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<section class="sphx-glr-example-title" id="entropic-wasserstein-component-analysis">
<span id="sphx-glr-auto-examples-others-plot-ewca-py"></span><h1>Entropic Wasserstein Component Analysis<a class="headerlink" href="#entropic-wasserstein-component-analysis" title="Link to this heading"></a></h1>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>Example added in release: 0.9.1.</p>
</div>
<p>This example illustrates the use of EWCA as proposed in [52].</p>
<p>[52] Collas, A., Vayer, T., Flamary, F., & Breloy, A. (2023).
Entropic Wasserstein Component Analysis.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Author: Antoine Collas <antoine.collas@inria.fr></span>
<span class="c1">#</span>
<span class="c1"># License: MIT License</span>
<span class="c1"># sphinx_gallery_thumbnail_number = 2</span>
<span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
<span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pylab</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">pl</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">ot.dr</span><span class="w"> </span><span class="kn">import</span> <a href="../../gen_modules/ot.dr.html#id4" title="ot.dr.ewca" class="sphx-glr-backref-module-ot-dr sphx-glr-backref-type-py-function"><span class="n">ewca</span></a>
<span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.datasets</span><span class="w"> </span><span class="kn">import</span> <span class="n">make_blobs</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">matplotlib</span><span class="w"> </span><span class="kn">import</span> <span class="n">ticker</span> <span class="k">as</span> <span class="n">mticker</span>
<span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.patches</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">patches</span>
<span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib</span>
</pre></div>
</div>
<section id="generate-data">
<h2>Generate data<a class="headerlink" href="#generate-data" title="Link to this heading"></a></h2>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n_samples</span></a> <span class="o">=</span> <span class="mi">20</span>
<a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">esp</span></a> <span class="o">=</span> <span class="mf">0.8</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">centers</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.array.html#numpy.array" title="numpy.array" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">array</span></a><span class="p">([[</span><a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">esp</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">esp</span></a><span class="p">],</span> <span class="p">[</span><span class="o">-</span><a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">esp</span></a><span class="p">,</span> <span class="o">-</span><a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">esp</span></a><span class="p">]])</span>
<a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">cluster_std</span></a> <span class="o">=</span> <span class="mf">0.4</span>
<a href="https://numpy.org/doc/stable/reference/random/legacy.html#numpy.random.RandomState" title="numpy.random.RandomState" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">rng</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/random/legacy.html#numpy.random.RandomState" title="numpy.random.RandomState" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-class"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">RandomState</span></a><span class="p">(</span><span class="mi">42</span><span class="p">)</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">X</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">y</span></a> <span class="o">=</span> <span class="n">make_blobs</span><span class="p">(</span>
<a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n_samples</span></a><span class="o">=</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n_samples</span></a><span class="p">,</span>
<span class="n">n_features</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">centers</span></a><span class="o">=</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">centers</span></a><span class="p">,</span>
<a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">cluster_std</span></a><span class="o">=</span><a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">cluster_std</span></a><span class="p">,</span>
<span class="n">shuffle</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
<span class="n">random_state</span><span class="o">=</span><a href="https://numpy.org/doc/stable/reference/random/legacy.html#numpy.random.RandomState" title="numpy.random.RandomState" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">rng</span></a><span class="p">,</span>
<span class="p">)</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">X</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">X</span></a> <span class="o">-</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">X</span></a><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
</pre></div>
</div>
</section>
<section id="plot-data">
<h2>Plot data<a class="headerlink" href="#plot-data" title="Link to this heading"></a></h2>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.figure.Figure.html#matplotlib.figure.Figure" title="matplotlib.figure.Figure" class="sphx-glr-backref-module-matplotlib-figure sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">fig</span></a> <span class="o">=</span> <span class="n">pl</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.colors.ListedColormap.html#matplotlib.colors.ListedColormap" title="matplotlib.colors.ListedColormap" class="sphx-glr-backref-module-matplotlib-colors sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">cmap</span></a> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/cm_api.html#matplotlib.cm.ColormapRegistry.get_cmap" title="matplotlib.cm.ColormapRegistry.get_cmap" class="sphx-glr-backref-module-matplotlib-cm sphx-glr-backref-type-py-method"><span class="n">matplotlib</span><span class="o">.</span><span class="n">colormaps</span><span class="o">.</span><span class="n">get_cmap</span></a><span class="p">(</span><span class="s2">"tab10"</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">X</span></a><span class="p">[:</span> <a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n_samples</span></a> <span class="o">//</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">X</span></a><span class="p">[:</span> <a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n_samples</span></a> <span class="o">//</span> <span class="mi">2</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="p">[</span><a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.colors.ListedColormap.html#matplotlib.colors.ListedColormap" title="matplotlib.colors.ListedColormap" class="sphx-glr-backref-module-matplotlib-colors sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">cmap</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">y</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">i</span></a><span class="p">]</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">i</span></a> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n_samples</span></a> <span class="o">//</span> <span class="mi">2</span><span class="p">)],</span>
<span class="n">alpha</span><span class="o">=</span><span class="mf">0.4</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="s2">"Class 1"</span><span class="p">,</span>
<span class="n">zorder</span><span class="o">=</span><span class="mi">30</span><span class="p">,</span>
<span class="n">s</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">X</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n_samples</span></a> <span class="o">//</span> <span class="mi">2</span> <span class="p">:,</span> <span class="mi">0</span><span class="p">],</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">X</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n_samples</span></a> <span class="o">//</span> <span class="mi">2</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="p">[</span><a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.colors.ListedColormap.html#matplotlib.colors.ListedColormap" title="matplotlib.colors.ListedColormap" class="sphx-glr-backref-module-matplotlib-colors sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">cmap</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">y</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">i</span></a><span class="p">]</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">i</span></a> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n_samples</span></a> <span class="o">//</span> <span class="mi">2</span><span class="p">,</span> <a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n_samples</span></a><span class="p">)],</span>
<span class="n">alpha</span><span class="o">=</span><span class="mf">0.4</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="s2">"Class 2"</span><span class="p">,</span>
<span class="n">zorder</span><span class="o">=</span><span class="mi">30</span><span class="p">,</span>
<span class="n">s</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span>
<span class="p">)</span>
<a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x_y_lim</span></a> <span class="o">=</span> <span class="mf">2.5</span>
<a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">fs</span></a> <span class="o">=</span> <span class="mi">15</span>
<span class="n">pl</span><span class="o">.</span><span class="n">xlim</span><span class="p">(</span><span class="o">-</span><a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x_y_lim</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x_y_lim</span></a><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">xticks</span><span class="p">([])</span>
<span class="n">pl</span><span class="o">.</span><span class="n">ylim</span><span class="p">(</span><span class="o">-</span><a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x_y_lim</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x_y_lim</span></a><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">yticks</span><span class="p">([])</span>
<span class="n">pl</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">fontsize</span><span class="o">=</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">fs</span></a><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"Data"</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">fs</span></a><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_EWCA_001.png" srcset="../../_images/sphx_glr_plot_EWCA_001.png" alt="Data" class = "sphx-glr-single-img"/></section>
<section id="compute-ewca">
<h2>Compute EWCA<a class="headerlink" href="#compute-ewca" title="Link to this heading"></a></h2>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">pi</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">U</span></a> <span class="o">=</span> <a href="../../gen_modules/ot.dr.html#id4" title="ot.dr.ewca" class="sphx-glr-backref-module-ot-dr sphx-glr-backref-type-py-function"><span class="n">ewca</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">X</span></a><span class="p">,</span> <span class="n">k</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">reg</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span>
</pre></div>
</div>
</section>
<section id="plot-data-first-component-and-projected-data">
<h2>Plot data, first component, and projected data<a class="headerlink" href="#plot-data-first-component-and-projected-data" title="Link to this heading"></a></h2>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.figure.Figure.html#matplotlib.figure.Figure" title="matplotlib.figure.Figure" class="sphx-glr-backref-module-matplotlib-figure sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">fig</span></a> <span class="o">=</span> <span class="n">pl</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
<a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">scale</span></a> <span class="o">=</span> <span class="mi">3</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">u</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">U</span></a><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span>
<span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span>
<span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">scale</span></a> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">u</span></a><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="o">-</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">scale</span></a> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">u</span></a><span class="p">[</span><span class="mi">0</span><span class="p">]],</span>
<span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">scale</span></a> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">u</span></a><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="o">-</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">scale</span></a> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">u</span></a><span class="p">[</span><span class="mi">1</span><span class="p">]],</span>
<span class="n">color</span><span class="o">=</span><span class="s2">"grey"</span><span class="p">,</span>
<span class="n">linestyle</span><span class="o">=</span><span class="s2">"--"</span><span class="p">,</span>
<span class="n">lw</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span>
<span class="n">alpha</span><span class="o">=</span><span class="mf">0.3</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s2">"$\mathbf</span><span class="si">{U}</span><span class="s2">$"</span><span class="p">,</span>
<span class="p">)</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">X1</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">X</span></a> <span class="o">@</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">u</span></a><span class="p">[:,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">@</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">u</span></a><span class="p">[:,</span> <span class="kc">None</span><span class="p">]</span><span class="o">.</span><span class="n">T</span>
<span class="k">for</span> <a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">i</span></a> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n_samples</span></a><span class="p">):</span>
<span class="k">for</span> <a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">j</span></a> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n_samples</span></a><span class="p">):</span>
<a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.float64" title="numpy.float64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">v</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">pi</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">i</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">j</span></a><span class="p">]</span> <span class="o">/</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">pi</span></a><span class="o">.</span><span class="n">max</span><span class="p">()</span>
<span class="k">if</span> <a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.float64" title="numpy.float64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">v</span></a> <span class="o">>=</span> <span class="mf">0.15</span> <span class="ow">or</span> <span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">i</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">j</span></a><span class="p">)</span> <span class="o">==</span> <span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n_samples</span></a> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n_samples</span></a> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
<span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span>
<span class="p">[</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">X</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">i</span></a><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">X1</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">j</span></a><span class="p">,</span> <span class="mi">0</span><span class="p">]],</span>
<span class="p">[</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">X</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">i</span></a><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">X1</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">j</span></a><span class="p">,</span> <span class="mi">1</span><span class="p">]],</span>
<span class="n">alpha</span><span class="o">=</span><a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.float64" title="numpy.float64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">v</span></a><span class="p">,</span>
<span class="n">linestyle</span><span class="o">=</span><span class="s2">"-"</span><span class="p">,</span>
<span class="n">c</span><span class="o">=</span><span class="s2">"C0"</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s2">"$\pi_</span><span class="si">{ij}</span><span class="s2">$"</span>
<span class="k">if</span> <span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">i</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">j</span></a><span class="p">)</span> <span class="o">==</span> <span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n_samples</span></a> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n_samples</span></a> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
<span class="k">else</span> <span class="kc">None</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">X</span></a><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">X</span></a><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span>
<span class="n">color</span><span class="o">=</span><span class="p">[</span><a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.colors.ListedColormap.html#matplotlib.colors.ListedColormap" title="matplotlib.colors.ListedColormap" class="sphx-glr-backref-module-matplotlib-colors sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">cmap</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">y</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">i</span></a><span class="p">]</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">i</span></a> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n_samples</span></a><span class="p">)],</span>
<span class="n">alpha</span><span class="o">=</span><span class="mf">0.4</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s2">"$\mathbf</span><span class="si">{x}</span><span class="s2">_i$"</span><span class="p">,</span>
<span class="n">zorder</span><span class="o">=</span><span class="mi">30</span><span class="p">,</span>
<span class="n">s</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">X1</span></a><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">X1</span></a><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span>
<span class="n">color</span><span class="o">=</span><span class="p">[</span><a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.colors.ListedColormap.html#matplotlib.colors.ListedColormap" title="matplotlib.colors.ListedColormap" class="sphx-glr-backref-module-matplotlib-colors sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">cmap</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">y</span></a><span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">i</span></a><span class="p">]</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">i</span></a> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n_samples</span></a><span class="p">)],</span>
<span class="n">alpha</span><span class="o">=</span><span class="mf">0.9</span><span class="p">,</span>
<span class="n">s</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span>
<span class="n">marker</span><span class="o">=</span><span class="s2">"+"</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s2">"$\mathbf</span><span class="si">{U}</span><span class="s2">\mathbf</span><span class="si">{U}</span><span class="s2">^{\top}\mathbf</span><span class="si">{x}</span><span class="s2">_i$"</span><span class="p">,</span>
<span class="n">zorder</span><span class="o">=</span><span class="mi">30</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"Data and projections"</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">fs</span></a><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">xlim</span><span class="p">(</span><span class="o">-</span><a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x_y_lim</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x_y_lim</span></a><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">xticks</span><span class="p">([])</span>
<span class="n">pl</span><span class="o">.</span><span class="n">ylim</span><span class="p">(</span><span class="o">-</span><a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x_y_lim</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x_y_lim</span></a><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">yticks</span><span class="p">([])</span>
<span class="n">pl</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">fontsize</span><span class="o">=</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">fs</span></a><span class="p">,</span> <span class="n">loc</span><span class="o">=</span><span class="s2">"upper left"</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_EWCA_002.png" srcset="../../_images/sphx_glr_plot_EWCA_002.png" alt="Data and projections" class = "sphx-glr-single-img"/></section>
<section id="plot-transport-plan">
<h2>Plot transport plan<a class="headerlink" href="#plot-transport-plan" title="Link to this heading"></a></h2>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.figure.Figure.html#matplotlib.figure.Figure" title="matplotlib.figure.Figure" class="sphx-glr-backref-module-matplotlib-figure sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">fig</span></a> <span class="o">=</span> <span class="n">pl</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.colors.PowerNorm.html#matplotlib.colors.PowerNorm" title="matplotlib.colors.PowerNorm" class="sphx-glr-backref-module-matplotlib-colors sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">norm</span></a> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.colors.PowerNorm.html#matplotlib.colors.PowerNorm" title="matplotlib.colors.PowerNorm" class="sphx-glr-backref-module-matplotlib-colors sphx-glr-backref-type-py-class"><span class="n">matplotlib</span><span class="o">.</span><span class="n">colors</span><span class="o">.</span><span class="n">PowerNorm</span></a><span class="p">(</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">vmin</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">vmax</span><span class="o">=</span><span class="mi">100</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/image_api.html#matplotlib.image.AxesImage" title="matplotlib.image.AxesImage" class="sphx-glr-backref-module-matplotlib-image sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">im</span></a> <span class="o">=</span> <span class="n">pl</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n_samples</span></a> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">pi</span></a> <span class="o">*</span> <span class="mi">100</span><span class="p">,</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.colors.ListedColormap.html#matplotlib.colors.ListedColormap" title="matplotlib.colors.ListedColormap" class="sphx-glr-backref-module-matplotlib-colors sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">cmap</span></a><span class="o">=</span><a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.colors.LinearSegmentedColormap.html#matplotlib.colors.LinearSegmentedColormap" title="matplotlib.colors.LinearSegmentedColormap" class="sphx-glr-backref-module-matplotlib-colors sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">pl</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">Blues</span></a><span class="p">,</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.colors.PowerNorm.html#matplotlib.colors.PowerNorm" title="matplotlib.colors.PowerNorm" class="sphx-glr-backref-module-matplotlib-colors sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">norm</span></a><span class="o">=</span><a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.colors.PowerNorm.html#matplotlib.colors.PowerNorm" title="matplotlib.colors.PowerNorm" class="sphx-glr-backref-module-matplotlib-colors sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">norm</span></a><span class="p">,</span> <span class="n">aspect</span><span class="o">=</span><span class="s2">"auto"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/colorbar_api.html#matplotlib.colorbar.Colorbar" title="matplotlib.colorbar.Colorbar" class="sphx-glr-backref-module-matplotlib-colorbar sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">cb</span></a> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.figure.Figure.colorbar.html#matplotlib.figure.Figure.colorbar" title="matplotlib.figure.Figure.colorbar" class="sphx-glr-backref-module-matplotlib-figure sphx-glr-backref-type-py-method"><span class="n">fig</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><a href="https://matplotlib.org/stable/api/image_api.html#matplotlib.image.AxesImage" title="matplotlib.image.AxesImage" class="sphx-glr-backref-module-matplotlib-image sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">im</span></a><span class="p">,</span> <span class="n">orientation</span><span class="o">=</span><span class="s2">"vertical"</span><span class="p">,</span> <span class="n">shrink</span><span class="o">=</span><span class="mf">0.8</span><span class="p">)</span>
<a href="https://docs.python.org/3/library/stdtypes.html#list" title="builtins.list" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ticks_loc</span></a> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.get_yticks.html#matplotlib.axes.Axes.get_yticks" title="matplotlib.axes.Axes.get_yticks" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">cb</span><span class="o">.</span><span class="n">ax</span><span class="o">.</span><span class="n">get_yticks</span></a><span class="p">()</span><span class="o">.</span><span class="n">tolist</span><span class="p">()</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.axis.Axis.set_major_locator.html#matplotlib.axis.Axis.set_major_locator" title="matplotlib.axis.Axis.set_major_locator" class="sphx-glr-backref-module-matplotlib-axis sphx-glr-backref-type-py-method"><span class="n">cb</span><span class="o">.</span><span class="n">ax</span><span class="o">.</span><span class="n">yaxis</span><span class="o">.</span><span class="n">set_major_locator</span></a><span class="p">(</span><a href="https://matplotlib.org/stable/api/ticker_api.html#matplotlib.ticker.FixedLocator" title="matplotlib.ticker.FixedLocator" class="sphx-glr-backref-module-matplotlib-ticker sphx-glr-backref-type-py-class"><span class="n">mticker</span><span class="o">.</span><span class="n">FixedLocator</span></a><span class="p">(</span><a href="https://docs.python.org/3/library/stdtypes.html#list" title="builtins.list" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ticks_loc</span></a><span class="p">))</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.set_yticklabels.html#matplotlib.axes.Axes.set_yticklabels" title="matplotlib.axes.Axes.set_yticklabels" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">cb</span><span class="o">.</span><span class="n">ax</span><span class="o">.</span><span class="n">set_yticklabels</span></a><span class="p">([</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="nb">int</span><span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">i</span></a><span class="p">)</span><span class="si">}</span><span class="s2">%"</span> <span class="k">for</span> <a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">i</span></a> <span class="ow">in</span> <a href="https://matplotlib.org/stable/api/colorbar_api.html#matplotlib.colorbar.Colorbar.get_ticks" title="matplotlib.colorbar.Colorbar.get_ticks" class="sphx-glr-backref-module-matplotlib-colorbar sphx-glr-backref-type-py-method"><span class="n">cb</span><span class="o">.</span><span class="n">get_ticks</span></a><span class="p">()])</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.tick_params.html#matplotlib.axes.Axes.tick_params" title="matplotlib.axes.Axes.tick_params" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">cb</span><span class="o">.</span><span class="n">ax</span><span class="o">.</span><span class="n">tick_params</span></a><span class="p">(</span><span class="n">labelsize</span><span class="o">=</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">fs</span></a><span class="p">)</span>
<span class="k">for</span> <a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">i</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">class_</span></a> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.sort.html#numpy.sort" title="numpy.sort" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">sort</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.unique.html#numpy.unique" title="numpy.unique" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">unique</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">y</span></a><span class="p">))):</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">indices</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">y</span></a> <span class="o">==</span> <a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">class_</span></a>
<a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">idx_min</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.min.html#numpy.min" title="numpy.min" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">min</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.arange.html#numpy.arange" title="numpy.arange" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">arange</span></a><span class="p">(</span><span class="nb">len</span><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">y</span></a><span class="p">))[</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">indices</span></a><span class="p">])</span>
<a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">idx_max</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.max.html#numpy.max" title="numpy.max" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">max</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.arange.html#numpy.arange" title="numpy.arange" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">arange</span></a><span class="p">(</span><span class="nb">len</span><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">y</span></a><span class="p">))[</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">indices</span></a><span class="p">])</span>
<a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">width</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">idx_max</span></a> <span class="o">-</span> <a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">idx_min</span></a> <span class="o">+</span> <span class="mi">1</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.patches.Rectangle.html#matplotlib.patches.Rectangle" title="matplotlib.patches.Rectangle" class="sphx-glr-backref-module-matplotlib-patches sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">rect</span></a> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.patches.Rectangle.html#matplotlib.patches.Rectangle" title="matplotlib.patches.Rectangle" class="sphx-glr-backref-module-matplotlib-patches sphx-glr-backref-type-py-class"><span class="n">patches</span><span class="o">.</span><span class="n">Rectangle</span></a><span class="p">(</span>
<span class="p">(</span><a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">idx_min</span></a> <span class="o">-</span> <span class="mf">0.5</span><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">idx_min</span></a> <span class="o">-</span> <span class="mf">0.5</span><span class="p">),</span>
<a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">width</span></a><span class="p">,</span>
<a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">width</span></a><span class="p">,</span>
<span class="n">linewidth</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
<span class="n">edgecolor</span><span class="o">=</span><span class="s2">"r"</span><span class="p">,</span>
<span class="n">facecolor</span><span class="o">=</span><span class="s2">"none"</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">gca</span><span class="p">()</span><span class="o">.</span><span class="n">add_patch</span><span class="p">(</span><a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.patches.Rectangle.html#matplotlib.patches.Rectangle" title="matplotlib.patches.Rectangle" class="sphx-glr-backref-module-matplotlib-patches sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">rect</span></a><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"OT plan"</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">fs</span></a><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="sa">r</span><span class="s2">"($\mathbf</span><span class="si">{x}</span><span class="s2">_1, \cdots, \mathbf</span><span class="si">{x}</span><span class="s2">_n$)"</span><span class="p">)</span>
<a href="https://docs.python.org/3/library/stdtypes.html#str" title="builtins.str" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x_label</span></a> <span class="o">=</span> <span class="sa">r</span><span class="s2">"($\mathbf</span><span class="si">{U}</span><span class="s2">\mathbf</span><span class="si">{U}</span><span class="s2">^{\top}\mathbf</span><span class="si">{x}</span><span class="s2">_1, \cdots,"</span>
<a href="https://docs.python.org/3/library/stdtypes.html#str" title="builtins.str" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x_label</span></a> <span class="o">+=</span> <span class="sa">r</span><span class="s2">"\mathbf</span><span class="si">{U}</span><span class="s2">\mathbf</span><span class="si">{U}</span><span class="s2">^{\top}\mathbf</span><span class="si">{x}</span><span class="s2">_n$)"</span>
<span class="n">pl</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><a href="https://docs.python.org/3/library/stdtypes.html#str" title="builtins.str" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">x_label</span></a><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
<span class="n">pl</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"scaled"</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
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