From d28c3150882a6b71603af885a728ba7e5b561e38 Mon Sep 17 00:00:00 2001
From: "github-actions[bot]"
 <41898282+github-actions[bot]@users.noreply.github.com>
Date: Wed, 20 Dec 2023 16:39:01 +0000
Subject: [PATCH] Update documentation

---
 nightly/.doctrees/environment.pickle          | Bin 2958882 -> 2970225 bytes
 nightly/.doctrees/optimisation.doctree        | Bin 1475508 -> 1483321 bytes
 .../SymmetrisedGradientOperator.html          |  75 ++++++++++++------
 nightly/optimisation.html                     |  55 ++++++++++---
 nightly/searchindex.js                        |   2 +-
 5 files changed, 95 insertions(+), 37 deletions(-)

diff --git a/nightly/.doctrees/environment.pickle b/nightly/.doctrees/environment.pickle
index 8a69b392a46d3702201f399eed6097ae5f73b639..372b13f675f3edb084981aa8cd54bed7a96981b7 100644
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diff --git a/nightly/.doctrees/optimisation.doctree b/nightly/.doctrees/optimisation.doctree
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diff --git a/nightly/_modules/cil/optimisation/operators/SymmetrisedGradientOperator.html b/nightly/_modules/cil/optimisation/operators/SymmetrisedGradientOperator.html
index c70991c8bf..5ba19a5b81 100644
--- a/nightly/_modules/cil/optimisation/operators/SymmetrisedGradientOperator.html
+++ b/nightly/_modules/cil/optimisation/operators/SymmetrisedGradientOperator.html
@@ -218,38 +218,48 @@ <h1>Source code for cil.optimisation.operators.SymmetrisedGradientOperator</h1><
 
 <div class="viewcode-block" id="SymmetrisedGradientOperator"><a class="viewcode-back" href="../../../../optimisation.html#cil.optimisation.operators.SymmetrisedGradientOperator">[docs]</a><span class="k">class</span> <span class="nc">SymmetrisedGradientOperator</span><span class="p">(</span><span class="n">LinearOperator</span><span class="p">):</span>
 <span class="w">    </span>
-<span class="w">    </span><span class="sa">r</span><span class="sd">&#39;&#39;&#39;Symmetrized Gradient Operator:  E: V -&gt; W</span>
+<span class="w">    </span><span class="sa">r</span><span class="sd">&#39;&#39;&#39; The symmetrised gradient is the operator, :math:`E`, defined by :math:`E: V \rightarrow W` where `V` is `BlockGeometry` and  `W` is the range of the Symmetrised Gradient and </span>
 <span class="sd">        </span>
-<span class="sd">        V : range of the Gradient Operator</span>
-<span class="sd">        W : range of the Symmetrized Gradient          </span>
-
-<span class="sd">        Example (2D): </span>
+<span class="sd">        .. math::</span>
+<span class="sd">        </span>
+<span class="sd">            E(v) = 0.5  ( \nabla v + (\nabla v)^{T} ) \\</span>
+<span class="sd">                        </span>
+<span class="sd">        </span>
+<span class="sd">    In 2 dimensions, let :math:`v(x,y)=(v_1(x,y),v_2(x,y))` which gives</span>
 <span class="sd">        </span>
 <span class="sd">        .. math::</span>
-<span class="sd">            v = (v1, v2) \\</span>
 <span class="sd">        </span>
-<span class="sd">            Ev = 0.5 * ( \nabla\cdot v + (\nabla\cdot c)^{T} ) \\</span>
-<span class="sd">            </span>
-<span class="sd">            \begin{matrix} </span>
-<span class="sd">                \partial_{y} v1 &amp; 0.5 * (\partial_{x} v1 + \partial_{y} v2) \\</span>
-<span class="sd">                0.5 * (\partial_{x} v1 + \partial_{y} v2) &amp; \partial_{x} v2 </span>
-<span class="sd">            \end{matrix}</span>
-<span class="sd">                                                                  </span>
+<span class="sd">            \nabla v =\left( \begin{matrix} </span>
+<span class="sd">                \partial_{x} v_1 &amp; \partial_x v_2\\</span>
+<span class="sd">                \partial_{y}v_1 &amp; \partial_y v_2</span>
+<span class="sd">            \end{matrix}\right)</span>
+<span class="sd">        </span>
+<span class="sd">    and thus </span>
+<span class="sd">        </span>
+<span class="sd">        .. math::</span>
+<span class="sd">        </span>
+<span class="sd">            E(v) = 0.5  ( \nabla v + (\nabla v)^{T} )       </span>
+<span class="sd">            =\left( \begin{matrix} </span>
+<span class="sd">                \partial_{x} v_1 &amp; 0.5  (\partial_{y} v_1 + \partial_{x} v_2) \\</span>
+<span class="sd">                0.5  (\partial_{x} v_1 + \partial_{y} v_2) &amp; \partial_{y} v_2 </span>
+<span class="sd">            \end{matrix}\right)</span>
+<span class="sd">                          </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    domain_geometry: `BlockGeometry` with shape (2,1) or (3,1)</span>
+<span class="sd">        Set up the domain of the function. </span>
+<span class="sd">    bnd_cond: str, optional, default :code:`Neumann`</span>
+<span class="sd">        Boundary condition either :code:`Neumann` or :code:`Periodic`</span>
+<span class="sd">    correlation: str, optional, default :code:`Channel`</span>
+<span class="sd">        Correlation either :code:`SpaceChannel` or :code:`Channel`</span>
+<span class="sd">        </span>
 <span class="sd">    &#39;&#39;&#39;</span>
     
     <span class="n">CORRELATION_SPACE</span> <span class="o">=</span> <span class="s2">&quot;Space&quot;</span>
     <span class="n">CORRELATION_SPACECHANNEL</span> <span class="o">=</span> <span class="s2">&quot;SpaceChannels&quot;</span>
     
     <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">domain_geometry</span><span class="p">,</span> <span class="n">bnd_cond</span> <span class="o">=</span> <span class="s1">&#39;Neumann&#39;</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
-<span class="w">        </span><span class="sd">&#39;&#39;&#39;creator</span>
-<span class="sd">        </span>
-<span class="sd">        :param domain_geometry: domain of the operator</span>
-<span class="sd">        :param bnd_cond: boundary condition, either :code:`Neumann` or :code:`Periodic`.</span>
-<span class="sd">        :type bnd_cond: str, optional, default :code:`Neumann`</span>
-<span class="sd">        :param correlation: :code:`SpaceChannel` or :code:`Channel`</span>
-<span class="sd">        :type correlation: str, optional, default :code:`Channel`</span>
-<span class="sd">        &#39;&#39;&#39;</span>
-        
+
         <span class="bp">self</span><span class="o">.</span><span class="n">bnd_cond</span> <span class="o">=</span> <span class="n">bnd_cond</span>
         <span class="bp">self</span><span class="o">.</span><span class="n">correlation</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;correlation&#39;</span><span class="p">,</span><span class="n">SymmetrisedGradientOperator</span><span class="o">.</span><span class="n">CORRELATION_SPACE</span><span class="p">)</span>
                 
@@ -272,7 +282,15 @@ <h1>Source code for cil.optimisation.operators.SymmetrisedGradientOperator</h1><
         
 <div class="viewcode-block" id="SymmetrisedGradientOperator.direct"><a class="viewcode-back" href="../../../../optimisation.html#cil.optimisation.operators.SymmetrisedGradientOperator.direct">[docs]</a>    <span class="k">def</span> <span class="nf">direct</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">out</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
 <span class="w">        </span>
-<span class="w">        </span><span class="sd">&#39;&#39;&#39;Returns E(v)&#39;&#39;&#39;</span>        
+<span class="w">        </span><span class="sa">r</span><span class="sd">&#39;&#39;&#39;Returns :math:`E(v) = 0.5 * ( \nabla v + (\nabla v)^{T} )` </span>
+<span class="sd">        </span>
+<span class="sd">        Parameters:</span>
+<span class="sd">        -------------</span>
+<span class="sd">        </span>
+<span class="sd">        x: BlockDataContainer</span>
+<span class="sd">        out: BlockDataContainer, default None</span>
+<span class="sd">            If out is not None the output of direct will be filled in out, otherwise a new object is instantiated and returned.</span>
+<span class="sd">        &#39;&#39;&#39;</span>        
         
         <span class="k">if</span> <span class="n">out</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
             
@@ -301,7 +319,16 @@ <h1>Source code for cil.optimisation.operators.SymmetrisedGradientOperator</h1><
             
                                                
 <div class="viewcode-block" id="SymmetrisedGradientOperator.adjoint"><a class="viewcode-back" href="../../../../optimisation.html#cil.optimisation.operators.SymmetrisedGradientOperator.adjoint">[docs]</a>    <span class="k">def</span> <span class="nf">adjoint</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">out</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
-        
+<span class="w">        </span><span class="sa">r</span><span class="sd">&#39;&#39;&#39;Returns the adjoint of the symmetrised gradient operator</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters:</span>
+<span class="sd">        -------------</span>
+<span class="sd">        </span>
+<span class="sd">        x: BlockDataContainer</span>
+<span class="sd">        out: BlockDataContainer, default None</span>
+<span class="sd">            If out is not None the output of adjoint will be filled in out, otherwise a new object is instantiated and returned.</span>
+<span class="sd">        &#39;&#39;&#39;</span>         
+       
         <span class="k">if</span> <span class="n">out</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
             
             <span class="n">tmp</span> <span class="o">=</span> <span class="p">[</span><span class="kc">None</span><span class="p">]</span><span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">domain_geometry</span><span class="p">()</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
diff --git a/nightly/optimisation.html b/nightly/optimisation.html
index 7884016dc0..2c156ecea6 100644
--- a/nightly/optimisation.html
+++ b/nightly/optimisation.html
@@ -3159,26 +3159,57 @@ <h3>GradientOperator<a class="headerlink" href="#gradientoperator" title="Permal
 <dl class="py class">
 <dt id="cil.optimisation.operators.SymmetrisedGradientOperator">
 <em class="property"><span class="pre">class</span> </em><code class="sig-prename descclassname"><span class="pre">cil.optimisation.operators.</span></code><code class="sig-name descname"><span class="pre">SymmetrisedGradientOperator</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">domain_geometry</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bnd_cond</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'Neumann'</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/cil/optimisation/operators/SymmetrisedGradientOperator.html#SymmetrisedGradientOperator"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#cil.optimisation.operators.SymmetrisedGradientOperator" title="Permalink to this definition">#</a></dt>
-<dd><p>Symmetrized Gradient Operator:  E: V -&gt; W</p>
-<p>V : range of the Gradient Operator
-W : range of the Symmetrized Gradient</p>
-<p>Example (2D):</p>
-<div class="math notranslate nohighlight">
-\[ \begin{align}\begin{aligned}\begin{split}v = (v1, v2) \\\end{split}\\\begin{split}Ev = 0.5 * ( \nabla\cdot v + (\nabla\cdot c)^{T} ) \\\end{split}\\\begin{split}\begin{matrix}
-    \partial_{y} v1 &amp; 0.5 * (\partial_{x} v1 + \partial_{y} v2) \\
-    0.5 * (\partial_{x} v1 + \partial_{y} v2) &amp; \partial_{x} v2
-\end{matrix}\end{split}\end{aligned}\end{align} \]</div>
+<dd><p>The symmetrised gradient is the operator, <span class="math notranslate nohighlight">\(E\)</span>, defined by <span class="math notranslate nohighlight">\(E: V \rightarrow W\)</span> where <cite>V</cite> is <cite>BlockGeometry</cite> and  <cite>W</cite> is the range of the Symmetrised Gradient and</p>
+<blockquote>
+<div><div class="math notranslate nohighlight">
+\[\begin{split}E(v) = 0.5  ( \nabla v + (\nabla v)^{T} ) \\\end{split}\]</div>
+</div></blockquote>
+<p>In 2 dimensions, let <span class="math notranslate nohighlight">\(v(x,y)=(v_1(x,y),v_2(x,y))\)</span> which gives</p>
+<blockquote>
+<div><div class="math notranslate nohighlight">
+\[\begin{split}\nabla v =\left( \begin{matrix}
+    \partial_{x} v_1 &amp; \partial_x v_2\\
+    \partial_{y}v_1 &amp; \partial_y v_2
+\end{matrix}\right)\end{split}\]</div>
+</div></blockquote>
+<p>and thus</p>
+<blockquote>
+<div><div class="math notranslate nohighlight">
+\[\begin{split}E(v) = 0.5  ( \nabla v + (\nabla v)^{T} )
+=\left( \begin{matrix}
+    \partial_{x} v_1 &amp; 0.5  (\partial_{y} v_1 + \partial_{x} v_2) \\
+    0.5  (\partial_{x} v_1 + \partial_{y} v_2) &amp; \partial_{y} v_2
+\end{matrix}\right)\end{split}\]</div>
+</div></blockquote>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>domain_geometry</strong> (<cite>BlockGeometry</cite> with shape (2,1) or (3,1)) – Set up the domain of the function.</p></li>
+<li><p><strong>bnd_cond</strong> (str, optional, default <code class="code docutils literal notranslate"><span class="pre">Neumann</span></code>) – Boundary condition either <code class="code docutils literal notranslate"><span class="pre">Neumann</span></code> or <code class="code docutils literal notranslate"><span class="pre">Periodic</span></code></p></li>
+<li><p><strong>correlation</strong> (str, optional, default <code class="code docutils literal notranslate"><span class="pre">Channel</span></code>) – Correlation either <code class="code docutils literal notranslate"><span class="pre">SpaceChannel</span></code> or <code class="code docutils literal notranslate"><span class="pre">Channel</span></code></p></li>
+</ul>
+</dd>
+</dl>
 <dl class="py method">
 <dt id="cil.optimisation.operators.SymmetrisedGradientOperator.direct">
 <code class="sig-name descname"><span class="pre">direct</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">out</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/cil/optimisation/operators/SymmetrisedGradientOperator.html#SymmetrisedGradientOperator.direct"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#cil.optimisation.operators.SymmetrisedGradientOperator.direct" title="Permalink to this definition">#</a></dt>
-<dd><p>Returns E(v)</p>
+<dd><p>Returns <span class="math notranslate nohighlight">\(E(v) = 0.5 * ( \nabla v + (\nabla v)^{T} )\)</span></p>
+<p>x: BlockDataContainer
+out: BlockDataContainer, default None</p>
+<blockquote>
+<div><p>If out is not None the output of direct will be filled in out, otherwise a new object is instantiated and returned.</p>
+</div></blockquote>
 </dd></dl>
 
 <dl class="py method">
 <dt id="cil.optimisation.operators.SymmetrisedGradientOperator.adjoint">
 <code class="sig-name descname"><span class="pre">adjoint</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">out</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/cil/optimisation/operators/SymmetrisedGradientOperator.html#SymmetrisedGradientOperator.adjoint"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#cil.optimisation.operators.SymmetrisedGradientOperator.adjoint" title="Permalink to this definition">#</a></dt>
-<dd><p>returns the adjoint/inverse operation</p>
-<p>only available to linear operators</p>
+<dd><p>Returns the adjoint of the symmetrised gradient operator</p>
+<p>x: BlockDataContainer
+out: BlockDataContainer, default None</p>
+<blockquote>
+<div><p>If out is not None the output of adjoint will be filled in out, otherwise a new object is instantiated and returned.</p>
+</div></blockquote>
 </dd></dl>
 
 </dd></dl>
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index 5fd7c4f20b..8a62c9ce65 100644
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