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<section class="sphx-glr-example-title" id="gmm-flow">
<span id="sphx-glr-auto-examples-others-plot-gmm-flow-py"></span><h1>GMM Flow<a class="headerlink" href="#gmm-flow" title="Link to this heading"></a></h1>
<p>Illustration of the flow of a Gaussian Mixture with
respect to its GMM-OT distance with respect to a
fixed GMM.</p>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Author: Eloi Tanguy <eloi.tanguy@u-paris></span>
<span class="c1"># Remi Flamary <remi.flamary@polytehnique.edu></span>
<span class="c1"># Julie Delon <julie.delon@math.cnrs.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">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">colormaps</span> <span class="k">as</span> <a href="https://matplotlib.org/stable/api/cm_api.html#matplotlib.cm.ColormapRegistry" title="matplotlib.cm.ColormapRegistry" class="sphx-glr-backref-module-matplotlib-cm sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">cm</span></a>
<span class="kn">import</span> <span class="nn">ot</span>
<span class="kn">import</span> <span class="nn">ot.plot</span>
<span class="kn">from</span> <span class="nn">ot.utils</span> <span class="kn">import</span> <a href="../../gen_modules/ot.utils.html#id65" title="ot.utils.proj_SDP" class="sphx-glr-backref-module-ot-utils sphx-glr-backref-type-py-function"><span class="n">proj_SDP</span></a><span class="p">,</span> <a href="../../gen_modules/ot.utils.html#id66" title="ot.utils.proj_simplex" class="sphx-glr-backref-module-ot-utils sphx-glr-backref-type-py-function"><span class="n">proj_simplex</span></a>
<span class="kn">from</span> <span class="nn">ot.gmm</span> <span class="kn">import</span> <a href="../../gen_modules/ot.gmm.html#id10" title="ot.gmm.gmm_ot_loss" class="sphx-glr-backref-module-ot-gmm sphx-glr-backref-type-py-function"><span class="n">gmm_ot_loss</span></a>
<span class="kn">import</span> <span class="nn">torch</span>
<span class="kn">from</span> <span class="nn">torch.optim</span> <span class="kn">import</span> <a href="https://pytorch.org/docs/stable/generated/torch.optim.Adam.html#torch.optim.Adam" title="torch.optim.Adam" class="sphx-glr-backref-module-torch-optim sphx-glr-backref-type-py-class"><span class="n">Adam</span></a>
<span class="kn">from</span> <span class="nn">matplotlib.patches</span> <span class="kn">import</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.patches.Ellipse.html#matplotlib.patches.Ellipse" title="matplotlib.patches.Ellipse" class="sphx-glr-backref-module-matplotlib-patches sphx-glr-backref-type-py-class"><span class="n">Ellipse</span></a>
</pre></div>
</div>
<section id="generate-data-and-plot-it">
<h2>Generate data and plot it<a class="headerlink" href="#generate-data-and-plot-it" title="Link to this heading"></a></h2>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><a href="https://pytorch.org/docs/stable/generated/torch.manual_seed.html#torch.manual_seed" title="torch.manual_seed" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-function"><span class="n">torch</span><span class="o">.</span><span class="n">manual_seed</span></a><span class="p">(</span><span class="mi">3</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">ks</span></a> <span class="o">=</span> <span class="mi">3</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">kt</span></a> <span class="o">=</span> <span class="mi">2</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">d</span></a> <span class="o">=</span> <span class="mi">2</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">eps</span></a> <span class="o">=</span> <span class="mf">0.1</span>
<a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">m_s</span></a> <span class="o">=</span> <a href="https://pytorch.org/docs/stable/generated/torch.randn.html#torch.randn" title="torch.randn" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-function"><span class="n">torch</span><span class="o">.</span><span class="n">randn</span></a><span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ks</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">d</span></a><span class="p">)</span>
<a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">m_s</span></a><span class="o">.</span><span class="n">requires_grad_</span><span class="p">()</span>
<a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">m_t</span></a> <span class="o">=</span> <a href="https://pytorch.org/docs/stable/generated/torch.randn.html#torch.randn" title="torch.randn" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-function"><span class="n">torch</span><span class="o">.</span><span class="n">randn</span></a><span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">kt</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">d</span></a><span class="p">)</span>
<a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">C_s</span></a> <span class="o">=</span> <a href="https://pytorch.org/docs/stable/generated/torch.randn.html#torch.randn" title="torch.randn" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-function"><span class="n">torch</span><span class="o">.</span><span class="n">randn</span></a><span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ks</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">d</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">d</span></a><span class="p">)</span>
<a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">C_s</span></a> <span class="o">=</span> <a href="https://pytorch.org/docs/stable/generated/torch.matmul.html#torch.matmul" title="torch.matmul" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-function"><span class="n">torch</span><span class="o">.</span><span class="n">matmul</span></a><span class="p">(</span><a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">C_s</span></a><span class="p">,</span> <a href="https://pytorch.org/docs/stable/generated/torch.transpose.html#torch.transpose" title="torch.transpose" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-function"><span class="n">torch</span><span class="o">.</span><span class="n">transpose</span></a><span class="p">(</span><a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">C_s</span></a><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
<a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">C_s</span></a> <span class="o">+=</span> <a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">eps</span></a> <span class="o">*</span> <a href="https://pytorch.org/docs/stable/generated/torch.eye.html#torch.eye" title="torch.eye" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-function"><span class="n">torch</span><span class="o">.</span><span class="n">eye</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">d</span></a><span class="p">)[</span><span class="kc">None</span><span class="p">,</span> <span class="p">:,</span> <span class="p">:]</span> <span class="o">*</span> <a href="https://pytorch.org/docs/stable/generated/torch.ones.html#torch.ones" title="torch.ones" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-function"><span class="n">torch</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">ks</span></a><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">C_s</span></a><span class="o">.</span><span class="n">requires_grad_</span><span class="p">()</span>
<a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">C_t</span></a> <span class="o">=</span> <a href="https://pytorch.org/docs/stable/generated/torch.randn.html#torch.randn" title="torch.randn" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-function"><span class="n">torch</span><span class="o">.</span><span class="n">randn</span></a><span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">kt</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">d</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">d</span></a><span class="p">)</span>
<a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">C_t</span></a> <span class="o">=</span> <a href="https://pytorch.org/docs/stable/generated/torch.matmul.html#torch.matmul" title="torch.matmul" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-function"><span class="n">torch</span><span class="o">.</span><span class="n">matmul</span></a><span class="p">(</span><a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">C_t</span></a><span class="p">,</span> <a href="https://pytorch.org/docs/stable/generated/torch.transpose.html#torch.transpose" title="torch.transpose" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-function"><span class="n">torch</span><span class="o">.</span><span class="n">transpose</span></a><span class="p">(</span><a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">C_t</span></a><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
<a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">C_t</span></a> <span class="o">+=</span> <a href="https://docs.python.org/3/library/functions.html#float" title="builtins.float" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">eps</span></a> <span class="o">*</span> <a href="https://pytorch.org/docs/stable/generated/torch.eye.html#torch.eye" title="torch.eye" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-function"><span class="n">torch</span><span class="o">.</span><span class="n">eye</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">d</span></a><span class="p">)[</span><span class="kc">None</span><span class="p">,</span> <span class="p">:,</span> <span class="p">:]</span> <span class="o">*</span> <a href="https://pytorch.org/docs/stable/generated/torch.ones.html#torch.ones" title="torch.ones" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-function"><span class="n">torch</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">kt</span></a><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">w_s</span></a> <span class="o">=</span> <a href="https://pytorch.org/docs/stable/generated/torch.randn.html#torch.randn" title="torch.randn" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-function"><span class="n">torch</span><span class="o">.</span><span class="n">randn</span></a><span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">ks</span></a><span class="p">)</span>
<a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">w_s</span></a> <span class="o">=</span> <a href="../../gen_modules/ot.utils.html#id66" title="ot.utils.proj_simplex" class="sphx-glr-backref-module-ot-utils sphx-glr-backref-type-py-function"><span class="n">proj_simplex</span></a><span class="p">(</span><a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">w_s</span></a><span class="p">)</span>
<a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">w_s</span></a><span class="o">.</span><span class="n">requires_grad_</span><span class="p">()</span>
<a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">w_t</span></a> <span class="o">=</span> <a href="https://pytorch.org/docs/stable/generated/torch.tensor.html#torch.tensor" title="torch.tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-function"><span class="n">torch</span><span class="o">.</span><span class="n">tensor</span></a><span class="p">(</span><a href="../../all.html#ot.unif" title="ot.unif" class="sphx-glr-backref-module-ot sphx-glr-backref-type-py-function"><span class="n">ot</span><span class="o">.</span><span class="n">unif</span></a><span class="p">(</span><a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">kt</span></a><span class="p">))</span>
<span class="k">def</span> <span class="nf">draw_cov</span><span class="p">(</span><span class="n">mu</span><span class="p">,</span> <span class="n">C</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">nstd</span><span class="o">=</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>
<span class="k">def</span> <span class="nf">eigsorted</span><span class="p">(</span><span class="n">cov</span><span class="p">):</span>
<span class="k">if</span> <a href="https://pytorch.org/docs/stable/generated/torch.is_tensor.html#torch.is_tensor" title="torch.is_tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-function"><span class="n">torch</span><span class="o">.</span><span class="n">is_tensor</span></a><span class="p">(</span><span class="n">cov</span><span class="p">):</span>
<span class="n">cov</span> <span class="o">=</span> <span class="n">cov</span><span class="o">.</span><span class="n">detach</span><span class="p">()</span><span class="o">.</span><span class="n">numpy</span><span class="p">()</span>
<span class="n">vals</span><span class="p">,</span> <span class="n">vecs</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.linalg.eigh.html#numpy.linalg.eigh" title="numpy.linalg.eigh" class="sphx-glr-backref-module-numpy-linalg sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">eigh</span></a><span class="p">(</span><span class="n">cov</span><span class="p">)</span>
<span class="n">order</span> <span class="o">=</span> <span class="n">vals</span><span class="o">.</span><span class="n">argsort</span><span class="p">()[::</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
<span class="k">return</span> <span class="n">vals</span><span class="p">[</span><span class="n">order</span><span class="p">],</span> <span class="n">vecs</span><span class="p">[:,</span> <span class="n">order</span><span class="p">]</span>
<span class="n">vals</span><span class="p">,</span> <span class="n">vecs</span> <span class="o">=</span> <span class="n">eigsorted</span><span class="p">(</span><span class="n">C</span><span class="p">)</span>
<span class="n">theta</span> <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">degrees</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">arctan2</span></a><span class="p">(</span><span class="o">*</span><span class="n">vecs</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">][::</span><span class="o">-</span><span class="mi">1</span><span class="p">]))</span>
<span class="n">w</span><span class="p">,</span> <span class="n">h</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">nstd</span> <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">sqrt</span></a><span class="p">(</span><span class="n">vals</span><span class="p">)</span>
<span class="n">ell</span> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.patches.Ellipse.html#matplotlib.patches.Ellipse" title="matplotlib.patches.Ellipse" class="sphx-glr-backref-module-matplotlib-patches sphx-glr-backref-type-py-class"><span class="n">Ellipse</span></a><span class="p">(</span>
<span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="n">mu</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">mu</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span>
<span class="n">width</span><span class="o">=</span><span class="n">w</span><span class="p">,</span>
<span class="n">height</span><span class="o">=</span><span class="n">h</span><span class="p">,</span>
<span class="n">alpha</span><span class="o">=</span><span class="n">alpha</span><span class="p">,</span>
<span class="n">angle</span><span class="o">=</span><span class="n">theta</span><span class="p">,</span>
<span class="n">facecolor</span><span class="o">=</span><span class="n">color</span><span class="p">,</span>
<span class="n">edgecolor</span><span class="o">=</span><span class="n">color</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="n">label</span><span class="p">,</span>
<span class="n">fill</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">gca</span><span class="p">()</span><span class="o">.</span><span class="n">add_artist</span><span class="p">(</span><span class="n">ell</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">draw_gmm</span><span class="p">(</span><span class="n">ms</span><span class="p">,</span> <span class="n">Cs</span><span class="p">,</span> <span class="n">ws</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">nstd</span><span class="o">=</span><span class="mf">0.5</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="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><span class="n">ms</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]):</span>
<span class="n">draw_cov</span><span class="p">(</span><span class="n">ms</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">k</span></a><span class="p">],</span> <span class="n">Cs</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">k</span></a><span class="p">],</span> <span class="n">color</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="n">nstd</span><span class="p">,</span> <span class="n">alpha</span> <span class="o">*</span> <span class="n">ws</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">k</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">axis</span></a> <span class="o">=</span> <span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="o">-</span><span class="mi">3</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">figure</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">10</span><span class="p">))</span>
<span class="n">pl</span><span class="o">.</span><span class="n">clf</span><span class="p">()</span>
<span class="n">pl</span><span class="o">.</span><span class="n">subplot</span><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="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">m_s</span></a><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">detach</span><span class="p">(),</span> <a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">m_s</span></a><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">detach</span><span class="p">(),</span> <span class="n">color</span><span class="o">=</span><span class="s2">"C0"</span><span class="p">)</span>
<span class="n">draw_gmm</span><span class="p">(</span><a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">m_s</span></a><span class="o">.</span><span class="n">detach</span><span class="p">(),</span> <a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">C_s</span></a><span class="o">.</span><span class="n">detach</span><span class="p">(),</span> <a href="https://pytorch.org/docs/stable/generated/torch.softmax.html#torch.softmax" title="torch.softmax" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-function"><span class="n">torch</span><span class="o">.</span><span class="n">softmax</span></a><span class="p">(</span><a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">w_s</span></a><span class="p">,</span> <span class="mi">0</span><span class="p">)</span><span class="o">.</span><span class="n">detach</span><span class="p">()</span><span class="o">.</span><span class="n">numpy</span><span class="p">(),</span> <span class="n">color</span><span class="o">=</span><span class="s2">"C0"</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</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">axis</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">axis</span></a><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"Source GMM"</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">subplot</span><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="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">m_t</span></a><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">detach</span><span class="p">(),</span> <a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">m_t</span></a><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">detach</span><span class="p">(),</span> <span class="n">color</span><span class="o">=</span><span class="s2">"C1"</span><span class="p">)</span>
<span class="n">draw_gmm</span><span class="p">(</span><a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">m_t</span></a><span class="o">.</span><span class="n">detach</span><span class="p">(),</span> <a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">C_t</span></a><span class="o">.</span><span class="n">detach</span><span class="p">(),</span> <a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">w_t</span></a><span class="o">.</span><span class="n">numpy</span><span class="p">(),</span> <span class="n">color</span><span class="o">=</span><span class="s2">"C1"</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</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">axis</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">axis</span></a><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"Target GMM"</span><span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_GMM_flow_001.png" srcset="../../_images/sphx_glr_plot_GMM_flow_001.png" alt="Source GMM, Target GMM" class = "sphx-glr-single-img"/><div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>Text(0.5, 1.0, 'Target GMM')
</pre></div>
</div>
</section>
<section id="gradient-descent-loop">
<h2>Gradient descent loop<a class="headerlink" href="#gradient-descent-loop" 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_gd_its</span></a> <span class="o">=</span> <span class="mi">100</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">lr</span></a> <span class="o">=</span> <span class="mf">3e-2</span>
<a href="https://pytorch.org/docs/stable/generated/torch.optim.Adam.html#torch.optim.Adam" title="torch.optim.Adam" class="sphx-glr-backref-module-torch-optim sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">opt</span></a> <span class="o">=</span> <a href="https://pytorch.org/docs/stable/generated/torch.optim.Adam.html#torch.optim.Adam" title="torch.optim.Adam" class="sphx-glr-backref-module-torch-optim sphx-glr-backref-type-py-class"><span class="n">Adam</span></a><span class="p">(</span>
<span class="p">[</span>
<span class="p">{</span><span class="s2">"params"</span><span class="p">:</span> <a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">m_s</span></a><span class="p">,</span> <span class="s2">"lr"</span><span class="p">:</span> <span class="mi">2</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">lr</span></a><span class="p">},</span>
<span class="p">{</span><span class="s2">"params"</span><span class="p">:</span> <a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">C_s</span></a><span class="p">,</span> <span class="s2">"lr"</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">lr</span></a><span class="p">},</span>
<span class="p">{</span><span class="s2">"params"</span><span class="p">:</span> <a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">w_s</span></a><span class="p">,</span> <span class="s2">"lr"</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">lr</span></a><span class="p">},</span>
<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">m_list</span></a> <span class="o">=</span> <span class="p">[</span><a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">m_s</span></a><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">numpy</span><span class="p">()</span><span class="o">.</span><span class="n">copy</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">C_list</span></a> <span class="o">=</span> <span class="p">[</span><a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">C_s</span><span class="o">.</span><span class="n">data</span></a><span class="o">.</span><span class="n">numpy</span><span class="p">()</span><span class="o">.</span><span class="n">copy</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">w_list</span></a> <span class="o">=</span> <span class="p">[</span><a href="https://pytorch.org/docs/stable/generated/torch.softmax.html#torch.softmax" title="torch.softmax" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-function"><span class="n">torch</span><span class="o">.</span><span class="n">softmax</span></a><span class="p">(</span><a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">w_s</span></a><span class="p">,</span> <span class="mi">0</span><span class="p">)</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">numpy</span><span class="p">()</span><span class="o">.</span><span class="n">copy</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">loss_list</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">_</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_gd_its</span></a><span class="p">):</span>
<a href="https://pytorch.org/docs/stable/generated/torch.optim.Adam.html#torch.optim.Adam.zero_grad" title="torch.optim.Adam.zero_grad" class="sphx-glr-backref-module-torch-optim sphx-glr-backref-type-py-method"><span class="n">opt</span><span class="o">.</span><span class="n">zero_grad</span></a><span class="p">()</span>
<a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">loss</span></a> <span class="o">=</span> <a href="../../gen_modules/ot.gmm.html#id10" title="ot.gmm.gmm_ot_loss" class="sphx-glr-backref-module-ot-gmm sphx-glr-backref-type-py-function"><span class="n">gmm_ot_loss</span></a><span class="p">(</span><a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">m_s</span></a><span class="p">,</span> <a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">m_t</span></a><span class="p">,</span> <a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">C_s</span></a><span class="p">,</span> <a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">C_t</span></a><span class="p">,</span> <a href="https://pytorch.org/docs/stable/generated/torch.softmax.html#torch.softmax" title="torch.softmax" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-function"><span class="n">torch</span><span class="o">.</span><span class="n">softmax</span></a><span class="p">(</span><a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">w_s</span></a><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">w_t</span></a><span class="p">)</span>
<a href="https://pytorch.org/docs/stable/generated/torch.Tensor.backward.html#torch.Tensor.backward" title="torch.Tensor.backward" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-method"><span class="n">loss</span><span class="o">.</span><span class="n">backward</span></a><span class="p">()</span>
<a href="https://pytorch.org/docs/stable/generated/torch.optim.Adam.html#torch.optim.Adam.step" title="torch.optim.Adam.step" class="sphx-glr-backref-module-torch-optim sphx-glr-backref-type-py-method"><span class="n">opt</span><span class="o">.</span><span class="n">step</span></a><span class="p">()</span>
<span class="k">with</span> <a href="https://pytorch.org/docs/stable/generated/torch.no_grad.html#torch.no_grad" title="torch.no_grad" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class"><span class="n">torch</span><span class="o">.</span><span class="n">no_grad</span></a><span class="p">():</span>
<a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">C_s</span><span class="o">.</span><span class="n">data</span></a> <span class="o">=</span> <a href="../../gen_modules/ot.utils.html#id65" title="ot.utils.proj_SDP" class="sphx-glr-backref-module-ot-utils sphx-glr-backref-type-py-function"><span class="n">proj_SDP</span></a><span class="p">(</span><a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">C_s</span><span class="o">.</span><span class="n">data</span></a><span class="p">,</span> <span class="n">vmin</span><span class="o">=</span><span class="mf">1e-6</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">m_list</span></a><span class="o">.</span><span class="n">append</span><span class="p">(</span><a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">m_s</span></a><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">numpy</span><span class="p">()</span><span class="o">.</span><span class="n">copy</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">C_list</span></a><span class="o">.</span><span class="n">append</span><span class="p">(</span><a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">C_s</span><span class="o">.</span><span class="n">data</span></a><span class="o">.</span><span class="n">numpy</span><span class="p">()</span><span class="o">.</span><span class="n">copy</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">w_list</span></a><span class="o">.</span><span class="n">append</span><span class="p">(</span><a href="https://pytorch.org/docs/stable/generated/torch.softmax.html#torch.softmax" title="torch.softmax" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-function"><span class="n">torch</span><span class="o">.</span><span class="n">softmax</span></a><span class="p">(</span><a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">w_s</span></a><span class="p">,</span> <span class="mi">0</span><span class="p">)</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">numpy</span><span class="p">()</span><span class="o">.</span><span class="n">copy</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">loss_list</span></a><span class="o">.</span><span class="n">append</span><span class="p">(</span><a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">loss</span></a><span class="o">.</span><span class="n">item</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">clf</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://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">loss_list</span></a><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"Loss"</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s2">"its"</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s2">"loss"</span><span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_GMM_flow_002.png" srcset="../../_images/sphx_glr_plot_GMM_flow_002.png" alt="Loss" class = "sphx-glr-single-img"/><div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>Text(55.847222222222214, 0.5, 'loss')
</pre></div>
</div>
</section>
<section id="last-step-visualisation">
<h2>Last step visualisation<a class="headerlink" href="#last-step-visualisation" title="Link to this heading"></a></h2>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><a href="https://docs.python.org/3/library/stdtypes.html#list" title="builtins.list" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">axis</span></a> <span class="o">=</span> <span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="o">-</span><span class="mi">3</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">figure</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">10</span><span class="p">))</span>
<span class="n">pl</span><span class="o">.</span><span class="n">clf</span><span class="p">()</span>
<span class="n">pl</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"GMM flow, last step"</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><a href="https://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">m_list</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://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">m_list</span></a><span class="p">[</span><span class="mi">0</span><span class="p">][:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">color</span><span class="o">=</span><span class="s2">"C0"</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Source"</span><span class="p">)</span>
<span class="n">draw_gmm</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">m_list</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">C_list</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">w_list</span></a><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">color</span><span class="o">=</span><span class="s2">"C0"</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</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">axis</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">axis</span></a><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">m_t</span></a><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">detach</span><span class="p">(),</span> <a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">m_t</span></a><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">detach</span><span class="p">(),</span> <span class="n">color</span><span class="o">=</span><span class="s2">"C1"</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Target"</span><span class="p">)</span>
<span class="n">draw_gmm</span><span class="p">(</span><a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">m_t</span></a><span class="o">.</span><span class="n">detach</span><span class="p">(),</span> <a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">C_t</span></a><span class="o">.</span><span class="n">detach</span><span class="p">(),</span> <a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">w_t</span></a><span class="o">.</span><span class="n">numpy</span><span class="p">(),</span> <span class="n">color</span><span class="o">=</span><span class="s2">"C1"</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</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">axis</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">axis</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</span></a> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span>
<span class="n">pl</span><span class="o">.</span><span class="n">scatter</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">m_list</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</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">m_list</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</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">"C2"</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">label</span><span class="o">=</span><span class="s2">"Last step"</span><span class="p">)</span>
<span class="n">draw_gmm</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">m_list</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</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">C_list</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</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">w_list</span></a><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">color</span><span class="o">=</span><span class="s2">"C2"</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">pl</span><span class="o">.</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">axis</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">axis</span></a><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">fontsize</span><span class="o">=</span><span class="mi">15</span><span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_GMM_flow_003.png" srcset="../../_images/sphx_glr_plot_GMM_flow_003.png" alt="GMM flow, last step" class = "sphx-glr-single-img"/><div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span><matplotlib.legend.Legend object at 0x7f58eaf21120>
</pre></div>
</div>
</section>
<section id="steps-visualisation">
<h2>Steps visualisation<a class="headerlink" href="#steps-visualisation" title="Link to this heading"></a></h2>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">index_to_color</span><span class="p">(</span><span class="n">i</span><span class="p">):</span>
<span class="k">return</span> <span class="nb">int</span><span class="p">(</span><span class="n">i</span><span class="o">**</span><span class="mf">0.5</span><span class="p">)</span>
<a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n_steps_visu</span></a> <span class="o">=</span> <span class="mi">100</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="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">10</span><span class="p">))</span>
<span class="n">pl</span><span class="o">.</span><span class="n">clf</span><span class="p">()</span>
<span class="n">pl</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"GMM flow, all steps"</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">its_to_show</span></a> <span class="o">=</span> <span class="p">[</span><span class="nb">int</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</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="mi">1</span><span class="p">,</span> <a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n_gd_its</span></a> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <a href="https://docs.python.org/3/library/functions.html#int" title="builtins.int" class="sphx-glr-backref-module-builtins sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">n_steps_visu</span></a><span class="p">)]</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.colors.ListedColormap.html#matplotlib.colors.ListedColormap" title="matplotlib.colors.ListedColormap" class="sphx-glr-backref-module-matplotlib-colors sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">cmp</span></a> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/cm_api.html#matplotlib.cm.ColormapRegistry" title="matplotlib.cm.ColormapRegistry" class="sphx-glr-backref-module-matplotlib-cm sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">cm</span></a><span class="p">[</span><span class="s2">"plasma"</span><span class="p">]</span><span class="o">.</span><span class="n">resampled</span><span class="p">(</span><span class="n">index_to_color</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_steps_visu</span></a><span class="p">))</span>
<span class="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span>
<a href="https://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">m_list</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://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">m_list</span></a><span class="p">[</span><span class="mi">0</span><span class="p">][:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">color</span><span class="o">=</span><a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.colors.ListedColormap.html#matplotlib.colors.ListedColormap" title="matplotlib.colors.ListedColormap" class="sphx-glr-backref-module-matplotlib-colors sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">cmp</span></a><span class="p">(</span><span class="n">index_to_color</span><span class="p">(</span><span class="mi">0</span><span class="p">)),</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Source"</span>
<span class="p">)</span>
<span class="n">draw_gmm</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">m_list</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">C_list</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">w_list</span></a><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">color</span><span class="o">=</span><a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.colors.ListedColormap.html#matplotlib.colors.ListedColormap" title="matplotlib.colors.ListedColormap" class="sphx-glr-backref-module-matplotlib-colors sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">cmp</span></a><span class="p">(</span><span class="n">index_to_color</span><span class="p">(</span><span class="mi">0</span><span class="p">)))</span>
<span class="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span>
<a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">m_t</span></a><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">detach</span><span class="p">(),</span>
<a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">m_t</span></a><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">detach</span><span class="p">(),</span>
<span class="n">color</span><span class="o">=</span><a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.colors.ListedColormap.html#matplotlib.colors.ListedColormap" title="matplotlib.colors.ListedColormap" class="sphx-glr-backref-module-matplotlib-colors sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">cmp</span></a><span class="p">(</span><span class="n">index_to_color</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_steps_visu</span></a> <span class="o">-</span> <span class="mi">1</span><span class="p">)),</span>
<span class="n">label</span><span class="o">=</span><span class="s2">"Target"</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">draw_gmm</span><span class="p">(</span>
<a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">m_t</span></a><span class="o">.</span><span class="n">detach</span><span class="p">(),</span> <a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">C_t</span></a><span class="o">.</span><span class="n">detach</span><span class="p">(),</span> <a href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="torch.Tensor" class="sphx-glr-backref-module-torch sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">w_t</span></a><span class="o">.</span><span class="n">numpy</span><span class="p">(),</span> <span class="n">color</span><span class="o">=</span><a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.colors.ListedColormap.html#matplotlib.colors.ListedColormap" title="matplotlib.colors.ListedColormap" class="sphx-glr-backref-module-matplotlib-colors sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">cmp</span></a><span class="p">(</span><span class="n">index_to_color</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_steps_visu</span></a> <span class="o">-</span> <span class="mi">1</span><span class="p">))</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> <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">its_to_show</span></a><span class="p">:</span>
<span class="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span>
<a href="https://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">m_list</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</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">m_list</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</span></a><span class="p">][:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">color</span><span class="o">=</span><a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.colors.ListedColormap.html#matplotlib.colors.ListedColormap" title="matplotlib.colors.ListedColormap" class="sphx-glr-backref-module-matplotlib-colors sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">cmp</span></a><span class="p">(</span><span class="n">index_to_color</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">k</span></a><span class="p">)),</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.8</span>
<span class="p">)</span>
<span class="n">draw_gmm</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">m_list</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</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">C_list</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</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">w_list</span></a><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">color</span><span class="o">=</span><a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.colors.ListedColormap.html#matplotlib.colors.ListedColormap" title="matplotlib.colors.ListedColormap" class="sphx-glr-backref-module-matplotlib-colors sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">cmp</span></a><span class="p">(</span><span class="n">index_to_color</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">k</span></a><span class="p">)),</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.04</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</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">axis</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">axis</span></a><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">fontsize</span><span class="o">=</span><span class="mi">15</span><span class="p">)</span>
</pre></div>
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