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<h1>Source code for torch.distributions.dirichlet</h1><div class="highlight"><pre>
<span></span><span class="kn">import</span> <span class="nn">torch</span>
<span class="kn">from</span> <span class="nn">torch.autograd</span> <span class="kn">import</span> <span class="n">Function</span>
<span class="kn">from</span> <span class="nn">torch.autograd.function</span> <span class="kn">import</span> <span class="n">once_differentiable</span>
<span class="kn">from</span> <span class="nn">torch.distributions</span> <span class="kn">import</span> <span class="n">constraints</span>
<span class="kn">from</span> <span class="nn">torch.distributions.exp_family</span> <span class="kn">import</span> <span class="n">ExponentialFamily</span>
<span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"Dirichlet"</span><span class="p">]</span>
<span class="c1"># This helper is exposed for testing.</span>
<span class="k">def</span> <span class="nf">_Dirichlet_backward</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">concentration</span><span class="p">,</span> <span class="n">grad_output</span><span class="p">):</span>
<span class="n">total</span> <span class="o">=</span> <span class="n">concentration</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="kc">True</span><span class="p">)</span><span class="o">.</span><span class="n">expand_as</span><span class="p">(</span><span class="n">concentration</span><span class="p">)</span>
<span class="n">grad</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">_dirichlet_grad</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">concentration</span><span class="p">,</span> <span class="n">total</span><span class="p">)</span>
<span class="k">return</span> <span class="n">grad</span> <span class="o">*</span> <span class="p">(</span><span class="n">grad_output</span> <span class="o">-</span> <span class="p">(</span><span class="n">x</span> <span class="o">*</span> <span class="n">grad_output</span><span class="p">)</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="kc">True</span><span class="p">))</span>
<span class="k">class</span> <span class="nc">_Dirichlet</span><span class="p">(</span><span class="n">Function</span><span class="p">):</span>
<span class="nd">@staticmethod</span>
<span class="k">def</span> <span class="nf">forward</span><span class="p">(</span><span class="n">ctx</span><span class="p">,</span> <span class="n">concentration</span><span class="p">):</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">_sample_dirichlet</span><span class="p">(</span><span class="n">concentration</span><span class="p">)</span>
<span class="n">ctx</span><span class="o">.</span><span class="n">save_for_backward</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">concentration</span><span class="p">)</span>
<span class="k">return</span> <span class="n">x</span>
<span class="nd">@staticmethod</span>
<span class="nd">@once_differentiable</span>
<span class="k">def</span> <span class="nf">backward</span><span class="p">(</span><span class="n">ctx</span><span class="p">,</span> <span class="n">grad_output</span><span class="p">):</span>
<span class="n">x</span><span class="p">,</span> <span class="n">concentration</span> <span class="o">=</span> <span class="n">ctx</span><span class="o">.</span><span class="n">saved_tensors</span>
<span class="k">return</span> <span class="n">_Dirichlet_backward</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">concentration</span><span class="p">,</span> <span class="n">grad_output</span><span class="p">)</span>
<div class="viewcode-block" id="Dirichlet"><a class="viewcode-back" href="../../../distributions.html#torch.distributions.dirichlet.Dirichlet">[docs]</a><span class="k">class</span> <span class="nc">Dirichlet</span><span class="p">(</span><span class="n">ExponentialFamily</span><span class="p">):</span>
<span class="w"> </span><span class="sa">r</span><span class="sd">"""</span>
<span class="sd"> Creates a Dirichlet distribution parameterized by concentration :attr:`concentration`.</span>
<span class="sd"> Example::</span>
<span class="sd"> >>> # xdoctest: +IGNORE_WANT("non-deterministic")</span>
<span class="sd"> >>> m = Dirichlet(torch.tensor([0.5, 0.5]))</span>
<span class="sd"> >>> m.sample() # Dirichlet distributed with concentration [0.5, 0.5]</span>
<span class="sd"> tensor([ 0.1046, 0.8954])</span>
<span class="sd"> Args:</span>
<span class="sd"> concentration (Tensor): concentration parameter of the distribution</span>
<span class="sd"> (often referred to as alpha)</span>
<span class="sd"> """</span>
<span class="n">arg_constraints</span> <span class="o">=</span> <span class="p">{</span>
<span class="s2">"concentration"</span><span class="p">:</span> <span class="n">constraints</span><span class="o">.</span><span class="n">independent</span><span class="p">(</span><span class="n">constraints</span><span class="o">.</span><span class="n">positive</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="p">}</span>
<span class="n">support</span> <span class="o">=</span> <span class="n">constraints</span><span class="o">.</span><span class="n">simplex</span>
<span class="n">has_rsample</span> <span class="o">=</span> <span class="kc">True</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">concentration</span><span class="p">,</span> <span class="n">validate_args</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="k">if</span> <span class="n">concentration</span><span class="o">.</span><span class="n">dim</span><span class="p">()</span> <span class="o"><</span> <span class="mi">1</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
<span class="s2">"`concentration` parameter must be at least one-dimensional."</span>
<span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">concentration</span> <span class="o">=</span> <span class="n">concentration</span>
<span class="n">batch_shape</span><span class="p">,</span> <span class="n">event_shape</span> <span class="o">=</span> <span class="n">concentration</span><span class="o">.</span><span class="n">shape</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">concentration</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">:]</span>
<span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">batch_shape</span><span class="p">,</span> <span class="n">event_shape</span><span class="p">,</span> <span class="n">validate_args</span><span class="o">=</span><span class="n">validate_args</span><span class="p">)</span>
<div class="viewcode-block" id="Dirichlet.expand"><a class="viewcode-back" href="../../../distributions.html#torch.distributions.dirichlet.Dirichlet.expand">[docs]</a> <span class="k">def</span> <span class="nf">expand</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">batch_shape</span><span class="p">,</span> <span class="n">_instance</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="n">new</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_get_checked_instance</span><span class="p">(</span><span class="n">Dirichlet</span><span class="p">,</span> <span class="n">_instance</span><span class="p">)</span>
<span class="n">batch_shape</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">Size</span><span class="p">(</span><span class="n">batch_shape</span><span class="p">)</span>
<span class="n">new</span><span class="o">.</span><span class="n">concentration</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">concentration</span><span class="o">.</span><span class="n">expand</span><span class="p">(</span><span class="n">batch_shape</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">event_shape</span><span class="p">)</span>
<span class="nb">super</span><span class="p">(</span><span class="n">Dirichlet</span><span class="p">,</span> <span class="n">new</span><span class="p">)</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span>
<span class="n">batch_shape</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">event_shape</span><span class="p">,</span> <span class="n">validate_args</span><span class="o">=</span><span class="kc">False</span>
<span class="p">)</span>
<span class="n">new</span><span class="o">.</span><span class="n">_validate_args</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_validate_args</span>
<span class="k">return</span> <span class="n">new</span></div>
<div class="viewcode-block" id="Dirichlet.rsample"><a class="viewcode-back" href="../../../distributions.html#torch.distributions.dirichlet.Dirichlet.rsample">[docs]</a> <span class="k">def</span> <span class="nf">rsample</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">sample_shape</span><span class="o">=</span><span class="p">()):</span>
<span class="n">shape</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_extended_shape</span><span class="p">(</span><span class="n">sample_shape</span><span class="p">)</span>
<span class="n">concentration</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">concentration</span><span class="o">.</span><span class="n">expand</span><span class="p">(</span><span class="n">shape</span><span class="p">)</span>
<span class="k">return</span> <span class="n">_Dirichlet</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">concentration</span><span class="p">)</span></div>
<div class="viewcode-block" id="Dirichlet.log_prob"><a class="viewcode-back" href="../../../distributions.html#torch.distributions.dirichlet.Dirichlet.log_prob">[docs]</a> <span class="k">def</span> <span class="nf">log_prob</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_validate_args</span><span class="p">:</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_validate_sample</span><span class="p">(</span><span class="n">value</span><span class="p">)</span>
<span class="k">return</span> <span class="p">(</span>
<span class="n">torch</span><span class="o">.</span><span class="n">xlogy</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">concentration</span> <span class="o">-</span> <span class="mf">1.0</span><span class="p">,</span> <span class="n">value</span><span class="p">)</span><span class="o">.</span><span class="n">sum</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">torch</span><span class="o">.</span><span class="n">lgamma</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">concentration</span><span class="o">.</span><span class="n">sum</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">torch</span><span class="o">.</span><span class="n">lgamma</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">concentration</span><span class="p">)</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="p">)</span></div>
<span class="nd">@property</span>
<span class="k">def</span> <span class="nf">mean</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">concentration</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">concentration</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="kc">True</span><span class="p">)</span>
<span class="nd">@property</span>
<span class="k">def</span> <span class="nf">mode</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="n">concentrationm1</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">concentration</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">clamp</span><span class="p">(</span><span class="nb">min</span><span class="o">=</span><span class="mf">0.0</span><span class="p">)</span>
<span class="n">mode</span> <span class="o">=</span> <span class="n">concentrationm1</span> <span class="o">/</span> <span class="n">concentrationm1</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="kc">True</span><span class="p">)</span>
<span class="n">mask</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">concentration</span> <span class="o"><</span> <span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">all</span><span class="p">(</span><span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
<span class="n">mode</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">functional</span><span class="o">.</span><span class="n">one_hot</span><span class="p">(</span>
<span class="n">mode</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span><span class="o">.</span><span class="n">argmax</span><span class="p">(</span><span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">),</span> <span class="n">concentrationm1</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<span class="p">)</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">mode</span><span class="p">)</span>
<span class="k">return</span> <span class="n">mode</span>
<span class="nd">@property</span>
<span class="k">def</span> <span class="nf">variance</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="n">con0</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">concentration</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="kc">True</span><span class="p">)</span>
<span class="k">return</span> <span class="p">(</span>
<span class="bp">self</span><span class="o">.</span><span class="n">concentration</span>
<span class="o">*</span> <span class="p">(</span><span class="n">con0</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">concentration</span><span class="p">)</span>
<span class="o">/</span> <span class="p">(</span><span class="n">con0</span><span class="o">.</span><span class="n">pow</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">con0</span> <span class="o">+</span> <span class="mi">1</span><span class="p">))</span>
<span class="p">)</span>
<div class="viewcode-block" id="Dirichlet.entropy"><a class="viewcode-back" href="../../../distributions.html#torch.distributions.dirichlet.Dirichlet.entropy">[docs]</a> <span class="k">def</span> <span class="nf">entropy</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="n">k</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">concentration</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="n">a0</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">concentration</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="k">return</span> <span class="p">(</span>
<span class="n">torch</span><span class="o">.</span><span class="n">lgamma</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">concentration</span><span class="p">)</span><span class="o">.</span><span class="n">sum</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">torch</span><span class="o">.</span><span class="n">lgamma</span><span class="p">(</span><span class="n">a0</span><span class="p">)</span>
<span class="o">-</span> <span class="p">(</span><span class="n">k</span> <span class="o">-</span> <span class="n">a0</span><span class="p">)</span> <span class="o">*</span> <span class="n">torch</span><span class="o">.</span><span class="n">digamma</span><span class="p">(</span><span class="n">a0</span><span class="p">)</span>
<span class="o">-</span> <span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">concentration</span> <span class="o">-</span> <span class="mf">1.0</span><span class="p">)</span> <span class="o">*</span> <span class="n">torch</span><span class="o">.</span><span class="n">digamma</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">concentration</span><span class="p">))</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="p">)</span></div>
<span class="nd">@property</span>
<span class="k">def</span> <span class="nf">_natural_params</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="k">return</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">concentration</span><span class="p">,)</span>
<span class="k">def</span> <span class="nf">_log_normalizer</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
<span class="k">return</span> <span class="n">x</span><span class="o">.</span><span class="n">lgamma</span><span class="p">()</span><span class="o">.</span><span class="n">sum</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">torch</span><span class="o">.</span><span class="n">lgamma</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">))</span></div>
</pre></div>
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