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<h1>Source code for torch.distributions.studentT</h1><div class="highlight"><pre>
<span></span><span class="kn">import</span> <span class="nn">math</span>
<span class="kn">import</span> <span class="nn">torch</span>
<span class="kn">from</span> <span class="nn">torch</span> <span class="kn">import</span> <span class="n">inf</span><span class="p">,</span> <span class="n">nan</span>
<span class="kn">from</span> <span class="nn">torch.distributions</span> <span class="kn">import</span> <span class="n">Chi2</span><span class="p">,</span> <span class="n">constraints</span>
<span class="kn">from</span> <span class="nn">torch.distributions.distribution</span> <span class="kn">import</span> <span class="n">Distribution</span>
<span class="kn">from</span> <span class="nn">torch.distributions.utils</span> <span class="kn">import</span> <span class="n">_standard_normal</span><span class="p">,</span> <span class="n">broadcast_all</span>
<span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span><span class="s1">'StudentT'</span><span class="p">]</span>
<div class="viewcode-block" id="StudentT"><a class="viewcode-back" href="../../../distributions.html#torch.distributions.studentT.StudentT">[docs]</a><span class="k">class</span> <span class="nc">StudentT</span><span class="p">(</span><span class="n">Distribution</span><span class="p">):</span>
<span class="sa">r</span><span class="sd">"""</span>
<span class="sd"> Creates a Student's t-distribution parameterized by degree of</span>
<span class="sd"> freedom :attr:`df`, mean :attr:`loc` and scale :attr:`scale`.</span>
<span class="sd"> Example::</span>
<span class="sd"> >>> # xdoctest: +IGNORE_WANT("non-deterinistic")</span>
<span class="sd"> >>> m = StudentT(torch.tensor([2.0]))</span>
<span class="sd"> >>> m.sample() # Student's t-distributed with degrees of freedom=2</span>
<span class="sd"> tensor([ 0.1046])</span>
<span class="sd"> Args:</span>
<span class="sd"> df (float or Tensor): degrees of freedom</span>
<span class="sd"> loc (float or Tensor): mean of the distribution</span>
<span class="sd"> scale (float or Tensor): scale of the distribution</span>
<span class="sd"> """</span>
<span class="n">arg_constraints</span> <span class="o">=</span> <span class="p">{</span><span class="s1">'df'</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="s1">'loc'</span><span class="p">:</span> <span class="n">constraints</span><span class="o">.</span><span class="n">real</span><span class="p">,</span> <span class="s1">'scale'</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="n">support</span> <span class="o">=</span> <span class="n">constraints</span><span class="o">.</span><span class="n">real</span>
<span class="n">has_rsample</span> <span class="o">=</span> <span class="kc">True</span>
<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="n">m</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">loc</span><span class="o">.</span><span class="n">clone</span><span class="p">(</span><span class="n">memory_format</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">contiguous_format</span><span class="p">)</span>
<span class="n">m</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">df</span> <span class="o"><=</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">nan</span>
<span class="k">return</span> <span class="n">m</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="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">loc</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">m</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">df</span><span class="o">.</span><span class="n">clone</span><span class="p">(</span><span class="n">memory_format</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">contiguous_format</span><span class="p">)</span>
<span class="n">m</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">df</span> <span class="o">></span> <span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">scale</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">df</span> <span class="o">></span> <span class="mi">2</span><span class="p">]</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="bp">self</span><span class="o">.</span><span class="n">df</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">df</span> <span class="o">></span> <span class="mi">2</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">df</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">df</span> <span class="o">></span> <span class="mi">2</span><span class="p">]</span> <span class="o">-</span> <span class="mi">2</span><span class="p">)</span>
<span class="n">m</span><span class="p">[(</span><span class="bp">self</span><span class="o">.</span><span class="n">df</span> <span class="o"><=</span> <span class="mi">2</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">df</span> <span class="o">></span> <span class="mi">1</span><span class="p">)]</span> <span class="o">=</span> <span class="n">inf</span>
<span class="n">m</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">df</span> <span class="o"><=</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">nan</span>
<span class="k">return</span> <span class="n">m</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">df</span><span class="p">,</span> <span class="n">loc</span><span class="o">=</span><span class="mf">0.</span><span class="p">,</span> <span class="n">scale</span><span class="o">=</span><span class="mf">1.</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="bp">self</span><span class="o">.</span><span class="n">df</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">loc</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">scale</span> <span class="o">=</span> <span class="n">broadcast_all</span><span class="p">(</span><span class="n">df</span><span class="p">,</span> <span class="n">loc</span><span class="p">,</span> <span class="n">scale</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_chi2</span> <span class="o">=</span> <span class="n">Chi2</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">df</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">df</span><span class="o">.</span><span class="n">size</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">validate_args</span><span class="o">=</span><span class="n">validate_args</span><span class="p">)</span>
<div class="viewcode-block" id="StudentT.expand"><a class="viewcode-back" href="../../../distributions.html#torch.distributions.studentT.StudentT.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">StudentT</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">df</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">df</span><span class="o">.</span><span class="n">expand</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">loc</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">loc</span><span class="o">.</span><span class="n">expand</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">scale</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">scale</span><span class="o">.</span><span class="n">expand</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">_chi2</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_chi2</span><span class="o">.</span><span class="n">expand</span><span class="p">(</span><span class="n">batch_shape</span><span class="p">)</span>
<span class="nb">super</span><span class="p">(</span><span class="n">StudentT</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="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="StudentT.rsample"><a class="viewcode-back" href="../../../distributions.html#torch.distributions.studentT.StudentT.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="n">torch</span><span class="o">.</span><span class="n">Size</span><span class="p">()):</span>
<span class="c1"># NOTE: This does not agree with scipy implementation as much as other distributions.</span>
<span class="c1"># (see https://github.com/fritzo/notebooks/blob/master/debug-student-t.ipynb). Using DoubleTensor</span>
<span class="c1"># parameters seems to help.</span>
<span class="c1"># X ~ Normal(0, 1)</span>
<span class="c1"># Z ~ Chi2(df)</span>
<span class="c1"># Y = X / sqrt(Z / df) ~ StudentT(df)</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">X</span> <span class="o">=</span> <span class="n">_standard_normal</span><span class="p">(</span><span class="n">shape</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">df</span><span class="o">.</span><span class="n">dtype</span><span class="p">,</span> <span class="n">device</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">df</span><span class="o">.</span><span class="n">device</span><span class="p">)</span>
<span class="n">Z</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_chi2</span><span class="o">.</span><span class="n">rsample</span><span class="p">(</span><span class="n">sample_shape</span><span class="p">)</span>
<span class="n">Y</span> <span class="o">=</span> <span class="n">X</span> <span class="o">*</span> <span class="n">torch</span><span class="o">.</span><span class="n">rsqrt</span><span class="p">(</span><span class="n">Z</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">df</span><span class="p">)</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">loc</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">scale</span> <span class="o">*</span> <span class="n">Y</span></div>
<div class="viewcode-block" id="StudentT.log_prob"><a class="viewcode-back" href="../../../distributions.html#torch.distributions.studentT.StudentT.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="n">y</span> <span class="o">=</span> <span class="p">(</span><span class="n">value</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">loc</span><span class="p">)</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">scale</span>
<span class="n">Z</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">scale</span><span class="o">.</span><span class="n">log</span><span class="p">()</span> <span class="o">+</span>
<span class="mf">0.5</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">df</span><span class="o">.</span><span class="n">log</span><span class="p">()</span> <span class="o">+</span>
<span class="mf">0.5</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">math</span><span class="o">.</span><span class="n">pi</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="mf">0.5</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">df</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="mf">0.5</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">df</span> <span class="o">+</span> <span class="mf">1.</span><span class="p">)))</span>
<span class="k">return</span> <span class="o">-</span><span class="mf">0.5</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">df</span> <span class="o">+</span> <span class="mf">1.</span><span class="p">)</span> <span class="o">*</span> <span class="n">torch</span><span class="o">.</span><span class="n">log1p</span><span class="p">(</span><span class="n">y</span><span class="o">**</span><span class="mf">2.</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">df</span><span class="p">)</span> <span class="o">-</span> <span class="n">Z</span></div>
<div class="viewcode-block" id="StudentT.entropy"><a class="viewcode-back" href="../../../distributions.html#torch.distributions.studentT.StudentT.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">lbeta</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="mf">0.5</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">df</span><span class="p">)</span> <span class="o">+</span> <span class="n">math</span><span class="o">.</span><span class="n">lgamma</span><span class="p">(</span><span class="mf">0.5</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="mf">0.5</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">df</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="bp">self</span><span class="o">.</span><span class="n">scale</span><span class="o">.</span><span class="n">log</span><span class="p">()</span> <span class="o">+</span>
<span class="mf">0.5</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">df</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span>
<span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">digamma</span><span class="p">(</span><span class="mf">0.5</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">df</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">digamma</span><span class="p">(</span><span class="mf">0.5</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">df</span><span class="p">))</span> <span class="o">+</span>
<span class="mf">0.5</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">df</span><span class="o">.</span><span class="n">log</span><span class="p">()</span> <span class="o">+</span> <span class="n">lbeta</span><span class="p">)</span></div></div>
</pre></div>
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