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<p><a class="reference internal" href="#sphx-glr-download-auto-examples-gromov-plot-fgw-py"><span class="std std-ref">Go to the end</span></a>
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<section class="sphx-glr-example-title" id="plot-fused-gromov-wasserstein">
<span id="sphx-glr-auto-examples-gromov-plot-fgw-py"></span><h1>Plot Fused-Gromov-Wasserstein<a class="headerlink" href="#plot-fused-gromov-wasserstein" title="Link to this heading"></a></h1>
<p>This example first illustrates the computation of FGW for 1D measures estimated
using a Conditional Gradient solver [24].</p>
<p>[24] Vayer Titouan, Chapel Laetitia, Flamary Rémi, Tavenard Romain
and Courty Nicolas
“Optimal Transport for structured data with application on graphs”
International Conference on Machine Learning (ICML). 2019.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Author: Titouan Vayer <titouan.vayer@irisa.fr></span>
<span class="c1">#</span>
<span class="c1"># License: MIT License</span>
<span class="c1"># sphinx_gallery_thumbnail_number = 3</span>
<span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">pl</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">ot</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">ot.gromov</span><span class="w"> </span><span class="kn">import</span> <a href="../../all.html#ot.gromov_wasserstein" title="ot.gromov_wasserstein" class="sphx-glr-backref-module-ot sphx-glr-backref-type-py-function"><span class="n">gromov_wasserstein</span></a><span class="p">,</span> <a href="../../all.html#ot.fused_gromov_wasserstein" title="ot.fused_gromov_wasserstein" class="sphx-glr-backref-module-ot sphx-glr-backref-type-py-function"><span class="n">fused_gromov_wasserstein</span></a>
</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><span class="c1"># parameters</span>
<span class="c1"># We create two 1D random measures</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</span></a> <span class="o">=</span> <span class="mi">20</span> <span class="c1"># number of points in the first distribution</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">n2</span></a> <span class="o">=</span> <span class="mi">30</span> <span class="c1"># number of points in the second distribution</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">sig</span></a> <span class="o">=</span> <span class="mi">1</span> <span class="c1"># std of first distribution</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">sig2</span></a> <span class="o">=</span> <span class="mf">0.1</span> <span class="c1"># std of second distribution</span>
<a href="https://numpy.org/doc/stable/reference/random/generated/numpy.random.seed.html#numpy.random.seed" title="numpy.random.seed" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</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">phi</span></a> <span class="o">=</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><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</span></a><span class="p">)[:,</span> <span class="kc">None</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">xs</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">phi</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">sig</span></a> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/random/generated/numpy.random.randn.html#numpy.random.randn" title="numpy.random.randn" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</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</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">ys</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.vstack.html#numpy.vstack" title="numpy.vstack" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">vstack</span></a><span class="p">(</span>
<span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ones.html#numpy.ones" title="numpy.ones" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">ones</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</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="mi">0</span> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ones.html#numpy.ones" title="numpy.ones" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">ones</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</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="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">sig2</span></a> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/random/generated/numpy.random.randn.html#numpy.random.randn" title="numpy.random.randn" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</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</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">phi2</span></a> <span class="o">=</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><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">n2</span></a><span class="p">)[:,</span> <span class="kc">None</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">xt</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">phi2</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">sig</span></a> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/random/generated/numpy.random.randn.html#numpy.random.randn" title="numpy.random.randn" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</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">n2</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">yt</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.vstack.html#numpy.vstack" title="numpy.vstack" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">vstack</span></a><span class="p">(</span>
<span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ones.html#numpy.ones" title="numpy.ones" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">ones</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">n2</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="mi">0</span> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ones.html#numpy.ones" title="numpy.ones" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">ones</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">n2</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="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">sig2</span></a> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/random/generated/numpy.random.randn.html#numpy.random.randn" title="numpy.random.randn" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</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">n2</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">yt</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">yt</span></a><span class="p">[::</span><span class="o">-</span><span class="mi">1</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">p</span></a> <span class="o">=</span> <a href="../../all.html#ot.unif" title="ot.unif" class="sphx-glr-backref-module-ot sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">unif</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</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">q</span></a> <span class="o">=</span> <a href="../../all.html#ot.unif" title="ot.unif" class="sphx-glr-backref-module-ot sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">unif</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">n2</span></a><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><span class="c1"># plot the distributions</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">figure</span></a><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="p">(</span><span class="mi">7</span><span class="p">,</span> <span class="mi">7</span><span class="p">))</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.scatter.html#matplotlib.pyplot.scatter" title="matplotlib.pyplot.scatter" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">scatter</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">ys</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">xs</span></a><span class="p">,</span> <span class="n">c</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">phi</span></a><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mi">70</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.ylabel.html#matplotlib.pyplot.ylabel" title="matplotlib.pyplot.ylabel" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">ylabel</span></a><span class="p">(</span><span class="s2">"Feature value a"</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s2">"$\mu=\sum_i \delta_{x_i,a_i}$"</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">25</span><span class="p">,</span> <span class="n">y</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.xticks.html#matplotlib.pyplot.xticks" title="matplotlib.pyplot.xticks" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">xticks</span></a><span class="p">(())</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.yticks.html#matplotlib.pyplot.yticks" title="matplotlib.pyplot.yticks" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">yticks</span></a><span class="p">(())</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.scatter.html#matplotlib.pyplot.scatter" title="matplotlib.pyplot.scatter" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">scatter</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">yt</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">xt</span></a><span class="p">,</span> <span class="n">c</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">phi2</span></a><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mi">70</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.xlabel.html#matplotlib.pyplot.xlabel" title="matplotlib.pyplot.xlabel" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">xlabel</span></a><span class="p">(</span><span class="s2">"coordinates x/y"</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">25</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.ylabel.html#matplotlib.pyplot.ylabel" title="matplotlib.pyplot.ylabel" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">ylabel</span></a><span class="p">(</span><span class="s2">"Feature value b"</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s2">"$</span><span class="se">\\</span><span class="s2">nu=\sum_j \delta_{y_j,b_j}$"</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">25</span><span class="p">,</span> <span class="n">y</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.yticks.html#matplotlib.pyplot.yticks" title="matplotlib.pyplot.yticks" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">yticks</span></a><span class="p">(())</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.tight_layout.html#matplotlib.pyplot.tight_layout" title="matplotlib.pyplot.tight_layout" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">tight_layout</span></a><span class="p">()</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_fgw_001.png" srcset="../../_images/sphx_glr_plot_fgw_001.png" alt="$\mu=\sum_i \delta_{x_i,a_i}$, $\nu=\sum_j \delta_{y_j,b_j}$" class = "sphx-glr-single-img"/><div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>/home/circleci/project/examples/gromov/plot_fgw.py:70: SyntaxWarning: invalid escape sequence '\m'
pl.title("$\mu=\sum_i \delta_{x_i,a_i}$", fontsize=25, y=1)
/home/circleci/project/examples/gromov/plot_fgw.py:77: SyntaxWarning: invalid escape sequence '\s'
pl.title("$\\nu=\sum_j \delta_{y_j,b_j}$", fontsize=25, y=1)
</pre></div>
</div>
</section>
<section id="create-structure-matrices-and-across-feature-distance-matrix">
<h2>Create structure matrices and across-feature distance matrix<a class="headerlink" href="#create-structure-matrices-and-across-feature-distance-matrix" title="Link to this heading"></a></h2>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Structure matrices and across-features distance matrix</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">C1</span></a> <span class="o">=</span> <a href="../../all.html#ot.dist" title="ot.dist" class="sphx-glr-backref-module-ot sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">dist</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">xs</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">C2</span></a> <span class="o">=</span> <a href="../../all.html#ot.dist" title="ot.dist" class="sphx-glr-backref-module-ot sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">dist</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">xt</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">M</span></a> <span class="o">=</span> <a href="../../all.html#ot.dist" title="ot.dist" class="sphx-glr-backref-module-ot sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">dist</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">ys</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">yt</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">w1</span></a> <span class="o">=</span> <a href="../../all.html#ot.unif" title="ot.unif" class="sphx-glr-backref-module-ot sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">unif</span></a><span class="p">(</span><a href="https://docs.python.org/3/library/stdtypes.html#tuple" title="builtins.tuple" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">C1</span><span class="o">.</span><span class="n">shape</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">w2</span></a> <span class="o">=</span> <a href="../../all.html#ot.unif" title="ot.unif" class="sphx-glr-backref-module-ot sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">unif</span></a><span class="p">(</span><a href="https://docs.python.org/3/library/stdtypes.html#tuple" title="builtins.tuple" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">C2</span><span class="o">.</span><span class="n">shape</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">Got</span></a> <span class="o">=</span> <a href="../../all.html#ot.emd" title="ot.emd" class="sphx-glr-backref-module-ot sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">emd</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">M</span></a><span class="p">)</span>
</pre></div>
</div>
</section>
<section id="plot-matrices">
<h2>Plot matrices<a class="headerlink" href="#plot-matrices" 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/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">cmap</span></a> <span class="o">=</span> <span class="s2">"Reds"</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">figure</span></a><span class="p">(</span><span class="mi">2</span><span class="p">,</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://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>
<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">l_x</span></a> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">15</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">l_y</span></a> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">15</span><span class="p">,</span> <span class="mi">20</span><span class="p">,</span> <span class="mi">25</span><span class="p">]</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.gridspec.GridSpec.html#matplotlib.gridspec.GridSpec" title="matplotlib.gridspec.GridSpec" class="sphx-glr-backref-module-matplotlib-gridspec sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">gs</span></a> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.gridspec.GridSpec.html#matplotlib.gridspec.GridSpec" title="matplotlib.gridspec.GridSpec" class="sphx-glr-backref-module-matplotlib-gridspec sphx-glr-backref-type-py-class"><span class="n">pl</span><span class="o">.</span><span class="n">GridSpec</span></a><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.axes.Axes.html#matplotlib.axes.Axes" title="matplotlib.axes.Axes" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ax1</span></a> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.gridspec.GridSpec.html#matplotlib.gridspec.GridSpec" title="matplotlib.gridspec.GridSpec" class="sphx-glr-backref-module-matplotlib-gridspec sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">gs</span></a><span class="p">[</span><span class="mi">3</span><span class="p">:,</span> <span class="p">:</span><span class="mi">2</span><span class="p">])</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">imshow</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">C1</span></a><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">cmap</span></a><span class="o">=</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">cmap</span></a><span class="p">,</span> <span class="n">interpolation</span><span class="o">=</span><span class="s2">"nearest"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s2">"$C_1$"</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>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.xlabel.html#matplotlib.pyplot.xlabel" title="matplotlib.pyplot.xlabel" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">xlabel</span></a><span class="p">(</span><span class="s2">"$k$"</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>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.ylabel.html#matplotlib.pyplot.ylabel" title="matplotlib.pyplot.ylabel" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">ylabel</span></a><span class="p">(</span><span class="s2">"$i$"</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>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.xticks.html#matplotlib.pyplot.xticks" title="matplotlib.pyplot.xticks" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">xticks</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">l_x</span></a><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.yticks.html#matplotlib.pyplot.yticks" title="matplotlib.pyplot.yticks" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">yticks</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">l_x</span></a><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes" title="matplotlib.axes.Axes" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ax2</span></a> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.gridspec.GridSpec.html#matplotlib.gridspec.GridSpec" title="matplotlib.gridspec.GridSpec" class="sphx-glr-backref-module-matplotlib-gridspec sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">gs</span></a><span class="p">[:</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">:])</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">imshow</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">C2</span></a><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">cmap</span></a><span class="o">=</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">cmap</span></a><span class="p">,</span> <span class="n">interpolation</span><span class="o">=</span><span class="s2">"nearest"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s2">"$C_2$"</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>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.ylabel.html#matplotlib.pyplot.ylabel" title="matplotlib.pyplot.ylabel" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">ylabel</span></a><span class="p">(</span><span class="s2">"$l$"</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>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.xticks.html#matplotlib.pyplot.xticks" title="matplotlib.pyplot.xticks" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">xticks</span></a><span class="p">(())</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.yticks.html#matplotlib.pyplot.yticks" title="matplotlib.pyplot.yticks" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">yticks</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">l_y</span></a><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.set_aspect.html#matplotlib.axes.Axes.set_aspect" title="matplotlib.axes.Axes.set_aspect" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax2</span><span class="o">.</span><span class="n">set_aspect</span></a><span class="p">(</span><span class="s2">"auto"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes" title="matplotlib.axes.Axes" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ax3</span></a> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.gridspec.GridSpec.html#matplotlib.gridspec.GridSpec" title="matplotlib.gridspec.GridSpec" class="sphx-glr-backref-module-matplotlib-gridspec sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">gs</span></a><span class="p">[</span><span class="mi">3</span><span class="p">:,</span> <span class="mi">2</span><span class="p">:],</span> <span class="n">sharex</span><span class="o">=</span><a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes" title="matplotlib.axes.Axes" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ax2</span></a><span class="p">,</span> <span class="n">sharey</span><span class="o">=</span><a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes" title="matplotlib.axes.Axes" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ax1</span></a><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">imshow</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">M</span></a><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">cmap</span></a><span class="o">=</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">cmap</span></a><span class="p">,</span> <span class="n">interpolation</span><span class="o">=</span><span class="s2">"nearest"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.yticks.html#matplotlib.pyplot.yticks" title="matplotlib.pyplot.yticks" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">yticks</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">l_x</span></a><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.xticks.html#matplotlib.pyplot.xticks" title="matplotlib.pyplot.xticks" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">xticks</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">l_y</span></a><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.ylabel.html#matplotlib.pyplot.ylabel" title="matplotlib.pyplot.ylabel" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">ylabel</span></a><span class="p">(</span><span class="s2">"$i$"</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>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s2">"$M_</span><span class="si">{AB}</span><span class="s2">$"</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>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.xlabel.html#matplotlib.pyplot.xlabel" title="matplotlib.pyplot.xlabel" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">xlabel</span></a><span class="p">(</span><span class="s2">"$j$"</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>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.tight_layout.html#matplotlib.pyplot.tight_layout" title="matplotlib.pyplot.tight_layout" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">tight_layout</span></a><span class="p">()</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.set_aspect.html#matplotlib.axes.Axes.set_aspect" title="matplotlib.axes.Axes.set_aspect" class="sphx-glr-backref-module-matplotlib-axes sphx-glr-backref-type-py-method"><span class="n">ax3</span><span class="o">.</span><span class="n">set_aspect</span></a><span class="p">(</span><span class="s2">"auto"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_fgw_002.png" srcset="../../_images/sphx_glr_plot_fgw_002.png" alt="$C_1$, $C_2$, $M_{AB}$" class = "sphx-glr-single-img"/></section>
<section id="compute-fgw-gw">
<h2>Compute FGW/GW<a class="headerlink" href="#compute-fgw-gw" title="Link to this heading"></a></h2>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Computing FGW and GW</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">alpha</span></a> <span class="o">=</span> <span class="mf">1e-3</span>
<a href="../../all.html#ot.tic" title="ot.tic" class="sphx-glr-backref-module-ot sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">tic</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">Gwg</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/stdtypes.html#dict" title="builtins.dict" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">logw</span></a> <span class="o">=</span> <a href="../../all.html#ot.fused_gromov_wasserstein" title="ot.fused_gromov_wasserstein" class="sphx-glr-backref-module-ot sphx-glr-backref-type-py-function"><span class="n">fused_gromov_wasserstein</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">M</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">C1</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">C2</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">p</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">q</span></a><span class="p">,</span> <span class="n">loss_fun</span><span class="o">=</span><span class="s2">"square_loss"</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">alpha</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">alpha</span></a><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <a href="https://docs.python.org/3/library/stdtypes.html#dict" title="builtins.dict" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">log</span></a><span class="o">=</span><span class="kc">True</span>
<span class="p">)</span>
<a href="../../all.html#ot.toc" title="ot.toc" class="sphx-glr-backref-module-ot sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">toc</span></a><span class="p">()</span>
<span class="c1"># reload_ext WGW</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">Gg</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/stdtypes.html#dict" title="builtins.dict" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">log</span></a> <span class="o">=</span> <a href="../../all.html#ot.gromov_wasserstein" title="ot.gromov_wasserstein" class="sphx-glr-backref-module-ot sphx-glr-backref-type-py-function"><span class="n">gromov_wasserstein</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">C1</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">C2</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">p</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">q</span></a><span class="p">,</span> <span class="n">loss_fun</span><span class="o">=</span><span class="s2">"square_loss"</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <a href="https://docs.python.org/3/library/stdtypes.html#dict" title="builtins.dict" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">log</span></a><span class="o">=</span><span class="kc">True</span>
<span class="p">)</span>
</pre></div>
</div>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>It. |Loss |Relative loss|Absolute loss
------------------------------------------------
0|4.734412e+01|0.000000e+00|0.000000e+00
1|2.508254e+01|8.875326e-01|2.226158e+01
2|2.189327e+01|1.456740e-01|3.189279e+00
3|2.189327e+01|0.000000e+00|0.000000e+00
Elapsed time : 0.001593882000179292 s
It. |Loss |Relative loss|Absolute loss
------------------------------------------------
0|4.683978e+04|0.000000e+00|0.000000e+00
1|3.860061e+04|2.134468e-01|8.239175e+03
2|2.182948e+04|7.682787e-01|1.677113e+04
3|2.182948e+04|0.000000e+00|0.000000e+00
</pre></div>
</div>
</section>
<section id="visualize-transport-matrices">
<h2>Visualize transport matrices<a class="headerlink" href="#visualize-transport-matrices" title="Link to this heading"></a></h2>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="c1"># visu OT matrix</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">cmap</span></a> <span class="o">=</span> <span class="s2">"Blues"</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>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">figure</span></a><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="p">(</span><span class="mi">13</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.clf.html#matplotlib.pyplot.clf" title="matplotlib.pyplot.clf" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">clf</span></a><span class="p">()</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">imshow</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">Got</span></a><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">cmap</span></a><span class="o">=</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">cmap</span></a><span class="p">,</span> <span class="n">interpolation</span><span class="o">=</span><span class="s2">"nearest"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.ylabel.html#matplotlib.pyplot.ylabel" title="matplotlib.pyplot.ylabel" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">ylabel</span></a><span class="p">(</span><span class="s2">"$i$"</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>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.xticks.html#matplotlib.pyplot.xticks" title="matplotlib.pyplot.xticks" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">xticks</span></a><span class="p">(())</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s2">"Wasserstein ($M$ only)"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">imshow</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">Gg</span></a><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">cmap</span></a><span class="o">=</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">cmap</span></a><span class="p">,</span> <span class="n">interpolation</span><span class="o">=</span><span class="s2">"nearest"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s2">"Gromov ($C_1,C_2$ only)"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.xticks.html#matplotlib.pyplot.xticks" title="matplotlib.pyplot.xticks" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">xticks</span></a><span class="p">(())</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">imshow</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">Gwg</span></a><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">cmap</span></a><span class="o">=</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">cmap</span></a><span class="p">,</span> <span class="n">interpolation</span><span class="o">=</span><span class="s2">"nearest"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s2">"FGW ($M+C_1,C_2$)"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.xlabel.html#matplotlib.pyplot.xlabel" title="matplotlib.pyplot.xlabel" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">xlabel</span></a><span class="p">(</span><span class="s2">"$j$"</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>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.ylabel.html#matplotlib.pyplot.ylabel" title="matplotlib.pyplot.ylabel" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">ylabel</span></a><span class="p">(</span><span class="s2">"$i$"</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>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.tight_layout.html#matplotlib.pyplot.tight_layout" title="matplotlib.pyplot.tight_layout" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">tight_layout</span></a><span class="p">()</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">pl</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
</pre></div>
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<img src="../../_images/sphx_glr_plot_fgw_003.png" srcset="../../_images/sphx_glr_plot_fgw_003.png" alt="Wasserstein ($M$ only), Gromov ($C_1,C_2$ only), FGW ($M+C_1,C_2$)" class = "sphx-glr-single-img"/><p class="sphx-glr-timing"><strong>Total running time of the script:</strong> (0 minutes 0.610 seconds)</p>
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