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<div class="section" id="pylab-examples-example-code-boxplot-demo2-py">
<span id="pylab-examples-boxplot-demo2"></span><h1>pylab_examples example code: boxplot_demo2.py<a class="headerlink" href="#pylab-examples-example-code-boxplot-demo2-py" title="Permalink to this headline">ΒΆ</a></h1>
<p>(<a class="reference external" href="../../mpl_examples/pylab_examples/boxplot_demo2.py">Source code</a>, <a class="reference external" href="../../mpl_examples/pylab_examples/boxplot_demo2.png">png</a>, <a class="reference external" href="../../mpl_examples/pylab_examples/boxplot_demo2.hires.png">hires.png</a>, <a class="reference external" href="../../mpl_examples/pylab_examples/boxplot_demo2.pdf">pdf</a>)</p>
<div class="figure">
<img alt="../../_images/boxplot_demo2.png" src="../../_images/boxplot_demo2.png" />
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<div class="highlight-python"><div class="highlight"><pre><span class="sd">"""</span>
<span class="sd">Thanks Josh Hemann for the example</span>
<span class="sd">"""</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">matplotlib.patches</span> <span class="kn">import</span> <span class="n">Polygon</span>
<span class="c"># Generate some data from five different probability distributions,</span>
<span class="c"># each with different characteristics. We want to play with how an IID</span>
<span class="c"># bootstrap resample of the data preserves the distributional</span>
<span class="c"># properties of the original sample, and a boxplot is one visual tool</span>
<span class="c"># to make this assessment</span>
<span class="n">numDists</span> <span class="o">=</span> <span class="mi">5</span>
<span class="n">randomDists</span> <span class="o">=</span> <span class="p">[</span><span class="s">'Normal(1,1)'</span><span class="p">,</span><span class="s">' Lognormal(1,1)'</span><span class="p">,</span> <span class="s">'Exp(1)'</span><span class="p">,</span> <span class="s">'Gumbel(6,4)'</span><span class="p">,</span>
<span class="s">'Triangular(2,9,11)'</span><span class="p">]</span>
<span class="n">N</span> <span class="o">=</span> <span class="mi">500</span>
<span class="n">norm</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">normal</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span> <span class="n">N</span><span class="p">)</span>
<span class="n">logn</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">lognormal</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span> <span class="n">N</span><span class="p">)</span>
<span class="n">expo</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">exponential</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">N</span><span class="p">)</span>
<span class="n">gumb</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">gumbel</span><span class="p">(</span><span class="mi">6</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="n">N</span><span class="p">)</span>
<span class="n">tria</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">triangular</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">9</span><span class="p">,</span> <span class="mi">11</span><span class="p">,</span> <span class="n">N</span><span class="p">)</span>
<span class="c"># Generate some random indices that we'll use to resample the original data</span>
<span class="c"># arrays. For code brevity, just use the same random indices for each array</span>
<span class="n">bootstrapIndices</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">random_integers</span><span class="p">(</span><span class="mi">0</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="n">N</span><span class="p">)</span>
<span class="n">normBoot</span> <span class="o">=</span> <span class="n">norm</span><span class="p">[</span><span class="n">bootstrapIndices</span><span class="p">]</span>
<span class="n">expoBoot</span> <span class="o">=</span> <span class="n">expo</span><span class="p">[</span><span class="n">bootstrapIndices</span><span class="p">]</span>
<span class="n">gumbBoot</span> <span class="o">=</span> <span class="n">gumb</span><span class="p">[</span><span class="n">bootstrapIndices</span><span class="p">]</span>
<span class="n">lognBoot</span> <span class="o">=</span> <span class="n">logn</span><span class="p">[</span><span class="n">bootstrapIndices</span><span class="p">]</span>
<span class="n">triaBoot</span> <span class="o">=</span> <span class="n">tria</span><span class="p">[</span><span class="n">bootstrapIndices</span><span class="p">]</span>
<span class="n">data</span> <span class="o">=</span> <span class="p">[</span><span class="n">norm</span><span class="p">,</span> <span class="n">normBoot</span><span class="p">,</span> <span class="n">logn</span><span class="p">,</span> <span class="n">lognBoot</span><span class="p">,</span> <span class="n">expo</span><span class="p">,</span> <span class="n">expoBoot</span><span class="p">,</span> <span class="n">gumb</span><span class="p">,</span> <span class="n">gumbBoot</span><span class="p">,</span>
<span class="n">tria</span><span class="p">,</span> <span class="n">triaBoot</span><span class="p">]</span>
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span><span class="mi">6</span><span class="p">))</span>
<span class="n">fig</span><span class="o">.</span><span class="n">canvas</span><span class="o">.</span><span class="n">set_window_title</span><span class="p">(</span><span class="s">'A Boxplot Example'</span><span class="p">)</span>
<span class="n">ax1</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">subplots_adjust</span><span class="p">(</span><span class="n">left</span><span class="o">=</span><span class="mf">0.075</span><span class="p">,</span> <span class="n">right</span><span class="o">=</span><span class="mf">0.95</span><span class="p">,</span> <span class="n">top</span><span class="o">=</span><span class="mf">0.9</span><span class="p">,</span> <span class="n">bottom</span><span class="o">=</span><span class="mf">0.25</span><span class="p">)</span>
<span class="n">bp</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">boxplot</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">notch</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">sym</span><span class="o">=</span><span class="s">'+'</span><span class="p">,</span> <span class="n">vert</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">whis</span><span class="o">=</span><span class="mf">1.5</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">setp</span><span class="p">(</span><span class="n">bp</span><span class="p">[</span><span class="s">'boxes'</span><span class="p">],</span> <span class="n">color</span><span class="o">=</span><span class="s">'black'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">setp</span><span class="p">(</span><span class="n">bp</span><span class="p">[</span><span class="s">'whiskers'</span><span class="p">],</span> <span class="n">color</span><span class="o">=</span><span class="s">'black'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">setp</span><span class="p">(</span><span class="n">bp</span><span class="p">[</span><span class="s">'fliers'</span><span class="p">],</span> <span class="n">color</span><span class="o">=</span><span class="s">'red'</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span><span class="s">'+'</span><span class="p">)</span>
<span class="c"># Add a horizontal grid to the plot, but make it very light in color</span>
<span class="c"># so we can use it for reading data values but not be distracting</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">yaxis</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="bp">True</span><span class="p">,</span> <span class="n">linestyle</span><span class="o">=</span><span class="s">'-'</span><span class="p">,</span> <span class="n">which</span><span class="o">=</span><span class="s">'major'</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">'lightgrey'</span><span class="p">,</span>
<span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span>
<span class="c"># Hide these grid behind plot objects</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">set_axisbelow</span><span class="p">(</span><span class="bp">True</span><span class="p">)</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s">'Comparison of IID Bootstrap Resampling Across Five Distributions'</span><span class="p">)</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s">'Distribution'</span><span class="p">)</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s">'Value'</span><span class="p">)</span>
<span class="c"># Now fill the boxes with desired colors</span>
<span class="n">boxColors</span> <span class="o">=</span> <span class="p">[</span><span class="s">'darkkhaki'</span><span class="p">,</span><span class="s">'royalblue'</span><span class="p">]</span>
<span class="n">numBoxes</span> <span class="o">=</span> <span class="n">numDists</span><span class="o">*</span><span class="mi">2</span>
<span class="n">medians</span> <span class="o">=</span> <span class="nb">range</span><span class="p">(</span><span class="n">numBoxes</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">numBoxes</span><span class="p">):</span>
<span class="n">box</span> <span class="o">=</span> <span class="n">bp</span><span class="p">[</span><span class="s">'boxes'</span><span class="p">][</span><span class="n">i</span><span class="p">]</span>
<span class="n">boxX</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">boxY</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">5</span><span class="p">):</span>
<span class="n">boxX</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">box</span><span class="o">.</span><span class="n">get_xdata</span><span class="p">()[</span><span class="n">j</span><span class="p">])</span>
<span class="n">boxY</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">box</span><span class="o">.</span><span class="n">get_ydata</span><span class="p">()[</span><span class="n">j</span><span class="p">])</span>
<span class="n">boxCoords</span> <span class="o">=</span> <span class="nb">zip</span><span class="p">(</span><span class="n">boxX</span><span class="p">,</span><span class="n">boxY</span><span class="p">)</span>
<span class="c"># Alternate between Dark Khaki and Royal Blue</span>
<span class="n">k</span> <span class="o">=</span> <span class="n">i</span> <span class="o">%</span> <span class="mi">2</span>
<span class="n">boxPolygon</span> <span class="o">=</span> <span class="n">Polygon</span><span class="p">(</span><span class="n">boxCoords</span><span class="p">,</span> <span class="n">facecolor</span><span class="o">=</span><span class="n">boxColors</span><span class="p">[</span><span class="n">k</span><span class="p">])</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">add_patch</span><span class="p">(</span><span class="n">boxPolygon</span><span class="p">)</span>
<span class="c"># Now draw the median lines back over what we just filled in</span>
<span class="n">med</span> <span class="o">=</span> <span class="n">bp</span><span class="p">[</span><span class="s">'medians'</span><span class="p">][</span><span class="n">i</span><span class="p">]</span>
<span class="n">medianX</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">medianY</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="p">):</span>
<span class="n">medianX</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">med</span><span class="o">.</span><span class="n">get_xdata</span><span class="p">()[</span><span class="n">j</span><span class="p">])</span>
<span class="n">medianY</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">med</span><span class="o">.</span><span class="n">get_ydata</span><span class="p">()[</span><span class="n">j</span><span class="p">])</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">medianX</span><span class="p">,</span> <span class="n">medianY</span><span class="p">,</span> <span class="s">'k'</span><span class="p">)</span>
<span class="n">medians</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">medianY</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="c"># Finally, overplot the sample averages, with horixzontal alignment</span>
<span class="c"># in the center of each box</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="n">np</span><span class="o">.</span><span class="n">average</span><span class="p">(</span><span class="n">med</span><span class="o">.</span><span class="n">get_xdata</span><span class="p">())],</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">average</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">i</span><span class="p">])],</span>
<span class="n">color</span><span class="o">=</span><span class="s">'w'</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span><span class="s">'*'</span><span class="p">,</span> <span class="n">markeredgecolor</span><span class="o">=</span><span class="s">'k'</span><span class="p">)</span>
<span class="c"># Set the axes ranges and axes labels</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">(</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">numBoxes</span><span class="o">+</span><span class="mf">0.5</span><span class="p">)</span>
<span class="n">top</span> <span class="o">=</span> <span class="mi">40</span>
<span class="n">bottom</span> <span class="o">=</span> <span class="o">-</span><span class="mi">5</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">(</span><span class="n">bottom</span><span class="p">,</span> <span class="n">top</span><span class="p">)</span>
<span class="n">xtickNames</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">setp</span><span class="p">(</span><span class="n">ax1</span><span class="p">,</span> <span class="n">xticklabels</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">repeat</span><span class="p">(</span><span class="n">randomDists</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">setp</span><span class="p">(</span><span class="n">xtickNames</span><span class="p">,</span> <span class="n">rotation</span><span class="o">=</span><span class="mi">45</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">8</span><span class="p">)</span>
<span class="c"># Due to the Y-axis scale being different across samples, it can be</span>
<span class="c"># hard to compare differences in medians across the samples. Add upper</span>
<span class="c"># X-axis tick labels with the sample medians to aid in comparison</span>
<span class="c"># (just use two decimal places of precision)</span>
<span class="n">pos</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="n">numBoxes</span><span class="p">)</span><span class="o">+</span><span class="mi">1</span>
<span class="n">upperLabels</span> <span class="o">=</span> <span class="p">[</span><span class="nb">str</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">round</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span> <span class="k">for</span> <span class="n">s</span> <span class="ow">in</span> <span class="n">medians</span><span class="p">]</span>
<span class="n">weights</span> <span class="o">=</span> <span class="p">[</span><span class="s">'bold'</span><span class="p">,</span> <span class="s">'semibold'</span><span class="p">]</span>
<span class="k">for</span> <span class="n">tick</span><span class="p">,</span><span class="n">label</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">numBoxes</span><span class="p">),</span><span class="n">ax1</span><span class="o">.</span><span class="n">get_xticklabels</span><span class="p">()):</span>
<span class="n">k</span> <span class="o">=</span> <span class="n">tick</span> <span class="o">%</span> <span class="mi">2</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="n">pos</span><span class="p">[</span><span class="n">tick</span><span class="p">],</span> <span class="n">top</span><span class="o">-</span><span class="p">(</span><span class="n">top</span><span class="o">*</span><span class="mf">0.05</span><span class="p">),</span> <span class="n">upperLabels</span><span class="p">[</span><span class="n">tick</span><span class="p">],</span>
<span class="n">horizontalalignment</span><span class="o">=</span><span class="s">'center'</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="s">'x-small'</span><span class="p">,</span> <span class="n">weight</span><span class="o">=</span><span class="n">weights</span><span class="p">[</span><span class="n">k</span><span class="p">],</span>
<span class="n">color</span><span class="o">=</span><span class="n">boxColors</span><span class="p">[</span><span class="n">k</span><span class="p">])</span>
<span class="c"># Finally, add a basic legend</span>
<span class="n">plt</span><span class="o">.</span><span class="n">figtext</span><span class="p">(</span><span class="mf">0.80</span><span class="p">,</span> <span class="mf">0.08</span><span class="p">,</span> <span class="nb">str</span><span class="p">(</span><span class="n">N</span><span class="p">)</span> <span class="o">+</span> <span class="s">' Random Numbers'</span> <span class="p">,</span>
<span class="n">backgroundcolor</span><span class="o">=</span><span class="n">boxColors</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">color</span><span class="o">=</span><span class="s">'black'</span><span class="p">,</span> <span class="n">weight</span><span class="o">=</span><span class="s">'roman'</span><span class="p">,</span>
<span class="n">size</span><span class="o">=</span><span class="s">'x-small'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">figtext</span><span class="p">(</span><span class="mf">0.80</span><span class="p">,</span> <span class="mf">0.045</span><span class="p">,</span> <span class="s">'IID Bootstrap Resample'</span><span class="p">,</span>
<span class="n">backgroundcolor</span><span class="o">=</span><span class="n">boxColors</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span>
<span class="n">color</span><span class="o">=</span><span class="s">'white'</span><span class="p">,</span> <span class="n">weight</span><span class="o">=</span><span class="s">'roman'</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="s">'x-small'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">figtext</span><span class="p">(</span><span class="mf">0.80</span><span class="p">,</span> <span class="mf">0.015</span><span class="p">,</span> <span class="s">'*'</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">'white'</span><span class="p">,</span> <span class="n">backgroundcolor</span><span class="o">=</span><span class="s">'silver'</span><span class="p">,</span>
<span class="n">weight</span><span class="o">=</span><span class="s">'roman'</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="s">'medium'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">figtext</span><span class="p">(</span><span class="mf">0.815</span><span class="p">,</span> <span class="mf">0.013</span><span class="p">,</span> <span class="s">' Average Value'</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">'black'</span><span class="p">,</span> <span class="n">weight</span><span class="o">=</span><span class="s">'roman'</span><span class="p">,</span>
<span class="n">size</span><span class="o">=</span><span class="s">'x-small'</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
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<p>Keywords: python, matplotlib, pylab, example, codex (see <a class="reference internal" href="../../faq/howto_faq.html#how-to-search-examples"><em>Search examples</em></a>)</p>
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