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<div class="section" id="plotting">
<h1>Plotting<a class="headerlink" href="#plotting" title="Permalink to this headline">¶</a></h1>
<p>If <a class="reference external" href="http://matplotlib.sourceforge.net/">matplotlib</a> is available, the functions <tt class="docutils literal"><span class="pre">plot</span></tt> and <tt class="docutils literal"><span class="pre">cplot</span></tt> in mpmath can be used to plot functions respectively as x-y graphs and in the complex plane. Also, <tt class="docutils literal"><span class="pre">splot</span></tt> can be used to produce 3D surface plots.</p>
<div class="section" id="function-curve-plots">
<h2>Function curve plots<a class="headerlink" href="#function-curve-plots" title="Permalink to this headline">¶</a></h2>
<img alt="_images/plot.png" src="_images/plot.png" />
<p>Output of <tt class="docutils literal"><span class="pre">plot([cos,</span> <span class="pre">sin],</span> <span class="pre">[-4,</span> <span class="pre">4])</span></tt></p>
<dl class="function">
<dt id="mpmath.plot">
<tt class="descclassname">mpmath.</tt><tt class="descname">plot</tt><big>(</big><em>ctx</em>, <em>f</em>, <em>xlim=</em><span class="optional">[</span>, <em>-5</em>, <em>5</em><span class="optional">]</span>, <em>ylim=None</em>, <em>points=200</em>, <em>file=None</em>, <em>dpi=None</em>, <em>singularities=</em><span class="optional">[</span><span class="optional">]</span>, <em>axes=None</em><big>)</big><a class="headerlink" href="#mpmath.plot" title="Permalink to this definition">¶</a></dt>
<dd><p>Shows a simple 2D plot of a function <img class="math" src="_images/math/c96dd6ec1dc4ad7520fbdc78fcdbec9edd068d0c.png" alt="f(x)"/> or list of functions
<img class="math" src="_images/math/1ad13c4e8c318e9bf1720a2bdbb6094260518fde.png" alt="[f_0(x), f_1(x), \ldots, f_n(x)]"/> over a given interval
specified by <em>xlim</em>. Some examples:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="n">plot</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">exp</span><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">*</span><span class="n">li</span><span class="p">(</span><span class="n">x</span><span class="p">),</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">])</span>
<span class="n">plot</span><span class="p">([</span><span class="n">cos</span><span class="p">,</span> <span class="n">sin</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">])</span>
<span class="n">plot</span><span class="p">([</span><span class="n">fresnels</span><span class="p">,</span> <span class="n">fresnelc</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">])</span>
<span class="n">plot</span><span class="p">([</span><span class="n">sqrt</span><span class="p">,</span> <span class="n">cbrt</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">])</span>
<span class="n">plot</span><span class="p">(</span><span class="k">lambda</span> <span class="n">t</span><span class="p">:</span> <span class="n">zeta</span><span class="p">(</span><span class="mf">0.5</span><span class="o">+</span><span class="n">t</span><span class="o">*</span><span class="n">j</span><span class="p">),</span> <span class="p">[</span><span class="o">-</span><span class="mi">20</span><span class="p">,</span> <span class="mi">20</span><span class="p">])</span>
<span class="n">plot</span><span class="p">([</span><span class="n">floor</span><span class="p">,</span> <span class="n">ceil</span><span class="p">,</span> <span class="nb">abs</span><span class="p">,</span> <span class="n">sign</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">])</span>
</pre></div>
</div>
<p>Points where the function raises a numerical exception or
returns an infinite value are removed from the graph.
Singularities can also be excluded explicitly
as follows (useful for removing erroneous vertical lines):</p>
<div class="highlight-python"><div class="highlight"><pre><span class="n">plot</span><span class="p">(</span><span class="n">cot</span><span class="p">,</span> <span class="n">ylim</span><span class="o">=</span><span class="p">[</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">])</span> <span class="c"># bad</span>
<span class="n">plot</span><span class="p">(</span><span class="n">cot</span><span class="p">,</span> <span class="n">ylim</span><span class="o">=</span><span class="p">[</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">],</span> <span class="n">singularities</span><span class="o">=</span><span class="p">[</span><span class="o">-</span><span class="n">pi</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">pi</span><span class="p">])</span> <span class="c"># good</span>
</pre></div>
</div>
<p>For parts where the function assumes complex values, the
real part is plotted with dashes and the imaginary part
is plotted with dots.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">This function requires matplotlib (pylab).</p>
</div>
</dd></dl>
</div>
<div class="section" id="complex-function-plots">
<h2>Complex function plots<a class="headerlink" href="#complex-function-plots" title="Permalink to this headline">¶</a></h2>
<img alt="_images/cplot.png" src="_images/cplot.png" />
<p>Output of <tt class="docutils literal"><span class="pre">fp.cplot(fp.gamma,</span> <span class="pre">points=100000)</span></tt></p>
<dl class="function">
<dt id="mpmath.cplot">
<tt class="descclassname">mpmath.</tt><tt class="descname">cplot</tt><big>(</big><em>ctx</em>, <em>f</em>, <em>re=</em><span class="optional">[</span>, <em>-5</em>, <em>5</em><span class="optional">]</span>, <em>im=</em><span class="optional">[</span>, <em>-5</em>, <em>5</em><span class="optional">]</span>, <em>points=2000</em>, <em>color=None</em>, <em>verbose=False</em>, <em>file=None</em>, <em>dpi=None</em>, <em>axes=None</em><big>)</big><a class="headerlink" href="#mpmath.cplot" title="Permalink to this definition">¶</a></dt>
<dd><p>Plots the given complex-valued function <em>f</em> over a rectangular part
of the complex plane specified by the pairs of intervals <em>re</em> and <em>im</em>.
For example:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="n">cplot</span><span class="p">(</span><span class="k">lambda</span> <span class="n">z</span><span class="p">:</span> <span class="n">z</span><span class="p">,</span> <span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">10</span><span class="p">,</span> <span class="mi">10</span><span class="p">])</span>
<span class="n">cplot</span><span class="p">(</span><span class="n">exp</span><span class="p">)</span>
<span class="n">cplot</span><span class="p">(</span><span class="n">zeta</span><span class="p">,</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">50</span><span class="p">])</span>
</pre></div>
</div>
<p>By default, the complex argument (phase) is shown as color (hue) and
the magnitude is show as brightness. You can also supply a
custom color function (<em>color</em>). This function should take a
complex number as input and return an RGB 3-tuple containing
floats in the range 0.0-1.0.</p>
<p>To obtain a sharp image, the number of points may need to be
increased to 100,000 or thereabout. Since evaluating the
function that many times is likely to be slow, the ‘verbose’
option is useful to display progress.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">This function requires matplotlib (pylab).</p>
</div>
</dd></dl>
</div>
<div class="section" id="d-surface-plots">
<h2>3D surface plots<a class="headerlink" href="#d-surface-plots" title="Permalink to this headline">¶</a></h2>
<img alt="_images/splot.png" src="_images/splot.png" />
<p>Output of <tt class="docutils literal"><span class="pre">splot</span></tt> for the donut example.</p>
<dl class="function">
<dt id="mpmath.splot">
<tt class="descclassname">mpmath.</tt><tt class="descname">splot</tt><big>(</big><em>ctx</em>, <em>f</em>, <em>u=</em><span class="optional">[</span>, <em>-5</em>, <em>5</em><span class="optional">]</span>, <em>v=</em><span class="optional">[</span>, <em>-5</em>, <em>5</em><span class="optional">]</span>, <em>points=100</em>, <em>keep_aspect=True</em>, <em>wireframe=False</em>, <em>file=None</em>, <em>dpi=None</em>, <em>axes=None</em><big>)</big><a class="headerlink" href="#mpmath.splot" title="Permalink to this definition">¶</a></dt>
<dd><p>Plots the surface defined by <img class="math" src="_images/math/bb2c93730dbb48558bb3c4738c956c4e8f816437.png" alt="f"/>.</p>
<p>If <img class="math" src="_images/math/bb2c93730dbb48558bb3c4738c956c4e8f816437.png" alt="f"/> returns a single component, then this plots the surface
defined by <img class="math" src="_images/math/c45f4d6822ca0dd7ea528041bf7079ff62ba3afb.png" alt="z = f(x,y)"/> over the rectangular domain with
<img class="math" src="_images/math/1a5f9274eefe45963c681d18e88951fd4d855b8d.png" alt="x = u"/> and <img class="math" src="_images/math/7b8577d72dc78ef2d19856895b18f28de3e80e8d.png" alt="y = v"/>.</p>
<p>If <img class="math" src="_images/math/bb2c93730dbb48558bb3c4738c956c4e8f816437.png" alt="f"/> returns three components, then this plots the parametric
surface <img class="math" src="_images/math/4c1c53bd0db4ab53f1731be43bf2e5e96c11e8ec.png" alt="x, y, z = f(u,v)"/> over the pairs of intervals <img class="math" src="_images/math/9ad99798ec4c38e165cf517cb9e02b1c9e824103.png" alt="u"/> and <img class="math" src="_images/math/a9f23bf124b6b2b2a993eb313c72e678664ac74a.png" alt="v"/>.</p>
<p>For example, to plot a simple function:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">mpmath</span> <span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">f</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">:</span> <span class="n">sin</span><span class="p">(</span><span class="n">x</span><span class="o">+</span><span class="n">y</span><span class="p">)</span><span class="o">*</span><span class="n">cos</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">splot</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="p">[</span><span class="o">-</span><span class="n">pi</span><span class="p">,</span><span class="n">pi</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="n">pi</span><span class="p">,</span><span class="n">pi</span><span class="p">])</span> <span class="c"># doctest: +SKIP</span>
</pre></div>
</div>
<p>Plotting a donut:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">r</span><span class="p">,</span> <span class="n">R</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span> <span class="mf">2.5</span>
<span class="gp">>>> </span><span class="n">f</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">:</span> <span class="p">[</span><span class="n">r</span><span class="o">*</span><span class="n">cos</span><span class="p">(</span><span class="n">u</span><span class="p">),</span> <span class="p">(</span><span class="n">R</span><span class="o">+</span><span class="n">r</span><span class="o">*</span><span class="n">sin</span><span class="p">(</span><span class="n">u</span><span class="p">))</span><span class="o">*</span><span class="n">cos</span><span class="p">(</span><span class="n">v</span><span class="p">),</span> <span class="p">(</span><span class="n">R</span><span class="o">+</span><span class="n">r</span><span class="o">*</span><span class="n">sin</span><span class="p">(</span><span class="n">u</span><span class="p">))</span><span class="o">*</span><span class="n">sin</span><span class="p">(</span><span class="n">v</span><span class="p">)]</span>
<span class="gp">>>> </span><span class="n">splot</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="o">*</span><span class="n">pi</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="o">*</span><span class="n">pi</span><span class="p">])</span> <span class="c"># doctest: +SKIP</span>
</pre></div>
</div>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">This function requires matplotlib (pylab) 0.98.5.3 or higher.</p>
</div>
</dd></dl>
</div>
</div>
</div>
</div>
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<h3><a href="index.html">Table Of Contents</a></h3>
<ul>
<li><a class="reference external" href="#">Plotting</a><ul>
<li><a class="reference external" href="#function-curve-plots">Function curve plots</a></li>
<li><a class="reference external" href="#complex-function-plots">Complex function plots</a></li>
<li><a class="reference external" href="#d-surface-plots">3D surface plots</a></li>
</ul>
</li>
</ul>
<h4>Previous topic</h4>
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title="previous chapter">Utility functions</a></p>
<h4>Next topic</h4>
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title="next chapter">Mathematical functions</a></p>
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