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<h1>Source code for quapy.plot</h1><div class="highlight"><pre>
<span></span><span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">defaultdict</span>
<span class="kn">import</span> <span class="nn">math</span>
<span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">cm</span>
<span class="kn">import</span> <span class="nn">matplotlib.colors</span> <span class="k">as</span> <span class="nn">mcolors</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">matplotlib.colors</span> <span class="kn">import</span> <span class="n">LinearSegmentedColormap</span><span class="p">,</span> <span class="n">ListedColormap</span>
<span class="kn">from</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">import</span> <span class="n">get_cmap</span>
<span class="kn">from</span> <span class="nn">matplotlib.ticker</span> <span class="kn">import</span> <span class="n">ScalarFormatter</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">scipy.stats</span> <span class="kn">import</span> <span class="n">ttest_ind_from_stats</span>
<span class="kn">import</span> <span class="nn">quapy</span> <span class="k">as</span> <span class="nn">qp</span>
<span class="n">plt</span><span class="o">.</span><span class="n">rcParams</span><span class="p">[</span><span class="s1">&#39;figure.figsize&#39;</span><span class="p">]</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">plt</span><span class="o">.</span><span class="n">rcParams</span><span class="p">[</span><span class="s1">&#39;figure.dpi&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="mi">200</span>
<span class="n">plt</span><span class="o">.</span><span class="n">rcParams</span><span class="p">[</span><span class="s1">&#39;font.size&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="mi">18</span>
<div class="viewcode-block" id="binary_diagonal">
<a class="viewcode-back" href="../../quapy.html#quapy.plot.binary_diagonal">[docs]</a>
<span class="k">def</span> <span class="nf">binary_diagonal</span><span class="p">(</span><span class="n">method_names</span><span class="p">,</span> <span class="n">true_prevs</span><span class="p">,</span> <span class="n">estim_prevs</span><span class="p">,</span> <span class="n">pos_class</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">title</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">show_std</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">legend</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
<span class="n">train_prev</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">savepath</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">method_order</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> The diagonal plot displays the predicted prevalence values (along the y-axis) as a function of the true prevalence</span>
<span class="sd"> values (along the x-axis). The optimal quantifier is described by the diagonal (0,0)-(1,1) of the plot (hence the</span>
<span class="sd"> name). It is convenient for binary quantification problems, though it can be used for multiclass problems by</span>
<span class="sd"> indicating which class is to be taken as the positive class. (For multiclass quantification problems, other plots</span>
<span class="sd"> like the :meth:`error_by_drift` might be preferable though).</span>
<span class="sd"> The format convention is as follows: `method_names`, `true_prevs`, and `estim_prevs` are array-like of the same</span>
<span class="sd"> length, with the ith element describing the output of an independent experiment. The elements of `true_prevs`, and</span>
<span class="sd"> `estim_prevs` are `ndarrays` with coherent shape for the same experiment. Experiments for the same method on</span>
<span class="sd"> different datasets can be used, in which case the method name can appear more than once in `method_names`.</span>
<span class="sd"> :param method_names: array-like with the method names for each experiment</span>
<span class="sd"> :param true_prevs: array-like with the true prevalence values for each experiment. Each entry is a ndarray of</span>
<span class="sd"> shape `(n_samples, n_classes)` components.</span>
<span class="sd"> :param estim_prevs: array-like with the estimated prevalence values for each experiment. Each entry is a ndarray of</span>
<span class="sd"> shape `(n_samples, n_classes)` components and `n_samples` must coincide with the corresponding entry in</span>
<span class="sd"> `true_prevs`.</span>
<span class="sd"> :param pos_class: index of the positive class (default 1)</span>
<span class="sd"> :param title: the title to be displayed in the plot (default None)</span>
<span class="sd"> :param show_std: whether to show standard deviations (represented by color bands). This might be inconvenient</span>
<span class="sd"> for cases in which many methods are compared, or when the standard deviations are high -- default True)</span>
<span class="sd"> :param legend: whether to display the legend (default True)</span>
<span class="sd"> :param train_prev: if indicated (default is None), the training prevalence (for the positive class) is highlighted</span>
<span class="sd"> in the plot. This is convenient when all the experiments have been conducted in the same dataset, or in</span>
<span class="sd"> datasets with the same training prevalence.</span>
<span class="sd"> :param savepath: path where to save the plot. If not indicated (as default), the plot is shown.</span>
<span class="sd"> :param method_order: if indicated (default is None), imposes the order in which the methods are processed (i.e.,</span>
<span class="sd"> listed in the legend and associated with matplotlib colors).</span>
<span class="sd"> :return: returns (fig, ax) matplotlib objects for eventual customisation</span>
<span class="sd"> &quot;&quot;&quot;</span>
<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">set_aspect</span><span class="p">(</span><span class="s1">&#39;equal&#39;</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="n">ax</span><span class="o">.</span><span class="n">plot</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">1</span><span class="p">],</span> <span class="s1">&#39;--k&#39;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;ideal&#39;</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">method_names</span><span class="p">,</span> <span class="n">true_prevs</span><span class="p">,</span> <span class="n">estim_prevs</span> <span class="o">=</span> <span class="n">_merge</span><span class="p">(</span><span class="n">method_names</span><span class="p">,</span> <span class="n">true_prevs</span><span class="p">,</span> <span class="n">estim_prevs</span><span class="p">)</span>
<span class="n">order</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="n">method_names</span><span class="p">,</span> <span class="n">true_prevs</span><span class="p">,</span> <span class="n">estim_prevs</span><span class="p">))</span>
<span class="k">if</span> <span class="n">method_order</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">table</span> <span class="o">=</span> <span class="p">{</span><span class="n">method_name</span><span class="p">:[</span><span class="n">true_prev</span><span class="p">,</span> <span class="n">estim_prev</span><span class="p">]</span> <span class="k">for</span> <span class="n">method_name</span><span class="p">,</span> <span class="n">true_prev</span><span class="p">,</span> <span class="n">estim_prev</span> <span class="ow">in</span> <span class="n">order</span><span class="p">}</span>
<span class="n">order</span> <span class="o">=</span> <span class="p">[(</span><span class="n">method_name</span><span class="p">,</span> <span class="o">*</span><span class="n">table</span><span class="p">[</span><span class="n">method_name</span><span class="p">])</span> <span class="k">for</span> <span class="n">method_name</span> <span class="ow">in</span> <span class="n">method_order</span><span class="p">]</span>
<span class="n">NUM_COLORS</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">method_names</span><span class="p">)</span>
<span class="k">if</span> <span class="n">NUM_COLORS</span><span class="o">&gt;</span><span class="mi">10</span><span class="p">:</span>
<span class="n">cm</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">get_cmap</span><span class="p">(</span><span class="s1">&#39;tab20&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_prop_cycle</span><span class="p">(</span><span class="n">color</span><span class="o">=</span><span class="p">[</span><span class="n">cm</span><span class="p">(</span><span class="mf">1.</span> <span class="o">*</span> <span class="n">i</span> <span class="o">/</span> <span class="n">NUM_COLORS</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">NUM_COLORS</span><span class="p">)])</span>
<span class="k">for</span> <span class="n">method</span><span class="p">,</span> <span class="n">true_prev</span><span class="p">,</span> <span class="n">estim_prev</span> <span class="ow">in</span> <span class="n">order</span><span class="p">:</span>
<span class="n">true_prev</span> <span class="o">=</span> <span class="n">true_prev</span><span class="p">[:,</span><span class="n">pos_class</span><span class="p">]</span>
<span class="n">estim_prev</span> <span class="o">=</span> <span class="n">estim_prev</span><span class="p">[:,</span><span class="n">pos_class</span><span class="p">]</span>
<span class="n">x_ticks</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">unique</span><span class="p">(</span><span class="n">true_prev</span><span class="p">)</span>
<span class="n">x_ticks</span><span class="o">.</span><span class="n">sort</span><span class="p">()</span>
<span class="n">y_ave</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">([</span><span class="n">estim_prev</span><span class="p">[</span><span class="n">true_prev</span> <span class="o">==</span> <span class="n">x</span><span class="p">]</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">x_ticks</span><span class="p">])</span>
<span class="n">y_std</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">([</span><span class="n">estim_prev</span><span class="p">[</span><span class="n">true_prev</span> <span class="o">==</span> <span class="n">x</span><span class="p">]</span><span class="o">.</span><span class="n">std</span><span class="p">()</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">x_ticks</span><span class="p">])</span>
<span class="n">ax</span><span class="o">.</span><span class="n">errorbar</span><span class="p">(</span><span class="n">x_ticks</span><span class="p">,</span> <span class="n">y_ave</span><span class="p">,</span> <span class="n">fmt</span><span class="o">=</span><span class="s1">&#39;-&#39;</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span><span class="s1">&#39;o&#39;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="n">method</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="k">if</span> <span class="n">show_std</span><span class="p">:</span>
<span class="n">ax</span><span class="o">.</span><span class="n">fill_between</span><span class="p">(</span><span class="n">x_ticks</span><span class="p">,</span> <span class="n">y_ave</span> <span class="o">-</span> <span class="n">y_std</span><span class="p">,</span> <span class="n">y_ave</span> <span class="o">+</span> <span class="n">y_std</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.25</span><span class="p">)</span>
<span class="k">if</span> <span class="n">train_prev</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">train_prev</span> <span class="o">=</span> <span class="n">train_prev</span><span class="p">[</span><span class="n">pos_class</span><span class="p">]</span>
<span class="n">ax</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">train_prev</span><span class="p">,</span> <span class="n">train_prev</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s1">&#39;c&#39;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;tr-prev&#39;</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">edgecolor</span><span class="o">=</span><span class="s1">&#39;k&#39;</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set</span><span class="p">(</span><span class="n">xlabel</span><span class="o">=</span><span class="s1">&#39;true prevalence&#39;</span><span class="p">,</span> <span class="n">ylabel</span><span class="o">=</span><span class="s1">&#39;estimated prevalence&#39;</span><span class="p">,</span> <span class="n">title</span><span class="o">=</span><span class="n">title</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylim</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="n">ax</span><span class="o">.</span><span class="n">set_xlim</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="k">if</span> <span class="n">legend</span><span class="p">:</span>
<span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s1">&#39;center left&#39;</span><span class="p">,</span> <span class="n">bbox_to_anchor</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">))</span>
<span class="n">_save_or_show</span><span class="p">(</span><span class="n">savepath</span><span class="p">)</span>
<span class="k">return</span> <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span></div>
<div class="viewcode-block" id="binary_bias_global">
<a class="viewcode-back" href="../../quapy.html#quapy.plot.binary_bias_global">[docs]</a>
<span class="k">def</span> <span class="nf">binary_bias_global</span><span class="p">(</span><span class="n">method_names</span><span class="p">,</span> <span class="n">true_prevs</span><span class="p">,</span> <span class="n">estim_prevs</span><span class="p">,</span> <span class="n">pos_class</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">title</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">savepath</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Box-plots displaying the global bias (i.e., signed error computed as the estimated value minus the true value)</span>
<span class="sd"> for each quantification method with respect to a given positive class.</span>
<span class="sd"> The format convention is as follows: `method_names`, `true_prevs`, and `estim_prevs` are array-like of the same</span>
<span class="sd"> length, with the ith element describing the output of an independent experiment. The elements of `true_prevs`, and</span>
<span class="sd"> `estim_prevs` are `ndarrays` with coherent shape for the same experiment. Experiments for the same method on</span>
<span class="sd"> different datasets can be used, in which case the method name can appear more than once in `method_names`.</span>
<span class="sd"> :param method_names: array-like with the method names for each experiment</span>
<span class="sd"> :param true_prevs: array-like with the true prevalence values for each experiment. Each entry is a ndarray of</span>
<span class="sd"> shape `(n_samples, n_classes)` components.</span>
<span class="sd"> :param estim_prevs: array-like with the estimated prevalence values for each experiment. Each entry is a ndarray of</span>
<span class="sd"> shape `(n_samples, n_classes)` components and `n_samples` must coincide with the corresponding entry in</span>
<span class="sd"> `true_prevs`.</span>
<span class="sd"> :param pos_class: index of the positive class</span>
<span class="sd"> :param title: the title to be displayed in the plot (default None)</span>
<span class="sd"> :param savepath: path where to save the plot. If not indicated (as default), the plot is shown.</span>
<span class="sd"> :return: returns (fig, ax) matplotlib objects for eventual customisation</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="n">method_names</span><span class="p">,</span> <span class="n">true_prevs</span><span class="p">,</span> <span class="n">estim_prevs</span> <span class="o">=</span> <span class="n">_merge</span><span class="p">(</span><span class="n">method_names</span><span class="p">,</span> <span class="n">true_prevs</span><span class="p">,</span> <span class="n">estim_prevs</span><span class="p">)</span>
<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">grid</span><span class="p">()</span>
<span class="n">data</span><span class="p">,</span> <span class="n">labels</span> <span class="o">=</span> <span class="p">[],</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">method</span><span class="p">,</span> <span class="n">true_prev</span><span class="p">,</span> <span class="n">estim_prev</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">method_names</span><span class="p">,</span> <span class="n">true_prevs</span><span class="p">,</span> <span class="n">estim_prevs</span><span class="p">):</span>
<span class="n">true_prev</span> <span class="o">=</span> <span class="n">true_prev</span><span class="p">[:,</span><span class="n">pos_class</span><span class="p">]</span>
<span class="n">estim_prev</span> <span class="o">=</span> <span class="n">estim_prev</span><span class="p">[:,</span><span class="n">pos_class</span><span class="p">]</span>
<span class="n">data</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">estim_prev</span><span class="o">-</span><span class="n">true_prev</span><span class="p">)</span>
<span class="n">labels</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">method</span><span class="p">)</span>
<span class="n">ax</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">labels</span><span class="o">=</span><span class="n">labels</span><span class="p">,</span> <span class="n">patch_artist</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">showmeans</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xticks</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">ax</span><span class="o">.</span><span class="n">set</span><span class="p">(</span><span class="n">ylabel</span><span class="o">=</span><span class="s1">&#39;error bias&#39;</span><span class="p">,</span> <span class="n">title</span><span class="o">=</span><span class="n">title</span><span class="p">)</span>
<span class="n">_save_or_show</span><span class="p">(</span><span class="n">savepath</span><span class="p">)</span>
<span class="k">return</span> <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span></div>
<div class="viewcode-block" id="binary_bias_bins">
<a class="viewcode-back" href="../../quapy.html#quapy.plot.binary_bias_bins">[docs]</a>
<span class="k">def</span> <span class="nf">binary_bias_bins</span><span class="p">(</span><span class="n">method_names</span><span class="p">,</span> <span class="n">true_prevs</span><span class="p">,</span> <span class="n">estim_prevs</span><span class="p">,</span> <span class="n">pos_class</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">title</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">nbins</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">colormap</span><span class="o">=</span><span class="n">cm</span><span class="o">.</span><span class="n">tab10</span><span class="p">,</span>
<span class="n">vertical_xticks</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">legend</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">savepath</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Box-plots displaying the local bias (i.e., signed error computed as the estimated value minus the true value)</span>
<span class="sd"> for different bins of (true) prevalence of the positive class, for each quantification method.</span>
<span class="sd"> The format convention is as follows: `method_names`, `true_prevs`, and `estim_prevs` are array-like of the same</span>
<span class="sd"> length, with the ith element describing the output of an independent experiment. The elements of `true_prevs`, and</span>
<span class="sd"> `estim_prevs` are `ndarrays` with coherent shape for the same experiment. Experiments for the same method on</span>
<span class="sd"> different datasets can be used, in which case the method name can appear more than once in `method_names`.</span>
<span class="sd"> :param method_names: array-like with the method names for each experiment</span>
<span class="sd"> :param true_prevs: array-like with the true prevalence values for each experiment. Each entry is a ndarray of</span>
<span class="sd"> shape `(n_samples, n_classes)` components.</span>
<span class="sd"> :param estim_prevs: array-like with the estimated prevalence values for each experiment. Each entry is a ndarray of</span>
<span class="sd"> shape `(n_samples, n_classes)` components and `n_samples` must coincide with the corresponding entry in</span>
<span class="sd"> `true_prevs`.</span>
<span class="sd"> :param pos_class: index of the positive class</span>
<span class="sd"> :param title: the title to be displayed in the plot (default None)</span>
<span class="sd"> :param nbins: number of bins (default 5)</span>
<span class="sd"> :param colormap: the matplotlib colormap to use (default cm.tab10)</span>
<span class="sd"> :param vertical_xticks: whether or not to add secondary grid (default is False)</span>
<span class="sd"> :param legend: whether or not to display the legend (default is True)</span>
<span class="sd"> :param savepath: path where to save the plot. If not indicated (as default), the plot is shown.</span>
<span class="sd"> :return: returns (fig, ax) matplotlib objects for eventual customisation</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="kn">from</span> <span class="nn">pylab</span> <span class="kn">import</span> <span class="n">boxplot</span><span class="p">,</span> <span class="n">plot</span><span class="p">,</span> <span class="n">setp</span>
<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">grid</span><span class="p">()</span>
<span class="n">method_names</span><span class="p">,</span> <span class="n">true_prevs</span><span class="p">,</span> <span class="n">estim_prevs</span> <span class="o">=</span> <span class="n">_merge</span><span class="p">(</span><span class="n">method_names</span><span class="p">,</span> <span class="n">true_prevs</span><span class="p">,</span> <span class="n">estim_prevs</span><span class="p">)</span>
<span class="n">bins</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</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="n">nbins</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<span class="n">binwidth</span> <span class="o">=</span> <span class="mi">1</span><span class="o">/</span><span class="n">nbins</span>
<span class="n">data</span> <span class="o">=</span> <span class="p">{}</span>
<span class="k">for</span> <span class="n">method</span><span class="p">,</span> <span class="n">true_prev</span><span class="p">,</span> <span class="n">estim_prev</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">method_names</span><span class="p">,</span> <span class="n">true_prevs</span><span class="p">,</span> <span class="n">estim_prevs</span><span class="p">):</span>
<span class="n">true_prev</span> <span class="o">=</span> <span class="n">true_prev</span><span class="p">[:,</span><span class="n">pos_class</span><span class="p">]</span>
<span class="n">estim_prev</span> <span class="o">=</span> <span class="n">estim_prev</span><span class="p">[:,</span><span class="n">pos_class</span><span class="p">]</span>
<span class="n">data</span><span class="p">[</span><span class="n">method</span><span class="p">]</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">inds</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">digitize</span><span class="p">(</span><span class="n">true_prev</span><span class="p">,</span> <span class="n">bins</span><span class="p">,</span> <span class="n">right</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="k">for</span> <span class="n">ind</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">bins</span><span class="p">)):</span>
<span class="n">selected</span> <span class="o">=</span> <span class="n">inds</span><span class="o">==</span><span class="n">ind</span>
<span class="n">data</span><span class="p">[</span><span class="n">method</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">estim_prev</span><span class="p">[</span><span class="n">selected</span><span class="p">]</span> <span class="o">-</span> <span class="n">true_prev</span><span class="p">[</span><span class="n">selected</span><span class="p">])</span>
<span class="n">nmethods</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">method_names</span><span class="p">)</span>
<span class="n">boxwidth</span> <span class="o">=</span> <span class="n">binwidth</span><span class="o">/</span><span class="p">(</span><span class="n">nmethods</span><span class="o">+</span><span class="mi">4</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span><span class="nb">bin</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">bins</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]):</span>
<span class="n">boxdata</span> <span class="o">=</span> <span class="p">[</span><span class="n">data</span><span class="p">[</span><span class="n">method</span><span class="p">][</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">method</span> <span class="ow">in</span> <span class="n">method_names</span><span class="p">]</span>
<span class="n">positions</span> <span class="o">=</span> <span class="p">[</span><span class="nb">bin</span><span class="o">+</span><span class="p">(</span><span class="n">i</span><span class="o">*</span><span class="n">boxwidth</span><span class="p">)</span><span class="o">+</span><span class="mi">2</span><span class="o">*</span><span class="n">boxwidth</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span><span class="n">_</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">method_names</span><span class="p">)]</span>
<span class="n">box</span> <span class="o">=</span> <span class="n">boxplot</span><span class="p">(</span><span class="n">boxdata</span><span class="p">,</span> <span class="n">showmeans</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">positions</span><span class="o">=</span><span class="n">positions</span><span class="p">,</span> <span class="n">widths</span> <span class="o">=</span> <span class="n">boxwidth</span><span class="p">,</span> <span class="n">sym</span><span class="o">=</span><span class="s1">&#39;+&#39;</span><span class="p">,</span> <span class="n">patch_artist</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="k">for</span> <span class="n">boxid</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">method_names</span><span class="p">)):</span>
<span class="n">c</span> <span class="o">=</span> <span class="n">colormap</span><span class="o">.</span><span class="n">colors</span><span class="p">[</span><span class="n">boxid</span><span class="o">%</span><span class="nb">len</span><span class="p">(</span><span class="n">colormap</span><span class="o">.</span><span class="n">colors</span><span class="p">)]</span>
<span class="n">setp</span><span class="p">(</span><span class="n">box</span><span class="p">[</span><span class="s1">&#39;fliers&#39;</span><span class="p">][</span><span class="n">boxid</span><span class="p">],</span> <span class="n">color</span><span class="o">=</span><span class="n">c</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span><span class="s1">&#39;+&#39;</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mf">3.</span><span class="p">,</span> <span class="n">markeredgecolor</span><span class="o">=</span><span class="n">c</span><span class="p">)</span>
<span class="n">setp</span><span class="p">(</span><span class="n">box</span><span class="p">[</span><span class="s1">&#39;boxes&#39;</span><span class="p">][</span><span class="n">boxid</span><span class="p">],</span> <span class="n">color</span><span class="o">=</span><span class="n">c</span><span class="p">)</span>
<span class="n">setp</span><span class="p">(</span><span class="n">box</span><span class="p">[</span><span class="s1">&#39;medians&#39;</span><span class="p">][</span><span class="n">boxid</span><span class="p">],</span> <span class="n">color</span><span class="o">=</span><span class="s1">&#39;k&#39;</span><span class="p">)</span>
<span class="n">major_xticks_positions</span><span class="p">,</span> <span class="n">minor_xticks_positions</span> <span class="o">=</span> <span class="p">[],</span> <span class="p">[]</span>
<span class="n">major_xticks_labels</span><span class="p">,</span> <span class="n">minor_xticks_labels</span> <span class="o">=</span> <span class="p">[],</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span><span class="n">b</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">bins</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]):</span>
<span class="n">major_xticks_positions</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>
<span class="n">minor_xticks_positions</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">b</span> <span class="o">+</span> <span class="n">binwidth</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span>
<span class="n">major_xticks_labels</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="s1">&#39;&#39;</span><span class="p">)</span>
<span class="n">minor_xticks_labels</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;[</span><span class="si">{</span><span class="n">bins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="si">:</span><span class="s1">.2f</span><span class="si">}</span><span class="s1">-</span><span class="si">{</span><span class="n">bins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="si">:</span><span class="s1">.2f</span><span class="si">}</span><span class="s1">)&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(</span><span class="n">major_xticks_positions</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(</span><span class="n">minor_xticks_positions</span><span class="p">,</span> <span class="n">minor</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xticklabels</span><span class="p">(</span><span class="n">major_xticks_labels</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xticklabels</span><span class="p">(</span><span class="n">minor_xticks_labels</span><span class="p">,</span> <span class="n">minor</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">rotation</span><span class="o">=</span><span class="s1">&#39;vertical&#39;</span> <span class="k">if</span> <span class="n">vertical_xticks</span> <span class="k">else</span> <span class="s1">&#39;horizontal&#39;</span><span class="p">)</span>
<span class="k">if</span> <span class="n">vertical_xticks</span><span class="p">:</span>
<span class="c1"># Pad margins so that markers don&#39;t get clipped by the axes</span>
<span class="n">plt</span><span class="o">.</span><span class="n">margins</span><span class="p">(</span><span class="mf">0.2</span><span class="p">)</span>
<span class="c1"># Tweak spacing to prevent clipping of tick-labels</span>
<span class="n">plt</span><span class="o">.</span><span class="n">subplots_adjust</span><span class="p">(</span><span class="n">bottom</span><span class="o">=</span><span class="mf">0.15</span><span class="p">)</span>
<span class="k">if</span> <span class="n">legend</span><span class="p">:</span>
<span class="c1"># adds the legend to the list hs, initialized with the &quot;ideal&quot; quantifier (one that has 0 bias across all bins. i.e.</span>
<span class="c1"># a line from (0,0) to (1,0). The other elements are simply labelled dot-plots that are to be removed (setting</span>
<span class="c1"># set_visible to False for all but the first element) after the legend has been placed</span>
<span class="n">hs</span><span class="o">=</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="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">0</span><span class="p">],</span> <span class="s1">&#39;-k&#39;</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">2</span><span class="p">)[</span><span class="mi">0</span><span class="p">]]</span>
<span class="k">for</span> <span class="n">colorid</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">method_names</span><span class="p">)):</span>
<span class="n">color</span><span class="o">=</span><span class="n">colormap</span><span class="o">.</span><span class="n">colors</span><span class="p">[</span><span class="n">colorid</span> <span class="o">%</span> <span class="nb">len</span><span class="p">(</span><span class="n">colormap</span><span class="o">.</span><span class="n">colors</span><span class="p">)]</span>
<span class="n">h</span><span class="p">,</span> <span class="o">=</span> <span class="n">plot</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="s1">&#39;-s&#39;</span><span class="p">,</span> <span class="n">markerfacecolor</span><span class="o">=</span><span class="n">color</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">&#39;k&#39;</span><span class="p">,</span><span class="n">mec</span><span class="o">=</span><span class="n">color</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mf">1.</span><span class="p">)</span>
<span class="n">hs</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">h</span><span class="p">)</span>
<span class="n">box</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">get_position</span><span class="p">()</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_position</span><span class="p">([</span><span class="n">box</span><span class="o">.</span><span class="n">x0</span><span class="p">,</span> <span class="n">box</span><span class="o">.</span><span class="n">y0</span><span class="p">,</span> <span class="n">box</span><span class="o">.</span><span class="n">width</span> <span class="o">*</span> <span class="mf">0.8</span><span class="p">,</span> <span class="n">box</span><span class="o">.</span><span class="n">height</span><span class="p">])</span>
<span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">hs</span><span class="p">,</span> <span class="p">[</span><span class="s1">&#39;ideal&#39;</span><span class="p">]</span><span class="o">+</span><span class="n">method_names</span><span class="p">,</span> <span class="n">loc</span><span class="o">=</span><span class="s1">&#39;center left&#39;</span><span class="p">,</span> <span class="n">bbox_to_anchor</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">))</span>
<span class="p">[</span><span class="n">h</span><span class="o">.</span><span class="n">set_visible</span><span class="p">(</span><span class="kc">False</span><span class="p">)</span> <span class="k">for</span> <span class="n">h</span> <span class="ow">in</span> <span class="n">hs</span><span class="p">[</span><span class="mi">1</span><span class="p">:]]</span>
<span class="c1"># x-axis and y-axis labels and limits</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set</span><span class="p">(</span><span class="n">xlabel</span><span class="o">=</span><span class="s1">&#39;prevalence&#39;</span><span class="p">,</span> <span class="n">ylabel</span><span class="o">=</span><span class="s1">&#39;error bias&#39;</span><span class="p">,</span> <span class="n">title</span><span class="o">=</span><span class="n">title</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlim</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="n">_save_or_show</span><span class="p">(</span><span class="n">savepath</span><span class="p">)</span>
<span class="k">return</span> <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span></div>
<div class="viewcode-block" id="error_by_drift">
<a class="viewcode-back" href="../../quapy.html#quapy.plot.error_by_drift">[docs]</a>
<span class="k">def</span> <span class="nf">error_by_drift</span><span class="p">(</span><span class="n">method_names</span><span class="p">,</span> <span class="n">true_prevs</span><span class="p">,</span> <span class="n">estim_prevs</span><span class="p">,</span> <span class="n">tr_prevs</span><span class="p">,</span>
<span class="n">n_bins</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">error_name</span><span class="o">=</span><span class="s1">&#39;ae&#39;</span><span class="p">,</span> <span class="n">show_std</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
<span class="n">show_density</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
<span class="n">show_legend</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
<span class="n">logscale</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
<span class="n">title</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">vlines</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">method_order</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">savepath</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Plots the error (along the x-axis, as measured in terms of `error_name`) as a function of the train-test shift</span>
<span class="sd"> (along the y-axis, as measured in terms of :meth:`quapy.error.ae`). This plot is useful especially for multiclass</span>
<span class="sd"> problems, in which &quot;diagonal plots&quot; may be cumbersone, and in order to gain understanding about how methods</span>
<span class="sd"> fare in different regions of the prior probability shift spectrum (e.g., in the low-shift regime vs. in the</span>
<span class="sd"> high-shift regime).</span>
<span class="sd"> The format convention is as follows: `method_names`, `true_prevs`, and `estim_prevs` are array-like of the same</span>
<span class="sd"> length, with the ith element describing the output of an independent experiment. The elements of `true_prevs`, and</span>
<span class="sd"> `estim_prevs` are `ndarrays` with coherent shape for the same experiment. Experiments for the same method on</span>
<span class="sd"> different datasets can be used, in which case the method name can appear more than once in `method_names`.</span>
<span class="sd"> :param method_names: array-like with the method names for each experiment</span>
<span class="sd"> :param true_prevs: array-like with the true prevalence values for each experiment. Each entry is a ndarray of</span>
<span class="sd"> shape `(n_samples, n_classes)` components.</span>
<span class="sd"> :param estim_prevs: array-like with the estimated prevalence values for each experiment. Each entry is a ndarray of</span>
<span class="sd"> shape `(n_samples, n_classes)` components and `n_samples` must coincide with the corresponding entry in</span>
<span class="sd"> `true_prevs`.</span>
<span class="sd"> :param tr_prevs: training prevalence of each experiment</span>
<span class="sd"> :param n_bins: number of bins in which the y-axis is to be divided (default is 20)</span>
<span class="sd"> :param error_name: a string representing the name of an error function (as defined in `quapy.error`, default is &quot;ae&quot;)</span>
<span class="sd"> :param show_std: whether or not to show standard deviations as color bands (default is False)</span>
<span class="sd"> :param show_density: whether or not to display the distribution of experiments for each bin (default is True)</span>
<span class="sd"> :param show_density: whether or not to display the legend of the chart (default is True)</span>
<span class="sd"> :param logscale: whether or not to log-scale the y-error measure (default is False)</span>
<span class="sd"> :param title: title of the plot (default is None)</span>
<span class="sd"> :param vlines: array-like list of values (default is None). If indicated, highlights some regions of the space</span>
<span class="sd"> using vertical dotted lines.</span>
<span class="sd"> :param method_order: if indicated (default is None), imposes the order in which the methods are processed (i.e.,</span>
<span class="sd"> listed in the legend and associated with matplotlib colors).</span>
<span class="sd"> :param savepath: path where to save the plot. If not indicated (as default), the plot is shown.</span>
<span class="sd"> :return: returns (fig, ax) matplotlib objects for eventual customisation</span>
<span class="sd"> &quot;&quot;&quot;</span>
<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">grid</span><span class="p">()</span>
<span class="n">x_error</span> <span class="o">=</span> <span class="n">qp</span><span class="o">.</span><span class="n">error</span><span class="o">.</span><span class="n">ae</span>
<span class="n">y_error</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">qp</span><span class="o">.</span><span class="n">error</span><span class="p">,</span> <span class="n">error_name</span><span class="p">)</span>
<span class="k">if</span> <span class="n">method_order</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">method_order</span> <span class="o">=</span> <span class="p">[]</span>
<span class="c1"># get all data as a dictionary {&#39;m&#39;:{&#39;x&#39;:ndarray, &#39;y&#39;:ndarray}} where &#39;m&#39; is a method name (in the same</span>
<span class="c1"># order as in method_order (if specified), and where &#39;x&#39; are the train-test shifts (computed as according to</span>
<span class="c1"># x_error function) and &#39;y&#39; is the estim-test shift (computed as according to y_error)</span>
<span class="n">data</span> <span class="o">=</span> <span class="n">_join_data_by_drift</span><span class="p">(</span><span class="n">method_names</span><span class="p">,</span> <span class="n">true_prevs</span><span class="p">,</span> <span class="n">estim_prevs</span><span class="p">,</span> <span class="n">tr_prevs</span><span class="p">,</span> <span class="n">x_error</span><span class="p">,</span> <span class="n">y_error</span><span class="p">,</span> <span class="n">method_order</span><span class="p">)</span>
<span class="n">_set_colors</span><span class="p">(</span><span class="n">ax</span><span class="p">,</span> <span class="n">n_methods</span><span class="o">=</span><span class="nb">len</span><span class="p">(</span><span class="n">method_order</span><span class="p">))</span>
<span class="n">bins</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</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="n">n_bins</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<span class="n">binwidth</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="n">n_bins</span>
<span class="n">min_x</span><span class="p">,</span> <span class="n">max_x</span><span class="p">,</span> <span class="n">min_y</span><span class="p">,</span> <span class="n">max_y</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span>
<span class="n">npoints</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">bins</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">float</span><span class="p">)</span>
<span class="k">for</span> <span class="n">method</span> <span class="ow">in</span> <span class="n">method_order</span><span class="p">:</span>
<span class="n">tr_test_drifts</span> <span class="o">=</span> <span class="n">data</span><span class="p">[</span><span class="n">method</span><span class="p">][</span><span class="s1">&#39;x&#39;</span><span class="p">]</span>
<span class="n">method_drifts</span> <span class="o">=</span> <span class="n">data</span><span class="p">[</span><span class="n">method</span><span class="p">][</span><span class="s1">&#39;y&#39;</span><span class="p">]</span>
<span class="k">if</span> <span class="n">logscale</span><span class="p">:</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_yscale</span><span class="p">(</span><span class="s2">&quot;log&quot;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">yaxis</span><span class="o">.</span><span class="n">set_major_formatter</span><span class="p">(</span><span class="n">ScalarFormatter</span><span class="p">())</span>
<span class="n">ax</span><span class="o">.</span><span class="n">yaxis</span><span class="o">.</span><span class="n">get_major_formatter</span><span class="p">()</span><span class="o">.</span><span class="n">set_scientific</span><span class="p">(</span><span class="kc">False</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">minorticks_off</span><span class="p">()</span>
<span class="n">inds</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">digitize</span><span class="p">(</span><span class="n">tr_test_drifts</span><span class="p">,</span> <span class="n">bins</span><span class="p">,</span> <span class="n">right</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">xs</span><span class="p">,</span> <span class="n">ys</span><span class="p">,</span> <span class="n">ystds</span> <span class="o">=</span> <span class="p">[],</span> <span class="p">[],</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">p</span><span class="p">,</span><span class="n">ind</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">bins</span><span class="p">))):</span>
<span class="n">selected</span> <span class="o">=</span> <span class="n">inds</span><span class="o">==</span><span class="n">ind</span>
<span class="k">if</span> <span class="n">selected</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">xs</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">ind</span><span class="o">*</span><span class="n">binwidth</span><span class="o">-</span><span class="n">binwidth</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span>
<span class="n">ys</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">method_drifts</span><span class="p">[</span><span class="n">selected</span><span class="p">]))</span>
<span class="n">ystds</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">std</span><span class="p">(</span><span class="n">method_drifts</span><span class="p">[</span><span class="n">selected</span><span class="p">]))</span>
<span class="n">npoints</span><span class="p">[</span><span class="n">p</span><span class="p">]</span> <span class="o">+=</span> <span class="nb">len</span><span class="p">(</span><span class="n">method_drifts</span><span class="p">[</span><span class="n">selected</span><span class="p">])</span>
<span class="n">xs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">xs</span><span class="p">)</span>
<span class="n">ys</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">ys</span><span class="p">)</span>
<span class="n">ystds</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">ystds</span><span class="p">)</span>
<span class="n">min_x_method</span><span class="p">,</span> <span class="n">max_x_method</span><span class="p">,</span> <span class="n">min_y_method</span><span class="p">,</span> <span class="n">max_y_method</span> <span class="o">=</span> <span class="n">xs</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span> <span class="n">xs</span><span class="o">.</span><span class="n">max</span><span class="p">(),</span> <span class="n">ys</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span> <span class="n">ys</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
<span class="n">min_x</span> <span class="o">=</span> <span class="n">min_x_method</span> <span class="k">if</span> <span class="n">min_x</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">min_x_method</span> <span class="o">&lt;</span> <span class="n">min_x</span> <span class="k">else</span> <span class="n">min_x</span>
<span class="n">max_x</span> <span class="o">=</span> <span class="n">max_x_method</span> <span class="k">if</span> <span class="n">max_x</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">max_x_method</span> <span class="o">&gt;</span> <span class="n">max_x</span> <span class="k">else</span> <span class="n">max_x</span>
<span class="n">max_y</span> <span class="o">=</span> <span class="n">max_y_method</span> <span class="k">if</span> <span class="n">max_y</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">max_y_method</span> <span class="o">&gt;</span> <span class="n">max_y</span> <span class="k">else</span> <span class="n">max_y</span>
<span class="n">min_y</span> <span class="o">=</span> <span class="n">min_y_method</span> <span class="k">if</span> <span class="n">min_y</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">min_y_method</span> <span class="o">&lt;</span> <span class="n">min_y</span> <span class="k">else</span> <span class="n">min_y</span>
<span class="n">max_y</span> <span class="o">=</span> <span class="n">max_y_method</span> <span class="k">if</span> <span class="n">max_y</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">max_y_method</span> <span class="o">&gt;</span> <span class="n">max_y</span> <span class="k">else</span> <span class="n">max_y</span>
<span class="n">ax</span><span class="o">.</span><span class="n">errorbar</span><span class="p">(</span><span class="n">xs</span><span class="p">,</span> <span class="n">ys</span><span class="p">,</span> <span class="n">fmt</span><span class="o">=</span><span class="s1">&#39;-&#39;</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span><span class="s1">&#39;o&#39;</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">&#39;w&#39;</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">8</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">4</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">errorbar</span><span class="p">(</span><span class="n">xs</span><span class="p">,</span> <span class="n">ys</span><span class="p">,</span> <span class="n">fmt</span><span class="o">=</span><span class="s1">&#39;-&#39;</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span><span class="s1">&#39;o&#39;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="n">method</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">6</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="k">if</span> <span class="n">show_std</span><span class="p">:</span>
<span class="n">ax</span><span class="o">.</span><span class="n">fill_between</span><span class="p">(</span><span class="n">xs</span><span class="p">,</span> <span class="n">ys</span><span class="o">-</span><span class="n">ystds</span><span class="p">,</span> <span class="n">ys</span><span class="o">+</span><span class="n">ystds</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.25</span><span class="p">)</span>
<span class="k">if</span> <span class="n">show_density</span><span class="p">:</span>
<span class="n">ax2</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">twinx</span><span class="p">()</span>
<span class="n">densities</span> <span class="o">=</span> <span class="n">npoints</span><span class="o">/</span><span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">npoints</span><span class="p">)</span>
<span class="n">ax2</span><span class="o">.</span><span class="n">bar</span><span class="p">([</span><span class="n">ind</span> <span class="o">*</span> <span class="n">binwidth</span><span class="o">-</span><span class="n">binwidth</span><span class="o">/</span><span class="mi">2</span> <span class="k">for</span> <span class="n">ind</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">bins</span><span class="p">))],</span>
<span class="n">densities</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.15</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">&#39;g&#39;</span><span class="p">,</span> <span class="n">width</span><span class="o">=</span><span class="n">binwidth</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;density&#39;</span><span class="p">)</span>
<span class="n">ax2</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="nb">max</span><span class="p">(</span><span class="n">densities</span><span class="p">))</span>
<span class="n">ax2</span><span class="o">.</span><span class="n">spines</span><span class="p">[</span><span class="s1">&#39;right&#39;</span><span class="p">]</span><span class="o">.</span><span class="n">set_color</span><span class="p">(</span><span class="s1">&#39;g&#39;</span><span class="p">)</span>
<span class="n">ax2</span><span class="o">.</span><span class="n">tick_params</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="s1">&#39;y&#39;</span><span class="p">,</span> <span class="n">colors</span><span class="o">=</span><span class="s1">&#39;g&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set</span><span class="p">(</span><span class="n">xlabel</span><span class="o">=</span><span class="sa">f</span><span class="s1">&#39;Prior shift between training set and test sample&#39;</span><span class="p">,</span>
<span class="n">ylabel</span><span class="o">=</span><span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">error_name</span><span class="o">.</span><span class="n">upper</span><span class="p">()</span><span class="si">}</span><span class="s1"> (true prev, predicted prev)&#39;</span><span class="p">,</span>
<span class="n">title</span><span class="o">=</span><span class="n">title</span><span class="p">)</span>
<span class="c1"># box = ax.get_position()</span>
<span class="c1"># ax.set_position([box.x0, box.y0, box.width * 0.8, box.height])</span>
<span class="k">if</span> <span class="n">vlines</span><span class="p">:</span>
<span class="k">for</span> <span class="n">vline</span> <span class="ow">in</span> <span class="n">vlines</span><span class="p">:</span>
<span class="n">ax</span><span class="o">.</span><span class="n">axvline</span><span class="p">(</span><span class="n">vline</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="n">linestyle</span><span class="o">=</span><span class="s1">&#39;--&#39;</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">&#39;k&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">(</span><span class="n">min_x</span><span class="p">,</span> <span class="n">max_x</span><span class="p">)</span>
<span class="k">if</span> <span class="n">logscale</span><span class="p">:</span>
<span class="c1">#nice scale for the logaritmic axis</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">10</span> <span class="o">**</span> <span class="n">math</span><span class="o">.</span><span class="n">ceil</span><span class="p">(</span><span class="n">math</span><span class="o">.</span><span class="n">log10</span><span class="p">(</span><span class="n">max_y</span><span class="p">)))</span>
<span class="k">if</span> <span class="n">show_legend</span><span class="p">:</span>
<span class="n">fig</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s1">&#39;center left&#39;</span><span class="p">,</span>
<span class="n">bbox_to_anchor</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">),</span>
<span class="n">ncol</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">_save_or_show</span><span class="p">(</span><span class="n">savepath</span><span class="p">)</span>
<span class="k">return</span> <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span></div>
<div class="viewcode-block" id="brokenbar_supremacy_by_drift">
<a class="viewcode-back" href="../../quapy.html#quapy.plot.brokenbar_supremacy_by_drift">[docs]</a>
<span class="k">def</span> <span class="nf">brokenbar_supremacy_by_drift</span><span class="p">(</span><span class="n">method_names</span><span class="p">,</span> <span class="n">true_prevs</span><span class="p">,</span> <span class="n">estim_prevs</span><span class="p">,</span> <span class="n">tr_prevs</span><span class="p">,</span>
<span class="n">n_bins</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">binning</span><span class="o">=</span><span class="s1">&#39;isomerous&#39;</span><span class="p">,</span>
<span class="n">x_error</span><span class="o">=</span><span class="s1">&#39;ae&#39;</span><span class="p">,</span> <span class="n">y_error</span><span class="o">=</span><span class="s1">&#39;ae&#39;</span><span class="p">,</span> <span class="n">ttest_alpha</span><span class="o">=</span><span class="mf">0.005</span><span class="p">,</span> <span class="n">tail_density_threshold</span><span class="o">=</span><span class="mf">0.005</span><span class="p">,</span>
<span class="n">method_order</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">savepath</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Displays (only) the top performing methods for different regions of the train-test shift in form of a broken</span>
<span class="sd"> bar chart, in which each method has bars only for those regions in which either one of the following conditions</span>
<span class="sd"> hold: (i) it is the best method (in average) for the bin, or (ii) it is not statistically significantly different</span>
<span class="sd"> (in average) as according to a two-sided t-test on independent samples at confidence `ttest_alpha`.</span>
<span class="sd"> The binning can be made &quot;isometric&quot; (same size), or &quot;isomerous&quot; (same number of experiments -- default). A second</span>
<span class="sd"> plot is displayed on top, that displays the distribution of experiments for each bin (when binning=&quot;isometric&quot;) or</span>
<span class="sd"> the percentiles points of the distribution (when binning=&quot;isomerous&quot;).</span>
<span class="sd"> The format convention is as follows: `method_names`, `true_prevs`, and `estim_prevs` are array-like of the same</span>
<span class="sd"> length, with the ith element describing the output of an independent experiment. The elements of `true_prevs`, and</span>
<span class="sd"> `estim_prevs` are `ndarrays` with coherent shape for the same experiment. Experiments for the same method on</span>
<span class="sd"> different datasets can be used, in which case the method name can appear more than once in `method_names`.</span>
<span class="sd"> :param method_names: array-like with the method names for each experiment</span>
<span class="sd"> :param true_prevs: array-like with the true prevalence values for each experiment. Each entry is a ndarray of</span>
<span class="sd"> shape `(n_samples, n_classes)` components.</span>
<span class="sd"> :param estim_prevs: array-like with the estimated prevalence values for each experiment. Each entry is a ndarray of</span>
<span class="sd"> shape `(n_samples, n_classes)` components and `n_samples` must coincide with the corresponding entry in</span>
<span class="sd"> `true_prevs`.</span>
<span class="sd"> :param tr_prevs: training prevalence of each experiment</span>
<span class="sd"> :param n_bins: number of bins in which the y-axis is to be divided (default is 20)</span>
<span class="sd"> :param binning: type of binning, either &quot;isomerous&quot; (default) or &quot;isometric&quot;</span>
<span class="sd"> :param x_error: a string representing the name of an error function (as defined in `quapy.error`) to be used for</span>
<span class="sd"> measuring the amount of train-test shift (default is &quot;ae&quot;)</span>
<span class="sd"> :param y_error: a string representing the name of an error function (as defined in `quapy.error`) to be used for</span>
<span class="sd"> measuring the amount of error in the prevalence estimations (default is &quot;ae&quot;)</span>
<span class="sd"> :param ttest_alpha: the confidence interval above which a p-value (two-sided t-test on independent samples) is</span>
<span class="sd"> to be considered as an indicator that the two means are not statistically significantly different. Default is</span>
<span class="sd"> 0.005, meaning that a `p-value &gt; 0.005` indicates the two methods involved are to be considered similar</span>
<span class="sd"> :param tail_density_threshold: sets a threshold on the density of experiments (over the total number of experiments)</span>
<span class="sd"> below which a bin in the tail (i.e., the right-most ones) will be discarded. This is in order to avoid some</span>
<span class="sd"> bins to be shown for train-test outliers.</span>
<span class="sd"> :param method_order: if indicated (default is None), imposes the order in which the methods are processed (i.e.,</span>
<span class="sd"> listed in the legend and associated with matplotlib colors).</span>
<span class="sd"> :param savepath: path where to save the plot. If not indicated (as default), the plot is shown.</span>
<span class="sd"> :return: returns (fig, ax) matplotlib objects for eventual customisation</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">assert</span> <span class="n">binning</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;isomerous&#39;</span><span class="p">,</span> <span class="s1">&#39;isometric&#39;</span><span class="p">],</span> <span class="s1">&#39;unknown binning type; valid types are &quot;isomerous&quot; and &quot;isometric&quot;&#39;</span>
<span class="n">x_error</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">qp</span><span class="o">.</span><span class="n">error</span><span class="p">,</span> <span class="n">x_error</span><span class="p">)</span>
<span class="n">y_error</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">qp</span><span class="o">.</span><span class="n">error</span><span class="p">,</span> <span class="n">y_error</span><span class="p">)</span>
<span class="k">if</span> <span class="n">method_order</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">method_order</span> <span class="o">=</span> <span class="p">[]</span>
<span class="c1"># get all data as a dictionary {&#39;m&#39;:{&#39;x&#39;:ndarray, &#39;y&#39;:ndarray}} where &#39;m&#39; is a method name (in the same</span>
<span class="c1"># order as in method_order (if specified), and where &#39;x&#39; are the train-test shifts (computed as according to</span>
<span class="c1"># x_error function) and &#39;y&#39; is the estim-test shift (computed as according to y_error)</span>
<span class="n">data</span> <span class="o">=</span> <span class="n">_join_data_by_drift</span><span class="p">(</span><span class="n">method_names</span><span class="p">,</span> <span class="n">true_prevs</span><span class="p">,</span> <span class="n">estim_prevs</span><span class="p">,</span> <span class="n">tr_prevs</span><span class="p">,</span> <span class="n">x_error</span><span class="p">,</span> <span class="n">y_error</span><span class="p">,</span> <span class="n">method_order</span><span class="p">)</span>
<span class="k">if</span> <span class="n">method_order</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">method_order</span> <span class="o">=</span> <span class="n">method_names</span>
<span class="k">if</span> <span class="n">binning</span> <span class="o">==</span> <span class="s1">&#39;isomerous&#39;</span><span class="p">:</span>
<span class="c1"># take bins containing the same amount of examples</span>
<span class="n">tr_test_drifts</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">([</span><span class="n">data</span><span class="p">[</span><span class="n">m</span><span class="p">][</span><span class="s1">&#39;x&#39;</span><span class="p">]</span> <span class="k">for</span> <span class="n">m</span> <span class="ow">in</span> <span class="n">method_order</span><span class="p">])</span>
<span class="n">bins</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">quantile</span><span class="p">(</span><span class="n">tr_test_drifts</span><span class="p">,</span> <span class="n">q</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">linspace</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="n">n_bins</span><span class="o">+</span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">flatten</span><span class="p">()</span>
<span class="k">else</span><span class="p">:</span>
<span class="c1"># take equidistant bins</span>
<span class="n">bins</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</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="n">n_bins</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
<span class="n">bins</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="o">-</span><span class="mf">0.001</span>
<span class="n">bins</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">+=</span> <span class="mf">0.001</span>
<span class="c1"># we use this to keep track of how many datapoits contribute to each bin</span>
<span class="n">inds_histogram_global</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">n_bins</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">float</span><span class="p">)</span>
<span class="n">n_methods</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">method_order</span><span class="p">)</span>
<span class="n">buckets</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="n">n_methods</span><span class="p">,</span> <span class="n">n_bins</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">method</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">method_order</span><span class="p">):</span>
<span class="n">tr_test_drifts</span> <span class="o">=</span> <span class="n">data</span><span class="p">[</span><span class="n">method</span><span class="p">][</span><span class="s1">&#39;x&#39;</span><span class="p">]</span>
<span class="n">method_drifts</span> <span class="o">=</span> <span class="n">data</span><span class="p">[</span><span class="n">method</span><span class="p">][</span><span class="s1">&#39;y&#39;</span><span class="p">]</span>
<span class="n">inds</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">digitize</span><span class="p">(</span><span class="n">tr_test_drifts</span><span class="p">,</span> <span class="n">bins</span><span class="p">,</span> <span class="n">right</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="n">inds_histogram_global</span> <span class="o">+=</span> <span class="n">np</span><span class="o">.</span><span class="n">histogram</span><span class="p">(</span><span class="n">tr_test_drifts</span><span class="p">,</span> <span class="n">density</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="n">bins</span><span class="p">)[</span><span class="mi">0</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="nb">len</span><span class="p">(</span><span class="n">bins</span><span class="p">)):</span>
<span class="n">selected</span> <span class="o">=</span> <span class="n">inds</span> <span class="o">==</span> <span class="n">j</span>
<span class="k">if</span> <span class="n">selected</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">method_drifts</span><span class="p">[</span><span class="n">selected</span><span class="p">])</span>
<span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">std</span><span class="p">(</span><span class="n">method_drifts</span><span class="p">[</span><span class="n">selected</span><span class="p">])</span>
<span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="n">selected</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
<span class="c1"># cancel last buckets with low density</span>
<span class="n">histogram</span> <span class="o">=</span> <span class="n">inds_histogram_global</span> <span class="o">/</span> <span class="n">inds_histogram_global</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
<span class="k">for</span> <span class="n">tail</span> <span class="ow">in</span> <span class="nb">reversed</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">histogram</span><span class="p">))):</span>
<span class="k">if</span> <span class="n">histogram</span><span class="p">[</span><span class="n">tail</span><span class="p">]</span> <span class="o">&lt;</span> <span class="n">tail_density_threshold</span><span class="p">:</span>
<span class="n">buckets</span><span class="p">[:,</span><span class="n">tail</span><span class="p">,</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">break</span>
<span class="n">salient_methods</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
<span class="n">best_methods</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">bucket</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">buckets</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]):</span>
<span class="n">nc</span> <span class="o">=</span> <span class="n">buckets</span><span class="p">[:,</span> <span class="n">bucket</span><span class="p">,</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="k">if</span> <span class="n">nc</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">best_methods</span><span class="o">.</span><span class="n">append</span><span class="p">([])</span>
<span class="k">continue</span>
<span class="n">order</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">argsort</span><span class="p">(</span><span class="n">buckets</span><span class="p">[:,</span> <span class="n">bucket</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
<span class="n">rank1</span> <span class="o">=</span> <span class="n">order</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">best_bucket_methods</span> <span class="o">=</span> <span class="p">[</span><span class="n">method_order</span><span class="p">[</span><span class="n">rank1</span><span class="p">]]</span>
<span class="n">best_mean</span><span class="p">,</span> <span class="n">best_std</span><span class="p">,</span> <span class="n">best_nc</span> <span class="o">=</span> <span class="n">buckets</span><span class="p">[</span><span class="n">rank1</span><span class="p">,</span> <span class="n">bucket</span><span class="p">,</span> <span class="p">:]</span>
<span class="k">for</span> <span class="n">method_index</span> <span class="ow">in</span> <span class="n">order</span><span class="p">[</span><span class="mi">1</span><span class="p">:]:</span>
<span class="n">method_mean</span><span class="p">,</span> <span class="n">method_std</span><span class="p">,</span> <span class="n">method_nc</span> <span class="o">=</span> <span class="n">buckets</span><span class="p">[</span><span class="n">method_index</span><span class="p">,</span> <span class="n">bucket</span><span class="p">,</span> <span class="p">:]</span>
<span class="n">_</span><span class="p">,</span> <span class="n">pval</span> <span class="o">=</span> <span class="n">ttest_ind_from_stats</span><span class="p">(</span><span class="n">best_mean</span><span class="p">,</span> <span class="n">best_std</span><span class="p">,</span> <span class="n">best_nc</span><span class="p">,</span> <span class="n">method_mean</span><span class="p">,</span> <span class="n">method_std</span><span class="p">,</span> <span class="n">method_nc</span><span class="p">)</span>
<span class="k">if</span> <span class="n">pval</span> <span class="o">&gt;</span> <span class="n">ttest_alpha</span><span class="p">:</span>
<span class="n">best_bucket_methods</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">method_order</span><span class="p">[</span><span class="n">method_index</span><span class="p">])</span>
<span class="n">best_methods</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">best_bucket_methods</span><span class="p">)</span>
<span class="n">salient_methods</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">best_bucket_methods</span><span class="p">)</span>
<span class="k">if</span> <span class="n">binning</span><span class="o">==</span><span class="s1">&#39;isomerous&#39;</span><span class="p">:</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">axes</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="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">gridspec_kw</span><span class="o">=</span><span class="p">{</span><span class="s1">&#39;height_ratios&#39;</span><span class="p">:</span> <span class="p">[</span><span class="mf">0.2</span><span class="p">,</span> <span class="mi">1</span><span class="p">]},</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">salient_methods</span><span class="p">)))</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">fig</span><span class="p">,</span> <span class="n">axes</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="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">gridspec_kw</span><span class="o">=</span><span class="p">{</span><span class="s1">&#39;height_ratios&#39;</span><span class="p">:</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">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">salient_methods</span><span class="p">)))</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">axes</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
<span class="n">high_from</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">yticks</span><span class="p">,</span> <span class="n">yticks_method_names</span> <span class="o">=</span> <span class="p">[],</span> <span class="p">[]</span>
<span class="n">color</span> <span class="o">=</span> <span class="n">get_cmap</span><span class="p">(</span><span class="s1">&#39;Accent&#39;</span><span class="p">)</span><span class="o">.</span><span class="n">colors</span>
<span class="n">vlines</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">bar_high</span> <span class="o">=</span> <span class="mi">1</span>
<span class="k">for</span> <span class="n">method</span> <span class="ow">in</span> <span class="p">[</span><span class="n">m</span> <span class="k">for</span> <span class="n">m</span> <span class="ow">in</span> <span class="n">method_order</span> <span class="k">if</span> <span class="n">m</span> <span class="ow">in</span> <span class="n">salient_methods</span><span class="p">]:</span>
<span class="n">broken_paths</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">path_start</span><span class="p">,</span> <span class="n">path_end</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">best_bucket_methods</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">best_methods</span><span class="p">):</span>
<span class="k">if</span> <span class="n">method</span> <span class="ow">in</span> <span class="n">best_bucket_methods</span><span class="p">:</span>
<span class="k">if</span> <span class="n">path_start</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">path_start</span> <span class="o">=</span> <span class="n">bins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<span class="n">path_end</span> <span class="o">=</span> <span class="n">bins</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">path_start</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">path_end</span> <span class="o">+=</span> <span class="n">bins</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">bins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">if</span> <span class="n">path_start</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">broken_paths</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">tuple</span><span class="p">((</span><span class="n">path_start</span><span class="p">,</span> <span class="n">path_end</span><span class="p">)))</span>
<span class="n">path_start</span><span class="p">,</span> <span class="n">path_end</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span>
<span class="k">if</span> <span class="n">path_start</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">broken_paths</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">tuple</span><span class="p">((</span><span class="n">path_start</span><span class="p">,</span> <span class="n">path_end</span><span class="p">)))</span>
<span class="n">ax</span><span class="o">.</span><span class="n">broken_barh</span><span class="p">(</span><span class="n">broken_paths</span><span class="p">,</span> <span class="p">(</span><span class="n">high_from</span><span class="p">,</span> <span class="n">bar_high</span><span class="p">),</span> <span class="n">facecolors</span><span class="o">=</span><span class="n">color</span><span class="p">[</span><span class="nb">len</span><span class="p">(</span><span class="n">yticks_method_names</span><span class="p">)])</span>
<span class="n">yticks</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">high_from</span><span class="o">+</span><span class="n">bar_high</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span>
<span class="n">high_from</span> <span class="o">+=</span> <span class="n">bar_high</span>
<span class="n">yticks_method_names</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">method</span><span class="p">)</span>
<span class="k">for</span> <span class="n">path_start</span><span class="p">,</span> <span class="n">path_end</span> <span class="ow">in</span> <span class="n">broken_paths</span><span class="p">:</span>
<span class="n">vlines</span><span class="o">.</span><span class="n">extend</span><span class="p">([</span><span class="n">path_start</span><span class="p">,</span> <span class="n">path_start</span><span class="o">+</span><span class="n">path_end</span><span class="p">])</span>
<span class="n">vlines</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">unique</span><span class="p">(</span><span class="n">vlines</span><span class="p">)</span>
<span class="n">vlines</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">vlines</span><span class="p">)</span>
<span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">vlines</span><span class="p">[</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="n">ax</span><span class="o">.</span><span class="n">axvline</span><span class="p">(</span><span class="n">x</span><span class="o">=</span><span class="n">v</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">&#39;k&#39;</span><span class="p">,</span> <span class="n">linestyle</span><span class="o">=</span><span class="s1">&#39;--&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">high_from</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">(</span><span class="n">vlines</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">vlines</span><span class="p">[</span><span class="o">-</span><span class="mi">1</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="s1">&#39;Distribution shift between training set and sample&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(</span><span class="n">yticks</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_yticklabels</span><span class="p">(</span><span class="n">yticks_method_names</span><span class="p">)</span>
<span class="c1"># upper plot (explaining distribution)</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="k">if</span> <span class="n">binning</span> <span class="o">==</span> <span class="s1">&#39;isometric&#39;</span><span class="p">:</span>
<span class="c1"># show the density for each region</span>
<span class="n">bins</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">=</span><span class="mi">0</span>
<span class="n">y_pos</span> <span class="o">=</span> <span class="p">[</span><span class="n">b</span><span class="o">+</span><span class="p">(</span><span class="n">bins</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">b</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span><span class="n">b</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">bins</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span> <span class="k">if</span> <span class="n">histogram</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">&gt;</span><span class="mi">0</span><span class="p">]</span>
<span class="n">bar_width</span> <span class="o">=</span> <span class="p">[</span><span class="n">bins</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">bins</span><span class="p">[</span><span class="n">i</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="nb">len</span><span class="p">(</span><span class="n">bins</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]))</span> <span class="k">if</span> <span class="n">histogram</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">&gt;</span><span class="mi">0</span><span class="p">]</span>
<span class="n">ax</span><span class="o">.</span><span class="n">bar</span><span class="p">(</span><span class="n">y_pos</span><span class="p">,</span> <span class="p">[</span><span class="n">n</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">histogram</span> <span class="k">if</span> <span class="n">n</span><span class="o">&gt;</span><span class="mi">0</span><span class="p">],</span> <span class="n">bar_width</span><span class="p">,</span> <span class="n">align</span><span class="o">=</span><span class="s1">&#39;center&#39;</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="n">color</span><span class="o">=</span><span class="s1">&#39;silver&#39;</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="s1">&#39;shift</span><span class="se">\n</span><span class="s1">distribution&#39;</span><span class="p">,</span> <span class="n">rotation</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">ha</span><span class="o">=</span><span class="s1">&#39;right&#39;</span><span class="p">,</span> <span class="n">va</span><span class="o">=</span><span class="s1">&#39;center&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">(</span><span class="n">vlines</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">vlines</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
<span class="n">ax</span><span class="o">.</span><span class="n">get_xaxis</span><span class="p">()</span><span class="o">.</span><span class="n">set_visible</span><span class="p">(</span><span class="kc">False</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">wspace</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">hspace</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="c1"># show the percentiles of the distribution</span>
<span class="n">cumsum</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">histogram</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="nb">len</span><span class="p">(</span><span class="n">bins</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">])):</span>
<span class="n">start</span><span class="p">,</span> <span class="n">width</span> <span class="o">=</span> <span class="n">bins</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">bins</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">bins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<span class="n">ax</span><span class="o">.</span><span class="n">broken_barh</span><span class="p">([</span><span class="nb">tuple</span><span class="p">((</span><span class="n">start</span><span class="p">,</span> <span class="n">width</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="n">facecolors</span><span class="o">=</span><span class="s1">&#39;whitesmoke&#39;</span> <span class="k">if</span> <span class="n">i</span><span class="o">%</span><span class="mi">2</span><span class="o">==</span><span class="mi">0</span> <span class="k">else</span> <span class="s1">&#39;silver&#39;</span><span class="p">)</span>
<span class="k">if</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="nb">len</span><span class="p">(</span><span class="n">bins</span><span class="p">)</span><span class="o">-</span><span class="mi">2</span><span class="p">:</span>
<span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="n">bins</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">],</span> <span class="mf">0.5</span><span class="p">,</span> <span class="s1">&#39;$P_{&#39;</span><span class="o">+</span><span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="nb">int</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">round</span><span class="p">(</span><span class="n">cumsum</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">*</span><span class="mi">100</span><span class="p">))</span><span class="si">}</span><span class="s1">&#39;</span><span class="o">+</span><span class="s1">&#39;}$&#39;</span><span class="p">,</span> <span class="n">ha</span><span class="o">=</span><span class="s1">&#39;center&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylim</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="n">ax</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">(</span><span class="n">vlines</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">vlines</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
<span class="n">ax</span><span class="o">.</span><span class="n">get_yaxis</span><span class="p">()</span><span class="o">.</span><span class="n">set_visible</span><span class="p">(</span><span class="kc">False</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">get_xaxis</span><span class="p">()</span><span class="o">.</span><span class="n">set_visible</span><span class="p">(</span><span class="kc">False</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">wspace</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">hspace</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">_save_or_show</span><span class="p">(</span><span class="n">savepath</span><span class="p">)</span>
<span class="k">return</span> <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span></div>
<div class="viewcode-block" id="plot_simplex">
<a class="viewcode-back" href="../../quapy.html#quapy.plot.plot_simplex">[docs]</a>
<span class="k">def</span> <span class="nf">plot_simplex</span><span class="p">(</span>
<span class="n">point_layers</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">region_layers</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">density_function</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">density_color</span><span class="o">=</span><span class="s1">&#39;#1f77b4&#39;</span><span class="p">,</span>
<span class="n">density_alpha</span><span class="o">=</span><span class="mf">1.0</span><span class="p">,</span>
<span class="n">resolution</span><span class="o">=</span><span class="mi">400</span><span class="p">,</span>
<span class="n">class_names</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">title</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">show_legend</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
<span class="n">legend_loc</span><span class="o">=</span><span class="s1">&#39;lower center&#39;</span><span class="p">,</span>
<span class="n">legend_bbox_to_anchor</span><span class="o">=</span><span class="p">(</span><span class="mf">0.5</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.08</span><span class="p">),</span>
<span class="n">legend_ncol</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
<span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mf">6.8</span><span class="p">,</span> <span class="mf">6.2</span><span class="p">),</span>
<span class="n">class_name_fontsize</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
<span class="n">title_fontsize</span><span class="o">=</span><span class="mi">11</span><span class="p">,</span>
<span class="n">legend_fontsize</span><span class="o">=</span><span class="mi">9</span><span class="p">,</span>
<span class="n">ax</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">savepath</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd"> Plots data on the ternary simplex for three-class quantification problems.</span>
<span class="sd"> This utility is convenient for visualising prevalence vectors, posterior triplets,</span>
<span class="sd"> confidence regions, or any other points that lie on the 2-dimensional probability</span>
<span class="sd"> simplex. The plot can combine three optional layer types:</span>
<span class="sd"> * `point_layers`: scatter layers for one or more prevalence clouds or reference points</span>
<span class="sd"> * `region_layers`: shaded regions defined by callables on prevalence vectors</span>
<span class="sd"> * `density_function`: a scalar function evaluated on the simplex and rendered as a heatmap</span>
<span class="sd"> Each entry in `point_layers` is a dictionary with a mandatory `points` field</span>
<span class="sd"> containing an array-like of shape `(n_points, 3)` or `(3,)`. Optional fields are</span>
<span class="sd"> `label` for the legend and `style` for matplotlib scatter keyword arguments.</span>
<span class="sd"> Each entry in `region_layers` is a dictionary with a mandatory `fn` field containing</span>
<span class="sd"> a callable that receives prevalence vectors and returns region-membership scores.</span>
<span class="sd"> Optional fields are `label`, `color`, and `alpha`.</span>
<span class="sd"> :param point_layers: optional list of point-layer dictionaries</span>
<span class="sd"> :param region_layers: optional list of region-layer dictionaries</span>
<span class="sd"> :param density_function: optional callable receiving prevalence vectors and returning</span>
<span class="sd"> scalar values</span>
<span class="sd"> :param density_color: color used for the density heatmap</span>
<span class="sd"> :param density_alpha: opacity for the density heatmap</span>
<span class="sd"> :param resolution: number of grid steps per axis used for rendering regions and densities</span>
<span class="sd"> :param class_names: optional list or tuple with the three class names</span>
<span class="sd"> :param title: optional plot title</span>
<span class="sd"> :param show_legend: whether to display the legend</span>
<span class="sd"> :param legend_loc: location string passed to matplotlib for the legend</span>
<span class="sd"> :param legend_bbox_to_anchor: optional legend anchor box</span>
<span class="sd"> :param legend_ncol: number of legend columns</span>
<span class="sd"> :param figsize: figure size used when `ax` is not provided</span>
<span class="sd"> :param class_name_fontsize: fontsize used for simplex vertex labels</span>
<span class="sd"> :param title_fontsize: fontsize used for the optional title</span>
<span class="sd"> :param legend_fontsize: fontsize used for the legend</span>
<span class="sd"> :param ax: optional matplotlib axes object; if not provided, a new figure is created</span>
<span class="sd"> :param savepath: path where to save the plot; if not indicated, the plot is shown when</span>
<span class="sd"> `ax` is not provided</span>
<span class="sd"> :return: returns `(fig, ax)` matplotlib objects for eventual customisation</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">if</span> <span class="n">class_names</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">class_names</span> <span class="o">=</span> <span class="p">(</span><span class="s1">&#39;Y=1&#39;</span><span class="p">,</span> <span class="s1">&#39;Y=2&#39;</span><span class="p">,</span> <span class="s1">&#39;Y=3&#39;</span><span class="p">)</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">class_names</span><span class="p">)</span> <span class="o">!=</span> <span class="mi">3</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;expected exactly 3 class names, got </span><span class="si">{</span><span class="nb">len</span><span class="p">(</span><span class="n">class_names</span><span class="p">)</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">)</span>
<span class="n">own_figure</span> <span class="o">=</span> <span class="n">ax</span> <span class="ow">is</span> <span class="kc">None</span>
<span class="k">if</span> <span class="n">own_figure</span><span class="p">:</span>
<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">figsize</span><span class="o">=</span><span class="n">figsize</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">fig</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">figure</span>
<span class="k">if</span> <span class="n">density_function</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">_plot_simplex_density</span><span class="p">(</span><span class="n">ax</span><span class="p">,</span> <span class="n">density_function</span><span class="p">,</span> <span class="n">resolution</span><span class="p">,</span> <span class="n">density_color</span><span class="p">,</span> <span class="n">density_alpha</span><span class="p">)</span>
<span class="k">if</span> <span class="n">region_layers</span><span class="p">:</span>
<span class="n">_plot_simplex_regions</span><span class="p">(</span><span class="n">ax</span><span class="p">,</span> <span class="n">region_layers</span><span class="p">,</span> <span class="n">resolution</span><span class="p">)</span>
<span class="k">if</span> <span class="n">point_layers</span><span class="p">:</span>
<span class="n">_plot_simplex_points</span><span class="p">(</span><span class="n">ax</span><span class="p">,</span> <span class="n">point_layers</span><span class="p">)</span>
<span class="n">simplex_ymax</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="mi">3</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span>
<span class="n">triangle</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span>
<span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">],</span>
<span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">],</span>
<span class="p">[</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">simplex_ymax</span><span class="p">],</span>
<span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">],</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">triangle</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">triangle</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="s1">&#39;black&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="o">-</span><span class="mf">0.05</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.05</span><span class="p">,</span> <span class="n">class_names</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">ha</span><span class="o">=</span><span class="s1">&#39;right&#39;</span><span class="p">,</span> <span class="n">va</span><span class="o">=</span><span class="s1">&#39;top&#39;</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="n">class_name_fontsize</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="mf">1.05</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.05</span><span class="p">,</span> <span class="n">class_names</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">ha</span><span class="o">=</span><span class="s1">&#39;left&#39;</span><span class="p">,</span> <span class="n">va</span><span class="o">=</span><span class="s1">&#39;top&#39;</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="n">class_name_fontsize</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">simplex_ymax</span> <span class="o">+</span> <span class="mf">0.05</span><span class="p">,</span> <span class="n">class_names</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">ha</span><span class="o">=</span><span class="s1">&#39;center&#39;</span><span class="p">,</span> <span class="n">va</span><span class="o">=</span><span class="s1">&#39;bottom&#39;</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="n">class_name_fontsize</span><span class="p">)</span>
<span class="k">if</span> <span class="n">title</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="n">title</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="n">title_fontsize</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_aspect</span><span class="p">(</span><span class="s1">&#39;equal&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">(</span><span class="o">-</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">1.1</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">(</span><span class="o">-</span><span class="mf">0.1</span><span class="p">,</span> <span class="n">simplex_ymax</span> <span class="o">+</span> <span class="mf">0.1</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s1">&#39;off&#39;</span><span class="p">)</span>
<span class="k">if</span> <span class="n">show_legend</span><span class="p">:</span>
<span class="n">_</span><span class="p">,</span> <span class="n">labels</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">get_legend_handles_labels</span><span class="p">()</span>
<span class="k">if</span> <span class="n">labels</span><span class="p">:</span>
<span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="n">legend_loc</span><span class="p">,</span> <span class="n">bbox_to_anchor</span><span class="o">=</span><span class="n">legend_bbox_to_anchor</span><span class="p">,</span> <span class="n">ncol</span><span class="o">=</span><span class="n">legend_ncol</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="n">legend_fontsize</span><span class="p">,</span> <span class="n">frameon</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="n">fig</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">(</span><span class="n">pad</span><span class="o">=</span><span class="mf">0.6</span><span class="p">)</span>
<span class="k">if</span> <span class="n">savepath</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">qp</span><span class="o">.</span><span class="n">util</span><span class="o">.</span><span class="n">create_parent_dir</span><span class="p">(</span><span class="n">savepath</span><span class="p">)</span>
<span class="n">fig</span><span class="o">.</span><span class="n">savefig</span><span class="p">(</span><span class="n">savepath</span><span class="p">,</span> <span class="n">bbox_inches</span><span class="o">=</span><span class="s1">&#39;tight&#39;</span><span class="p">)</span>
<span class="k">elif</span> <span class="n">own_figure</span><span class="p">:</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
<span class="k">return</span> <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span></div>
<span class="k">def</span> <span class="nf">_merge</span><span class="p">(</span><span class="n">method_names</span><span class="p">,</span> <span class="n">true_prevs</span><span class="p">,</span> <span class="n">estim_prevs</span><span class="p">):</span>
<span class="n">ndims</span> <span class="o">=</span> <span class="n">true_prevs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
<span class="n">data</span> <span class="o">=</span> <span class="n">defaultdict</span><span class="p">(</span><span class="k">lambda</span><span class="p">:</span> <span class="p">{</span><span class="s1">&#39;true&#39;</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">ndims</span><span class="p">)),</span> <span class="s1">&#39;estim&#39;</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">ndims</span><span class="p">))})</span>
<span class="n">method_order</span><span class="o">=</span><span class="p">[]</span>
<span class="k">for</span> <span class="n">method</span><span class="p">,</span> <span class="n">true_prev</span><span class="p">,</span> <span class="n">estim_prev</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">method_names</span><span class="p">,</span> <span class="n">true_prevs</span><span class="p">,</span> <span class="n">estim_prevs</span><span class="p">):</span>
<span class="n">data</span><span class="p">[</span><span class="n">method</span><span class="p">][</span><span class="s1">&#39;true&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">([</span><span class="n">data</span><span class="p">[</span><span class="n">method</span><span class="p">][</span><span class="s1">&#39;true&#39;</span><span class="p">],</span> <span class="n">true_prev</span><span class="p">])</span>
<span class="n">data</span><span class="p">[</span><span class="n">method</span><span class="p">][</span><span class="s1">&#39;estim&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">([</span><span class="n">data</span><span class="p">[</span><span class="n">method</span><span class="p">][</span><span class="s1">&#39;estim&#39;</span><span class="p">],</span> <span class="n">estim_prev</span><span class="p">])</span>
<span class="k">if</span> <span class="n">method</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">method_order</span><span class="p">:</span>
<span class="n">method_order</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">method</span><span class="p">)</span>
<span class="n">true_prevs_</span> <span class="o">=</span> <span class="p">[</span><span class="n">data</span><span class="p">[</span><span class="n">m</span><span class="p">][</span><span class="s1">&#39;true&#39;</span><span class="p">]</span> <span class="k">for</span> <span class="n">m</span> <span class="ow">in</span> <span class="n">method_order</span><span class="p">]</span>
<span class="n">estim_prevs_</span> <span class="o">=</span> <span class="p">[</span><span class="n">data</span><span class="p">[</span><span class="n">m</span><span class="p">][</span><span class="s1">&#39;estim&#39;</span><span class="p">]</span> <span class="k">for</span> <span class="n">m</span> <span class="ow">in</span> <span class="n">method_order</span><span class="p">]</span>
<span class="k">return</span> <span class="n">method_order</span><span class="p">,</span> <span class="n">true_prevs_</span><span class="p">,</span> <span class="n">estim_prevs_</span>
<span class="k">def</span> <span class="nf">_set_colors</span><span class="p">(</span><span class="n">ax</span><span class="p">,</span> <span class="n">n_methods</span><span class="p">):</span>
<span class="n">NUM_COLORS</span> <span class="o">=</span> <span class="n">n_methods</span>
<span class="k">if</span> <span class="n">NUM_COLORS</span><span class="o">&gt;</span><span class="mi">10</span><span class="p">:</span>
<span class="n">cm</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">get_cmap</span><span class="p">(</span><span class="s1">&#39;tab20&#39;</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_prop_cycle</span><span class="p">(</span><span class="n">color</span><span class="o">=</span><span class="p">[</span><span class="n">cm</span><span class="p">(</span><span class="mf">1.</span> <span class="o">*</span> <span class="n">i</span> <span class="o">/</span> <span class="n">NUM_COLORS</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">NUM_COLORS</span><span class="p">)])</span>
<span class="k">def</span> <span class="nf">_save_or_show</span><span class="p">(</span><span class="n">savepath</span><span class="p">):</span>
<span class="c1"># if savepath is specified, then saves the plot in that path; otherwise the plot is shown</span>
<span class="k">if</span> <span class="n">savepath</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">qp</span><span class="o">.</span><span class="n">util</span><span class="o">.</span><span class="n">create_parent_dir</span><span class="p">(</span><span class="n">savepath</span><span class="p">)</span>
<span class="c1"># plt.tight_layout()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">savefig</span><span class="p">(</span><span class="n">savepath</span><span class="p">,</span> <span class="n">bbox_inches</span><span class="o">=</span><span class="s1">&#39;tight&#39;</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
<span class="k">def</span> <span class="nf">_join_data_by_drift</span><span class="p">(</span><span class="n">method_names</span><span class="p">,</span> <span class="n">true_prevs</span><span class="p">,</span> <span class="n">estim_prevs</span><span class="p">,</span> <span class="n">tr_prevs</span><span class="p">,</span> <span class="n">x_error</span><span class="p">,</span> <span class="n">y_error</span><span class="p">,</span> <span class="n">method_order</span><span class="p">):</span>
<span class="n">data</span> <span class="o">=</span> <span class="n">defaultdict</span><span class="p">(</span><span class="k">lambda</span><span class="p">:</span> <span class="p">{</span><span class="s1">&#39;x&#39;</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">)),</span> <span class="s1">&#39;y&#39;</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">))})</span>
<span class="k">if</span> <span class="n">method_order</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">method_order</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">method</span><span class="p">,</span> <span class="n">test_prevs_i</span><span class="p">,</span> <span class="n">estim_prevs_i</span><span class="p">,</span> <span class="n">tr_prev_i</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">method_names</span><span class="p">,</span> <span class="n">true_prevs</span><span class="p">,</span> <span class="n">estim_prevs</span><span class="p">,</span> <span class="n">tr_prevs</span><span class="p">):</span>
<span class="n">tr_prev_i</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">tr_prev_i</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</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="n">repeats</span><span class="o">=</span><span class="n">test_prevs_i</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">tr_test_drifts</span> <span class="o">=</span> <span class="n">x_error</span><span class="p">(</span><span class="n">test_prevs_i</span><span class="p">,</span> <span class="n">tr_prev_i</span><span class="p">)</span>
<span class="n">data</span><span class="p">[</span><span class="n">method</span><span class="p">][</span><span class="s1">&#39;x&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">([</span><span class="n">data</span><span class="p">[</span><span class="n">method</span><span class="p">][</span><span class="s1">&#39;x&#39;</span><span class="p">],</span> <span class="n">tr_test_drifts</span><span class="p">])</span>
<span class="n">method_drifts</span> <span class="o">=</span> <span class="n">y_error</span><span class="p">(</span><span class="n">test_prevs_i</span><span class="p">,</span> <span class="n">estim_prevs_i</span><span class="p">)</span>
<span class="n">data</span><span class="p">[</span><span class="n">method</span><span class="p">][</span><span class="s1">&#39;y&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">([</span><span class="n">data</span><span class="p">[</span><span class="n">method</span><span class="p">][</span><span class="s1">&#39;y&#39;</span><span class="p">],</span> <span class="n">method_drifts</span><span class="p">])</span>
<span class="k">if</span> <span class="n">method</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">method_order</span><span class="p">:</span>
<span class="n">method_order</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">method</span><span class="p">)</span>
<span class="k">return</span> <span class="n">data</span>
<span class="k">def</span> <span class="nf">_simplex_to_cartesian</span><span class="p">(</span><span class="n">prevalences</span><span class="p">):</span>
<span class="n">prevalences</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">prevalences</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">float</span><span class="p">)</span>
<span class="n">prevalences</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">atleast_2d</span><span class="p">(</span><span class="n">prevalences</span><span class="p">)</span>
<span class="k">if</span> <span class="n">prevalences</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">!=</span> <span class="mi">3</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;plot_simplex expects prevalence vectors of shape (_, 3); found </span><span class="si">{</span><span class="n">prevalences</span><span class="o">.</span><span class="n">shape</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">)</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">prevalences</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="mf">0.5</span> <span class="o">*</span> <span class="n">prevalences</span><span class="p">[:,</span> <span class="mi">2</span><span class="p">]</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">prevalences</span><span class="p">[:,</span> <span class="mi">2</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span>
<span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span>
<span class="k">def</span> <span class="nf">_barycentric_from_xy</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
<span class="n">p3</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="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
<span class="n">p2</span> <span class="o">=</span> <span class="n">x</span> <span class="o">-</span> <span class="mf">0.5</span> <span class="o">*</span> <span class="n">p3</span>
<span class="n">p1</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">p2</span> <span class="o">-</span> <span class="n">p3</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">stack</span><span class="p">([</span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span><span class="p">,</span> <span class="n">p3</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="k">def</span> <span class="nf">_simplex_mesh</span><span class="p">(</span><span class="n">resolution</span><span class="p">):</span>
<span class="n">simplex_ymax</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="mi">3</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span>
<span class="n">xs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</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="n">resolution</span><span class="p">)</span>
<span class="n">ys</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">simplex_ymax</span><span class="p">,</span> <span class="n">resolution</span><span class="p">)</span>
<span class="n">grid_x</span><span class="p">,</span> <span class="n">grid_y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span><span class="p">(</span><span class="n">xs</span><span class="p">,</span> <span class="n">ys</span><span class="p">)</span>
<span class="n">pts_bary</span> <span class="o">=</span> <span class="n">_barycentric_from_xy</span><span class="p">(</span><span class="n">grid_x</span><span class="p">,</span> <span class="n">grid_y</span><span class="p">)</span>
<span class="n">mask</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">all</span><span class="p">(</span><span class="n">pts_bary</span> <span class="o">&gt;=</span> <span class="mi">0</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="k">return</span> <span class="n">xs</span><span class="p">,</span> <span class="n">ys</span><span class="p">,</span> <span class="n">pts_bary</span><span class="p">,</span> <span class="n">mask</span>
<span class="k">def</span> <span class="nf">_evaluate_simplex_function</span><span class="p">(</span><span class="n">function</span><span class="p">,</span> <span class="n">points</span><span class="p">):</span>
<span class="n">points</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">points</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">float</span><span class="p">)</span>
<span class="k">try</span><span class="p">:</span>
<span class="n">values</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">function</span><span class="p">(</span><span class="n">points</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">float</span><span class="p">)</span>
<span class="k">if</span> <span class="n">values</span><span class="o">.</span><span class="n">shape</span> <span class="o">==</span> <span class="p">(</span><span class="n">points</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">],):</span>
<span class="k">return</span> <span class="n">values</span>
<span class="k">if</span> <span class="n">values</span><span class="o">.</span><span class="n">shape</span> <span class="o">==</span> <span class="n">points</span><span class="o">.</span><span class="n">shape</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]:</span>
<span class="k">return</span> <span class="n">values</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="k">except</span> <span class="ne">Exception</span><span class="p">:</span>
<span class="k">pass</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">([</span><span class="n">function</span><span class="p">(</span><span class="n">point</span><span class="p">)</span> <span class="k">for</span> <span class="n">point</span> <span class="ow">in</span> <span class="n">points</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">float</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">_region_colormap</span><span class="p">(</span><span class="n">color</span><span class="o">=</span><span class="s1">&#39;blue&#39;</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.35</span><span class="p">):</span>
<span class="k">return</span> <span class="n">ListedColormap</span><span class="p">([</span>
<span class="p">(</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">),</span>
<span class="p">(</span><span class="o">*</span><span class="n">mcolors</span><span class="o">.</span><span class="n">to_rgb</span><span class="p">(</span><span class="n">color</span><span class="p">),</span> <span class="n">alpha</span><span class="p">),</span>
<span class="p">])</span>
<span class="k">def</span> <span class="nf">_plot_simplex_points</span><span class="p">(</span><span class="n">ax</span><span class="p">,</span> <span class="n">point_layers</span><span class="p">):</span>
<span class="k">for</span> <span class="n">layer</span> <span class="ow">in</span> <span class="n">point_layers</span><span class="p">:</span>
<span class="n">points</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">layer</span><span class="p">[</span><span class="s1">&#39;points&#39;</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">float</span><span class="p">)</span>
<span class="n">style</span> <span class="o">=</span> <span class="p">{</span><span class="s1">&#39;s&#39;</span><span class="p">:</span> <span class="mi">25</span><span class="p">,</span> <span class="s1">&#39;alpha&#39;</span><span class="p">:</span> <span class="mf">0.8</span><span class="p">}</span>
<span class="n">style</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">layer</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;style&#39;</span><span class="p">,</span> <span class="p">{}))</span>
<span class="n">ax</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="o">*</span><span class="n">_simplex_to_cartesian</span><span class="p">(</span><span class="n">points</span><span class="p">),</span> <span class="n">label</span><span class="o">=</span><span class="n">layer</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;label&#39;</span><span class="p">),</span> <span class="o">**</span><span class="n">style</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">_plot_simplex_regions</span><span class="p">(</span><span class="n">ax</span><span class="p">,</span> <span class="n">region_layers</span><span class="p">,</span> <span class="n">resolution</span><span class="p">):</span>
<span class="n">xs</span><span class="p">,</span> <span class="n">ys</span><span class="p">,</span> <span class="n">pts_bary</span><span class="p">,</span> <span class="n">simplex_mask</span> <span class="o">=</span> <span class="n">_simplex_mesh</span><span class="p">(</span><span class="n">resolution</span><span class="p">)</span>
<span class="n">valid_points</span> <span class="o">=</span> <span class="n">pts_bary</span><span class="p">[</span><span class="n">simplex_mask</span><span class="p">]</span>
<span class="k">for</span> <span class="n">layer</span> <span class="ow">in</span> <span class="n">region_layers</span><span class="p">:</span>
<span class="n">mask</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">simplex_mask</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">float</span><span class="p">)</span>
<span class="n">values</span> <span class="o">=</span> <span class="n">_evaluate_simplex_function</span><span class="p">(</span><span class="n">layer</span><span class="p">[</span><span class="s1">&#39;fn&#39;</span><span class="p">],</span> <span class="n">valid_points</span><span class="p">)</span>
<span class="n">mask</span><span class="p">[</span><span class="n">simplex_mask</span><span class="p">]</span> <span class="o">=</span> <span class="n">values</span>
<span class="n">ax</span><span class="o">.</span><span class="n">pcolormesh</span><span class="p">(</span>
<span class="n">xs</span><span class="p">,</span>
<span class="n">ys</span><span class="p">,</span>
<span class="n">mask</span><span class="p">,</span>
<span class="n">shading</span><span class="o">=</span><span class="s1">&#39;auto&#39;</span><span class="p">,</span>
<span class="n">cmap</span><span class="o">=</span><span class="n">_region_colormap</span><span class="p">(</span><span class="n">layer</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;color&#39;</span><span class="p">,</span> <span class="s1">&#39;blue&#39;</span><span class="p">),</span> <span class="n">layer</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;alpha&#39;</span><span class="p">,</span> <span class="mf">0.35</span><span class="p">)),</span>
<span class="p">)</span>
<span class="k">if</span> <span class="n">layer</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;label&#39;</span><span class="p">)</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">ax</span><span class="o">.</span><span class="n">scatter</span><span class="p">([],</span> <span class="p">[],</span> <span class="n">color</span><span class="o">=</span><span class="n">layer</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;color&#39;</span><span class="p">,</span> <span class="s1">&#39;blue&#39;</span><span class="p">),</span> <span class="n">alpha</span><span class="o">=</span><span class="n">layer</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;alpha&#39;</span><span class="p">,</span> <span class="mf">0.35</span><span class="p">),</span> <span class="n">label</span><span class="o">=</span><span class="n">layer</span><span class="p">[</span><span class="s1">&#39;label&#39;</span><span class="p">])</span>
<span class="k">def</span> <span class="nf">_plot_simplex_density</span><span class="p">(</span><span class="n">ax</span><span class="p">,</span> <span class="n">density_function</span><span class="p">,</span> <span class="n">resolution</span><span class="p">,</span> <span class="n">color</span><span class="p">,</span> <span class="n">alpha</span><span class="p">):</span>
<span class="n">xs</span><span class="p">,</span> <span class="n">ys</span><span class="p">,</span> <span class="n">pts_bary</span><span class="p">,</span> <span class="n">simplex_mask</span> <span class="o">=</span> <span class="n">_simplex_mesh</span><span class="p">(</span><span class="n">resolution</span><span class="p">)</span>
<span class="n">valid_points</span> <span class="o">=</span> <span class="n">pts_bary</span><span class="p">[</span><span class="n">simplex_mask</span><span class="p">]</span>
<span class="n">density</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">full</span><span class="p">(</span><span class="n">simplex_mask</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">float</span><span class="p">)</span>
<span class="n">values</span> <span class="o">=</span> <span class="n">_evaluate_simplex_function</span><span class="p">(</span><span class="n">density_function</span><span class="p">,</span> <span class="n">valid_points</span><span class="p">)</span>
<span class="n">min_v</span><span class="p">,</span> <span class="n">max_v</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">values</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">values</span><span class="p">)</span>
<span class="k">if</span> <span class="n">max_v</span> <span class="o">&gt;</span> <span class="n">min_v</span><span class="p">:</span>
<span class="n">values</span> <span class="o">=</span> <span class="p">(</span><span class="n">values</span> <span class="o">-</span> <span class="n">min_v</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">max_v</span> <span class="o">-</span> <span class="n">min_v</span><span class="p">)</span>
<span class="n">density</span><span class="p">[</span><span class="n">simplex_mask</span><span class="p">]</span> <span class="o">=</span> <span class="n">values</span>
<span class="n">cmap</span> <span class="o">=</span> <span class="n">LinearSegmentedColormap</span><span class="o">.</span><span class="n">from_list</span><span class="p">(</span><span class="s1">&#39;simplex_density&#39;</span><span class="p">,</span> <span class="p">[</span><span class="s1">&#39;white&#39;</span><span class="p">,</span> <span class="n">color</span><span class="p">])</span>
<span class="n">ax</span><span class="o">.</span><span class="n">pcolormesh</span><span class="p">(</span><span class="n">xs</span><span class="p">,</span> <span class="n">ys</span><span class="p">,</span> <span class="n">density</span><span class="p">,</span> <span class="n">shading</span><span class="o">=</span><span class="s1">&#39;auto&#39;</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">cmap</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="n">alpha</span><span class="p">)</span>
<div class="viewcode-block" id="calibration_plot">
<a class="viewcode-back" href="../../quapy.html#quapy.plot.calibration_plot">[docs]</a>
<span class="k">def</span> <span class="nf">calibration_plot</span><span class="p">(</span><span class="n">prob_classifier</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">nbins</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">savepath</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="n">posteriors</span> <span class="o">=</span> <span class="n">prob_classifier</span><span class="o">.</span><span class="n">predict_proba</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="k">assert</span> <span class="n">posteriors</span><span class="o">.</span><span class="n">ndim</span><span class="o">==</span><span class="mi">2</span><span class="p">,</span> <span class="s1">&#39;calibration plot only works for binary problems&#39;</span>
<span class="n">posteriors</span> <span class="o">=</span> <span class="n">posteriors</span><span class="p">[:,</span><span class="mi">1</span><span class="p">]</span>
<span class="n">pred_y</span> <span class="o">=</span> <span class="n">posteriors</span><span class="o">&gt;=</span><span class="mf">0.5</span>
<span class="n">bins</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</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="n">nbins</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">binned_values</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">digitize</span><span class="p">(</span><span class="n">posteriors</span><span class="p">,</span> <span class="n">bins</span><span class="p">,</span> <span class="n">right</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="n">correct</span> <span class="o">=</span> <span class="n">pred_y</span> <span class="o">==</span> <span class="n">y</span>
<span class="n">bin_centers</span> <span class="o">=</span> <span class="p">(</span><span class="n">bins</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">bins</span><span class="p">[</span><span class="mi">1</span><span class="p">:])</span> <span class="o">/</span> <span class="mi">2</span>
<span class="n">bins_names</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">nbins</span><span class="p">)</span>
<span class="n">y_axis</span> <span class="o">=</span> <span class="p">[</span><span class="n">correct</span><span class="p">[</span><span class="n">binned_values</span><span class="o">==</span><span class="nb">bin</span><span class="p">]</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span> <span class="k">for</span> <span class="nb">bin</span> <span class="ow">in</span> <span class="n">bins_names</span><span class="p">]</span>
<span class="n">y_axis</span> <span class="o">=</span> <span class="p">[</span><span class="n">v</span> <span class="k">if</span> <span class="ow">not</span> <span class="n">np</span><span class="o">.</span><span class="n">isnan</span><span class="p">(</span><span class="n">v</span><span class="p">)</span> <span class="k">else</span> <span class="mi">0</span> <span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">y_axis</span><span class="p">]</span>
<span class="c1"># Crear el gráfico de barras</span>
<span class="n">plt</span><span class="o">.</span><span class="n">bar</span><span class="p">(</span><span class="n">bin_centers</span><span class="p">,</span> <span class="n">y_axis</span><span class="p">,</span> <span class="n">width</span><span class="o">=</span><span class="n">bins</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">bins</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">edgecolor</span><span class="o">=</span><span class="s1">&#39;black&#39;</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.7</span><span class="p">)</span>
<span class="c1"># Etiquetas y título</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s2">&quot;Bin&quot;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s2">&quot;Value&quot;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">&quot;Bar plot of calculated values per bin&quot;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xticks</span><span class="p">(</span><span class="n">bin_centers</span><span class="p">,</span> <span class="p">[</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">b</span><span class="si">:</span><span class="s2">.2f</span><span class="si">}</span><span class="s2">&quot;</span> <span class="k">for</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">bin_centers</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="c1"># Mostrar el gráfico</span>
<span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span></div>
<span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s1">&#39;__main__&#39;</span><span class="p">:</span>
<span class="kn">import</span> <span class="nn">quapy</span> <span class="k">as</span> <span class="nn">qp</span>
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="kn">import</span> <span class="n">LogisticRegression</span>
<span class="n">data</span> <span class="o">=</span> <span class="n">qp</span><span class="o">.</span><span class="n">datasets</span><span class="o">.</span><span class="n">fetch_UCIBinaryDataset</span><span class="p">(</span><span class="n">qp</span><span class="o">.</span><span class="n">datasets</span><span class="o">.</span><span class="n">UCI_BINARY_DATASETS</span><span class="p">[</span><span class="mi">6</span><span class="p">])</span>
<span class="n">train</span><span class="p">,</span> <span class="n">test</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">train_test</span>
<span class="n">classifier</span> <span class="o">=</span> <span class="n">LogisticRegression</span><span class="p">()</span>
<span class="n">classifier</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="o">*</span><span class="n">train</span><span class="o">.</span><span class="n">Xy</span><span class="p">)</span>
<span class="n">calibration_plot</span><span class="p">(</span><span class="n">classifier</span><span class="p">,</span> <span class="o">*</span><span class="n">test</span><span class="o">.</span><span class="n">Xy</span><span class="p">)</span>
</pre></div>
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