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<article class="md-content__inner md-typeset">
<h1 id="solver">Solver</h1>
<div class="doc doc-object doc-module">
<h2 id="felice.solver" class="doc doc-heading">
<code class="doc-symbol doc-symbol-heading doc-symbol-module"></code> <code>felice.solver</code>
</h2>
<div class="doc doc-contents first">
<div class="doc doc-children">
<h3 id="felice.solver-classes">Classes</h3>
<div class="doc doc-object doc-class">
<h4 id="felice.solver.ClipSolver" class="doc doc-heading">
<code class="doc-symbol doc-symbol-heading doc-symbol-class"></code> <code>ClipSolver</code>
</h4>
<div class="doc doc-contents ">
<p class="doc doc-class-bases">
Bases: <code><span title="equinox.Module">Module</span></code></p>
<details class="mkdocstrings-source">
<summary>Source code in <code>felice/solver.py</code></summary>
<div class="language-python highlight"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre><span></span><span class="normal"><a href="#__codelineno-0-12">12</a></span>
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<span class="normal"><a href="#__codelineno-0-64">64</a></span></pre></div></td><td class="code"><div><pre><span></span><code><span id="__span-0-12"><a id="__codelineno-0-12" name="__codelineno-0-12"></a><span class="k">class</span><span class="w"> </span><span class="nc">ClipSolver</span><span class="p">(</span><span class="n">eqx</span><span class="o">.</span><span class="n">Module</span><span class="p">):</span>
</span><span id="__span-0-13"><a id="__codelineno-0-13" name="__codelineno-0-13"></a> <span class="n">solver</span><span class="p">:</span> <span class="n">AbstractSolver</span>
</span><span id="__span-0-14"><a id="__codelineno-0-14" name="__codelineno-0-14"></a>
</span><span id="__span-0-15"><a id="__codelineno-0-15" name="__codelineno-0-15"></a> <span class="k">def</span><span class="w"> </span><span class="fm">__getattr__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">):</span>
</span><span id="__span-0-16"><a id="__codelineno-0-16" name="__codelineno-0-16"></a> <span class="k">return</span> <span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">solver</span><span class="p">,</span> <span class="n">name</span><span class="p">)</span>
</span><span id="__span-0-17"><a id="__codelineno-0-17" name="__codelineno-0-17"></a>
</span><span id="__span-0-18"><a id="__codelineno-0-18" name="__codelineno-0-18"></a> <span class="k">def</span><span class="w"> </span><span class="nf">step</span><span class="p">(</span>
</span><span id="__span-0-19"><a id="__codelineno-0-19" name="__codelineno-0-19"></a> <span class="bp">self</span><span class="p">,</span>
</span><span id="__span-0-20"><a id="__codelineno-0-20" name="__codelineno-0-20"></a> <span class="n">terms</span><span class="p">:</span> <span class="n">PyTree</span><span class="p">[</span><span class="n">AbstractTerm</span><span class="p">],</span>
</span><span id="__span-0-21"><a id="__codelineno-0-21" name="__codelineno-0-21"></a> <span class="n">t0</span><span class="p">:</span> <span class="n">RealScalarLike</span><span class="p">,</span>
</span><span id="__span-0-22"><a id="__codelineno-0-22" name="__codelineno-0-22"></a> <span class="n">t1</span><span class="p">:</span> <span class="n">RealScalarLike</span><span class="p">,</span>
</span><span id="__span-0-23"><a id="__codelineno-0-23" name="__codelineno-0-23"></a> <span class="n">y0</span><span class="p">:</span> <span class="n">Y</span><span class="p">,</span>
</span><span id="__span-0-24"><a id="__codelineno-0-24" name="__codelineno-0-24"></a> <span class="n">args</span><span class="p">:</span> <span class="n">Args</span><span class="p">,</span>
</span><span id="__span-0-25"><a id="__codelineno-0-25" name="__codelineno-0-25"></a> <span class="n">solver_state</span><span class="p">:</span> <span class="n">_SolverState</span><span class="p">,</span>
</span><span id="__span-0-26"><a id="__codelineno-0-26" name="__codelineno-0-26"></a> <span class="n">made_jump</span><span class="p">:</span> <span class="n">BoolScalarLike</span><span class="p">,</span>
</span><span id="__span-0-27"><a id="__codelineno-0-27" name="__codelineno-0-27"></a> <span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">tuple</span><span class="p">[</span><span class="n">Y</span><span class="p">,</span> <span class="n">Optional</span><span class="p">[</span><span class="n">Y</span><span class="p">],</span> <span class="n">DenseInfo</span><span class="p">,</span> <span class="n">_SolverState</span><span class="p">,</span> <span class="n">RESULTS</span><span class="p">]:</span>
</span><span id="__span-0-28"><a id="__codelineno-0-28" name="__codelineno-0-28"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Make a single step of the solver.</span>
</span><span id="__span-0-29"><a id="__codelineno-0-29" name="__codelineno-0-29"></a>
</span><span id="__span-0-30"><a id="__codelineno-0-30" name="__codelineno-0-30"></a><span class="sd"> Each step is made over the specified interval $[t_0, t_1]$.</span>
</span><span id="__span-0-31"><a id="__codelineno-0-31" name="__codelineno-0-31"></a>
</span><span id="__span-0-32"><a id="__codelineno-0-32" name="__codelineno-0-32"></a><span class="sd"> **Arguments:**</span>
</span><span id="__span-0-33"><a id="__codelineno-0-33" name="__codelineno-0-33"></a>
</span><span id="__span-0-34"><a id="__codelineno-0-34" name="__codelineno-0-34"></a><span class="sd"> - `terms`: The PyTree of terms representing the vector fields and controls.</span>
</span><span id="__span-0-35"><a id="__codelineno-0-35" name="__codelineno-0-35"></a><span class="sd"> - `t0`: The start of the interval that the step is made over.</span>
</span><span id="__span-0-36"><a id="__codelineno-0-36" name="__codelineno-0-36"></a><span class="sd"> - `t1`: The end of the interval that the step is made over.</span>
</span><span id="__span-0-37"><a id="__codelineno-0-37" name="__codelineno-0-37"></a><span class="sd"> - `y0`: The current value of the solution at `t0`.</span>
</span><span id="__span-0-38"><a id="__codelineno-0-38" name="__codelineno-0-38"></a><span class="sd"> - `args`: Any extra arguments passed to the vector field.</span>
</span><span id="__span-0-39"><a id="__codelineno-0-39" name="__codelineno-0-39"></a><span class="sd"> - `solver_state`: Any evolving state for the solver itself, at `t0`.</span>
</span><span id="__span-0-40"><a id="__codelineno-0-40" name="__codelineno-0-40"></a><span class="sd"> - `made_jump`: Whether there was a discontinuity in the vector field at `t0`.</span>
</span><span id="__span-0-41"><a id="__codelineno-0-41" name="__codelineno-0-41"></a><span class="sd"> Some solvers (notably FSAL Runge--Kutta solvers) usually assume that there</span>
</span><span id="__span-0-42"><a id="__codelineno-0-42" name="__codelineno-0-42"></a><span class="sd"> are no jumps and for efficiency re-use information between steps; this</span>
</span><span id="__span-0-43"><a id="__codelineno-0-43" name="__codelineno-0-43"></a><span class="sd"> indicates that a jump has just occurred and this assumption is not true.</span>
</span><span id="__span-0-44"><a id="__codelineno-0-44" name="__codelineno-0-44"></a>
</span><span id="__span-0-45"><a id="__codelineno-0-45" name="__codelineno-0-45"></a><span class="sd"> **Returns:**</span>
</span><span id="__span-0-46"><a id="__codelineno-0-46" name="__codelineno-0-46"></a>
</span><span id="__span-0-47"><a id="__codelineno-0-47" name="__codelineno-0-47"></a><span class="sd"> A tuple of several objects:</span>
</span><span id="__span-0-48"><a id="__codelineno-0-48" name="__codelineno-0-48"></a>
</span><span id="__span-0-49"><a id="__codelineno-0-49" name="__codelineno-0-49"></a><span class="sd"> - The value of the solution at `t1`.</span>
</span><span id="__span-0-50"><a id="__codelineno-0-50" name="__codelineno-0-50"></a><span class="sd"> - A local error estimate made during the step. (Used by adaptive step size</span>
</span><span id="__span-0-51"><a id="__codelineno-0-51" name="__codelineno-0-51"></a><span class="sd"> controllers to change the step size.) May be `None` if no estimate was</span>
</span><span id="__span-0-52"><a id="__codelineno-0-52" name="__codelineno-0-52"></a><span class="sd"> made.</span>
</span><span id="__span-0-53"><a id="__codelineno-0-53" name="__codelineno-0-53"></a><span class="sd"> - Some dictionary of information that is passed to the solver&#39;s interpolation</span>
</span><span id="__span-0-54"><a id="__codelineno-0-54" name="__codelineno-0-54"></a><span class="sd"> routine to calculate dense output. (Used with `SaveAt(ts=...)` or</span>
</span><span id="__span-0-55"><a id="__codelineno-0-55" name="__codelineno-0-55"></a><span class="sd"> `SaveAt(dense=...)`.)</span>
</span><span id="__span-0-56"><a id="__codelineno-0-56" name="__codelineno-0-56"></a><span class="sd"> - The value of the solver state at `t1`.</span>
</span><span id="__span-0-57"><a id="__codelineno-0-57" name="__codelineno-0-57"></a><span class="sd"> - An integer (corresponding to `diffrax.RESULTS`) indicating whether the step</span>
</span><span id="__span-0-58"><a id="__codelineno-0-58" name="__codelineno-0-58"></a><span class="sd"> happened successfully, or if (unusually) it failed for some reason.</span>
</span><span id="__span-0-59"><a id="__codelineno-0-59" name="__codelineno-0-59"></a><span class="sd"> &quot;&quot;&quot;</span>
</span><span id="__span-0-60"><a id="__codelineno-0-60" name="__codelineno-0-60"></a> <span class="n">y1</span><span class="p">,</span> <span class="n">y_error</span><span class="p">,</span> <span class="n">dense_info</span><span class="p">,</span> <span class="n">solver_state</span><span class="p">,</span> <span class="n">result</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">solver</span><span class="o">.</span><span class="n">step</span><span class="p">(</span>
</span><span id="__span-0-61"><a id="__codelineno-0-61" name="__codelineno-0-61"></a> <span class="n">terms</span><span class="p">,</span> <span class="n">t0</span><span class="p">,</span> <span class="n">t1</span><span class="p">,</span> <span class="n">y0</span><span class="p">,</span> <span class="n">args</span><span class="p">,</span> <span class="n">solver_state</span><span class="p">,</span> <span class="n">made_jump</span>
</span><span id="__span-0-62"><a id="__codelineno-0-62" name="__codelineno-0-62"></a> <span class="p">)</span>
</span><span id="__span-0-63"><a id="__codelineno-0-63" name="__codelineno-0-63"></a> <span class="n">y1_clipped</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">tree_util</span><span class="o">.</span><span class="n">tree_map</span><span class="p">(</span><span class="n">jax</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">relu</span><span class="p">,</span> <span class="n">y1</span><span class="p">)</span>
</span><span id="__span-0-64"><a id="__codelineno-0-64" name="__codelineno-0-64"></a> <span class="k">return</span> <span class="n">y1_clipped</span><span class="p">,</span> <span class="n">y_error</span><span class="p">,</span> <span class="n">dense_info</span><span class="p">,</span> <span class="n">solver_state</span><span class="p">,</span> <span class="n">result</span>
</span></code></pre></div></td></tr></table></div>
</details>
<div class="doc doc-children">
<h5 id="felice.solver.ClipSolver-functions">Functions</h5>
<div class="doc doc-object doc-function">
<h6 id="felice.solver.ClipSolver.step" class="doc doc-heading">
<code class="doc-symbol doc-symbol-heading doc-symbol-method"></code> <code class="highlight language-python"><span class="n">step</span><span class="p">(</span><span class="n">terms</span><span class="p">:</span> <span class="n">PyTree</span><span class="p">[</span><span class="n">AbstractTerm</span><span class="p">],</span> <span class="n">t0</span><span class="p">:</span> <span class="n">RealScalarLike</span><span class="p">,</span> <span class="n">t1</span><span class="p">:</span> <span class="n">RealScalarLike</span><span class="p">,</span> <span class="n">y0</span><span class="p">:</span> <span class="n">Y</span><span class="p">,</span> <span class="n">args</span><span class="p">:</span> <span class="n">Args</span><span class="p">,</span> <span class="n">solver_state</span><span class="p">:</span> <span class="n">_SolverState</span><span class="p">,</span> <span class="n">made_jump</span><span class="p">:</span> <span class="n">BoolScalarLike</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">tuple</span><span class="p">[</span><span class="n">Y</span><span class="p">,</span> <span class="n">Optional</span><span class="p">[</span><span class="n">Y</span><span class="p">],</span> <span class="n">DenseInfo</span><span class="p">,</span> <span class="n">_SolverState</span><span class="p">,</span> <span class="n">RESULTS</span><span class="p">]</span></code>
</h6>
<div class="doc doc-contents ">
<p>Make a single step of the solver.</p>
<p>Each step is made over the specified interval <span class="arithmatex">\([t_0, t_1]\)</span>.</p>
<p><strong>Arguments:</strong></p>
<ul>
<li><code>terms</code>: The PyTree of terms representing the vector fields and controls.</li>
<li><code>t0</code>: The start of the interval that the step is made over.</li>
<li><code>t1</code>: The end of the interval that the step is made over.</li>
<li><code>y0</code>: The current value of the solution at <code>t0</code>.</li>
<li><code>args</code>: Any extra arguments passed to the vector field.</li>
<li><code>solver_state</code>: Any evolving state for the solver itself, at <code>t0</code>.</li>
<li><code>made_jump</code>: Whether there was a discontinuity in the vector field at <code>t0</code>.
Some solvers (notably FSAL Runge--Kutta solvers) usually assume that there
are no jumps and for efficiency re-use information between steps; this
indicates that a jump has just occurred and this assumption is not true.</li>
</ul>
<p><strong>Returns:</strong></p>
<p>A tuple of several objects:</p>
<ul>
<li>The value of the solution at <code>t1</code>.</li>
<li>A local error estimate made during the step. (Used by adaptive step size
controllers to change the step size.) May be <code>None</code> if no estimate was
made.</li>
<li>Some dictionary of information that is passed to the solver's interpolation
routine to calculate dense output. (Used with <code>SaveAt(ts=...)</code> or
<code>SaveAt(dense=...)</code>.)</li>
<li>The value of the solver state at <code>t1</code>.</li>
<li>An integer (corresponding to <code>diffrax.RESULTS</code>) indicating whether the step
happened successfully, or if (unusually) it failed for some reason.</li>
</ul>
<details class="mkdocstrings-source">
<summary>Source code in <code>felice/solver.py</code></summary>
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<span class="normal"><a href="#__codelineno-0-64">64</a></span></pre></div></td><td class="code"><div><pre><span></span><code><span id="__span-0-18"><a id="__codelineno-0-18" name="__codelineno-0-18"></a><span class="k">def</span><span class="w"> </span><span class="nf">step</span><span class="p">(</span>
</span><span id="__span-0-19"><a id="__codelineno-0-19" name="__codelineno-0-19"></a> <span class="bp">self</span><span class="p">,</span>
</span><span id="__span-0-20"><a id="__codelineno-0-20" name="__codelineno-0-20"></a> <span class="n">terms</span><span class="p">:</span> <span class="n">PyTree</span><span class="p">[</span><span class="n">AbstractTerm</span><span class="p">],</span>
</span><span id="__span-0-21"><a id="__codelineno-0-21" name="__codelineno-0-21"></a> <span class="n">t0</span><span class="p">:</span> <span class="n">RealScalarLike</span><span class="p">,</span>
</span><span id="__span-0-22"><a id="__codelineno-0-22" name="__codelineno-0-22"></a> <span class="n">t1</span><span class="p">:</span> <span class="n">RealScalarLike</span><span class="p">,</span>
</span><span id="__span-0-23"><a id="__codelineno-0-23" name="__codelineno-0-23"></a> <span class="n">y0</span><span class="p">:</span> <span class="n">Y</span><span class="p">,</span>
</span><span id="__span-0-24"><a id="__codelineno-0-24" name="__codelineno-0-24"></a> <span class="n">args</span><span class="p">:</span> <span class="n">Args</span><span class="p">,</span>
</span><span id="__span-0-25"><a id="__codelineno-0-25" name="__codelineno-0-25"></a> <span class="n">solver_state</span><span class="p">:</span> <span class="n">_SolverState</span><span class="p">,</span>
</span><span id="__span-0-26"><a id="__codelineno-0-26" name="__codelineno-0-26"></a> <span class="n">made_jump</span><span class="p">:</span> <span class="n">BoolScalarLike</span><span class="p">,</span>
</span><span id="__span-0-27"><a id="__codelineno-0-27" name="__codelineno-0-27"></a><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">tuple</span><span class="p">[</span><span class="n">Y</span><span class="p">,</span> <span class="n">Optional</span><span class="p">[</span><span class="n">Y</span><span class="p">],</span> <span class="n">DenseInfo</span><span class="p">,</span> <span class="n">_SolverState</span><span class="p">,</span> <span class="n">RESULTS</span><span class="p">]:</span>
</span><span id="__span-0-28"><a id="__codelineno-0-28" name="__codelineno-0-28"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Make a single step of the solver.</span>
</span><span id="__span-0-29"><a id="__codelineno-0-29" name="__codelineno-0-29"></a>
</span><span id="__span-0-30"><a id="__codelineno-0-30" name="__codelineno-0-30"></a><span class="sd"> Each step is made over the specified interval $[t_0, t_1]$.</span>
</span><span id="__span-0-31"><a id="__codelineno-0-31" name="__codelineno-0-31"></a>
</span><span id="__span-0-32"><a id="__codelineno-0-32" name="__codelineno-0-32"></a><span class="sd"> **Arguments:**</span>
</span><span id="__span-0-33"><a id="__codelineno-0-33" name="__codelineno-0-33"></a>
</span><span id="__span-0-34"><a id="__codelineno-0-34" name="__codelineno-0-34"></a><span class="sd"> - `terms`: The PyTree of terms representing the vector fields and controls.</span>
</span><span id="__span-0-35"><a id="__codelineno-0-35" name="__codelineno-0-35"></a><span class="sd"> - `t0`: The start of the interval that the step is made over.</span>
</span><span id="__span-0-36"><a id="__codelineno-0-36" name="__codelineno-0-36"></a><span class="sd"> - `t1`: The end of the interval that the step is made over.</span>
</span><span id="__span-0-37"><a id="__codelineno-0-37" name="__codelineno-0-37"></a><span class="sd"> - `y0`: The current value of the solution at `t0`.</span>
</span><span id="__span-0-38"><a id="__codelineno-0-38" name="__codelineno-0-38"></a><span class="sd"> - `args`: Any extra arguments passed to the vector field.</span>
</span><span id="__span-0-39"><a id="__codelineno-0-39" name="__codelineno-0-39"></a><span class="sd"> - `solver_state`: Any evolving state for the solver itself, at `t0`.</span>
</span><span id="__span-0-40"><a id="__codelineno-0-40" name="__codelineno-0-40"></a><span class="sd"> - `made_jump`: Whether there was a discontinuity in the vector field at `t0`.</span>
</span><span id="__span-0-41"><a id="__codelineno-0-41" name="__codelineno-0-41"></a><span class="sd"> Some solvers (notably FSAL Runge--Kutta solvers) usually assume that there</span>
</span><span id="__span-0-42"><a id="__codelineno-0-42" name="__codelineno-0-42"></a><span class="sd"> are no jumps and for efficiency re-use information between steps; this</span>
</span><span id="__span-0-43"><a id="__codelineno-0-43" name="__codelineno-0-43"></a><span class="sd"> indicates that a jump has just occurred and this assumption is not true.</span>
</span><span id="__span-0-44"><a id="__codelineno-0-44" name="__codelineno-0-44"></a>
</span><span id="__span-0-45"><a id="__codelineno-0-45" name="__codelineno-0-45"></a><span class="sd"> **Returns:**</span>
</span><span id="__span-0-46"><a id="__codelineno-0-46" name="__codelineno-0-46"></a>
</span><span id="__span-0-47"><a id="__codelineno-0-47" name="__codelineno-0-47"></a><span class="sd"> A tuple of several objects:</span>
</span><span id="__span-0-48"><a id="__codelineno-0-48" name="__codelineno-0-48"></a>
</span><span id="__span-0-49"><a id="__codelineno-0-49" name="__codelineno-0-49"></a><span class="sd"> - The value of the solution at `t1`.</span>
</span><span id="__span-0-50"><a id="__codelineno-0-50" name="__codelineno-0-50"></a><span class="sd"> - A local error estimate made during the step. (Used by adaptive step size</span>
</span><span id="__span-0-51"><a id="__codelineno-0-51" name="__codelineno-0-51"></a><span class="sd"> controllers to change the step size.) May be `None` if no estimate was</span>
</span><span id="__span-0-52"><a id="__codelineno-0-52" name="__codelineno-0-52"></a><span class="sd"> made.</span>
</span><span id="__span-0-53"><a id="__codelineno-0-53" name="__codelineno-0-53"></a><span class="sd"> - Some dictionary of information that is passed to the solver&#39;s interpolation</span>
</span><span id="__span-0-54"><a id="__codelineno-0-54" name="__codelineno-0-54"></a><span class="sd"> routine to calculate dense output. (Used with `SaveAt(ts=...)` or</span>
</span><span id="__span-0-55"><a id="__codelineno-0-55" name="__codelineno-0-55"></a><span class="sd"> `SaveAt(dense=...)`.)</span>
</span><span id="__span-0-56"><a id="__codelineno-0-56" name="__codelineno-0-56"></a><span class="sd"> - The value of the solver state at `t1`.</span>
</span><span id="__span-0-57"><a id="__codelineno-0-57" name="__codelineno-0-57"></a><span class="sd"> - An integer (corresponding to `diffrax.RESULTS`) indicating whether the step</span>
</span><span id="__span-0-58"><a id="__codelineno-0-58" name="__codelineno-0-58"></a><span class="sd"> happened successfully, or if (unusually) it failed for some reason.</span>
</span><span id="__span-0-59"><a id="__codelineno-0-59" name="__codelineno-0-59"></a><span class="sd"> &quot;&quot;&quot;</span>
</span><span id="__span-0-60"><a id="__codelineno-0-60" name="__codelineno-0-60"></a> <span class="n">y1</span><span class="p">,</span> <span class="n">y_error</span><span class="p">,</span> <span class="n">dense_info</span><span class="p">,</span> <span class="n">solver_state</span><span class="p">,</span> <span class="n">result</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">solver</span><span class="o">.</span><span class="n">step</span><span class="p">(</span>
</span><span id="__span-0-61"><a id="__codelineno-0-61" name="__codelineno-0-61"></a> <span class="n">terms</span><span class="p">,</span> <span class="n">t0</span><span class="p">,</span> <span class="n">t1</span><span class="p">,</span> <span class="n">y0</span><span class="p">,</span> <span class="n">args</span><span class="p">,</span> <span class="n">solver_state</span><span class="p">,</span> <span class="n">made_jump</span>
</span><span id="__span-0-62"><a id="__codelineno-0-62" name="__codelineno-0-62"></a> <span class="p">)</span>
</span><span id="__span-0-63"><a id="__codelineno-0-63" name="__codelineno-0-63"></a> <span class="n">y1_clipped</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">tree_util</span><span class="o">.</span><span class="n">tree_map</span><span class="p">(</span><span class="n">jax</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">relu</span><span class="p">,</span> <span class="n">y1</span><span class="p">)</span>
</span><span id="__span-0-64"><a id="__codelineno-0-64" name="__codelineno-0-64"></a> <span class="k">return</span> <span class="n">y1_clipped</span><span class="p">,</span> <span class="n">y_error</span><span class="p">,</span> <span class="n">dense_info</span><span class="p">,</span> <span class="n">solver_state</span><span class="p">,</span> <span class="n">result</span>
</span></code></pre></div></td></tr></table></div>
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