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<div class="sphx-glr-example-title section" id="d-optimal-transport-between-empirical-distributions">
<span id="sphx-glr-auto-examples-plot-ot-2d-samples-py"></span><h1>2D Optimal transport between empirical distributions<a class="headerlink" href="#d-optimal-transport-between-empirical-distributions" title="Permalink to this headline">¶</a></h1>
<p>Illustration of 2D optimal transport between discributions that are weighted
sum of diracs. The OT matrix is plotted with the samples.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># Author: Remi Flamary <remi.flamary@unice.fr></span>
<span class="c1"># Kilian Fatras <kilian.fatras@irisa.fr></span>
<span class="c1">#</span>
<span class="c1"># License: MIT License</span>
<span class="c1"># sphinx_gallery_thumbnail_number = 4</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pylab</span> <span class="k">as</span> <span class="nn">pl</span>
<span class="kn">import</span> <span class="nn">ot</span>
<span class="kn">import</span> <span class="nn">ot.plot</span>
</pre></div>
</div>
<div class="section" id="generate-data">
<h2>Generate data<a class="headerlink" href="#generate-data" title="Permalink to this headline">¶</a></h2>
<div class="highlight-default 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</span></a> <span class="o">=</span> <span class="mi">50</span> <span class="c1"># nb samples</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">mu_s</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><span class="mi">0</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">cov_s</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><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
<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">mu_t</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><span class="mi">4</span><span class="p">,</span> <span class="mi">4</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">cov_t</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><span class="mi">1</span><span class="p">,</span> <span class="o">-.</span><span class="mi">8</span><span class="p">],</span> <span class="p">[</span><span class="o">-.</span><span class="mi">8</span><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">xs</span></a> <span class="o">=</span> <a href="../gen_modules/ot.datasets.html#ot.datasets.make_2D_samples_gauss" title="ot.datasets.make_2D_samples_gauss" class="sphx-glr-backref-module-ot-datasets sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">datasets</span><span class="o">.</span><span class="n">make_2D_samples_gauss</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">mu_s</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">cov_s</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="o">=</span> <a href="../gen_modules/ot.datasets.html#ot.datasets.make_2D_samples_gauss" title="ot.datasets.make_2D_samples_gauss" class="sphx-glr-backref-module-ot-datasets sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">datasets</span><span class="o">.</span><span class="n">make_2D_samples_gauss</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">mu_t</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">cov_t</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">a</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">b</span></a> <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="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">n</span></a><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="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">n</span></a> <span class="c1"># uniform distribution on samples</span>
<span class="c1"># loss 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">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">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">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="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><span class="n">max</span><span class="p">()</span>
</pre></div>
</div>
</div>
<div class="section" id="plot-data">
<h2>Plot data<a class="headerlink" href="#plot-data" title="Permalink to this headline">¶</a></h2>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">pl</span><span class="o">.</span><span class="n">figure</span><span class="p">(</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><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="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">xs</span></a><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="s1">'+b'</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'Source samples'</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">plot</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="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">xt</span></a><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="s1">'xr'</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'Target samples'</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">loc</span><span class="o">=</span><span class="mi">0</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="s1">'Source and target distributions'</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">imshow</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> <span class="n">interpolation</span><span class="o">=</span><span class="s1">'nearest'</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="s1">'Cost matrix M'</span><span class="p">)</span>
</pre></div>
</div>
<ul class="sphx-glr-horizontal">
<li><img alt="Source and target distributions" class="sphx-glr-multi-img" src="../_images/sphx_glr_plot_OT_2D_samples_001.png" />
</li>
<li><img alt="Cost matrix M" class="sphx-glr-multi-img" src="../_images/sphx_glr_plot_OT_2D_samples_002.png" />
</li>
</ul>
<p class="sphx-glr-script-out">Out:</p>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>Text(0.5, 1.0, 'Cost matrix M')
</pre></div>
</div>
</div>
<div class="section" id="compute-emd">
<h2>Compute EMD<a class="headerlink" href="#compute-emd" title="Permalink to this headline">¶</a></h2>
<div class="highlight-default 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">G0</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><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">a</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">b</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>
<span class="n">pl</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">imshow</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">G0</span></a><span class="p">,</span> <span class="n">interpolation</span><span class="o">=</span><span class="s1">'nearest'</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="s1">'OT matrix G0'</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
<a href="../gen_modules/ot.plot.html#ot.plot.plot2D_samples_mat" title="ot.plot.plot2D_samples_mat" class="sphx-glr-backref-module-ot-plot sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">plot</span><span class="o">.</span><span class="n">plot2D_samples_mat</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">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">G0</span></a><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="p">[</span><span class="o">.</span><span class="mi">5</span><span class="p">,</span> <span class="o">.</span><span class="mi">5</span><span class="p">,</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><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="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">xs</span></a><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="s1">'+b'</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'Source samples'</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">plot</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="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">xt</span></a><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="s1">'xr'</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'Target samples'</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">loc</span><span class="o">=</span><span class="mi">0</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="s1">'OT matrix with samples'</span><span class="p">)</span>
</pre></div>
</div>
<ul class="sphx-glr-horizontal">
<li><img alt="OT matrix G0" class="sphx-glr-multi-img" src="../_images/sphx_glr_plot_OT_2D_samples_003.png" />
</li>
<li><img alt="OT matrix with samples" class="sphx-glr-multi-img" src="../_images/sphx_glr_plot_OT_2D_samples_004.png" />
</li>
</ul>
<p class="sphx-glr-script-out">Out:</p>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>Text(0.5, 1.0, 'OT matrix with samples')
</pre></div>
</div>
</div>
<div class="section" id="compute-sinkhorn">
<h2>Compute Sinkhorn<a class="headerlink" href="#compute-sinkhorn" title="Permalink to this headline">¶</a></h2>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># reg term</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">lambd</span></a> <span class="o">=</span> <span class="mf">1e-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">Gs</span></a> <span class="o">=</span> <a href="../all.html#ot.sinkhorn" title="ot.sinkhorn" class="sphx-glr-backref-module-ot sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">sinkhorn</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">a</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">b</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/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">lambd</span></a><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">imshow</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">Gs</span></a><span class="p">,</span> <span class="n">interpolation</span><span class="o">=</span><span class="s1">'nearest'</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="s1">'OT matrix sinkhorn'</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="mi">6</span><span class="p">)</span>
<a href="../gen_modules/ot.plot.html#ot.plot.plot2D_samples_mat" title="ot.plot.plot2D_samples_mat" class="sphx-glr-backref-module-ot-plot sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">plot</span><span class="o">.</span><span class="n">plot2D_samples_mat</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">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">Gs</span></a><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="p">[</span><span class="o">.</span><span class="mi">5</span><span class="p">,</span> <span class="o">.</span><span class="mi">5</span><span class="p">,</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><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="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">xs</span></a><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="s1">'+b'</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'Source samples'</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">plot</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="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">xt</span></a><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="s1">'xr'</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'Target samples'</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">loc</span><span class="o">=</span><span class="mi">0</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="s1">'OT matrix Sinkhorn with samples'</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>
</div>
<ul class="sphx-glr-horizontal">
<li><img alt="OT matrix sinkhorn" class="sphx-glr-multi-img" src="../_images/sphx_glr_plot_OT_2D_samples_005.png" />
</li>
<li><img alt="OT matrix Sinkhorn with samples" class="sphx-glr-multi-img" src="../_images/sphx_glr_plot_OT_2D_samples_006.png" />
</li>
</ul>
</div>
<div class="section" id="emprirical-sinkhorn">
<h2>Emprirical Sinkhorn<a class="headerlink" href="#emprirical-sinkhorn" title="Permalink to this headline">¶</a></h2>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># reg term</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">lambd</span></a> <span class="o">=</span> <span class="mf">1e-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">Ges</span></a> <span class="o">=</span> <a href="../gen_modules/ot.bregman.html#ot.bregman.empirical_sinkhorn" title="ot.bregman.empirical_sinkhorn" class="sphx-glr-backref-module-ot-bregman sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">bregman</span><span class="o">.</span><span class="n">empirical_sinkhorn</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">xt</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">lambd</span></a><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="mi">7</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">imshow</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">Ges</span></a><span class="p">,</span> <span class="n">interpolation</span><span class="o">=</span><span class="s1">'nearest'</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="s1">'OT matrix empirical sinkhorn'</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="mi">8</span><span class="p">)</span>
<a href="../gen_modules/ot.plot.html#ot.plot.plot2D_samples_mat" title="ot.plot.plot2D_samples_mat" class="sphx-glr-backref-module-ot-plot sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">plot</span><span class="o">.</span><span class="n">plot2D_samples_mat</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">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">Ges</span></a><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="p">[</span><span class="o">.</span><span class="mi">5</span><span class="p">,</span> <span class="o">.</span><span class="mi">5</span><span class="p">,</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><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="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">xs</span></a><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="s1">'+b'</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'Source samples'</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">plot</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="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">xt</span></a><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="s1">'xr'</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'Target samples'</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">loc</span><span class="o">=</span><span class="mi">0</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="s1">'OT matrix Sinkhorn from samples'</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>
</div>
<ul class="sphx-glr-horizontal">
<li><img alt="OT matrix empirical sinkhorn" class="sphx-glr-multi-img" src="../_images/sphx_glr_plot_OT_2D_samples_007.png" />
</li>
<li><img alt="OT matrix Sinkhorn from samples" class="sphx-glr-multi-img" src="../_images/sphx_glr_plot_OT_2D_samples_008.png" />
</li>
</ul>
<p class="sphx-glr-script-out">Out:</p>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>/home/circleci/project/ot/bregman.py:363: RuntimeWarning: divide by zero encountered in true_divide
v = np.divide(b, KtransposeU)
Warning: numerical errors at iteration 0
/home/circleci/project/ot/plot.py:90: RuntimeWarning: invalid value encountered in double_scalars
if G[i, j] / mx > thr:
</pre></div>
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