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14 changes: 7 additions & 7 deletions api/operator.interop.html
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Expand Up @@ -818,15 +818,15 @@ <h2><a class="toc-backref" href="#id6" role="doc-backlink">PyTorch</a><a class="
<p>Moreover, the methods above <strong>must</strong> accept stacking dimensions in <code class="docutils literal notranslate"><span class="pre">arr</span></code>. If this does not hold, consider
populating <code class="code docutils literal notranslate"><span class="pre">vectorize</span></code>.</p>
</li>
<li><p><code class="xref py py-class docutils literal notranslate"><span class="pre">*</span> <span class="pre">Auto-vectorization</span> <span class="pre">consists</span> <span class="pre">in</span> <span class="pre">decorating</span> <span class="pre">`kwargs</span></code>-specified arithmetic methods with <a class="reference external" href="https://pytorch.org/docs/stable/generated/torch.vmap.html#torch.vmap" title="(in PyTorch v2.4)"><code class="xref py py-func docutils literal notranslate"><span class="pre">torch.vmap()</span></code></a>. See` – the <a class="reference external" href="https://pytorch.org/docs/stable/func.ux_limitations.html#vmap-limitations">PyTorch documentation</a> for known
<li><p><code class="xref py py-class docutils literal notranslate"><span class="pre">*</span> <span class="pre">Auto-vectorization</span> <span class="pre">consists</span> <span class="pre">in</span> <span class="pre">decorating</span> <span class="pre">`kwargs</span></code>-specified arithmetic methods with <a class="reference external" href="https://pytorch.org/docs/stable/generated/torch.vmap.html#torch.vmap" title="(in PyTorch v2.5)"><code class="xref py py-func docutils literal notranslate"><span class="pre">torch.vmap()</span></code></a>. See` – the <a class="reference external" href="https://pytorch.org/docs/stable/func.ux_limitations.html#vmap-limitations">PyTorch documentation</a> for known
limitations.</p></li>
<li><p><code class="xref py py-class docutils literal notranslate"><span class="pre">*</span> <span class="pre">Arithmetic</span> <span class="pre">methods</span> <span class="pre">are</span> <span class="pre">**not</span> <span class="pre">currently</span> <span class="pre">JIT-ed**</span> <span class="pre">even</span> <span class="pre">if</span> <span class="pre">`jit</span></code> is set` to <code class="docutils literal notranslate"><span class="pre">True</span></code>. This is because of <code class="xref py py-class docutils literal notranslate"><span class="pre">the</span></code> – undocumented and currently poor interaction between <a class="reference external" href="https://pytorch.org/docs/stable/func.api.html#module-torch.func" title="(in PyTorch v2.4)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">torch.func</span></code></a> transforms and <a class="reference external" href="https://pytorch.org/docs/stable/generated/torch.compile.html#torch.compile" title="(in PyTorch v2.4)"><code class="xref py py-func docutils literal notranslate"><span class="pre">torch.compile()</span></code></a>.
<li><p><code class="xref py py-class docutils literal notranslate"><span class="pre">*</span> <span class="pre">Arithmetic</span> <span class="pre">methods</span> <span class="pre">are</span> <span class="pre">**not</span> <span class="pre">currently</span> <span class="pre">JIT-ed**</span> <span class="pre">even</span> <span class="pre">if</span> <span class="pre">`jit</span></code> is set` to <code class="docutils literal notranslate"><span class="pre">True</span></code>. This is because of <code class="xref py py-class docutils literal notranslate"><span class="pre">the</span></code> – undocumented and currently poor interaction between <a class="reference external" href="https://pytorch.org/docs/stable/func.api.html#module-torch.func" title="(in PyTorch v2.5)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">torch.func</span></code></a> transforms and <a class="reference external" href="https://pytorch.org/docs/stable/generated/torch.compile.html#torch.compile" title="(in PyTorch v2.5)"><code class="xref py py-func docutils literal notranslate"><span class="pre">torch.compile()</span></code></a>.
See <a class="reference external" href="https://github.com/pytorch/pytorch/issues/98822">this issue</a> for additional details.</p></li>
<li><p><code class="xref py py-class docutils literal notranslate"><span class="pre">*</span> <span class="pre">For</span> <span class="pre">:py:class:`~pyxu.abc.DiffMap</span></code> (or subclasses thereof)`, <code class="xref py py-class docutils literal notranslate"><span class="pre">the</span> <span class="pre">methods</span> <span class="pre">:py:meth:`~pyxu.abc.DiffMap.jacobian</span></code>,` – <a class="reference internal" href="abc.html#pyxu.abc.DiffFunc.grad" title="pyxu.abc.DiffFunc.grad"><code class="xref py py-meth docutils literal notranslate"><span class="pre">grad()</span></code></a> and <a class="reference internal" href="abc.html#pyxu.abc.LinOp.adjoint" title="pyxu.abc.LinOp.adjoint"><code class="xref py py-meth docutils literal notranslate"><span class="pre">adjoint()</span></code></a> are defined implicitly if not provided
using the auto-differentiation transforms from <a class="reference external" href="https://pytorch.org/docs/stable/func.api.html#module-torch.func" title="(in PyTorch v2.4)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">torch.func</span></code></a>. As detailed <a class="reference external" href="https://pytorch.org/docs/stable/func.ux_limitations.html">on this page</a>, such transforms work well on pure functions (that
using the auto-differentiation transforms from <a class="reference external" href="https://pytorch.org/docs/stable/func.api.html#module-torch.func" title="(in PyTorch v2.5)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">torch.func</span></code></a>. As detailed <a class="reference external" href="https://pytorch.org/docs/stable/func.ux_limitations.html">on this page</a>, such transforms work well on pure functions (that
is, functions where the output is completely determined by the input and that do not involve side effects like
mutation), but may fail on more complex functions. Moreover, <a class="reference external" href="https://pytorch.org/docs/stable/func.api.html#module-torch.func" title="(in PyTorch v2.4)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">torch.func</span></code></a> does not yet have full coverage
over PyTorch operations. For functions that call a <a class="reference external" href="https://pytorch.org/docs/stable/generated/torch.nn.Module.html#torch.nn.Module" title="(in PyTorch v2.4)"><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.nn.Module</span></code></a>, see <a class="reference external" href="https://pytorch.org/docs/stable/func.api.html#utilities-for-working-with-torch-nn-modules">here</a> for some utilities.</p></li>
mutation), but may fail on more complex functions. Moreover, <a class="reference external" href="https://pytorch.org/docs/stable/func.api.html#module-torch.func" title="(in PyTorch v2.5)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">torch.func</span></code></a> does not yet have full coverage
over PyTorch operations. For functions that call a <a class="reference external" href="https://pytorch.org/docs/stable/generated/torch.nn.Module.html#torch.nn.Module" title="(in PyTorch v2.5)"><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.nn.Module</span></code></a>, see <a class="reference external" href="https://pytorch.org/docs/stable/func.api.html#utilities-for-working-with-torch-nn-modules">here</a> for some utilities.</p></li>
<li><p><code class="xref py py-class docutils literal notranslate"> <span class="pre">Warning::</span></code> – Operators created with this wrapper do not support Dask inputs for now.</p></li>
</ul>
</p>
Expand All @@ -844,7 +844,7 @@ <h2><a class="toc-backref" href="#id6" role="doc-backlink">PyTorch</a><a class="
<p>Convert a PyTorch tensor into a NumPy-like array, sharing data, dtype and device.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>tensor</strong> (<a class="reference external" href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="(in PyTorch v2.4)"><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.Tensor</span></code></a>) – Input tensor.</p>
<dd class="field-odd"><p><strong>tensor</strong> (<a class="reference external" href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="(in PyTorch v2.5)"><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.Tensor</span></code></a>) – Input tensor.</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p><strong>arr</strong> – Output array.</p>
Expand Down Expand Up @@ -874,7 +874,7 @@ <h2><a class="toc-backref" href="#id6" role="doc-backlink">PyTorch</a><a class="
<dd class="field-even"><p><strong>tensor</strong> – Output tensor.</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p><a class="reference external" href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="(in PyTorch v2.4)"><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.Tensor</span></code></a></p>
<dd class="field-odd"><p><a class="reference external" href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="(in PyTorch v2.5)"><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.Tensor</span></code></a></p>
</dd>
</dl>
<p class="rubric">Notes</p>
Expand Down
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Expand Up @@ -292,7 +292,7 @@ <h2>Partial Derivatives<a class="headerlink" href="#Partial-Derivatives" title="
<div class="math notranslate nohighlight">
\[\mathbf{D} f [n] = f[n+1] - f[n]\]</div>
<p>As we will see below, this is the forward finite difference approximation. This could be implemented in <strong>matrix-form</strong>, in which case it would look like this:</p>
<center><p><img alt="875bb48c2d064c2e96edd550b6d7e188" class="no-scaled-link" src="../_images/matrix-form.png" style="width: 400px;"/></p>
<center><p><img alt="f47ddc01c4a44acf91190c92942a9ad6" class="no-scaled-link" src="../_images/matrix-form.png" style="width: 400px;"/></p>
</center><p>Or, it could be instead implemented via a for loop, in which the case of large input signals, would not require storing a large matrix:</p>
<div class="nbinput nblast docutils container">
<div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[1]:
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