You can refer to <a class="reference external" href="http://www.pythonlikeyoumeanit.com/Module5_OddsAndEnds/Matplotlib.html#Plotting-and-Saving-a-Figure">this segment of PLYMI</a> to see how to create a simple line plot.</p>
</div>
<div class="section" id="Tips">
<h2>Tips<a class="headerlink" href="#Tips" title="Permalink to this headline">¶</a></h2>
<p>It is helpful to know about NumPy’s <a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.cumsum.html">cumulative-sum function</a>, <code class="docutils literal notranslate"><span class="pre">numpy.cumsum</span></code>. This is useful for keeping a running tally - i.e. keeping the history of the number of darts that have fallen within the circle, and not just the current count.</p>
</div>
<div class="section" id="Solution-(Unvectorized)">
<h2>Solution (Unvectorized)<a class="headerlink" href="#Solution-(Unvectorized)" title="Permalink to this headline">¶</a></h2>
<p>To start, we want to generate the <span class="math notranslate nohighlight">\((x, y)\)</span> coordinates for our <span class="math notranslate nohighlight">\(N = 10,000\)</span> darts. Using <code class="docutils literal notranslate"><span class="pre">numpy.random.rand(N,</span> <span class="pre">2)</span></code>, we can generate a 2D array with <span class="math notranslate nohighlight">\(N\)</span> rows - each row contains the <span class="math notranslate nohighlight">\((x, y)\)</span> coordinate for a single dart.</p>
<p>We want the <span class="math notranslate nohighlight">\(x\)</span> and <span class="math notranslate nohighlight">\(y\)</span> coordinate of each dart to fall within <span class="math notranslate nohighlight">\([-1, 1]\)</span>, respectively. <code class="docutils literal notranslate"><span class="pre">numpy.random.rand</span></code> generates numbers on the interval <span class="math notranslate nohighlight">\([0, 1)\)</span>. We can multiply the generated numbers by two and then subtract one to instead generate numbers on the interval <span class="math notranslate nohighlight">\([-1, 1)\)</span>.</p>
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<span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="n">N</span> <span class="o">=</span> <span class="mi">10000</span>
<span class="n">dart_positions</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span> <span class="c1"># generates numbers in [-1, 1]</span>
</pre></div>
</div>
</div>
<p>Now we can loop over the dart positions, determine if whether a given dart fell within the circle, and update <span class="math notranslate nohighlight">\(N_{circle}\)</span> accordingly.</p>
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<span></span><span class="n">Ncircle</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="c1"># start the count with 0 to make our loop-logic easier</span>
<span class="k">for</span> <span class="n">x</span><span class="p">,</span><span class="n">y</span> <span class="ow">in</span> <span class="n">dart_positions</span><span class="p">:</span>
<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">y</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o"><</span> <span class="mi">1</span><span class="p">:</span>
<span class="n">Ncircle</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">Ncircle</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="c1"># another dart has fallen in the circle</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">Ncircle</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">Ncircle</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span> <span class="c1"># the dart fell outside of the circle - Ncircle is unchanged</span>
</pre></div>
</div>
</div>
<p>Now lets use our list, <code class="docutils literal notranslate"><span class="pre">Ncircle</span></code>, to compute the running approximation for <span class="math notranslate nohighlight">\(\pi\)</span>. We will</p>
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<span></span><span class="n">running_estimate</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">n_total</span><span class="p">,</span> <span class="n">n_circle</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">Ncircle</span><span class="p">[</span><span class="mi">1</span><span class="p">:]):</span> <span class="c1"># skip the inital 0-count</span>
<span class="c1"># n_total starts at 0, so we need to add 1</span>
<span class="n">running_estimate</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">4</span> <span class="o">*</span> <span class="n">n_circle</span> <span class="o">/</span> <span class="p">(</span><span class="n">n_total</span> <span class="o">+</span> <span class="mi">1</span><span class="p">))</span>
</pre></div>
</div>
</div>
<p>Let’s print our estimate for our first 10 throws and our last 10 throws. We should see that our estimate is extremely crude and noisy for the first 10 throws and is much more tightly bound for the last 10 throws.</p>
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<span></span><span class="n">running_estimate</span><span class="p">[:</span><span class="mi">10</span><span class="p">]</span>
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[4.0,
4.0,
2.6666666666666665,
2.0,
2.4,
2.6666666666666665,
2.2857142857142856,
2.5,
2.6666666666666665,
2.8]
</pre></div></div>
</div>
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<span></span><span class="n">running_estimate</span><span class="p">[</span><span class="o">-</span><span class="mi">10</span><span class="p">:]</span>
</pre></div>
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</div>
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[3.1184065659093183,
3.1184947958366696,
3.118583008105674,
3.118671202721633,
3.1187593796898447,
3.118847539015606,
3.1189356807042112,
3.119023804760952,
3.119111911191119,
3.1192]
</pre></div></div>
</div>
</div>
<div class="section" id="Solution-(Vectorized)">
<h2>Solution (Vectorized)<a class="headerlink" href="#Solution-(Vectorized)" title="Permalink to this headline">¶</a></h2>
<p>To start, we want to generate the <span class="math notranslate nohighlight">\((x, y)\)</span> coordinates for our <span class="math notranslate nohighlight">\(N = 10,000\)</span> darts. Using <code class="docutils literal notranslate"><span class="pre">numpy.random.rand(N,</span> <span class="pre">2)</span></code>, we can generate a 2D array with <span class="math notranslate nohighlight">\(N\)</span> rows - each row contains the <span class="math notranslate nohighlight">\((x, y)\)</span> coordinate for a single dart.</p>
<p>We want the <span class="math notranslate nohighlight">\(x\)</span> and <span class="math notranslate nohighlight">\(y\)</span> coordinate of each dart to fall within <span class="math notranslate nohighlight">\([-1, 1]\)</span>, respectively. <code class="docutils literal notranslate"><span class="pre">numpy.random.rand</span></code> generates numbers on the interval <span class="math notranslate nohighlight">\([0, 1)\)</span>. We can multiply the generated numbers by two and then subtract one to instead generate numbers on the interval <span class="math notranslate nohighlight">\([-1, 1)\)</span>.</p>
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<span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="n">N</span> <span class="o">=</span> <span class="mi">10000</span>
<span class="n">dart_positions</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span> <span class="c1"># generates numbers in [-1, 1]</span>
</pre></div>
</div>
</div>
<p>Now we want to compute the distance from the origin, <span class="math notranslate nohighlight">\(\sqrt{x^2 + y^2}\)</span>, for every dart in <code class="docutils literal notranslate"><span class="pre">dart_positions</span></code>. We can do this by squaring each element of <code class="docutils literal notranslate"><span class="pre">dart_positions</span></code> and summing across its <em>columns</em> (axis-1), and then taking the square root of the result. This will produce a shape-<span class="math notranslate nohighlight">\((N,)\)</span> array that stores the distance of each dart from the origin.</p>
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<span></span><span class="n">dist_from_origin</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">((</span><span class="n">dart_positions</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">))</span> <span class="c1"># shape-(N,) array</span>
</pre></div>
</div>
</div>
<p>More concisely, you can use the built-in function <code class="docutils literal notranslate"><span class="pre">np.linalg.norm</span></code> to the same effect.</p>
<p>Now we want to determine which of those darts fall within the circle. That is, find where <span class="math notranslate nohighlight">\(\sqrt{x^2 + y^2} < 1\)</span>. We can simply use <code class="docutils literal notranslate"><span class="pre"><</span></code> to perform an elementwise comparison. This will produce a <em>boolean-valued</em> array whose value is <code class="docutils literal notranslate"><span class="pre">True</span></code> for each dart that fell within the circle and <code class="docutils literal notranslate"><span class="pre">False</span></code> for those that didn’t.</p>
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<span></span><span class="n">is_in_circle</span> <span class="o">=</span> <span class="n">dist_from_origin</span> <span class="o"><</span> <span class="mi">1</span> <span class="c1"># shape-(N,) boolean array</span>
</pre></div>
</div>
</div>
<p>Finally, we want to compute the total number of darts that had landed within the circle at each given point in the sequence of throws. <a class="reference external" href="https://www.pythonlikeyoumeanit.com/Module2_EssentialsOfPython/Basic_Objects.html#Boolean-Objects-are-Integers">Recall that</a> <code class="docutils literal notranslate"><span class="pre">True</span></code> behaves like <code class="docutils literal notranslate"><span class="pre">1</span></code> and <code class="docutils literal notranslate"><span class="pre">False</span></code> behaves like <code class="docutils literal notranslate"><span class="pre">0</span></code>. Thus we can perform a cumulative sum on <code class="docutils literal notranslate"><span class="pre">in_circle</span></code> to perform this tally.</p>
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<span></span><span class="c1"># cumulative sum: num_in_circle[i] = sum(is_in_circle[:i])</span>
<span class="n">num_in_circle</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cumsum</span><span class="p">(</span><span class="n">is_in_circle</span><span class="p">)</span>
<span class="n">num_thrown</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">N</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span> <span class="c1"># 1, 2, ..., N</span>
</pre></div>
</div>
</div>
<p>Finally we can compute our approximated value of <span class="math notranslate nohighlight">\(\pi\)</span> for each dart thrown via <span class="math notranslate nohighlight">\(N_{circle} / N_{total} \approx \pi / 4\)</span>.</p>
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<span></span><span class="n">running_estimate</span> <span class="o">=</span> <span class="mi">4</span> <span class="o">*</span> <span class="n">num_in_circle</span> <span class="o">/</span> <span class="n">num_thrown</span>
</pre></div>
</div>
</div>
<p>Let’s inspect our results by plotting them. We will create a simple line plot, and will include the actual value of pi as a dashed horizontal line. Because we are throwing so many darts, it is useful to plot the number of darts thrown on a log-scale. This will let us to see how our approximation improves on the scale of throwing tens of darts versus hundred versus thousands, etc.</p>
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<span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="o">%</span><span class="k">matplotlib</span> notebook
<span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">num_thrown</span><span class="p">,</span> <span class="n">running_estimate</span><span class="p">);</span>
<span class="n">ax</span><span class="o">.</span><span class="n">hlines</span><span class="p">(</span><span class="n">y</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">,</span> <span class="n">xmin</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">xmax</span><span class="o">=</span><span class="n">N</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span> <span class="n">linestyles</span><span class="o">=</span><span class="s2">"--"</span><span class="p">)</span> <span class="c1"># horizontal line at true value of pi</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xscale</span><span class="p">(</span><span class="s2">"log"</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="sa">r</span><span class="s2">"Estimated value of $\pi$"</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">"Number of randomly-thrown darts (log-scale)"</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
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'text-align: center; padding: 3px;"/>');
titlebar.append(titletext)
this.root.append(titlebar);
this.header = titletext[0];
}
mpl.figure.prototype._canvas_extra_style = function(canvas_div) {
}
mpl.figure.prototype._root_extra_style = function(canvas_div) {
}
mpl.figure.prototype._init_canvas = function() {
var fig = this;
var canvas_div = $('<div/>');
canvas_div.attr('style', 'position: relative; clear: both; outline: 0');
function canvas_keyboard_event(event) {
return fig.key_event(event, event['data']);
}
canvas_div.keydown('key_press', canvas_keyboard_event);
canvas_div.keyup('key_release', canvas_keyboard_event);
this.canvas_div = canvas_div
this._canvas_extra_style(canvas_div)
this.root.append(canvas_div);
var canvas = $('<canvas/>');
canvas.addClass('mpl-canvas');
canvas.attr('style', "left: 0; top: 0; z-index: 0; outline: 0")
this.canvas = canvas[0];
this.context = canvas[0].getContext("2d");
var backingStore = this.context.backingStorePixelRatio ||
this.context.webkitBackingStorePixelRatio ||
this.context.mozBackingStorePixelRatio ||
this.context.msBackingStorePixelRatio ||
this.context.oBackingStorePixelRatio ||
this.context.backingStorePixelRatio || 1;
mpl.ratio = (window.devicePixelRatio || 1) / backingStore;
var rubberband = $('<canvas/>');
rubberband.attr('style', "position: absolute; left: 0; top: 0; z-index: 1;")
var pass_mouse_events = true;
canvas_div.resizable({
start: function(event, ui) {
pass_mouse_events = false;
},
resize: function(event, ui) {
fig.request_resize(ui.size.width, ui.size.height);
},
stop: function(event, ui) {
pass_mouse_events = true;
fig.request_resize(ui.size.width, ui.size.height);
},
});
function mouse_event_fn(event) {
if (pass_mouse_events)
return fig.mouse_event(event, event['data']);
}
rubberband.mousedown('button_press', mouse_event_fn);
rubberband.mouseup('button_release', mouse_event_fn);
// Throttle sequential mouse events to 1 every 20ms.
rubberband.mousemove('motion_notify', mouse_event_fn);
rubberband.mouseenter('figure_enter', mouse_event_fn);
rubberband.mouseleave('figure_leave', mouse_event_fn);
canvas_div.on("wheel", function (event) {
event = event.originalEvent;
event['data'] = 'scroll'
if (event.deltaY < 0) {
event.step = 1;
} else {
event.step = -1;
}
mouse_event_fn(event);
});
canvas_div.append(canvas);
canvas_div.append(rubberband);
this.rubberband = rubberband;
this.rubberband_canvas = rubberband[0];
this.rubberband_context = rubberband[0].getContext("2d");
this.rubberband_context.strokeStyle = "#000000";
this._resize_canvas = function(width, height) {
// Keep the size of the canvas, canvas container, and rubber band
// canvas in synch.
canvas_div.css('width', width)
canvas_div.css('height', height)
canvas.attr('width', width * mpl.ratio);
canvas.attr('height', height * mpl.ratio);
canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');
rubberband.attr('width', width);
rubberband.attr('height', height);
}
// Set the figure to an initial 600x600px, this will subsequently be updated
// upon first draw.
this._resize_canvas(600, 600);
// Disable right mouse context menu.
$(this.rubberband_canvas).bind("contextmenu",function(e){
return false;
});
function set_focus () {
canvas.focus();
canvas_div.focus();
}
window.setTimeout(set_focus, 100);
}
mpl.figure.prototype._init_toolbar = function() {
var fig = this;
var nav_element = $('<div/>')
nav_element.attr('style', 'width: 100%');
this.root.append(nav_element);
// Define a callback function for later on.
function toolbar_event(event) {
return fig.toolbar_button_onclick(event['data']);
}
function toolbar_mouse_event(event) {
return fig.toolbar_button_onmouseover(event['data']);
}
for(var toolbar_ind in mpl.toolbar_items) {
var name = mpl.toolbar_items[toolbar_ind][0];
var tooltip = mpl.toolbar_items[toolbar_ind][1];
var image = mpl.toolbar_items[toolbar_ind][2];
var method_name = mpl.toolbar_items[toolbar_ind][3];
if (!name) {
// put a spacer in here.
continue;
}
var button = $('<button/>');
button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +
'ui-button-icon-only');
button.attr('role', 'button');
button.attr('aria-disabled', 'false');
button.click(method_name, toolbar_event);
button.mouseover(tooltip, toolbar_mouse_event);
var icon_img = $('<span/>');
icon_img.addClass('ui-button-icon-primary ui-icon');
icon_img.addClass(image);
icon_img.addClass('ui-corner-all');
var tooltip_span = $('<span/>');
tooltip_span.addClass('ui-button-text');
tooltip_span.html(tooltip);
button.append(icon_img);
button.append(tooltip_span);
nav_element.append(button);
}
var fmt_picker_span = $('<span/>');
var fmt_picker = $('<select/>');
fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');
fmt_picker_span.append(fmt_picker);
nav_element.append(fmt_picker_span);
this.format_dropdown = fmt_picker[0];
for (var ind in mpl.extensions) {
var fmt = mpl.extensions[ind];
var option = $(
'<option/>', {selected: fmt === mpl.default_extension}).html(fmt);
fmt_picker.append(option)
}
// Add hover states to the ui-buttons
$( ".ui-button" ).hover(
function() { $(this).addClass("ui-state-hover");},
function() { $(this).removeClass("ui-state-hover");}
);
var status_bar = $('<span class="mpl-message"/>');
nav_element.append(status_bar);
this.message = status_bar[0];
}
mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {
// Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,
// which will in turn request a refresh of the image.
this.send_message('resize', {'width': x_pixels, 'height': y_pixels});
}
mpl.figure.prototype.send_message = function(type, properties) {
properties['type'] = type;
properties['figure_id'] = this.id;
this.ws.send(JSON.stringify(properties));
}
mpl.figure.prototype.send_draw_message = function() {
if (!this.waiting) {
this.waiting = true;
this.ws.send(JSON.stringify({type: "draw", figure_id: this.id}));
}
}
mpl.figure.prototype.handle_save = function(fig, msg) {
var format_dropdown = fig.format_dropdown;
var format = format_dropdown.options[format_dropdown.selectedIndex].value;
fig.ondownload(fig, format);
}
mpl.figure.prototype.handle_resize = function(fig, msg) {
var size = msg['size'];
if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {
fig._resize_canvas(size[0], size[1]);
fig.send_message("refresh", {});
};
}
mpl.figure.prototype.handle_rubberband = function(fig, msg) {
var x0 = msg['x0'] / mpl.ratio;
var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;
var x1 = msg['x1'] / mpl.ratio;
var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;
x0 = Math.floor(x0) + 0.5;
y0 = Math.floor(y0) + 0.5;
x1 = Math.floor(x1) + 0.5;
y1 = Math.floor(y1) + 0.5;
var min_x = Math.min(x0, x1);
var min_y = Math.min(y0, y1);
var width = Math.abs(x1 - x0);
var height = Math.abs(y1 - y0);
fig.rubberband_context.clearRect(
0, 0, fig.canvas.width, fig.canvas.height);
fig.rubberband_context.strokeRect(min_x, min_y, width, height);
}
mpl.figure.prototype.handle_figure_label = function(fig, msg) {
// Updates the figure title.