update to v1.0.9

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diff --git a/.buildinfo b/.buildinfo
@@ -1,4 +1,4 @@
 # Sphinx build info version 1
 # This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
-config: 05484e4b16d6e2f115fa5a1eeed7ab5d
+config: 95db85924c6a491dc9e425285e7f1063
 tags: 645f666f9bcd5a90fca523b33c5a78b7
diff --git a/_modules/escnn/group/directproduct.html b/_modules/escnn/group/directproduct.html
@@ -3,7 +3,7 @@
 <head>
  <meta charset="utf-8" />
  <meta name="viewport" content="width=device-width, initial-scale=1.0" />
- <title>escnn.group.directproduct &mdash; escnn 1.0.7 documentation</title>
+ <title>escnn.group.directproduct &mdash; escnn 1.0.9 documentation</title>
  <link rel="stylesheet" href="../../../_static/pygments.css" type="text/css" />
  <link rel="stylesheet" href="../../../_static/css/theme.css" type="text/css" />
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@@ -28,7 +28,7 @@
  <a href="../../../index.html" class="icon icon-home"> escnn
  </a>
  <div class="version">
- 1.0.7
+ 1.0.9
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 <div role="search">
  <form id="rtd-search-form" class="wy-form" action="../../../search.html" method="get">

diff --git a/_modules/escnn/group/doublegroup.html b/_modules/escnn/group/doublegroup.html
@@ -3,7 +3,7 @@
 <head>
  <meta charset="utf-8" />
  <meta name="viewport" content="width=device-width, initial-scale=1.0" />
- <title>escnn.group.doublegroup &mdash; escnn 1.0.7 documentation</title>
+ <title>escnn.group.doublegroup &mdash; escnn 1.0.9 documentation</title>
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@@ -28,7 +28,7 @@
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  <div class="version">
- 1.0.7
+ 1.0.9
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 <div role="search">
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diff --git a/_modules/escnn/group/group.html b/_modules/escnn/group/group.html
@@ -3,7 +3,7 @@
 <head>
  <meta charset="utf-8" />
  <meta name="viewport" content="width=device-width, initial-scale=1.0" />
- <title>escnn.group.group &mdash; escnn 1.0.7 documentation</title>
+ <title>escnn.group.group &mdash; escnn 1.0.9 documentation</title>
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@@ -28,7 +28,7 @@
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- 1.0.7
+ 1.0.9
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diff --git a/_modules/escnn/group/groups/cyclicgroup.html b/_modules/escnn/group/groups/cyclicgroup.html
@@ -3,7 +3,7 @@
 <head>
  <meta charset="utf-8" />
  <meta name="viewport" content="width=device-width, initial-scale=1.0" />
- <title>escnn.group.groups.cyclicgroup &mdash; escnn 1.0.7 documentation</title>
+ <title>escnn.group.groups.cyclicgroup &mdash; escnn 1.0.9 documentation</title>
  <link rel="stylesheet" href="../../../../_static/pygments.css" type="text/css" />
  <link rel="stylesheet" href="../../../../_static/css/theme.css" type="text/css" />
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@@ -28,7 +28,7 @@
  <a href="../../../../index.html" class="icon icon-home"> escnn
  </a>
  <div class="version">
- 1.0.7
+ 1.0.9
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 <div role="search">
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@@ -161,15 +161,21 @@ <h1>Source code for escnn.group.groups.cyclicgroup</h1><div class="highlight"><p
 <span class="sd"> </span>
 <span class="sd"> Args:</span>
 <span class="sd"> N (int): order of the group</span>
-<span class="sd"> </span>
+
+<span class="sd"> Attributes:</span>
+<span class="sd"> ~.rotation_order (int): the number of rotations, i.e. the order of the group</span>
+
 <span class="sd"> &quot;&quot;&quot;</span>
 
  <span class="k">assert</span> <span class="p">(</span><span class="nb">isinstance</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="ow">and</span> <span class="n">N</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">),</span> <span class="n">N</span>
 
  <span class="nb">super</span><span class="p">(</span><span class="n">CyclicGroup</span><span class="p">,</span> <span class="bp">self</span><span class="p">)</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="s2">&quot;C</span><span class="si">%d</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">N</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">True</span><span class="p">)</span>
 
  <span class="bp">self</span><span class="o">.</span><span class="n">N</span> <span class="o">=</span> <span class="n">N</span>
-
+
+ <span class="c1"># int: for consistency with the DihedralGroup, store the number of rotations also in this attribute</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">rotation_order</span> <span class="o">=</span> <span class="n">N</span>
+
  <span class="bp">self</span><span class="o">.</span><span class="n">_elements</span> <span class="o">=</span> <span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">element</span><span class="p">(</span><span class="n">i</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="n">N</span><span class="p">)]</span>
  <span class="c1"># self._elements_names = [&#39;e&#39;] + [&#39;r%d&#39; % i for i in range(1, N)]</span>
 

diff --git a/_modules/escnn/group/groups/dihedralgroup.html b/_modules/escnn/group/groups/dihedralgroup.html
@@ -3,7 +3,7 @@
 <head>
  <meta charset="utf-8" />
  <meta name="viewport" content="width=device-width, initial-scale=1.0" />
- <title>escnn.group.groups.dihedralgroup &mdash; escnn 1.0.7 documentation</title>
+ <title>escnn.group.groups.dihedralgroup &mdash; escnn 1.0.9 documentation</title>
  <link rel="stylesheet" href="../../../../_static/pygments.css" type="text/css" />
  <link rel="stylesheet" href="../../../../_static/css/theme.css" type="text/css" />
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@@ -28,7 +28,7 @@
  <a href="../../../../index.html" class="icon icon-home"> escnn
  </a>
  <div class="version">
- 1.0.7
+ 1.0.9
  </div>
 <div role="search">
  <form id="rtd-search-form" class="wy-form" action="../../../../search.html" method="get">

diff --git a/_modules/escnn/group/groups/factory.html b/_modules/escnn/group/groups/factory.html
@@ -3,7 +3,7 @@
 <head>
  <meta charset="utf-8" />
  <meta name="viewport" content="width=device-width, initial-scale=1.0" />
- <title>escnn.group.groups.factory &mdash; escnn 1.0.7 documentation</title>
+ <title>escnn.group.groups.factory &mdash; escnn 1.0.9 documentation</title>
  <link rel="stylesheet" href="../../../../_static/pygments.css" type="text/css" />
  <link rel="stylesheet" href="../../../../_static/css/theme.css" type="text/css" />
  <link rel="stylesheet" href="../../../../_static/custom.css" type="text/css" />
@@ -28,7 +28,7 @@
  <a href="../../../../index.html" class="icon icon-home"> escnn
  </a>
  <div class="version">
- 1.0.7
+ 1.0.9
  </div>
 <div role="search">
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@@ -134,6 +134,7 @@ <h1>Source code for escnn.group.groups.factory</h1><div class="highlight"><pre>
  <span class="s2">&quot;o2_group&quot;</span><span class="p">,</span>
  <span class="s2">&quot;so3_group&quot;</span><span class="p">,</span>
  <span class="s2">&quot;o3_group&quot;</span><span class="p">,</span>
+ <span class="s2">&quot;klein4_group&quot;</span><span class="p">,</span>
  <span class="s2">&quot;ico_group&quot;</span><span class="p">,</span>
  <span class="s2">&quot;octa_group&quot;</span><span class="p">,</span>
  <span class="s2">&quot;full_ico_group&quot;</span><span class="p">,</span>
@@ -288,6 +289,27 @@ <h1>Source code for escnn.group.groups.factory</h1><div class="highlight"><pre>
  <span class="k">return</span> <span class="n">O3</span><span class="o">.</span><span class="n">_generator</span><span class="p">(</span><span class="n">maximum_frequency</span><span class="p">)</span></div>
 
 
+<div class="viewcode-block" id="klein4_group"><a class="viewcode-back" href="../../../../api/escnn.group.html#escnn.group.klein4_group">[docs]</a><span class="k">def</span> <span class="nf">klein4_group</span><span class="p">():</span>
+ <span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
+
+<span class="sd"> Builds the group :math:`K_4 = C_2 \times C_2`. This group is most commonly associated with the symmetries of a</span>
+<span class="sd"> rectangle. I.e. a group generated by two perpendicular reflection and a rotation of 180 degrees.</span>
+<span class="sd"> The returned group instance has an additional 2D representation named ``&quot;rectangle&quot;``.</span>
+
+<span class="sd"> Returns:</span>
+<span class="sd"> the group :math:`K_4`</span>
+<span class="sd"> &quot;&quot;&quot;</span>
+ <span class="n">c2</span> <span class="o">=</span> <span class="n">cyclic_group</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
+ <span class="n">K4</span> <span class="o">=</span> <span class="n">direct_product</span><span class="p">(</span><span class="n">c2</span><span class="p">,</span> <span class="n">c2</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s1">&#39;Klein4&#39;</span><span class="p">)</span>
+ <span class="c1"># Klein4 group is mostly associated with the symmetries of the rectangle (2 perpendicular reflections (gx, gy) and a</span>
+ <span class="c1"># 180 deg rotation (gx · gy) in 2D space. We add this representation, constructed from the irreps of the group.</span>
+ <span class="c1"># rep2d_rectangle(e) = [[1, 0], [0, 1]], rep2d_rectangle(gx) = [[-1, 0], [0, 1]],</span>
+ <span class="c1"># rep2d_rectangle(gy) = [[1, 0], [0, -1]] rep2d_rectangle(gx · gy) = [[-1, 0], [0, -1]]</span>
+ <span class="n">rep2d_rectangle</span> <span class="o">=</span> <span class="n">K4</span><span class="o">.</span><span class="n">irrep</span><span class="p">((</span><span class="mi">1</span><span class="p">,),</span> <span class="p">(</span><span class="mi">0</span><span class="p">,))</span> <span class="o">+</span> <span class="n">K4</span><span class="o">.</span><span class="n">irrep</span><span class="p">((</span><span class="mi">0</span><span class="p">,),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,))</span>
+ <span class="n">K4</span><span class="o">.</span><span class="n">representations</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">rectangle</span><span class="o">=</span><span class="n">rep2d_rectangle</span><span class="p">)</span>
+ <span class="k">return</span> <span class="n">K4</span></div>
+
+
 <div class="viewcode-block" id="ico_group"><a class="viewcode-back" href="../../../../api/escnn.group.html#escnn.group.ico_group">[docs]</a><span class="k">def</span> <span class="nf">ico_group</span><span class="p">():</span>
  <span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 
@@ -314,7 +336,7 @@ <h1>Source code for escnn.group.groups.factory</h1><div class="highlight"><pre>
  <span class="k">return</span> <span class="n">direct_product</span><span class="p">(</span><span class="n">c2</span><span class="p">,</span> <span class="n">ico</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s1">&#39;FullIcosahedral&#39;</span><span class="p">)</span></div>
 
 
-<span class="k">def</span> <span class="nf">octa_group</span><span class="p">():</span>
+<div class="viewcode-block" id="octa_group"><a class="viewcode-back" href="../../../../api/escnn.group.html#escnn.group.octa_group">[docs]</a><span class="k">def</span> <span class="nf">octa_group</span><span class="p">():</span>
  <span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 
 <span class="sd"> Builds the group :math:`O`, i.e. the group of symmetries of the cube or octahedron</span>
@@ -323,10 +345,10 @@ <h1>Source code for escnn.group.groups.factory</h1><div class="highlight"><pre>
 <span class="sd"> the group :math:`O`</span>
 
 <span class="sd"> &quot;&quot;&quot;</span>
- <span class="k">return</span> <span class="n">Octahedral</span><span class="o">.</span><span class="n">_generator</span><span class="p">()</span>
+ <span class="k">return</span> <span class="n">Octahedral</span><span class="o">.</span><span class="n">_generator</span><span class="p">()</span></div>
 
 
-<span class="k">def</span> <span class="nf">full_octa_group</span><span class="p">():</span>
+<div class="viewcode-block" id="full_octa_group"><a class="viewcode-back" href="../../../../api/escnn.group.html#escnn.group.full_octa_group">[docs]</a><span class="k">def</span> <span class="nf">full_octa_group</span><span class="p">():</span>
  <span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 
 <span class="sd"> Builds the group :math:`O_h = C_2 \times O`, i.e. the group of all symmetries of the cube or octahedron</span>
@@ -337,7 +359,7 @@ <h1>Source code for escnn.group.groups.factory</h1><div class="highlight"><pre>
 <span class="sd"> &quot;&quot;&quot;</span>
  <span class="n">octa</span> <span class="o">=</span> <span class="n">octa_group</span><span class="p">()</span>
  <span class="n">c2</span> <span class="o">=</span> <span class="n">cyclic_group</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
- <span class="k">return</span> <span class="n">direct_product</span><span class="p">(</span><span class="n">c2</span><span class="p">,</span> <span class="n">octa</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s1">&#39;FullOctahedral&#39;</span><span class="p">)</span>
+ <span class="k">return</span> <span class="n">direct_product</span><span class="p">(</span><span class="n">c2</span><span class="p">,</span> <span class="n">octa</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s1">&#39;FullOctahedral&#39;</span><span class="p">)</span></div>
 
 
 <div class="viewcode-block" id="full_cylinder_group"><a class="viewcode-back" href="../../../../api/escnn.group.html#escnn.group.full_cylinder_group">[docs]</a><span class="k">def</span> <span class="nf">full_cylinder_group</span><span class="p">(</span><span class="n">maximum_frequency</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">3</span><span class="p">):</span>
@@ -445,6 +467,9 @@ <h1>Source code for escnn.group.groups.factory</h1><div class="highlight"><pre>
 <span class="sd"> the group :math:`C_2 \times C_n`</span>
 
 <span class="sd"> &quot;&quot;&quot;</span>
+ <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
+ <span class="k">return</span> <span class="n">klein4_group</span><span class="p">()</span>
+
  <span class="n">cn</span> <span class="o">=</span> <span class="n">cyclic_group</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
  <span class="n">c2</span> <span class="o">=</span> <span class="n">cyclic_group</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>