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<h1>Source code for torch.functional</h1><div class="highlight"><pre>
<span></span><span class="c1"># mypy: allow-untyped-defs</span>
<span class="kn">import</span> <span class="nn">itertools</span>
<span class="kn">import</span> <span class="nn">operator</span>
<span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Any</span><span class="p">,</span> <span class="n">List</span><span class="p">,</span> <span class="n">Optional</span><span class="p">,</span> <span class="n">Sequence</span><span class="p">,</span> <span class="n">Tuple</span><span class="p">,</span> <span class="n">TYPE_CHECKING</span><span class="p">,</span> <span class="n">Union</span>
<span class="kn">import</span> <span class="nn">torch</span>
<span class="kn">import</span> <span class="nn">torch.nn.functional</span> <span class="k">as</span> <span class="nn">F</span>
<span class="kn">from</span> <span class="nn">torch</span> <span class="kn">import</span> <span class="n">_VF</span><span class="p">,</span> <span class="n">Tensor</span>
<span class="kn">from</span> <span class="nn">torch._C</span> <span class="kn">import</span> <span class="n">_add_docstr</span>
<span class="kn">from</span> <span class="nn">torch._jit_internal</span> <span class="kn">import</span> <span class="n">_overload</span> <span class="k">as</span> <span class="n">overload</span><span class="p">,</span> <span class="n">boolean_dispatch</span>
<span class="kn">from</span> <span class="nn">torch._lowrank</span> <span class="kn">import</span> <span class="n">pca_lowrank</span><span class="p">,</span> <span class="n">svd_lowrank</span>
<span class="kn">from</span> <span class="nn">torch.overrides</span> <span class="kn">import</span> <span class="p">(</span>
<span class="n">handle_torch_function</span><span class="p">,</span>
<span class="n">has_torch_function</span><span class="p">,</span>
<span class="n">has_torch_function_unary</span><span class="p">,</span>
<span class="n">has_torch_function_variadic</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span>
<span class="s2">"atleast_1d"</span><span class="p">,</span>
<span class="s2">"atleast_2d"</span><span class="p">,</span>
<span class="s2">"atleast_3d"</span><span class="p">,</span>
<span class="s2">"align_tensors"</span><span class="p">,</span>
<span class="s2">"broadcast_shapes"</span><span class="p">,</span>
<span class="s2">"broadcast_tensors"</span><span class="p">,</span>
<span class="s2">"cartesian_prod"</span><span class="p">,</span>
<span class="s2">"block_diag"</span><span class="p">,</span>
<span class="s2">"cdist"</span><span class="p">,</span>
<span class="s2">"chain_matmul"</span><span class="p">,</span>
<span class="s2">"einsum"</span><span class="p">,</span>
<span class="s2">"istft"</span><span class="p">,</span>
<span class="s2">"lu"</span><span class="p">,</span>
<span class="s2">"norm"</span><span class="p">,</span>
<span class="s2">"meshgrid"</span><span class="p">,</span>
<span class="s2">"pca_lowrank"</span><span class="p">,</span>
<span class="s2">"split"</span><span class="p">,</span>
<span class="s2">"stft"</span><span class="p">,</span>
<span class="s2">"svd_lowrank"</span><span class="p">,</span>
<span class="s2">"tensordot"</span><span class="p">,</span>
<span class="s2">"unique"</span><span class="p">,</span>
<span class="s2">"unique_consecutive"</span><span class="p">,</span>
<span class="s2">"unravel_index"</span><span class="p">,</span>
<span class="p">]</span>
<div class="viewcode-block" id="broadcast_tensors"><a class="viewcode-back" href="../../generated/torch.broadcast_tensors.html#torch.broadcast_tensors">[docs]</a><span class="k">def</span> <span class="nf">broadcast_tensors</span><span class="p">(</span><span class="o">*</span><span class="n">tensors</span><span class="p">):</span>
<span class="w"> </span><span class="sa">r</span><span class="sd">"""broadcast_tensors(*tensors) -> List of Tensors</span>
<span class="sd"> Broadcasts the given tensors according to :ref:`broadcasting-semantics`.</span>
<span class="sd"> Args:</span>
<span class="sd"> *tensors: any number of tensors of the same type</span>
<span class="sd"> .. warning::</span>
<span class="sd"> More than one element of a broadcasted tensor may refer to a single</span>
<span class="sd"> memory location. As a result, in-place operations (especially ones that</span>
<span class="sd"> are vectorized) may result in incorrect behavior. If you need to write</span>
<span class="sd"> to the tensors, please clone them first.</span>
<span class="sd"> Example::</span>
<span class="sd"> >>> x = torch.arange(3).view(1, 3)</span>
<span class="sd"> >>> y = torch.arange(2).view(2, 1)</span>
<span class="sd"> >>> a, b = torch.broadcast_tensors(x, y)</span>
<span class="sd"> >>> a.size()</span>
<span class="sd"> torch.Size([2, 3])</span>
<span class="sd"> >>> a</span>
<span class="sd"> tensor([[0, 1, 2],</span>
<span class="sd"> [0, 1, 2]])</span>
<span class="sd"> """</span>
<span class="c1"># This wrapper exists to support variadic args.</span>
<span class="k">if</span> <span class="n">has_torch_function</span><span class="p">(</span><span class="n">tensors</span><span class="p">):</span>
<span class="k">return</span> <span class="n">handle_torch_function</span><span class="p">(</span><span class="n">broadcast_tensors</span><span class="p">,</span> <span class="n">tensors</span><span class="p">,</span> <span class="o">*</span><span class="n">tensors</span><span class="p">)</span>
<span class="k">return</span> <span class="n">_VF</span><span class="o">.</span><span class="n">broadcast_tensors</span><span class="p">(</span><span class="n">tensors</span><span class="p">)</span> <span class="c1"># type: ignore[attr-defined]</span></div>
<div class="viewcode-block" id="broadcast_shapes"><a class="viewcode-back" href="../../generated/torch.broadcast_shapes.html#torch.broadcast_shapes">[docs]</a><span class="k">def</span> <span class="nf">broadcast_shapes</span><span class="p">(</span><span class="o">*</span><span class="n">shapes</span><span class="p">):</span>
<span class="w"> </span><span class="sa">r</span><span class="sd">"""broadcast_shapes(*shapes) -> Size</span>
<span class="sd"> Similar to :func:`broadcast_tensors` but for shapes.</span>
<span class="sd"> This is equivalent to</span>
<span class="sd"> ``torch.broadcast_tensors(*map(torch.empty, shapes))[0].shape``</span>
<span class="sd"> but avoids the need create to intermediate tensors. This is useful for</span>
<span class="sd"> broadcasting tensors of common batch shape but different rightmost shape,</span>
<span class="sd"> e.g. to broadcast mean vectors with covariance matrices.</span>
<span class="sd"> Example::</span>
<span class="sd"> >>> torch.broadcast_shapes((2,), (3, 1), (1, 1, 1))</span>
<span class="sd"> torch.Size([1, 3, 2])</span>
<span class="sd"> Args:</span>
<span class="sd"> \*shapes (torch.Size): Shapes of tensors.</span>
<span class="sd"> Returns:</span>
<span class="sd"> shape (torch.Size): A shape compatible with all input shapes.</span>
<span class="sd"> Raises:</span>
<span class="sd"> RuntimeError: If shapes are incompatible.</span>
<span class="sd"> """</span>
<span class="c1"># This wrapper exists to support variadic args.</span>
<span class="c1"># TODO Move this to C++ once the jit has better support for torch.Size.</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">torch</span><span class="o">.</span><span class="n">jit</span><span class="o">.</span><span class="n">is_tracing</span><span class="p">():</span>
<span class="n">max_len</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">shape</span> <span class="ow">in</span> <span class="n">shapes</span><span class="p">:</span>
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">shape</span><span class="p">,</span> <span class="p">(</span><span class="nb">int</span><span class="p">,</span> <span class="n">torch</span><span class="o">.</span><span class="n">SymInt</span><span class="p">)):</span>
<span class="k">if</span> <span class="n">max_len</span> <span class="o"><</span> <span class="mi">1</span><span class="p">:</span>
<span class="n">max_len</span> <span class="o">=</span> <span class="mi">1</span>
<span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">shape</span><span class="p">,</span> <span class="p">(</span><span class="nb">tuple</span><span class="p">,</span> <span class="nb">list</span><span class="p">)):</span>
<span class="n">s</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">shape</span><span class="p">)</span>
<span class="k">if</span> <span class="n">max_len</span> <span class="o"><</span> <span class="n">s</span><span class="p">:</span>
<span class="n">max_len</span> <span class="o">=</span> <span class="n">s</span>
<span class="n">result</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">max_len</span>
<span class="kn">from</span> <span class="nn">torch.fx.experimental.symbolic_shapes</span> <span class="kn">import</span> <span class="n">guard_size_oblivious</span>
<span class="k">for</span> <span class="n">shape</span> <span class="ow">in</span> <span class="n">shapes</span><span class="p">:</span>
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">shape</span><span class="p">,</span> <span class="p">(</span><span class="nb">int</span><span class="p">,</span> <span class="n">torch</span><span class="o">.</span><span class="n">SymInt</span><span class="p">)):</span>
<span class="n">shape</span> <span class="o">=</span> <span class="p">(</span><span class="n">shape</span><span class="p">,)</span>
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">shape</span><span class="p">,</span> <span class="p">(</span><span class="nb">tuple</span><span class="p">,</span> <span class="nb">list</span><span class="p">)):</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</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="o">-</span> <span class="nb">len</span><span class="p">(</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="k">if</span> <span class="n">shape</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o"><</span> <span class="mi">0</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">"Trying to create tensor with negative dimension (</span><span class="si">{</span><span class="n">shape</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="si">}</span><span class="s2">): (</span><span class="si">{</span><span class="n">shape</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="si">}</span><span class="s2">)"</span>
<span class="p">)</span>
<span class="c1"># NB: result is initialized to 1 so this is effectively an</span>
<span class="c1"># equals one test</span>
<span class="k">if</span> <span class="n">guard_size_oblivious</span><span class="p">(</span><span class="n">shape</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">==</span> <span class="mi">1</span><span class="p">)</span> <span class="ow">or</span> <span class="n">guard_size_oblivious</span><span class="p">(</span>
<span class="n">shape</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">==</span> <span class="n">result</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<span class="p">):</span>
<span class="k">continue</span>
<span class="k">if</span> <span class="n">result</span><span class="p">[</span><span class="n">i</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">"Shape mismatch: objects cannot be broadcast to a single shape"</span>
<span class="p">)</span>
<span class="n">result</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">shape</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">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span>
<span class="s2">"Input shapes should be of type ints, a tuple of ints, or a list of ints, got "</span><span class="p">,</span>
<span class="n">shape</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">Size</span><span class="p">(</span><span class="n">result</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="c1"># with implementation above, torch.jit.trace hardcodes the sizes which makes subsequent replays fail</span>
<span class="k">with</span> <span class="n">torch</span><span class="o">.</span><span class="n">no_grad</span><span class="p">():</span>
<span class="n">scalar</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">zeros</span><span class="p">((),</span> <span class="n">device</span><span class="o">=</span><span class="s2">"cpu"</span><span class="p">)</span>
<span class="n">tensors</span> <span class="o">=</span> <span class="p">[</span><span class="n">scalar</span><span class="o">.</span><span class="n">expand</span><span class="p">(</span><span class="n">shape</span><span class="p">)</span> <span class="k">for</span> <span class="n">shape</span> <span class="ow">in</span> <span class="n">shapes</span><span class="p">]</span>
<span class="n">tensors</span> <span class="o">=</span> <span class="n">broadcast_tensors</span><span class="p">(</span><span class="o">*</span><span class="n">tensors</span><span class="p">)</span>
<span class="k">return</span> <span class="n">tensors</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">shape</span></div>
<div class="viewcode-block" id="split"><a class="viewcode-back" href="../../generated/torch.split.html#torch.split">[docs]</a><span class="k">def</span> <span class="nf">split</span><span class="p">(</span>
<span class="n">tensor</span><span class="p">:</span> <span class="n">Tensor</span><span class="p">,</span>
<span class="n">split_size_or_sections</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="n">List</span><span class="p">[</span><span class="nb">int</span><span class="p">]],</span>
<span class="n">dim</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span>
<span class="p">)</span> <span class="o">-></span> <span class="n">Tuple</span><span class="p">[</span><span class="n">Tensor</span><span class="p">,</span> <span class="o">...</span><span class="p">]:</span>
<span class="w"> </span><span class="sa">r</span><span class="sd">"""Splits the tensor into chunks. Each chunk is a view of the original tensor.</span>
<span class="sd"> If :attr:`split_size_or_sections` is an integer type, then :attr:`tensor` will</span>
<span class="sd"> be split into equally sized chunks (if possible). Last chunk will be smaller if</span>
<span class="sd"> the tensor size along the given dimension :attr:`dim` is not divisible by</span>
<span class="sd"> :attr:`split_size`.</span>
<span class="sd"> If :attr:`split_size_or_sections` is a list, then :attr:`tensor` will be split</span>
<span class="sd"> into ``len(split_size_or_sections)`` chunks with sizes in :attr:`dim` according</span>
<span class="sd"> to :attr:`split_size_or_sections`.</span>
<span class="sd"> Args:</span>
<span class="sd"> tensor (Tensor): tensor to split.</span>
<span class="sd"> split_size_or_sections (int) or (list(int)): size of a single chunk or</span>
<span class="sd"> list of sizes for each chunk</span>
<span class="sd"> dim (int): dimension along which to split the tensor.</span>
<span class="sd"> Example::</span>
<span class="sd"> >>> a = torch.arange(10).reshape(5, 2)</span>
<span class="sd"> >>> a</span>
<span class="sd"> tensor([[0, 1],</span>
<span class="sd"> [2, 3],</span>
<span class="sd"> [4, 5],</span>
<span class="sd"> [6, 7],</span>
<span class="sd"> [8, 9]])</span>
<span class="sd"> >>> torch.split(a, 2)</span>
<span class="sd"> (tensor([[0, 1],</span>
<span class="sd"> [2, 3]]),</span>
<span class="sd"> tensor([[4, 5],</span>
<span class="sd"> [6, 7]]),</span>
<span class="sd"> tensor([[8, 9]]))</span>
<span class="sd"> >>> torch.split(a, [1, 4])</span>
<span class="sd"> (tensor([[0, 1]]),</span>
<span class="sd"> tensor([[2, 3],</span>
<span class="sd"> [4, 5],</span>
<span class="sd"> [6, 7],</span>
<span class="sd"> [8, 9]]))</span>
<span class="sd"> """</span>
<span class="k">if</span> <span class="n">has_torch_function_unary</span><span class="p">(</span><span class="n">tensor</span><span class="p">):</span>
<span class="k">return</span> <span class="n">handle_torch_function</span><span class="p">(</span>
<span class="n">split</span><span class="p">,</span> <span class="p">(</span><span class="n">tensor</span><span class="p">,),</span> <span class="n">tensor</span><span class="p">,</span> <span class="n">split_size_or_sections</span><span class="p">,</span> <span class="n">dim</span><span class="o">=</span><span class="n">dim</span>
<span class="p">)</span>
<span class="c1"># Overwriting reason:</span>
<span class="c1"># This dispatches to two ATen functions depending on the type of</span>
<span class="c1"># split_size_or_sections. The branching code is in _tensor.py, which we</span>
<span class="c1"># call here.</span>
<span class="k">return</span> <span class="n">tensor</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="n">split_size_or_sections</span><span class="p">,</span> <span class="n">dim</span><span class="p">)</span></div>
<div class="viewcode-block" id="einsum"><a class="viewcode-back" href="../../generated/torch.einsum.html#torch.einsum">[docs]</a><span class="k">def</span> <span class="nf">einsum</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">:</span> <span class="n">Any</span><span class="p">)</span> <span class="o">-></span> <span class="n">Tensor</span><span class="p">:</span>
<span class="w"> </span><span class="sa">r</span><span class="sd">"""einsum(equation, *operands) -> Tensor</span>
<span class="sd"> Sums the product of the elements of the input :attr:`operands` along dimensions specified using a notation</span>
<span class="sd"> based on the Einstein summation convention.</span>
<span class="sd"> Einsum allows computing many common multi-dimensional linear algebraic array operations by representing them</span>
<span class="sd"> in a short-hand format based on the Einstein summation convention, given by :attr:`equation`. The details of</span>
<span class="sd"> this format are described below, but the general idea is to label every dimension of the input :attr:`operands`</span>
<span class="sd"> with some subscript and define which subscripts are part of the output. The output is then computed by summing</span>
<span class="sd"> the product of the elements of the :attr:`operands` along the dimensions whose subscripts are not part of the</span>
<span class="sd"> output. For example, matrix multiplication can be computed using einsum as `torch.einsum("ij,jk->ik", A, B)`.</span>
<span class="sd"> Here, j is the summation subscript and i and k the output subscripts (see section below for more details on why).</span>
<span class="sd"> Equation:</span>
<span class="sd"> The :attr:`equation` string specifies the subscripts (letters in `[a-zA-Z]`) for each dimension of</span>
<span class="sd"> the input :attr:`operands` in the same order as the dimensions, separating subscripts for each operand by a</span>
<span class="sd"> comma (','), e.g. `'ij,jk'` specify subscripts for two 2D operands. The dimensions labeled with the same subscript</span>
<span class="sd"> must be broadcastable, that is, their size must either match or be `1`. The exception is if a subscript is</span>
<span class="sd"> repeated for the same input operand, in which case the dimensions labeled with this subscript for this operand</span>
<span class="sd"> must match in size and the operand will be replaced by its diagonal along these dimensions. The subscripts that</span>
<span class="sd"> appear exactly once in the :attr:`equation` will be part of the output, sorted in increasing alphabetical order.</span>
<span class="sd"> The output is computed by multiplying the input :attr:`operands` element-wise, with their dimensions aligned based</span>
<span class="sd"> on the subscripts, and then summing out the dimensions whose subscripts are not part of the output.</span>
<span class="sd"> Optionally, the output subscripts can be explicitly defined by adding an arrow ('->') at the end of the equation</span>
<span class="sd"> followed by the subscripts for the output. For instance, the following equation computes the transpose of a</span>
<span class="sd"> matrix multiplication: 'ij,jk->ki'. The output subscripts must appear at least once for some input operand and</span>
<span class="sd"> at most once for the output.</span>
<span class="sd"> Ellipsis ('...') can be used in place of subscripts to broadcast the dimensions covered by the ellipsis.</span>
<span class="sd"> Each input operand may contain at most one ellipsis which will cover the dimensions not covered by subscripts,</span>
<span class="sd"> e.g. for an input operand with 5 dimensions, the ellipsis in the equation `'ab...c'` cover the third and fourth</span>
<span class="sd"> dimensions. The ellipsis does not need to cover the same number of dimensions across the :attr:`operands` but the</span>
<span class="sd"> 'shape' of the ellipsis (the size of the dimensions covered by them) must broadcast together. If the output is not</span>
<span class="sd"> explicitly defined with the arrow ('->') notation, the ellipsis will come first in the output (left-most dimensions),</span>
<span class="sd"> before the subscript labels that appear exactly once for the input operands. e.g. the following equation implements</span>
<span class="sd"> batch matrix multiplication `'...ij,...jk'`.</span>
<span class="sd"> A few final notes: the equation may contain whitespaces between the different elements (subscripts, ellipsis,</span>
<span class="sd"> arrow and comma) but something like `'. . .'` is not valid. An empty string `''` is valid for scalar operands.</span>
<span class="sd"> .. note::</span>
<span class="sd"> ``torch.einsum`` handles ellipsis ('...') differently from NumPy in that it allows dimensions</span>
<span class="sd"> covered by the ellipsis to be summed over, that is, ellipsis are not required to be part of the output.</span>
<span class="sd"> .. note::</span>
<span class="sd"> Please install opt-einsum (https://optimized-einsum.readthedocs.io/en/stable/) in order to enroll into a more</span>
<span class="sd"> performant einsum. You can install when installing torch like so: `pip install torch[opt-einsum]` or by itself</span>
<span class="sd"> with `pip install opt-einsum`.</span>
<span class="sd"> If opt-einsum is available, this function will automatically speed up computation and/or consume less memory</span>
<span class="sd"> by optimizing contraction order through our opt_einsum backend :mod:`torch.backends.opt_einsum` (The _ vs - is</span>
<span class="sd"> confusing, I know). This optimization occurs when there are at least three inputs, since the order does not matter</span>
<span class="sd"> otherwise. Note that finding `the` optimal path is an NP-hard problem, thus, opt-einsum relies on different</span>
<span class="sd"> heuristics to achieve near-optimal results. If opt-einsum is not available, the default order is to contract</span>
<span class="sd"> from left to right.</span>
<span class="sd"> To bypass this default behavior, add the following to disable opt_einsum and skip path calculation:</span>
<span class="sd"> ``torch.backends.opt_einsum.enabled = False``</span>
<span class="sd"> To specify which strategy you'd like for opt_einsum to compute the contraction path, add the following line:</span>
<span class="sd"> ``torch.backends.opt_einsum.strategy = 'auto'``. The default strategy is 'auto', and we also support 'greedy' and</span>
<span class="sd"> 'optimal'. Disclaimer that the runtime of 'optimal' is factorial in the number of inputs! See more details in</span>
<span class="sd"> the opt_einsum documentation (https://optimized-einsum.readthedocs.io/en/stable/path_finding.html).</span>
<span class="sd"> .. note::</span>
<span class="sd"> As of PyTorch 1.10 :func:`torch.einsum` also supports the sublist format (see examples below). In this format,</span>
<span class="sd"> subscripts for each operand are specified by sublists, list of integers in the range [0, 52). These sublists</span>
<span class="sd"> follow their operands, and an extra sublist can appear at the end of the input to specify the output's</span>
<span class="sd"> subscripts., e.g. `torch.einsum(op1, sublist1, op2, sublist2, ..., [subslist_out])`. Python's `Ellipsis` object</span>
<span class="sd"> may be provided in a sublist to enable broadcasting as described in the Equation section above.</span>
<span class="sd"> Args:</span>
<span class="sd"> equation (str): The subscripts for the Einstein summation.</span>
<span class="sd"> operands (List[Tensor]): The tensors to compute the Einstein summation of.</span>
<span class="sd"> Examples::</span>
<span class="sd"> >>> # xdoctest: +IGNORE_WANT("non-deterministic")</span>
<span class="sd"> >>> # trace</span>
<span class="sd"> >>> torch.einsum('ii', torch.randn(4, 4))</span>
<span class="sd"> tensor(-1.2104)</span>
<span class="sd"> >>> # xdoctest: +IGNORE_WANT("non-deterministic")</span>
<span class="sd"> >>> # diagonal</span>
<span class="sd"> >>> torch.einsum('ii->i', torch.randn(4, 4))</span>
<span class="sd"> tensor([-0.1034, 0.7952, -0.2433, 0.4545])</span>
<span class="sd"> >>> # xdoctest: +IGNORE_WANT("non-deterministic")</span>
<span class="sd"> >>> # outer product</span>
<span class="sd"> >>> x = torch.randn(5)</span>
<span class="sd"> >>> y = torch.randn(4)</span>
<span class="sd"> >>> torch.einsum('i,j->ij', x, y)</span>
<span class="sd"> tensor([[ 0.1156, -0.2897, -0.3918, 0.4963],</span>
<span class="sd"> [-0.3744, 0.9381, 1.2685, -1.6070],</span>
<span class="sd"> [ 0.7208, -1.8058, -2.4419, 3.0936],</span>
<span class="sd"> [ 0.1713, -0.4291, -0.5802, 0.7350],</span>
<span class="sd"> [ 0.5704, -1.4290, -1.9323, 2.4480]])</span>
<span class="sd"> >>> # xdoctest: +IGNORE_WANT("non-deterministic")</span>
<span class="sd"> >>> # batch matrix multiplication</span>
<span class="sd"> >>> As = torch.randn(3, 2, 5)</span>
<span class="sd"> >>> Bs = torch.randn(3, 5, 4)</span>
<span class="sd"> >>> torch.einsum('bij,bjk->bik', As, Bs)</span>
<span class="sd"> tensor([[[-1.0564, -1.5904, 3.2023, 3.1271],</span>
<span class="sd"> [-1.6706, -0.8097, -0.8025, -2.1183]],</span>
<span class="sd"> [[ 4.2239, 0.3107, -0.5756, -0.2354],</span>
<span class="sd"> [-1.4558, -0.3460, 1.5087, -0.8530]],</span>
<span class="sd"> [[ 2.8153, 1.8787, -4.3839, -1.2112],</span>
<span class="sd"> [ 0.3728, -2.1131, 0.0921, 0.8305]]])</span>
<span class="sd"> >>> # xdoctest: +IGNORE_WANT("non-deterministic")</span>
<span class="sd"> >>> # with sublist format and ellipsis</span>
<span class="sd"> >>> torch.einsum(As, [..., 0, 1], Bs, [..., 1, 2], [..., 0, 2])</span>
<span class="sd"> tensor([[[-1.0564, -1.5904, 3.2023, 3.1271],</span>
<span class="sd"> [-1.6706, -0.8097, -0.8025, -2.1183]],</span>
<span class="sd"> [[ 4.2239, 0.3107, -0.5756, -0.2354],</span>
<span class="sd"> [-1.4558, -0.3460, 1.5087, -0.8530]],</span>
<span class="sd"> [[ 2.8153, 1.8787, -4.3839, -1.2112],</span>
<span class="sd"> [ 0.3728, -2.1131, 0.0921, 0.8305]]])</span>
<span class="sd"> >>> # batch permute</span>
<span class="sd"> >>> A = torch.randn(2, 3, 4, 5)</span>
<span class="sd"> >>> torch.einsum('...ij->...ji', A).shape</span>
<span class="sd"> torch.Size([2, 3, 5, 4])</span>
<span class="sd"> >>> # equivalent to torch.nn.functional.bilinear</span>
<span class="sd"> >>> A = torch.randn(3, 5, 4)</span>
<span class="sd"> >>> l = torch.randn(2, 5)</span>
<span class="sd"> >>> r = torch.randn(2, 4)</span>
<span class="sd"> >>> torch.einsum('bn,anm,bm->ba', l, A, r)</span>
<span class="sd"> tensor([[-0.3430, -5.2405, 0.4494],</span>
<span class="sd"> [ 0.3311, 5.5201, -3.0356]])</span>
<span class="sd"> """</span>
<span class="kn">import</span> <span class="nn">torch.backends.opt_einsum</span> <span class="k">as</span> <span class="nn">opt_einsum</span>
<span class="c1"># This wrapper exists to support variadic args.</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">args</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">"einsum(): must specify the equation string and at least one operand, "</span>
<span class="s2">"or at least one operand and its subscripts list"</span>
<span class="p">)</span>
<span class="n">equation</span> <span class="o">=</span> <span class="kc">None</span>
<span class="n">operands</span> <span class="o">=</span> <span class="kc">None</span>
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</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="c1"># Convert the subscript list format which is an interleaving of operand and its subscripts</span>
<span class="c1"># list with an optional output subscripts list at the end (see documentation for more details on this)</span>
<span class="c1"># to the equation string format by creating the equation string from the subscripts list and grouping the</span>
<span class="c1"># input operands into a tensorlist (List[Tensor]).</span>
<span class="k">def</span> <span class="nf">parse_subscript</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-></span> <span class="nb">str</span><span class="p">:</span>
<span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="bp">Ellipsis</span><span class="p">:</span>
<span class="k">return</span> <span class="s2">"..."</span>
<span class="k">if</span> <span class="n">n</span> <span class="o">>=</span> <span class="mi">0</span> <span class="ow">and</span> <span class="n">n</span> <span class="o"><</span> <span class="mi">26</span><span class="p">:</span>
<span class="k">return</span> <span class="nb">chr</span><span class="p">(</span><span class="nb">ord</span><span class="p">(</span><span class="s2">"A"</span><span class="p">)</span> <span class="o">+</span> <span class="n">n</span><span class="p">)</span>
<span class="k">if</span> <span class="n">n</span> <span class="o">>=</span> <span class="mi">26</span> <span class="ow">and</span> <span class="n">n</span> <span class="o"><</span> <span class="mi">52</span><span class="p">:</span>
<span class="k">return</span> <span class="nb">chr</span><span class="p">(</span><span class="nb">ord</span><span class="p">(</span><span class="s2">"a"</span><span class="p">)</span> <span class="o">+</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">26</span><span class="p">)</span>
<span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
<span class="s2">"einsum(): subscript in subscript list is not within the valid range [0, 52)"</span>
<span class="p">)</span>
<span class="c1"># Parse subscripts for input operands</span>
<span class="n">equation</span> <span class="o">=</span> <span class="s2">","</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="s2">""</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">parse_subscript</span><span class="p">(</span><span class="n">s</span><span class="p">)</span> <span class="k">for</span> <span class="n">s</span> <span class="ow">in</span> <span class="n">l</span><span class="p">)</span> <span class="k">for</span> <span class="n">l</span> <span class="ow">in</span> <span class="n">args</span><span class="p">[</span><span class="mi">1</span><span class="p">::</span><span class="mi">2</span><span class="p">])</span>
<span class="c1"># Parse optional output subscripts (provided when the number of arguments is odd)</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">args</span><span class="p">)</span> <span class="o">%</span> <span class="mi">2</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
<span class="n">equation</span> <span class="o">+=</span> <span class="s2">"->"</span> <span class="o">+</span> <span class="s2">""</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">parse_subscript</span><span class="p">(</span><span class="n">s</span><span class="p">)</span> <span class="k">for</span> <span class="n">s</span> <span class="ow">in</span> <span class="n">args</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
<span class="n">operands</span> <span class="o">=</span> <span class="n">args</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">:</span><span class="mi">2</span><span class="p">]</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">operands</span> <span class="o">=</span> <span class="n">args</span><span class="p">[::</span><span class="mi">2</span><span class="p">]</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">equation</span> <span class="o">=</span> <span class="n">args</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="n">operands</span> <span class="o">=</span> <span class="n">args</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span>
<span class="k">if</span> <span class="n">has_torch_function</span><span class="p">(</span><span class="n">operands</span><span class="p">):</span>
<span class="k">return</span> <span class="n">handle_torch_function</span><span class="p">(</span><span class="n">einsum</span><span class="p">,</span> <span class="n">operands</span><span class="p">,</span> <span class="n">equation</span><span class="p">,</span> <span class="o">*</span><span class="n">operands</span><span class="p">)</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">operands</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">and</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">operands</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="p">(</span><span class="nb">list</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">)):</span>
<span class="c1"># the old interface of passing the operands as one list argument</span>
<span class="n">_operands</span> <span class="o">=</span> <span class="n">operands</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="c1"># recurse incase operands contains value that has torch function</span>
<span class="c1"># in the original implementation this line is omitted</span>
<span class="k">return</span> <span class="n">einsum</span><span class="p">(</span><span class="n">equation</span><span class="p">,</span> <span class="o">*</span><span class="n">_operands</span><span class="p">)</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">operands</span><span class="p">)</span> <span class="o"><=</span> <span class="mi">2</span> <span class="ow">or</span> <span class="ow">not</span> <span class="n">opt_einsum</span><span class="o">.</span><span class="n">enabled</span><span class="p">:</span>
<span class="c1"># the path for contracting 0 or 1 time(s) is already optimized</span>
<span class="c1"># or the user has disabled using opt_einsum</span>
<span class="k">return</span> <span class="n">_VF</span><span class="o">.</span><span class="n">einsum</span><span class="p">(</span><span class="n">equation</span><span class="p">,</span> <span class="n">operands</span><span class="p">)</span> <span class="c1"># type: ignore[attr-defined]</span>
<span class="n">path</span> <span class="o">=</span> <span class="kc">None</span>
<span class="k">if</span> <span class="n">opt_einsum</span><span class="o">.</span><span class="n">is_available</span><span class="p">():</span>
<span class="n">_opt_einsum</span> <span class="o">=</span> <span class="n">opt_einsum</span><span class="o">.</span><span class="n">get_opt_einsum</span><span class="p">()</span>
<span class="n">tupled_path</span> <span class="o">=</span> <span class="n">_opt_einsum</span><span class="o">.</span><span class="n">contract_path</span><span class="p">(</span>
<span class="n">equation</span><span class="p">,</span> <span class="o">*</span><span class="n">operands</span><span class="p">,</span> <span class="n">optimize</span><span class="o">=</span><span class="n">opt_einsum</span><span class="o">.</span><span class="n">strategy</span>
<span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
<span class="c1"># flatten path for dispatching to C++</span>
<span class="n">path</span> <span class="o">=</span> <span class="p">[</span><span class="n">item</span> <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="n">tupled_path</span> <span class="k">for</span> <span class="n">item</span> <span class="ow">in</span> <span class="n">pair</span><span class="p">]</span>
<span class="k">return</span> <span class="n">_VF</span><span class="o">.</span><span class="n">einsum</span><span class="p">(</span><span class="n">equation</span><span class="p">,</span> <span class="n">operands</span><span class="p">,</span> <span class="n">path</span><span class="o">=</span><span class="n">path</span><span class="p">)</span> <span class="c1"># type: ignore[attr-defined]</span></div>
<span class="c1"># This wrapper exists to support variadic args.</span>
<span class="k">if</span> <span class="n">TYPE_CHECKING</span><span class="p">:</span>
<span class="c1"># The JIT doesn't understand Union, so only add type annotation for mypy</span>
<span class="k">def</span> <span class="nf">meshgrid</span><span class="p">(</span>
<span class="o">*</span><span class="n">tensors</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="n">Tensor</span><span class="p">,</span> <span class="n">List</span><span class="p">[</span><span class="n">Tensor</span><span class="p">]],</span> <span class="n">indexing</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="nb">str</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span>