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<li class="toctree-l1"><a class="reference internal" href="../../../notes/amp_examples.html">CUDA Automatic Mixed Precision examples</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../../notes/autograd.html">Autograd mechanics</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../../notes/broadcasting.html">Broadcasting semantics</a></li>
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<h1>Source code for torch.distributions.wishart</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">warnings</span>
<span class="kn">from</span> <span class="nn">numbers</span> <span class="kn">import</span> <span class="n">Number</span>
<span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Union</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">nan</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="kn">from</span> <span class="nn">torch.distributions.utils</span> <span class="kn">import</span> <span class="n">lazy_property</span>
<span class="kn">from</span> <span class="nn">torch.distributions.multivariate_normal</span> <span class="kn">import</span> <span class="n">_precision_to_scale_tril</span>
<span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span><span class="s1">'Wishart'</span><span class="p">]</span>
<span class="n">_log_2</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="mi">2</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">_mvdigamma</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">,</span> <span class="n">p</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-></span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">:</span>
<span class="k">assert</span> <span class="n">x</span><span class="o">.</span><span class="n">gt</span><span class="p">((</span><span class="n">p</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span><span class="o">.</span><span class="n">all</span><span class="p">(),</span> <span class="s2">"Wrong domain for multivariate digamma function."</span>
<span class="k">return</span> <span class="n">torch</span><span class="o">.</span><span class="n">digamma</span><span class="p">(</span>
<span class="n">x</span><span class="o">.</span><span class="n">unsqueeze</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">arange</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">x</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="n">x</span><span class="o">.</span><span class="n">device</span><span class="p">)</span><span class="o">.</span><span class="n">div</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="o">.</span><span class="n">expand</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">shape</span> <span class="o">+</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">sum</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">_clamp_above_eps</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">)</span> <span class="o">-></span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">:</span>
<span class="c1"># We assume positive input for this function</span>
<span class="k">return</span> <span class="n">x</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="n">torch</span><span class="o">.</span><span class="n">finfo</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">dtype</span><span class="p">)</span><span class="o">.</span><span class="n">eps</span><span class="p">)</span>
<div class="viewcode-block" id="Wishart"><a class="viewcode-back" href="../../../distributions.html#torch.distributions.wishart.Wishart">[docs]</a><span class="k">class</span> <span class="nc">Wishart</span><span class="p">(</span><span class="n">ExponentialFamily</span><span class="p">):</span>
<span class="sa">r</span><span class="sd">"""</span>
<span class="sd"> Creates a Wishart distribution parameterized by a symmetric positive definite matrix :math:`\Sigma`,</span>
<span class="sd"> or its Cholesky decomposition :math:`\mathbf{\Sigma} = \mathbf{L}\mathbf{L}^\top`</span>
<span class="sd"> Example:</span>
<span class="sd"> >>> # xdoctest: +SKIP("FIXME: scale_tril must be at least two-dimensional")</span>
<span class="sd"> >>> m = Wishart(torch.eye(2), torch.Tensor([2]))</span>
<span class="sd"> >>> m.sample() # Wishart distributed with mean=`df * I` and</span>
<span class="sd"> >>> # variance(x_ij)=`df` for i != j and variance(x_ij)=`2 * df` for i == j</span>
<span class="sd"> Args:</span>
<span class="sd"> covariance_matrix (Tensor): positive-definite covariance matrix</span>
<span class="sd"> precision_matrix (Tensor): positive-definite precision matrix</span>
<span class="sd"> scale_tril (Tensor): lower-triangular factor of covariance, with positive-valued diagonal</span>
<span class="sd"> df (float or Tensor): real-valued parameter larger than the (dimension of Square matrix) - 1</span>
<span class="sd"> Note:</span>
<span class="sd"> Only one of :attr:`covariance_matrix` or :attr:`precision_matrix` or</span>
<span class="sd"> :attr:`scale_tril` can be specified.</span>
<span class="sd"> Using :attr:`scale_tril` will be more efficient: all computations internally</span>
<span class="sd"> are based on :attr:`scale_tril`. If :attr:`covariance_matrix` or</span>
<span class="sd"> :attr:`precision_matrix` is passed instead, it is only used to compute</span>
<span class="sd"> the corresponding lower triangular matrices using a Cholesky decomposition.</span>
<span class="sd"> 'torch.distributions.LKJCholesky' is a restricted Wishart distribution.[1]</span>
<span class="sd"> **References**</span>
<span class="sd"> [1] Wang, Z., Wu, Y. and Chu, H., 2018. `On equivalence of the LKJ distribution and the restricted Wishart distribution`.</span>
<span class="sd"> [2] Sawyer, S., 2007. `Wishart Distributions and Inverse-Wishart Sampling`.</span>
<span class="sd"> [3] Anderson, T. W., 2003. `An Introduction to Multivariate Statistical Analysis (3rd ed.)`.</span>
<span class="sd"> [4] Odell, P. L. & Feiveson, A. H., 1966. `A Numerical Procedure to Generate a SampleCovariance Matrix`. JASA, 61(313):199-203.</span>
<span class="sd"> [5] Ku, Y.-C. & Bloomfield, P., 2010. `Generating Random Wishart Matrices with Fractional Degrees of Freedom in OX`.</span>
<span class="sd"> """</span>
<span class="n">arg_constraints</span> <span class="o">=</span> <span class="p">{</span>
<span class="s1">'covariance_matrix'</span><span class="p">:</span> <span class="n">constraints</span><span class="o">.</span><span class="n">positive_definite</span><span class="p">,</span>
<span class="s1">'precision_matrix'</span><span class="p">:</span> <span class="n">constraints</span><span class="o">.</span><span class="n">positive_definite</span><span class="p">,</span>
<span class="s1">'scale_tril'</span><span class="p">:</span> <span class="n">constraints</span><span class="o">.</span><span class="n">lower_cholesky</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">greater_than</span><span class="p">(</span><span class="mi">0</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">positive_definite</span>
<span class="n">has_rsample</span> <span class="o">=</span> <span class="kc">True</span>
<span class="n">_mean_carrier_measure</span> <span class="o">=</span> <span class="mi">0</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">Union</span><span class="p">[</span><span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">,</span> <span class="n">Number</span><span class="p">],</span>
<span class="n">covariance_matrix</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
<span class="n">precision_matrix</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
<span class="n">scale_tril</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span> <span class="o">=</span> <span class="kc">None</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">assert</span> <span class="p">(</span><span class="n">covariance_matrix</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">)</span> <span class="o">+</span> <span class="p">(</span><span class="n">scale_tril</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">)</span> <span class="o">+</span> <span class="p">(</span><span class="n">precision_matrix</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">,</span> \
<span class="s2">"Exactly one of covariance_matrix or precision_matrix or scale_tril may be specified."</span>
<span class="n">param</span> <span class="o">=</span> <span class="nb">next</span><span class="p">(</span><span class="n">p</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="p">(</span><span class="n">covariance_matrix</span><span class="p">,</span> <span class="n">precision_matrix</span><span class="p">,</span> <span class="n">scale_tril</span><span class="p">)</span> <span class="k">if</span> <span class="n">p</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">)</span>
<span class="k">if</span> <span class="n">param</span><span class="o">.</span><span class="n">dim</span><span class="p">()</span> <span class="o"><</span> <span class="mi">2</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">"scale_tril must be at least two-dimensional, with optional leading batch dimensions"</span><span class="p">)</span>
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">df</span><span class="p">,</span> <span class="n">Number</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">param</span><span class="o">.</span><span class="n">shape</span><span class="p">[:</span><span class="o">-</span><span class="mi">2</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="n">torch</span><span class="o">.</span><span class="n">tensor</span><span class="p">(</span><span class="n">df</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">param</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="n">param</span><span class="o">.</span><span class="n">device</span><span class="p">)</span>
<span class="k">else</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">broadcast_shapes</span><span class="p">(</span><span class="n">param</span><span class="o">.</span><span class="n">shape</span><span class="p">[:</span><span class="o">-</span><span class="mi">2</span><span class="p">],</span> <span class="n">df</span><span class="o">.</span><span class="n">shape</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="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">event_shape</span> <span class="o">=</span> <span class="n">param</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">:]</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">df</span><span class="o">.</span><span class="n">le</span><span class="p">(</span><span class="n">event_shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</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">any</span><span class="p">():</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Value of df=</span><span class="si">{</span><span class="n">df</span><span class="si">}</span><span class="s2"> expected to be greater than ndim - 1 = </span><span class="si">{</span><span class="n">event_shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="mi">1</span><span class="si">}</span><span class="s2">."</span><span class="p">)</span>
<span class="k">if</span> <span class="n">scale_tril</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="bp">self</span><span class="o">.</span><span class="n">scale_tril</span> <span class="o">=</span> <span class="n">param</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="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">))</span>
<span class="k">elif</span> <span class="n">covariance_matrix</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="bp">self</span><span class="o">.</span><span class="n">covariance_matrix</span> <span class="o">=</span> <span class="n">param</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="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">))</span>
<span class="k">elif</span> <span class="n">precision_matrix</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="bp">self</span><span class="o">.</span><span class="n">precision_matrix</span> <span class="o">=</span> <span class="n">param</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="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">))</span>
<span class="bp">self</span><span class="o">.</span><span class="n">arg_constraints</span><span class="p">[</span><span class="s1">'df'</span><span class="p">]</span> <span class="o">=</span> <span class="n">constraints</span><span class="o">.</span><span class="n">greater_than</span><span class="p">(</span><span class="n">event_shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">df</span><span class="o">.</span><span class="n">lt</span><span class="p">(</span><span class="n">event_shape</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">any</span><span class="p">():</span>
<span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">"Low df values detected. Singular samples are highly likely to occur for ndim - 1 < df < ndim."</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>
<span class="bp">self</span><span class="o">.</span><span class="n">_batch_dims</span> <span class="o">=</span> <span class="p">[</span><span class="o">-</span><span class="p">(</span><span class="n">x</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_batch_shape</span><span class="p">))]</span>
<span class="k">if</span> <span class="n">scale_tril</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_unbroadcasted_scale_tril</span> <span class="o">=</span> <span class="n">scale_tril</span>
<span class="k">elif</span> <span class="n">covariance_matrix</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_unbroadcasted_scale_tril</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">cholesky</span><span class="p">(</span><span class="n">covariance_matrix</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span> <span class="c1"># precision_matrix is not None</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_unbroadcasted_scale_tril</span> <span class="o">=</span> <span class="n">_precision_to_scale_tril</span><span class="p">(</span><span class="n">precision_matrix</span><span class="p">)</span>
<span class="c1"># Chi2 distribution is needed for Bartlett decomposition sampling</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_dist_chi2</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">distributions</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="n">df</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="n">unsqueeze</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">arange</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="o">-</span><span class="mi">1</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">_unbroadcasted_scale_tril</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">_unbroadcasted_scale_tril</span><span class="o">.</span><span class="n">device</span><span class="p">,</span>
<span class="p">)</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="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,))</span>
<span class="p">)</span>
<span class="p">)</span>
<div class="viewcode-block" id="Wishart.expand"><a class="viewcode-back" href="../../../distributions.html#torch.distributions.wishart.Wishart.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">Wishart</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">cov_shape</span> <span class="o">=</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="n">new</span><span class="o">.</span><span class="n">_unbroadcasted_scale_tril</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_unbroadcasted_scale_tril</span><span class="o">.</span><span class="n">expand</span><span class="p">(</span><span class="n">cov_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">_batch_dims</span> <span class="o">=</span> <span class="p">[</span><span class="o">-</span><span class="p">(</span><span class="n">x</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">batch_shape</span><span class="p">))]</span>
<span class="k">if</span> <span class="s1">'covariance_matrix'</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__dict__</span><span class="p">:</span>
<span class="n">new</span><span class="o">.</span><span class="n">covariance_matrix</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">covariance_matrix</span><span class="o">.</span><span class="n">expand</span><span class="p">(</span><span class="n">cov_shape</span><span class="p">)</span>
<span class="k">if</span> <span class="s1">'scale_tril'</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__dict__</span><span class="p">:</span>
<span class="n">new</span><span class="o">.</span><span class="n">scale_tril</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">scale_tril</span><span class="o">.</span><span class="n">expand</span><span class="p">(</span><span class="n">cov_shape</span><span class="p">)</span>
<span class="k">if</span> <span class="s1">'precision_matrix'</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__dict__</span><span class="p">:</span>
<span class="n">new</span><span class="o">.</span><span class="n">precision_matrix</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">precision_matrix</span><span class="o">.</span><span class="n">expand</span><span class="p">(</span><span class="n">cov_shape</span><span class="p">)</span>
<span class="c1"># Chi2 distribution is needed for Bartlett decomposition sampling</span>
<span class="n">new</span><span class="o">.</span><span class="n">_dist_chi2</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">distributions</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="n">df</span><span class="o">=</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="n">unsqueeze</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">arange</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="o">-</span><span class="mi">1</span><span class="p">],</span>
<span class="n">dtype</span><span class="o">=</span><span class="n">new</span><span class="o">.</span><span class="n">_unbroadcasted_scale_tril</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="n">new</span><span class="o">.</span><span class="n">_unbroadcasted_scale_tril</span><span class="o">.</span><span class="n">device</span><span class="p">,</span>
<span class="p">)</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="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,))</span>
<span class="p">)</span>
<span class="p">)</span>
<span class="nb">super</span><span class="p">(</span><span class="n">Wishart</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>
<span class="nd">@lazy_property</span>
<span class="k">def</span> <span class="nf">scale_tril</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">_unbroadcasted_scale_tril</span><span class="o">.</span><span class="n">expand</span><span class="p">(</span>
<span class="bp">self</span><span class="o">.</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="nd">@lazy_property</span>
<span class="k">def</span> <span class="nf">covariance_matrix</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">_unbroadcasted_scale_tril</span> <span class="o">@</span> <span class="bp">self</span><span class="o">.</span><span class="n">_unbroadcasted_scale_tril</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="o">-</span><span class="mi">2</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">expand</span><span class="p">(</span><span class="bp">self</span><span class="o">.</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="nd">@lazy_property</span>
<span class="k">def</span> <span class="nf">precision_matrix</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="n">identity</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">eye</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="o">-</span><span class="mi">1</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">_unbroadcasted_scale_tril</span><span class="o">.</span><span class="n">device</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">_unbroadcasted_scale_tril</span><span class="o">.</span><span class="n">dtype</span><span class="p">,</span>
<span class="p">)</span>
<span class="k">return</span> <span class="n">torch</span><span class="o">.</span><span class="n">cholesky_solve</span><span class="p">(</span>
<span class="n">identity</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">_unbroadcasted_scale_tril</span>
<span class="p">)</span><span class="o">.</span><span class="n">expand</span><span class="p">(</span><span class="bp">self</span><span class="o">.</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="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">df</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_batch_shape</span> <span class="o">+</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">covariance_matrix</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">factor</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="bp">self</span><span class="o">.</span><span class="n">covariance_matrix</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="o">-</span> <span class="mi">1</span>
<span class="n">factor</span><span class="p">[</span><span class="n">factor</span> <span class="o"><=</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">nan</span>
<span class="k">return</span> <span class="n">factor</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_batch_shape</span> <span class="o">+</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">covariance_matrix</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">V</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">covariance_matrix</span> <span class="c1"># has shape (batch_shape x event_shape)</span>
<span class="n">diag_V</span> <span class="o">=</span> <span class="n">V</span><span class="o">.</span><span class="n">diagonal</span><span class="p">(</span><span class="n">dim1</span><span class="o">=-</span><span class="mi">2</span><span class="p">,</span> <span class="n">dim2</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">df</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_batch_shape</span> <span class="o">+</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span> <span class="o">*</span> <span class="p">(</span><span class="n">V</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="n">torch</span><span class="o">.</span><span class="n">einsum</span><span class="p">(</span><span class="s2">"...i,...j->...ij"</span><span class="p">,</span> <span class="n">diag_V</span><span class="p">,</span> <span class="n">diag_V</span><span class="p">))</span>
<span class="k">def</span> <span class="nf">_bartlett_sampling</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="n">p</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="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="c1"># has singleton shape</span>
<span class="c1"># Implemented Sampling using Bartlett decomposition</span>
<span class="n">noise</span> <span class="o">=</span> <span class="n">_clamp_above_eps</span><span class="p">(</span>
<span class="bp">self</span><span class="o">.</span><span class="n">_dist_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="o">.</span><span class="n">sqrt</span><span class="p">()</span>
<span class="p">)</span><span class="o">.</span><span class="n">diag_embed</span><span class="p">(</span><span class="n">dim1</span><span class="o">=-</span><span class="mi">2</span><span class="p">,</span> <span class="n">dim2</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
<span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">tril_indices</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">p</span><span class="p">,</span> <span class="n">offset</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
<span class="n">noise</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span>
<span class="n">torch</span><span class="o">.</span><span class="n">Size</span><span class="p">(</span><span class="n">sample_shape</span><span class="p">)</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">_batch_shape</span> <span class="o">+</span> <span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="n">p</span> <span class="o">*</span> <span class="p">(</span><span class="n">p</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span><span class="p">),),</span>
<span class="n">dtype</span><span class="o">=</span><span class="n">noise</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="n">noise</span><span class="o">.</span><span class="n">device</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">chol</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_unbroadcasted_scale_tril</span> <span class="o">@</span> <span class="n">noise</span>
<span class="k">return</span> <span class="n">chol</span> <span class="o">@</span> <span class="n">chol</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<div class="viewcode-block" id="Wishart.rsample"><a class="viewcode-back" href="../../../distributions.html#torch.distributions.wishart.Wishart.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="n">max_try_correction</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="sa">r</span><span class="sd">"""</span>
<span class="sd"> .. warning::</span>
<span class="sd"> In some cases, sampling algorithm based on Bartlett decomposition may return singular matrix samples.</span>
<span class="sd"> Several tries to correct singular samples are performed by default, but it may end up returning</span>
<span class="sd"> singular matrix samples. Singular samples may return `-inf` values in `.log_prob()`.</span>
<span class="sd"> In those cases, the user should validate the samples and either fix the value of `df`</span>
<span class="sd"> or adjust `max_try_correction` value for argument in `.rsample` accordingly.</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">max_try_correction</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">max_try_correction</span> <span class="o">=</span> <span class="mi">3</span> <span class="k">if</span> <span class="n">torch</span><span class="o">.</span><span class="n">_C</span><span class="o">.</span><span class="n">_get_tracing_state</span><span class="p">()</span> <span class="k">else</span> <span class="mi">10</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="n">sample_shape</span><span class="p">)</span>
<span class="n">sample</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_bartlett_sampling</span><span class="p">(</span><span class="n">sample_shape</span><span class="p">)</span>
<span class="c1"># Below part is to improve numerical stability temporally and should be removed in the future</span>
<span class="n">is_singular</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">support</span><span class="o">.</span><span class="n">check</span><span class="p">(</span><span class="n">sample</span><span class="p">)</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_batch_shape</span><span class="p">:</span>
<span class="n">is_singular</span> <span class="o">=</span> <span class="n">is_singular</span><span class="o">.</span><span class="n">amax</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_batch_dims</span><span class="p">)</span>
<span class="k">if</span> <span class="n">torch</span><span class="o">.</span><span class="n">_C</span><span class="o">.</span><span class="n">_get_tracing_state</span><span class="p">():</span>
<span class="c1"># Less optimized version for JIT</span>
<span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">max_try_correction</span><span class="p">):</span>
<span class="n">sample_new</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_bartlett_sampling</span><span class="p">(</span><span class="n">sample_shape</span><span class="p">)</span>
<span class="n">sample</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">is_singular</span><span class="p">,</span> <span class="n">sample_new</span><span class="p">,</span> <span class="n">sample</span><span class="p">)</span>
<span class="n">is_singular</span> <span class="o">=</span> <span class="o">~</span><span class="bp">self</span><span class="o">.</span><span class="n">support</span><span class="o">.</span><span class="n">check</span><span class="p">(</span><span class="n">sample</span><span class="p">)</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_batch_shape</span><span class="p">:</span>
<span class="n">is_singular</span> <span class="o">=</span> <span class="n">is_singular</span><span class="o">.</span><span class="n">amax</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_batch_dims</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="c1"># More optimized version with data-dependent control flow.</span>
<span class="k">if</span> <span class="n">is_singular</span><span class="o">.</span><span class="n">any</span><span class="p">():</span>
<span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">"Singular sample detected."</span><span class="p">)</span>
<span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">max_try_correction</span><span class="p">):</span>
<span class="n">sample_new</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_bartlett_sampling</span><span class="p">(</span><span class="n">is_singular</span><span class="p">[</span><span class="n">is_singular</span><span class="p">]</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="n">sample</span><span class="p">[</span><span class="n">is_singular</span><span class="p">]</span> <span class="o">=</span> <span class="n">sample_new</span>
<span class="n">is_singular_new</span> <span class="o">=</span> <span class="o">~</span><span class="bp">self</span><span class="o">.</span><span class="n">support</span><span class="o">.</span><span class="n">check</span><span class="p">(</span><span class="n">sample_new</span><span class="p">)</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_batch_shape</span><span class="p">:</span>
<span class="n">is_singular_new</span> <span class="o">=</span> <span class="n">is_singular_new</span><span class="o">.</span><span class="n">amax</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_batch_dims</span><span class="p">)</span>
<span class="n">is_singular</span><span class="p">[</span><span class="n">is_singular</span><span class="o">.</span><span class="n">clone</span><span class="p">()]</span> <span class="o">=</span> <span class="n">is_singular_new</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">is_singular</span><span class="o">.</span><span class="n">any</span><span class="p">():</span>
<span class="k">break</span>
<span class="k">return</span> <span class="n">sample</span></div>
<div class="viewcode-block" id="Wishart.log_prob"><a class="viewcode-back" href="../../../distributions.html#torch.distributions.wishart.Wishart.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">nu</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">df</span> <span class="c1"># has shape (batch_shape)</span>
<span class="n">p</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="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="c1"># has singleton shape</span>
<span class="k">return</span> <span class="p">(</span>
<span class="o">-</span> <span class="n">nu</span> <span class="o">*</span> <span class="p">(</span><span class="n">p</span> <span class="o">*</span> <span class="n">_log_2</span> <span class="o">/</span> <span class="mi">2</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">_unbroadcasted_scale_tril</span><span class="o">.</span><span class="n">diagonal</span><span class="p">(</span><span class="n">dim1</span><span class="o">=-</span><span class="mi">2</span><span class="p">,</span> <span class="n">dim2</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">log</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">mvlgamma</span><span class="p">(</span><span class="n">nu</span> <span class="o">/</span> <span class="mi">2</span><span class="p">,</span> <span class="n">p</span><span class="o">=</span><span class="n">p</span><span class="p">)</span>
<span class="o">+</span> <span class="p">(</span><span class="n">nu</span> <span class="o">-</span> <span class="n">p</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">torch</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">slogdet</span><span class="p">(</span><span class="n">value</span><span class="p">)</span><span class="o">.</span><span class="n">logabsdet</span>
<span class="o">-</span> <span class="n">torch</span><span class="o">.</span><span class="n">cholesky_solve</span><span class="p">(</span><span class="n">value</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">_unbroadcasted_scale_tril</span><span class="p">)</span><span class="o">.</span><span class="n">diagonal</span><span class="p">(</span><span class="n">dim1</span><span class="o">=-</span><span class="mi">2</span><span class="p">,</span> <span class="n">dim2</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">dim</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span>
<span class="p">)</span></div>
<div class="viewcode-block" id="Wishart.entropy"><a class="viewcode-back" href="../../../distributions.html#torch.distributions.wishart.Wishart.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">nu</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">df</span> <span class="c1"># has shape (batch_shape)</span>
<span class="n">p</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="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="c1"># has singleton shape</span>
<span class="n">V</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">covariance_matrix</span> <span class="c1"># has shape (batch_shape x event_shape)</span>
<span class="k">return</span> <span class="p">(</span>
<span class="p">(</span><span class="n">p</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">p</span> <span class="o">*</span> <span class="n">_log_2</span> <span class="o">/</span> <span class="mi">2</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">_unbroadcasted_scale_tril</span><span class="o">.</span><span class="n">diagonal</span><span class="p">(</span><span class="n">dim1</span><span class="o">=-</span><span class="mi">2</span><span class="p">,</span> <span class="n">dim2</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">log</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">mvlgamma</span><span class="p">(</span><span class="n">nu</span> <span class="o">/</span> <span class="mi">2</span><span class="p">,</span> <span class="n">p</span><span class="o">=</span><span class="n">p</span><span class="p">)</span>
<span class="o">-</span> <span class="p">(</span><span class="n">nu</span> <span class="o">-</span> <span class="n">p</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">_mvdigamma</span><span class="p">(</span><span class="n">nu</span> <span class="o">/</span> <span class="mi">2</span><span class="p">,</span> <span class="n">p</span><span class="o">=</span><span class="n">p</span><span class="p">)</span>
<span class="o">+</span> <span class="n">nu</span> <span class="o">*</span> <span class="n">p</span> <span class="o">/</span> <span class="mi">2</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="n">nu</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">df</span> <span class="c1"># has shape (batch_shape)</span>
<span class="n">p</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="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="c1"># has singleton shape</span>
<span class="k">return</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">precision_matrix</span> <span class="o">/</span> <span class="mi">2</span><span class="p">,</span> <span class="p">(</span><span class="n">nu</span> <span class="o">-</span> <span class="n">p</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</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="n">y</span><span class="p">):</span>
<span class="n">p</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="o">-</span><span class="mi">1</span><span class="p">]</span>
<span class="k">return</span> <span class="p">(</span>
<span class="p">(</span><span class="n">y</span> <span class="o">+</span> <span class="p">(</span><span class="n">p</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="o">-</span> <span class="n">torch</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">slogdet</span><span class="p">(</span><span class="o">-</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">logabsdet</span> <span class="o">+</span> <span class="n">_log_2</span> <span class="o">*</span> <span class="n">p</span><span class="p">)</span>
<span class="o">+</span> <span class="n">torch</span><span class="o">.</span><span class="n">mvlgamma</span><span class="p">(</span><span class="n">y</span> <span class="o">+</span> <span class="p">(</span><span class="n">p</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span><span class="p">,</span> <span class="n">p</span><span class="o">=</span><span class="n">p</span><span class="p">)</span>
<span class="p">)</span></div>
</pre></div>
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