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<h1>Source code for torch.autograd.functional</h1><div class="highlight"><pre>
<span></span><span class="c1"># mypy: allow-untyped-defs</span>
<span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">List</span><span class="p">,</span> <span class="n">Tuple</span>
<span class="kn">import</span> <span class="nn">torch</span>
<span class="kn">from</span> <span class="nn">torch._vmap_internals</span> <span class="kn">import</span> <span class="n">_vmap</span>
<span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">forward_ad</span> <span class="k">as</span> <span class="n">fwAD</span>
<span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"vjp"</span><span class="p">,</span> <span class="s2">"jvp"</span><span class="p">,</span> <span class="s2">"jacobian"</span><span class="p">,</span> <span class="s2">"hessian"</span><span class="p">,</span> <span class="s2">"hvp"</span><span class="p">,</span> <span class="s2">"vhp"</span><span class="p">]</span>
<span class="c1"># Utility functions</span>
<span class="k">def</span> <span class="nf">_as_tuple_nocheck</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
<span class="k">return</span> <span class="n">x</span>
<span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="nb">list</span><span class="p">):</span>
<span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="p">(</span><span class="n">x</span><span class="p">,)</span>
<span class="k">def</span> <span class="nf">_as_tuple</span><span class="p">(</span><span class="n">inp</span><span class="p">,</span> <span class="n">arg_name</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">fn_name</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="c1"># Ensures that inp is a tuple of Tensors</span>
<span class="c1"># Returns whether or not the original inp was a tuple and the tupled version of the input</span>
<span class="k">if</span> <span class="n">arg_name</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">and</span> <span class="n">fn_name</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">return</span> <span class="n">_as_tuple_nocheck</span><span class="p">(</span><span class="n">inp</span><span class="p">)</span>
<span class="n">is_inp_tuple</span> <span class="o">=</span> <span class="kc">True</span>
<span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">inp</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
<span class="n">inp</span> <span class="o">=</span> <span class="p">(</span><span class="n">inp</span><span class="p">,)</span>
<span class="n">is_inp_tuple</span> <span class="o">=</span> <span class="kc">False</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">el</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">inp</span><span class="p">):</span>
<span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">el</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="k">if</span> <span class="n">is_inp_tuple</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span>
<span class="sa">f</span><span class="s2">"The </span><span class="si">{</span><span class="n">arg_name</span><span class="si">}</span><span class="s2"> given to </span><span class="si">{</span><span class="n">fn_name</span><span class="si">}</span><span class="s2"> must be either a Tensor or a tuple of Tensors but the"</span>
<span class="sa">f</span><span class="s2">" value at index </span><span class="si">{</span><span class="n">i</span><span class="si">}</span><span class="s2"> has type </span><span class="si">{</span><span class="nb">type</span><span class="p">(</span><span class="n">el</span><span class="p">)</span><span class="si">}</span><span class="s2">."</span>
<span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span>
<span class="sa">f</span><span class="s2">"The </span><span class="si">{</span><span class="n">arg_name</span><span class="si">}</span><span class="s2"> given to </span><span class="si">{</span><span class="n">fn_name</span><span class="si">}</span><span class="s2"> must be either a Tensor or a tuple of Tensors but the"</span>
<span class="sa">f</span><span class="s2">" given </span><span class="si">{</span><span class="n">arg_name</span><span class="si">}</span><span class="s2"> has type </span><span class="si">{</span><span class="nb">type</span><span class="p">(</span><span class="n">el</span><span class="p">)</span><span class="si">}</span><span class="s2">."</span>
<span class="p">)</span>
<span class="k">return</span> <span class="n">is_inp_tuple</span><span class="p">,</span> <span class="n">inp</span>
<span class="k">def</span> <span class="nf">_tuple_postprocess</span><span class="p">(</span><span class="n">res</span><span class="p">,</span> <span class="n">to_unpack</span><span class="p">):</span>
<span class="c1"># Unpacks a potentially nested tuple of Tensors</span>
<span class="c1"># to_unpack should be a single boolean or a tuple of two booleans.</span>
<span class="c1"># It is used to:</span>
<span class="c1"># - invert _as_tuple when res should match the inp given to _as_tuple</span>
<span class="c1"># - optionally remove nesting of two tuples created by multiple calls to _as_tuple</span>
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">to_unpack</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
<span class="k">assert</span> <span class="nb">len</span><span class="p">(</span><span class="n">to_unpack</span><span class="p">)</span> <span class="o">==</span> <span class="mi">2</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">to_unpack</span><span class="p">[</span><span class="mi">1</span><span class="p">]:</span>
<span class="n">res</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">el</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="k">for</span> <span class="n">el</span> <span class="ow">in</span> <span class="n">res</span><span class="p">)</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">to_unpack</span><span class="p">[</span><span class="mi">0</span><span class="p">]:</span>
<span class="n">res</span> <span class="o">=</span> <span class="n">res</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">to_unpack</span><span class="p">:</span>
<span class="n">res</span> <span class="o">=</span> <span class="n">res</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="k">return</span> <span class="n">res</span>
<span class="k">def</span> <span class="nf">_grad_preprocess</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">create_graph</span><span class="p">,</span> <span class="n">need_graph</span><span class="p">):</span>
<span class="c1"># Preprocess the inputs to make sure they require gradient</span>
<span class="c1"># inputs is a tuple of Tensors to preprocess</span>
<span class="c1"># create_graph specifies if the user wants gradients to flow back to the Tensors in inputs</span>
<span class="c1"># need_graph specifies if we internally want gradients to flow back to the Tensors in res</span>
<span class="c1"># Note that we *always* create a new Tensor object to be able to see the difference between</span>
<span class="c1"># inputs given as arguments and the same Tensors automatically captured by the user function.</span>
<span class="c1"># Check this issue for more details on how that can happen: https://github.com/pytorch/pytorch/issues/32576</span>
<span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">inp</span> <span class="ow">in</span> <span class="n">inputs</span><span class="p">:</span>
<span class="k">if</span> <span class="n">create_graph</span> <span class="ow">and</span> <span class="n">inp</span><span class="o">.</span><span class="n">requires_grad</span><span class="p">:</span>
<span class="c1"># Create at least a new Tensor object in a differentiable way</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">inp</span><span class="o">.</span><span class="n">is_sparse</span><span class="p">:</span>
<span class="c1"># Use .view_as() to get a shallow copy</span>
<span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">inp</span><span class="o">.</span><span class="n">view_as</span><span class="p">(</span><span class="n">inp</span><span class="p">))</span>
<span class="k">else</span><span class="p">:</span>
<span class="c1"># We cannot use view for sparse Tensors so we clone</span>
<span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">inp</span><span class="o">.</span><span class="n">clone</span><span class="p">())</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">inp</span><span class="o">.</span><span class="n">detach</span><span class="p">()</span><span class="o">.</span><span class="n">requires_grad_</span><span class="p">(</span><span class="n">need_graph</span><span class="p">))</span>
<span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">res</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">_grad_postprocess</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">create_graph</span><span class="p">):</span>
<span class="c1"># Postprocess the generated Tensors to avoid returning Tensors with history when the user did not</span>
<span class="c1"># request it.</span>
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">inputs</span><span class="p">[</span><span class="mi">0</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="k">if</span> <span class="ow">not</span> <span class="n">create_graph</span><span class="p">:</span>
<span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">inp</span><span class="o">.</span><span class="n">detach</span><span class="p">()</span> <span class="k">for</span> <span class="n">inp</span> <span class="ow">in</span> <span class="n">inputs</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="n">inputs</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">_grad_postprocess</span><span class="p">(</span><span class="n">inp</span><span class="p">,</span> <span class="n">create_graph</span><span class="p">)</span> <span class="k">for</span> <span class="n">inp</span> <span class="ow">in</span> <span class="n">inputs</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">_validate_v</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="n">other</span><span class="p">,</span> <span class="n">is_other_tuple</span><span class="p">):</span>
<span class="c1"># This assumes that other is the correct shape, and v should match</span>
<span class="c1"># Both are assumed to be tuples of Tensors</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">other</span><span class="p">)</span> <span class="o">!=</span> <span class="nb">len</span><span class="p">(</span><span class="n">v</span><span class="p">):</span>
<span class="k">if</span> <span class="n">is_other_tuple</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span>
<span class="sa">f</span><span class="s2">"v is a tuple of invalid length: should be </span><span class="si">{</span><span class="nb">len</span><span class="p">(</span><span class="n">other</span><span class="p">)</span><span class="si">}</span><span class="s2"> but got </span><span class="si">{</span><span class="nb">len</span><span class="p">(</span><span class="n">v</span><span class="p">)</span><span class="si">}</span><span class="s2">."</span>
<span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s2">"The given v should contain a single Tensor."</span><span class="p">)</span>
<span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="p">(</span><span class="n">el_v</span><span class="p">,</span> <span class="n">el_other</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="n">other</span><span class="p">)):</span>
<span class="k">if</span> <span class="n">el_v</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="o">!=</span> <span class="n">el_other</span><span class="o">.</span><span class="n">size</span><span class="p">():</span>
<span class="n">prepend</span> <span class="o">=</span> <span class="s2">""</span>
<span class="k">if</span> <span class="n">is_other_tuple</span><span class="p">:</span>
<span class="n">prepend</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">"Entry </span><span class="si">{</span><span class="n">idx</span><span class="si">}</span><span class="s2"> in "</span>
<span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span>
<span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">prepend</span><span class="si">}</span><span class="s2">v has invalid size: should be </span><span class="si">{</span><span class="n">el_other</span><span class="o">.</span><span class="n">size</span><span class="p">()</span><span class="si">}</span><span class="s2"> but got </span><span class="si">{</span><span class="n">el_v</span><span class="o">.</span><span class="n">size</span><span class="p">()</span><span class="si">}</span><span class="s2">."</span>
<span class="p">)</span>
<span class="k">def</span> <span class="nf">_check_requires_grad</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">input_type</span><span class="p">,</span> <span class="n">strict</span><span class="p">):</span>
<span class="c1"># Used to make all the necessary checks to raise nice errors in strict mode.</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">strict</span><span class="p">:</span>
<span class="k">return</span>
<span class="k">if</span> <span class="n">input_type</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s2">"outputs"</span><span class="p">,</span> <span class="s2">"grad_inputs"</span><span class="p">,</span> <span class="s2">"jacobian"</span><span class="p">,</span> <span class="s2">"hessian"</span><span class="p">]:</span>
<span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s2">"Invalid input_type to _check_requires_grad"</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">inp</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">inputs</span><span class="p">):</span>
<span class="k">if</span> <span class="n">inp</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="c1"># This can only be reached for grad_inputs.</span>
<span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span>
<span class="sa">f</span><span class="s2">"The output of the user-provided function is independent of input </span><span class="si">{</span><span class="n">i</span><span class="si">}</span><span class="s2">."</span>
<span class="s2">" This is not allowed in strict mode."</span>
<span class="p">)</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">inp</span><span class="o">.</span><span class="n">requires_grad</span><span class="p">:</span>
<span class="k">if</span> <span class="n">input_type</span> <span class="o">==</span> <span class="s2">"hessian"</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span>
<span class="sa">f</span><span class="s2">"The hessian of the user-provided function with respect to input </span><span class="si">{</span><span class="n">i</span><span class="si">}</span><span class="s2">"</span>
<span class="s2">" is independent of the input. This is not allowed in strict mode."</span>
<span class="s2">" You should ensure that your function is thrice differentiable and that"</span>
<span class="s2">" the hessian depends on the inputs."</span>
<span class="p">)</span>
<span class="k">elif</span> <span class="n">input_type</span> <span class="o">==</span> <span class="s2">"jacobian"</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span>
<span class="s2">"While computing the hessian, found that the jacobian of the user-provided"</span>
<span class="sa">f</span><span class="s2">" function with respect to input </span><span class="si">{</span><span class="n">i</span><span class="si">}</span><span class="s2"> is independent of the input. This is not"</span>
<span class="s2">" allowed in strict mode. You should ensure that your function is twice"</span>
<span class="s2">" differentiable and that the jacobian depends on the inputs (this would be"</span>
<span class="s2">" violated by a linear function for example)."</span>
<span class="p">)</span>
<span class="k">elif</span> <span class="n">input_type</span> <span class="o">==</span> <span class="s2">"grad_inputs"</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span>
<span class="sa">f</span><span class="s2">"The gradient with respect to input </span><span class="si">{</span><span class="n">i</span><span class="si">}</span><span class="s2"> is independent of the inputs of the"</span>
<span class="s2">" user-provided function. This is not allowed in strict mode."</span>
<span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span>
<span class="sa">f</span><span class="s2">"Output </span><span class="si">{</span><span class="n">i</span><span class="si">}</span><span class="s2"> of the user-provided function does not require gradients."</span>
<span class="s2">" The outputs must be computed in a differentiable manner from the input"</span>
<span class="s2">" when running in strict mode."</span>
<span class="p">)</span>
<span class="k">def</span> <span class="nf">_autograd_grad</span><span class="p">(</span>
<span class="n">outputs</span><span class="p">,</span>
<span class="n">inputs</span><span class="p">,</span>
<span class="n">grad_outputs</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">create_graph</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
<span class="n">retain_graph</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
<span class="n">is_grads_batched</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
<span class="p">):</span>
<span class="c1"># Version of autograd.grad that accepts `None` in outputs and do not compute gradients for them.</span>
<span class="c1"># This has the extra constraint that inputs has to be a tuple</span>
<span class="k">assert</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">outputs</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">)</span>
<span class="k">if</span> <span class="n">grad_outputs</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">grad_outputs</span> <span class="o">=</span> <span class="p">(</span><span class="kc">None</span><span class="p">,)</span> <span class="o">*</span> <span class="nb">len</span><span class="p">(</span><span class="n">outputs</span><span class="p">)</span>
<span class="k">assert</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">grad_outputs</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">)</span>
<span class="k">assert</span> <span class="nb">len</span><span class="p">(</span><span class="n">outputs</span><span class="p">)</span> <span class="o">==</span> <span class="nb">len</span><span class="p">(</span><span class="n">grad_outputs</span><span class="p">)</span>
<span class="n">new_outputs</span><span class="p">:</span> <span class="n">Tuple</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="p">]</span> <span class="o">=</span> <span class="p">()</span>
<span class="n">new_grad_outputs</span><span class="p">:</span> <span class="n">Tuple</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="p">]</span> <span class="o">=</span> <span class="p">()</span>
<span class="k">for</span> <span class="n">out</span><span class="p">,</span> <span class="n">grad_out</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">outputs</span><span class="p">,</span> <span class="n">grad_outputs</span><span class="p">):</span>
<span class="k">if</span> <span class="n">out</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span> <span class="ow">and</span> <span class="n">out</span><span class="o">.</span><span class="n">requires_grad</span><span class="p">:</span>
<span class="n">new_outputs</span> <span class="o">+=</span> <span class="p">(</span><span class="n">out</span><span class="p">,)</span>
<span class="n">new_grad_outputs</span> <span class="o">+=</span> <span class="p">(</span><span class="n">grad_out</span><span class="p">,)</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">new_outputs</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="c1"># No differentiable output, we don't need to call the autograd engine</span>
<span class="k">return</span> <span class="p">(</span><span class="kc">None</span><span class="p">,)</span> <span class="o">*</span> <span class="nb">len</span><span class="p">(</span><span class="n">inputs</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="n">torch</span><span class="o">.</span><span class="n">autograd</span><span class="o">.</span><span class="n">grad</span><span class="p">(</span>
<span class="n">new_outputs</span><span class="p">,</span>
<span class="n">inputs</span><span class="p">,</span>
<span class="n">new_grad_outputs</span><span class="p">,</span>
<span class="n">allow_unused</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
<span class="n">create_graph</span><span class="o">=</span><span class="n">create_graph</span><span class="p">,</span>
<span class="n">retain_graph</span><span class="o">=</span><span class="n">retain_graph</span><span class="p">,</span>
<span class="n">is_grads_batched</span><span class="o">=</span><span class="n">is_grads_batched</span><span class="p">,</span>
<span class="p">)</span>
<span class="k">def</span> <span class="nf">_fill_in_zeros</span><span class="p">(</span><span class="n">grads</span><span class="p">,</span> <span class="n">refs</span><span class="p">,</span> <span class="n">strict</span><span class="p">,</span> <span class="n">create_graph</span><span class="p">,</span> <span class="n">stage</span><span class="p">):</span>
<span class="c1"># Used to detect None in the grads and depending on the flags, either replace them</span>
<span class="c1"># with Tensors full of 0s of the appropriate size based on the refs or raise an error.</span>
<span class="c1"># strict and create graph allow us to detect when it is appropriate to raise an error</span>
<span class="c1"># stage gives us information of which backward call we consider to give good error message</span>
<span class="k">if</span> <span class="n">stage</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="s2">"back"</span><span class="p">,</span> <span class="s2">"back_trick"</span><span class="p">,</span> <span class="s2">"double_back"</span><span class="p">,</span> <span class="s2">"double_back_trick"</span><span class="p">]:</span>
<span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Invalid stage argument '</span><span class="si">{</span><span class="n">stage</span><span class="si">}</span><span class="s2">' to _fill_in_zeros"</span><span class="p">)</span>
<span class="n">res</span><span class="p">:</span> <span class="n">Tuple</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="p">]</span> <span class="o">=</span> <span class="p">()</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">grads_i</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">grads</span><span class="p">):</span>
<span class="k">if</span> <span class="n">grads_i</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">if</span> <span class="n">strict</span><span class="p">:</span>
<span class="k">if</span> <span class="n">stage</span> <span class="o">==</span> <span class="s2">"back"</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span>
<span class="s2">"The output of the user-provided function is independent of "</span>
<span class="sa">f</span><span class="s2">"input </span><span class="si">{</span><span class="n">i</span><span class="si">}</span><span class="s2">. This is not allowed in strict mode."</span>
<span class="p">)</span>
<span class="k">elif</span> <span class="n">stage</span> <span class="o">==</span> <span class="s2">"back_trick"</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span>
<span class="sa">f</span><span class="s2">"The gradient with respect to the input is independent of entry </span><span class="si">{</span><span class="n">i</span><span class="si">}</span><span class="s2">"</span>
<span class="s2">" in the grad_outputs when using the double backward trick to compute"</span>
<span class="s2">" forward mode gradients. This is not allowed in strict mode."</span>
<span class="p">)</span>
<span class="k">elif</span> <span class="n">stage</span> <span class="o">==</span> <span class="s2">"double_back"</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span>
<span class="s2">"The jacobian of the user-provided function is independent of "</span>
<span class="sa">f</span><span class="s2">"input </span><span class="si">{</span><span class="n">i</span><span class="si">}</span><span class="s2">. This is not allowed in strict mode."</span>
<span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span>
<span class="s2">"The hessian of the user-provided function is independent of "</span>
<span class="sa">f</span><span class="s2">"entry </span><span class="si">{</span><span class="n">i</span><span class="si">}</span><span class="s2"> in the grad_jacobian. This is not allowed in strict "</span>
<span class="s2">"mode as it prevents from using the double backward trick to "</span>
<span class="s2">"replace forward mode AD."</span>
<span class="p">)</span>
<span class="n">grads_i</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">zeros_like</span><span class="p">(</span><span class="n">refs</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">if</span> <span class="n">strict</span> <span class="ow">and</span> <span class="n">create_graph</span> <span class="ow">and</span> <span class="ow">not</span> <span class="n">grads_i</span><span class="o">.</span><span class="n">requires_grad</span><span class="p">:</span>
<span class="k">if</span> <span class="s2">"double"</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">stage</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span>
<span class="s2">"The jacobian of the user-provided function is independent of "</span>
<span class="sa">f</span><span class="s2">"input </span><span class="si">{</span><span class="n">i</span><span class="si">}</span><span class="s2">. This is not allowed in strict mode when create_graph=True."</span>
<span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span>
<span class="s2">"The hessian of the user-provided function is independent of "</span>
<span class="sa">f</span><span class="s2">"input </span><span class="si">{</span><span class="n">i</span><span class="si">}</span><span class="s2">. This is not allowed in strict mode when create_graph=True."</span>
<span class="p">)</span>
<span class="n">res</span> <span class="o">+=</span> <span class="p">(</span><span class="n">grads_i</span><span class="p">,)</span>
<span class="k">return</span> <span class="n">res</span>
<span class="c1"># Public API</span>
<div class="viewcode-block" id="vjp"><a class="viewcode-back" href="../../../generated/torch.autograd.functional.vjp.html#torch.autograd.functional.vjp">[docs]</a><span class="k">def</span> <span class="nf">vjp</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="n">inputs</span><span class="p">,</span> <span class="n">v</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">create_graph</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">strict</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
<span class="w"> </span><span class="sa">r</span><span class="sd">"""Compute the dot product between a vector ``v`` and the Jacobian of the given function at the point given by the inputs.</span>
<span class="sd"> Args:</span>
<span class="sd"> func (function): a Python function that takes Tensor inputs and returns</span>
<span class="sd"> a tuple of Tensors or a Tensor.</span>
<span class="sd"> inputs (tuple of Tensors or Tensor): inputs to the function ``func``.</span>
<span class="sd"> v (tuple of Tensors or Tensor): The vector for which the vector</span>
<span class="sd"> Jacobian product is computed. Must be the same size as the output</span>
<span class="sd"> of ``func``. This argument is optional when the output of ``func``</span>
<span class="sd"> contains a single element and (if it is not provided) will be set</span>
<span class="sd"> as a Tensor containing a single ``1``.</span>
<span class="sd"> create_graph (bool, optional): If ``True``, both the output and result</span>
<span class="sd"> will be computed in a differentiable way. Note that when ``strict``</span>
<span class="sd"> is ``False``, the result can not require gradients or be</span>
<span class="sd"> disconnected from the inputs. Defaults to ``False``.</span>
<span class="sd"> strict (bool, optional): If ``True``, an error will be raised when we</span>
<span class="sd"> detect that there exists an input such that all the outputs are</span>
<span class="sd"> independent of it. If ``False``, we return a Tensor of zeros as the</span>
<span class="sd"> vjp for said inputs, which is the expected mathematical value.</span>
<span class="sd"> Defaults to ``False``.</span>
<span class="sd"> Returns:</span>
<span class="sd"> output (tuple): tuple with:</span>
<span class="sd"> func_output (tuple of Tensors or Tensor): output of ``func(inputs)``</span>
<span class="sd"> vjp (tuple of Tensors or Tensor): result of the dot product with</span>
<span class="sd"> the same shape as the inputs.</span>
<span class="sd"> Example:</span>
<span class="sd"> >>> # xdoctest: +REQUIRES(env:TORCH_DOCTEST_AUTOGRAD)</span>
<span class="sd"> >>> def exp_reducer(x):</span>
<span class="sd"> ... return x.exp().sum(dim=1)</span>
<span class="sd"> >>> inputs = torch.rand(4, 4)</span>
<span class="sd"> >>> v = torch.ones(4)</span>
<span class="sd"> >>> # xdoctest: +IGNORE_WANT("non-deterministic")</span>
<span class="sd"> >>> vjp(exp_reducer, inputs, v)</span>
<span class="sd"> (tensor([5.7817, 7.2458, 5.7830, 6.7782]),</span>
<span class="sd"> tensor([[1.4458, 1.3962, 1.3042, 1.6354],</span>
<span class="sd"> [2.1288, 1.0652, 1.5483, 2.5035],</span>
<span class="sd"> [2.2046, 1.1292, 1.1432, 1.3059],</span>
<span class="sd"> [1.3225, 1.6652, 1.7753, 2.0152]]))</span>
<span class="sd"> >>> vjp(exp_reducer, inputs, v, create_graph=True)</span>
<span class="sd"> (tensor([5.7817, 7.2458, 5.7830, 6.7782], grad_fn=<SumBackward1>),</span>
<span class="sd"> tensor([[1.4458, 1.3962, 1.3042, 1.6354],</span>
<span class="sd"> [2.1288, 1.0652, 1.5483, 2.5035],</span>
<span class="sd"> [2.2046, 1.1292, 1.1432, 1.3059],</span>
<span class="sd"> [1.3225, 1.6652, 1.7753, 2.0152]], grad_fn=<MulBackward0>))</span>
<span class="sd"> >>> def adder(x, y):</span>
<span class="sd"> ... return 2 * x + 3 * y</span>
<span class="sd"> >>> inputs = (torch.rand(2), torch.rand(2))</span>
<span class="sd"> >>> v = torch.ones(2)</span>
<span class="sd"> >>> vjp(adder, inputs, v)</span>
<span class="sd"> (tensor([2.4225, 2.3340]),</span>
<span class="sd"> (tensor([2., 2.]), tensor([3., 3.])))</span>
<span class="sd"> """</span>
<span class="k">with</span> <span class="n">torch</span><span class="o">.</span><span class="n">enable_grad</span><span class="p">():</span>
<span class="n">is_inputs_tuple</span><span class="p">,</span> <span class="n">inputs</span> <span class="o">=</span> <span class="n">_as_tuple</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="s2">"inputs"</span><span class="p">,</span> <span class="s2">"vjp"</span><span class="p">)</span>
<span class="n">inputs</span> <span class="o">=</span> <span class="n">_grad_preprocess</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">create_graph</span><span class="o">=</span><span class="n">create_graph</span><span class="p">,</span> <span class="n">need_graph</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">outputs</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="o">*</span><span class="n">inputs</span><span class="p">)</span>
<span class="n">is_outputs_tuple</span><span class="p">,</span> <span class="n">outputs</span> <span class="o">=</span> <span class="n">_as_tuple</span><span class="p">(</span>
<span class="n">outputs</span><span class="p">,</span> <span class="s2">"outputs of the user-provided function"</span><span class="p">,</span> <span class="s2">"vjp"</span>
<span class="p">)</span>
<span class="n">_check_requires_grad</span><span class="p">(</span><span class="n">outputs</span><span class="p">,</span> <span class="s2">"outputs"</span><span class="p">,</span> <span class="n">strict</span><span class="o">=</span><span class="n">strict</span><span class="p">)</span>
<span class="k">if</span> <span class="n">v</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">_</span><span class="p">,</span> <span class="n">v</span> <span class="o">=</span> <span class="n">_as_tuple</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="s2">"v"</span><span class="p">,</span> <span class="s2">"vjp"</span><span class="p">)</span>
<span class="n">v</span> <span class="o">=</span> <span class="n">_grad_preprocess</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="n">create_graph</span><span class="o">=</span><span class="n">create_graph</span><span class="p">,</span> <span class="n">need_graph</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="n">_validate_v</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="n">outputs</span><span class="p">,</span> <span class="n">is_outputs_tuple</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">outputs</span><span class="p">)</span> <span class="o">!=</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">outputs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">nelement</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">RuntimeError</span><span class="p">(</span>
<span class="s2">"The vector v can only be None if the "</span>
<span class="s2">"user-provided function returns "</span>
<span class="s2">"a single Tensor with a single element."</span>
<span class="p">)</span>
<span class="n">enable_grad</span> <span class="o">=</span> <span class="kc">True</span> <span class="k">if</span> <span class="n">create_graph</span> <span class="k">else</span> <span class="n">torch</span><span class="o">.</span><span class="n">is_grad_enabled</span><span class="p">()</span>
<span class="k">with</span> <span class="n">torch</span><span class="o">.</span><span class="n">set_grad_enabled</span><span class="p">(</span><span class="n">enable_grad</span><span class="p">):</span>
<span class="n">grad_res</span> <span class="o">=</span> <span class="n">_autograd_grad</span><span class="p">(</span><span class="n">outputs</span><span class="p">,</span> <span class="n">inputs</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">create_graph</span><span class="o">=</span><span class="n">create_graph</span><span class="p">)</span>
<span class="n">vjp</span> <span class="o">=</span> <span class="n">_fill_in_zeros</span><span class="p">(</span><span class="n">grad_res</span><span class="p">,</span> <span class="n">inputs</span><span class="p">,</span> <span class="n">strict</span><span class="p">,</span> <span class="n">create_graph</span><span class="p">,</span> <span class="s2">"back"</span><span class="p">)</span>
<span class="c1"># Cleanup objects and return them to the user</span>
<span class="n">outputs</span> <span class="o">=</span> <span class="n">_grad_postprocess</span><span class="p">(</span><span class="n">outputs</span><span class="p">,</span> <span class="n">create_graph</span><span class="p">)</span>
<span class="n">vjp</span> <span class="o">=</span> <span class="n">_grad_postprocess</span><span class="p">(</span><span class="n">vjp</span><span class="p">,</span> <span class="n">create_graph</span><span class="p">)</span>
<span class="k">return</span> <span class="n">_tuple_postprocess</span><span class="p">(</span><span class="n">outputs</span><span class="p">,</span> <span class="n">is_outputs_tuple</span><span class="p">),</span> <span class="n">_tuple_postprocess</span><span class="p">(</span>
<span class="n">vjp</span><span class="p">,</span> <span class="n">is_inputs_tuple</span>
<span class="p">)</span></div>
<div class="viewcode-block" id="jvp"><a class="viewcode-back" href="../../../generated/torch.autograd.functional.jvp.html#torch.autograd.functional.jvp">[docs]</a><span class="k">def</span> <span class="nf">jvp</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="n">inputs</span><span class="p">,</span> <span class="n">v</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">create_graph</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">strict</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
<span class="w"> </span><span class="sa">r</span><span class="sd">"""Compute the dot product between the Jacobian of the given function at the point given by the inputs and a vector ``v``.</span>
<span class="sd"> Args:</span>
<span class="sd"> func (function): a Python function that takes Tensor inputs and returns</span>
<span class="sd"> a tuple of Tensors or a Tensor.</span>
<span class="sd"> inputs (tuple of Tensors or Tensor): inputs to the function ``func``.</span>
<span class="sd"> v (tuple of Tensors or Tensor): The vector for which the Jacobian</span>
<span class="sd"> vector product is computed. Must be the same size as the input of</span>
<span class="sd"> ``func``. This argument is optional when the input to ``func``</span>
<span class="sd"> contains a single element and (if it is not provided) will be set</span>
<span class="sd"> as a Tensor containing a single ``1``.</span>
<span class="sd"> create_graph (bool, optional): If ``True``, both the output and result</span>
<span class="sd"> will be computed in a differentiable way. Note that when ``strict``</span>
<span class="sd"> is ``False``, the result can not require gradients or be</span>
<span class="sd"> disconnected from the inputs. Defaults to ``False``.</span>
<span class="sd"> strict (bool, optional): If ``True``, an error will be raised when we</span>
<span class="sd"> detect that there exists an input such that all the outputs are</span>
<span class="sd"> independent of it. If ``False``, we return a Tensor of zeros as the</span>
<span class="sd"> jvp for said inputs, which is the expected mathematical value.</span>
<span class="sd"> Defaults to ``False``.</span>
<span class="sd"> Returns:</span>
<span class="sd"> output (tuple): tuple with:</span>
<span class="sd"> func_output (tuple of Tensors or Tensor): output of ``func(inputs)``</span>
<span class="sd"> jvp (tuple of Tensors or Tensor): result of the dot product with</span>
<span class="sd"> the same shape as the output.</span>
<span class="sd"> Note:</span>
<span class="sd"> ``autograd.functional.jvp`` computes the jvp by using the backward of</span>
<span class="sd"> the backward (sometimes called the double backwards trick). This is not</span>
<span class="sd"> the most performant way of computing the jvp. Please consider using</span>
<span class="sd"> :func:`torch.func.jvp` or the</span>
<span class="sd"> :ref:`low-level forward-mode AD API <forward-mode-ad>` instead.</span>
<span class="sd"> Example:</span>
<span class="sd"> >>> # xdoctest: +REQUIRES(env:TORCH_DOCTEST_AUTOGRAD)</span>
<span class="sd"> >>> def exp_reducer(x):</span>
<span class="sd"> ... return x.exp().sum(dim=1)</span>
<span class="sd"> >>> inputs = torch.rand(4, 4)</span>
<span class="sd"> >>> v = torch.ones(4, 4)</span>
<span class="sd"> >>> # xdoctest: +IGNORE_WANT("non-deterministic")</span>
<span class="sd"> >>> jvp(exp_reducer, inputs, v)</span>
<span class="sd"> (tensor([6.3090, 4.6742, 7.9114, 8.2106]),</span>
<span class="sd"> tensor([6.3090, 4.6742, 7.9114, 8.2106]))</span>
<span class="sd"> >>> jvp(exp_reducer, inputs, v, create_graph=True)</span>
<span class="sd"> (tensor([6.3090, 4.6742, 7.9114, 8.2106], grad_fn=<SumBackward1>),</span>
<span class="sd"> tensor([6.3090, 4.6742, 7.9114, 8.2106], grad_fn=<SqueezeBackward1>))</span>
<span class="sd"> >>> def adder(x, y):</span>
<span class="sd"> ... return 2 * x + 3 * y</span>
<span class="sd"> >>> inputs = (torch.rand(2), torch.rand(2))</span>
<span class="sd"> >>> v = (torch.ones(2), torch.ones(2))</span>
<span class="sd"> >>> jvp(adder, inputs, v)</span>
<span class="sd"> (tensor([2.2399, 2.5005]),</span>
<span class="sd"> tensor([5., 5.]))</span>
<span class="sd"> """</span>
<span class="k">with</span> <span class="n">torch</span><span class="o">.</span><span class="n">enable_grad</span><span class="p">():</span>
<span class="n">is_inputs_tuple</span><span class="p">,</span> <span class="n">inputs</span> <span class="o">=</span> <span class="n">_as_tuple</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="s2">"inputs"</span><span class="p">,</span> <span class="s2">"jvp"</span><span class="p">)</span>
<span class="n">inputs</span> <span class="o">=</span> <span class="n">_grad_preprocess</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">create_graph</span><span class="o">=</span><span class="n">create_graph</span><span class="p">,</span> <span class="n">need_graph</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>