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<section class="sphx-glr-example-title" id="sparse-optimal-transport">
<span id="sphx-glr-auto-examples-plot-sparse-emd-py"></span><h1>Sparse Optimal Transport<a class="headerlink" href="#sparse-optimal-transport" title="Link to this heading"></a></h1>
<p>In many real-world optimal transport (OT) problems, the transport plan is
naturally sparse: only a small fraction of all possible source-target pairs
actually exchange mass. Using sparse OT solvers can provide significant
computational speedups and memory savings compared to dense solvers.</p>
<p>This example demonstrates how to use sparse cost matrices with POT’s EMD solver,
comparing sparse and dense formulations on both a minimal example and a larger
concentric circles dataset.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Author: Nathan Neike</span>
<span class="c1">#</span>
<span class="c1"># License: MIT License</span>
<span class="c1"># sphinx_gallery_thumbnail_number = 2</span>
<span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
<span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
<span class="kn">from</span><span class="w"> </span><span class="nn">scipy.sparse</span><span class="w"> </span><span class="kn">import</span> <a href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.coo_array.html#scipy.sparse.coo_array" title="scipy.sparse.coo_array" class="sphx-glr-backref-module-scipy-sparse sphx-glr-backref-type-py-class"><span class="n">coo_array</span></a>
<span class="kn">import</span><span class="w"> </span><span class="nn">ot</span>
</pre></div>
</div>
<section id="example-concentric-circles">
<h2>Example: concentric circles<a class="headerlink" href="#example-concentric-circles" title="Link to this heading"></a></h2>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n_clusters</span></a> <span class="o">=</span> <span class="mi">8</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">points_per_cluster</span></a> <span class="o">=</span> <span class="mi">25</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> <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_clusters</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">points_per_cluster</span></a>
<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">k_neighbors</span></a> <span class="o">=</span> <span class="mi">8</span>
<a href="https://numpy.org/doc/stable/reference/random/generator.html#numpy.random.Generator" title="numpy.random.Generator" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">rng</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/random/generator.html#numpy.random.default_rng" title="numpy.random.default_rng" 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">default_rng</span></a><span class="p">(</span><span class="mi">0</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">r_source</span></a> <span class="o">=</span> <span class="mf">1.0</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">r_target</span></a> <span class="o">=</span> <span class="mf">2.0</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">noise_scale</span></a> <span class="o">=</span> <span class="mf">0.06</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">theta</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">2.0</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">np</span><span class="o">.</span><span class="n">pi</span></a><span class="p">,</span> <a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n</span></a><span class="p">,</span> <span class="n">endpoint</span><span class="o">=</span><span class="kc">False</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">cluster_labels</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.repeat.html#numpy.repeat" title="numpy.repeat" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">repeat</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.arange.html#numpy.arange" title="numpy.arange" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">arange</span></a><span class="p">(</span><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_clusters</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">points_per_cluster</span></a><span class="p">)</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">X_large</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.column_stack.html#numpy.column_stack" title="numpy.column_stack" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">column_stack</span></a><span class="p">(</span>
<span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">r_source</span></a> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ufunc.html#numpy.ufunc" title="numpy.ufunc" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">np</span><span class="o">.</span><span class="n">cos</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">theta</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">r_source</span></a> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ufunc.html#numpy.ufunc" title="numpy.ufunc" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">np</span><span class="o">.</span><span class="n">sin</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">theta</span></a><span class="p">)]</span>
<span class="p">)</span> <span class="o">+</span> <a href="https://numpy.org/doc/stable/reference/random/generated/numpy.random.Generator.normal.html#numpy.random.Generator.normal" title="numpy.random.Generator.normal" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-method"><span class="n">rng</span><span class="o">.</span><span class="n">normal</span></a><span class="p">(</span><span class="n">scale</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">noise_scale</span></a><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n</span></a><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Y_large</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.column_stack.html#numpy.column_stack" title="numpy.column_stack" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">column_stack</span></a><span class="p">(</span>
<span class="p">[</span><a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">r_target</span></a> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ufunc.html#numpy.ufunc" title="numpy.ufunc" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">np</span><span class="o">.</span><span class="n">cos</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">theta</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">r_target</span></a> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ufunc.html#numpy.ufunc" title="numpy.ufunc" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">np</span><span class="o">.</span><span class="n">sin</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">theta</span></a><span class="p">)]</span>
<span class="p">)</span> <span class="o">+</span> <a href="https://numpy.org/doc/stable/reference/random/generated/numpy.random.Generator.normal.html#numpy.random.Generator.normal" title="numpy.random.Generator.normal" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-method"><span class="n">rng</span><span class="o">.</span><span class="n">normal</span></a><span class="p">(</span><span class="n">scale</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">noise_scale</span></a><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n</span></a><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
<a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">a_large</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.zeros.html#numpy.zeros" title="numpy.zeros" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">zeros</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">b_large</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.zeros.html#numpy.zeros" title="numpy.zeros" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">zeros</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="k">for</span> <a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">k</span></a> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n_clusters</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">idx</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.where.html#numpy.where" title="numpy.where" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">where</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">cluster_labels</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">k</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">a_large</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">idx</span></a><span class="p">]</span> <span class="o">=</span> <span class="mf">1.0</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_clusters</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">points_per_cluster</span></a>
<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_large</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">idx</span></a><span class="p">]</span> <span class="o">=</span> <span class="mf">1.0</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_clusters</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">points_per_cluster</span></a>
<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_full</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">X_large</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Y_large</span></a><span class="p">,</span> <span class="n">metric</span><span class="o">=</span><span class="s2">"euclidean"</span><span class="p">)</span>
<span class="c1"># Build sparse cost matrix: intra-cluster k-nearest neighbors</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">angles_X</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ufunc.html#numpy.ufunc" title="numpy.ufunc" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">np</span><span class="o">.</span><span class="n">arctan2</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">X_large</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">X_large</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">angles_Y</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ufunc.html#numpy.ufunc" title="numpy.ufunc" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">np</span><span class="o">.</span><span class="n">arctan2</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Y_large</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">Y_large</span></a><span class="p">[:,</span> <span class="mi">0</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">rows</span></a> <span class="o">=</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">cols</span></a> <span class="o">=</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">vals</span></a> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">k</span></a> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n_clusters</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">src_idx</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.where.html#numpy.where" title="numpy.where" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">where</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">cluster_labels</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">k</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">tgt_idx</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.where.html#numpy.where" title="numpy.where" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">where</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">cluster_labels</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">k</span></a><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
<span class="k">for</span> <a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">i</span></a> <span class="ow">in</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">src_idx</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">diff</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.angle.html#numpy.angle" title="numpy.angle" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">angle</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ufunc.html#numpy.ufunc" title="numpy.ufunc" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">np</span><span class="o">.</span><span class="n">exp</span></a><span class="p">(</span><span class="mi">1</span><a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">j</span></a> <span class="o">*</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">angles_Y</span></a><span class="p">[</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">tgt_idx</span></a><span class="p">]</span> <span class="o">-</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">angles_X</span></a><span class="p">[</span><a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">i</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">idx</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.argsort.html#numpy.argsort" title="numpy.argsort" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">argsort</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ufunc.html#numpy.ufunc" title="numpy.ufunc" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">np</span><span class="o">.</span><span class="n">abs</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">diff</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">k_neighbors</span></a><span class="p">]</span>
<span class="k">for</span> <a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">j_local</span></a> <span class="ow">in</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">idx</span></a><span class="p">:</span>
<a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">j</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">tgt_idx</span></a><span class="p">[</span><a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">j_local</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">rows</span></a><span class="o">.</span><span class="n">append</span><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">i</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">cols</span></a><span class="o">.</span><span class="n">append</span><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">j</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">vals</span></a><span class="o">.</span><span class="n">append</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_full</span></a><span class="p">[</span><a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">i</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">j</span></a><span class="p">])</span>
<a href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.coo_array.html#scipy.sparse.coo_array" title="scipy.sparse.coo_array" class="sphx-glr-backref-module-scipy-sparse sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">M_sparse_large</span></a> <span class="o">=</span> <a href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.coo_array.html#scipy.sparse.coo_array" title="scipy.sparse.coo_array" class="sphx-glr-backref-module-scipy-sparse sphx-glr-backref-type-py-class"><span class="n">coo_array</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">vals</span></a><span class="p">,</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">rows</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">cols</span></a><span class="p">)),</span> <span class="n">shape</span><span class="o">=</span><span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n</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://docs.python.org/3/library/stdtypes.html#set" title="builtins.set" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">allowed_sparse</span></a> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="nb">zip</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">rows</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">cols</span></a><span class="p">))</span>
</pre></div>
</div>
</section>
<section id="visualize-edge-structures">
<h2>Visualize edge structures<a class="headerlink" href="#visualize-edge-structures" title="Link to this heading"></a></h2>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.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">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">16</span><span class="p">,</span> <span class="mi">6</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">plt</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">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="k">for</span> <a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">i</span></a> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n</span></a><span class="p">):</span>
<span class="k">for</span> <a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">j</span></a> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n</span></a><span class="p">):</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="matplotlib.pyplot.plot" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span>
<span class="p">[</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">X_large</span></a><span class="p">[</span><a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">i</span></a><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Y_large</span></a><span class="p">[</span><a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">j</span></a><span class="p">,</span> <span class="mi">0</span><span class="p">]],</span>
<span class="p">[</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">X_large</span></a><span class="p">[</span><a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">i</span></a><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Y_large</span></a><span class="p">[</span><a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">j</span></a><span class="p">,</span> <span class="mi">1</span><span class="p">]],</span>
<span class="n">color</span><span class="o">=</span><span class="s2">"blue"</span><span class="p">,</span>
<span class="n">alpha</span><span class="o">=</span><span class="mf">0.2</span><span class="p">,</span>
<span class="n">linewidth</span><span class="o">=</span><span class="mf">0.05</span><span class="p">,</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">plt</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">X_large</span></a><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">X_large</span></a><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="s2">"r"</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span><span class="s2">"o"</span><span class="p">,</span> <span class="n">s</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.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">plt</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">Y_large</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">Y_large</span></a><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="s2">"b"</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span><span class="s2">"x"</span><span class="p">,</span> <span class="n">s</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.axis.html#matplotlib.pyplot.axis" title="matplotlib.pyplot.axis" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">axis</span></a><span class="p">(</span><span class="s2">"equal"</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">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s2">"Dense OT: All Possible Edges"</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">plt</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">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="k">for</span> <a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">i</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">j</span></a> <span class="ow">in</span> <a href="https://docs.python.org/3/library/stdtypes.html#set" title="builtins.set" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">allowed_sparse</span></a><span class="p">:</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="matplotlib.pyplot.plot" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span>
<span class="p">[</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">X_large</span></a><span class="p">[</span><a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">i</span></a><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Y_large</span></a><span class="p">[</span><a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">j</span></a><span class="p">,</span> <span class="mi">0</span><span class="p">]],</span>
<span class="p">[</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">X_large</span></a><span class="p">[</span><a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">i</span></a><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Y_large</span></a><span class="p">[</span><a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.int64" title="numpy.int64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">j</span></a><span class="p">,</span> <span class="mi">1</span><span class="p">]],</span>
<span class="n">color</span><span class="o">=</span><span class="s2">"blue"</span><span class="p">,</span>
<span class="n">alpha</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
<span class="n">linewidth</span><span class="o">=</span><span class="mf">0.05</span><span class="p">,</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">plt</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">X_large</span></a><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">X_large</span></a><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="s2">"r"</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span><span class="s2">"o"</span><span class="p">,</span> <span class="n">s</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.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">plt</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">Y_large</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">Y_large</span></a><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="s2">"b"</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span><span class="s2">"x"</span><span class="p">,</span> <span class="n">s</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.axis.html#matplotlib.pyplot.axis" title="matplotlib.pyplot.axis" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">axis</span></a><span class="p">(</span><span class="s2">"equal"</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">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s2">"Sparse OT: Intra-Cluster k-NN Edges"</span><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">plt</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">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
</pre></div>
</div>
<img src="../_images/sphx_glr_plot_sparse_emd_001.png" srcset="../_images/sphx_glr_plot_sparse_emd_001.png" alt="Dense OT: All Possible Edges, Sparse OT: Intra-Cluster k-NN Edges" class = "sphx-glr-single-img"/></section>
<section id="solve-and-visualize-transport-plans">
<h2>Solve and visualize transport plans<a class="headerlink" href="#solve-and-visualize-transport-plans" title="Link to this heading"></a></h2>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">G_dense</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_large</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_large</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_full</span></a><span class="p">)</span>
<a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.float64" title="numpy.float64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">cost_dense</span></a> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.sum.html#numpy.sum" title="numpy.sum" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">sum</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">G_dense</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_full</span></a><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Dense OT cost: </span><span class="si">{</span><a href="https://numpy.org/doc/stable/reference/arrays.scalars.html#numpy.float64" title="numpy.float64" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-attribute"><span class="n">cost_dense</span></a><span class="si">:</span><span class="s2">.6f</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
<a href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.coo_array.html#scipy.sparse.coo_array" title="scipy.sparse.coo_array" class="sphx-glr-backref-module-scipy-sparse sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">G_sparse</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_sparse</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_large</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_large</span></a><span class="p">,</span> <a href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.coo_array.html#scipy.sparse.coo_array" title="scipy.sparse.coo_array" class="sphx-glr-backref-module-scipy-sparse sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">M_sparse_large</span></a><span class="p">,</span> <span class="n">log</span><span class="o">=</span><span class="kc">True</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">cost_sparse</span></a> <span class="o">=</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_sparse</span></a><span class="p">[</span><span class="s2">"cost"</span><span class="p">]</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Sparse OT cost: </span><span class="si">{</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">cost_sparse</span></a><span class="si">:</span><span class="s2">.6f</span><span class="si">}</span><span class="s2">"</span><span class="p">)</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">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">16</span><span class="p">,</span> <span class="mi">6</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">plt</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">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<a href="../gen_modules/ot.plot.html#id1" 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">X_large</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Y_large</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">G_dense</span></a><span class="p">,</span> <span class="n">thr</span><span class="o">=</span><span class="mf">1e-10</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="p">[</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</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">plt</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">X_large</span></a><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">X_large</span></a><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="s2">"r"</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span><span class="s2">"o"</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">3</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">plt</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">Y_large</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">Y_large</span></a><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="s2">"b"</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span><span class="s2">"x"</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.axis.html#matplotlib.pyplot.axis" title="matplotlib.pyplot.axis" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">axis</span></a><span class="p">(</span><span class="s2">"equal"</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">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s2">"Dense OT: Optimal Transport Plan"</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">plt</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">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<a href="../gen_modules/ot.plot.html#id1" 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">X_large</span></a><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Y_large</span></a><span class="p">,</span> <a href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.coo_array.html#scipy.sparse.coo_array" title="scipy.sparse.coo_array" class="sphx-glr-backref-module-scipy-sparse sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">G_sparse</span></a><span class="p">,</span> <span class="n">thr</span><span class="o">=</span><span class="mf">1e-10</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="p">[</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</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">plt</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">X_large</span></a><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="numpy.ndarray" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">X_large</span></a><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="s2">"r"</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span><span class="s2">"o"</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">3</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">plt</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">Y_large</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">Y_large</span></a><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="s2">"b"</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span><span class="s2">"x"</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.axis.html#matplotlib.pyplot.axis" title="matplotlib.pyplot.axis" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">axis</span></a><span class="p">(</span><span class="s2">"equal"</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">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s2">"Sparse OT: Optimal Transport Plan"</span><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">plt</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">plt</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_sparse_emd_002.png" srcset="../_images/sphx_glr_plot_sparse_emd_002.png" alt="Dense OT: Optimal Transport Plan, Sparse OT: Optimal Transport Plan" class = "sphx-glr-single-img"/><div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>Dense OT cost: 0.992179
Sparse OT cost: 0.992290
</pre></div>
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