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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
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<div class="title">average.h</div> </div>
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<a href="average_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// Copyright (c) 2011, Hauke Strasdat</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// Copyright (c) 2012, Steven Lovegrove</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">// Copyright (c) 2021, farm-ng, inc.</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">//</span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">// Use of this source code is governed by an MIT-style</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// license that can be found in the LICENSE file or at</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">// https://opensource.org/licenses/MIT.</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"></span> </div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">/// @file</span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">/// Calculation of biinvariant means.</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment"></span> </div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor">#pragma once</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span>  </div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="preprocessor">#include "<a class="code" href="isometry2_8h.html">sophus/lie/isometry2.h</a>"</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="preprocessor">#include "<a class="code" href="isometry3_8h.html">sophus/lie/isometry3.h</a>"</span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="preprocessor">#include "<a class="code" href="rotation2_8h.html">sophus/lie/rotation2.h</a>"</span></div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="preprocessor">#include "<a class="code" href="rotation3_8h.html">sophus/lie/rotation3.h</a>"</span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="preprocessor">#include "<a class="code" href="scaling_8h.html">sophus/lie/scaling.h</a>"</span></div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="preprocessor">#include "<a class="code" href="scaling__translation_8h.html">sophus/lie/scaling_translation.h</a>"</span></div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="preprocessor">#include "<a class="code" href="similarity2_8h.html">sophus/lie/similarity2.h</a>"</span></div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="preprocessor">#include "<a class="code" href="similarity3_8h.html">sophus/lie/similarity3.h</a>"</span></div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="preprocessor">#include "<a class="code" href="spiral__similarity2_8h.html">sophus/lie/spiral_similarity2.h</a>"</span></div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="preprocessor">#include "<a class="code" href="spiral__similarity3_8h.html">sophus/lie/spiral_similarity3.h</a>"</span></div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="preprocessor">#include "<a class="code" href="translation_8h.html">sophus/lie/translation.h</a>"</span></div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  </div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="preprocessor">#include <complex></span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  </div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="keyword">namespace </span><a class="code" href="namespacesophus.html">sophus</a> {</div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment"></span> </div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment">/// Calculates mean iteratively.</span></div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment">///</span></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment">/// Returns ``nullopt`` if it does not converge.</span></div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment">///</span></div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment"></span><span class="keyword">template</span> <concepts::Range TSequenceContainer></div>
<div class="line"><a name="l00035"></a><span class="lineno"><a class="line" href="namespacesophus.html#a37dc98a953aee6515a775d7524382874"> 35</a></span> <span class="keyword">auto</span> <a class="code" href="namespacesophus.html#a37dc98a953aee6515a775d7524382874">iterativeMean</a>(</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  TSequenceContainer <span class="keyword">const</span>& foo_from_bar_transforms, <span class="keywordtype">int</span> max_num_iterations)</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  -> std::optional<typename TSequenceContainer::value_type> {</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  <span class="keywordtype">size_t</span> <span class="keyword">const</span> k_matrix_dim = std::distance(</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  std::begin(foo_from_bar_transforms), std::end(foo_from_bar_transforms));</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  SOPHUS_ASSERT(k_matrix_dim >= 1, <span class="stringliteral">"kMatrixDim must be >= 1."</span>);</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  </div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  <span class="keyword">using</span> Group = <span class="keyword">typename</span> TSequenceContainer::value_type;</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  <span class="keyword">using</span> Scalar = <span class="keyword">typename</span> Group::Scalar;</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <span class="keyword">using</span> <a class="code" href="namespacesophus_1_1concepts.html#a4144508616d6bff3e6cca31364bd2026">Tangent</a> = Eigen::Vector<Scalar, Group::kDof>;</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  </div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  <span class="comment">// This implements the algorithm in the beginning of Sec. 4.2 in</span></div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  <span class="comment">// ftp://ftp-sop.inria.fr/epidaure/Publications/Arsigny/arsigny_rr_biinvariant_average.pdf.</span></div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  Group foo_from_average = *std::begin(foo_from_bar_transforms);</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  Scalar w = Scalar(1. / k_matrix_dim);</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < max_num_iterations; ++i) {</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <a class="code" href="namespacesophus_1_1concepts.html#a4144508616d6bff3e6cca31364bd2026">Tangent</a> <a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a>;</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a>.setZero();</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="keywordflow">for</span> (Group <span class="keyword">const</span>& foo_from_bar : foo_from_bar_transforms) {</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a> += w * (foo_from_average.inverse() * foo_from_bar).log();</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  }</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  Group foo_from_newaverage = foo_from_average * Group::exp(<a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a>);</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <span class="keywordflow">if</span> (((foo_from_newaverage.inverse() * foo_from_average).log())</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  .squaredNorm() < kEpsilon<Scalar>) {</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <span class="keywordflow">return</span> foo_from_newaverage;</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  }</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  </div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  foo_from_average = foo_from_newaverage;</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  }</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="comment">// LCOV_EXCL_START</span></div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="keywordflow">return</span> std::nullopt;</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="comment">// LCOV_EXCL_STOP</span></div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span> }</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  </div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="preprocessor">#ifdef DOXYGEN_SHOULD_SKIP_THIS</span><span class="comment"></span></div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span> <span class="comment">/// Mean implementation for any Lie group.</span></div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="comment"></span><span class="keyword">template</span> <<span class="keyword">class</span> SequenceContainer, <span class="keyword">class</span> Scalar></div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span> optional<typename SequenceContainer::value_type> <a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a>(</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  SequenceContainer <span class="keyword">const</span>& foo_Ts_bar);</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="preprocessor">#else</span></div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  </div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span> <span class="comment">// Mean implementation for Translation.</span></div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="keyword">template</span> <</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  <a class="code" href="namespacesophus_1_1concepts.html#afad436533a1ee7ad7cf99d1182765e97">concepts::Range</a> TSequenceContainer,</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="keywordtype">int</span> kPointDim = TSequenceContainer::value_type::kDof,</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <span class="keyword">class </span>TScalar = <span class="keyword">typename</span> TSequenceContainer::value_type::Scalar></div>
<div class="line"><a name="l00081"></a><span class="lineno"><a class="line" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274"> 81</a></span> <span class="keyword">auto</span> <a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a>(TSequenceContainer <span class="keyword">const</span>& foo_from_bar_transforms)</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  -> std::enable_if_t<</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  std::is_same<</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="keyword">typename</span> TSequenceContainer::value_type,</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <a class="code" href="classsophus_1_1_translation.html">Translation<TScalar, kPointDim></a> >::value,</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  std::optional<typename TSequenceContainer::value_type> > {</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="keywordtype">size_t</span> <span class="keyword">const</span> k_matrix_dim = std::distance(</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  std::begin(foo_from_bar_transforms), std::end(foo_from_bar_transforms));</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  SOPHUS_ASSERT(k_matrix_dim >= 1, <span class="stringliteral">"kMatrixDim must be >= 1."</span>);</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  </div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  Eigen::Vector<TScalar, kPointDim> <a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a>;</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  <a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a>.setZero();</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="keywordflow">for</span> (<a class="code" href="classsophus_1_1_translation.html">Translation<TScalar, kPointDim></a> <span class="keyword">const</span>& foo_from_bar :</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  foo_from_bar_transforms) {</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a> += foo_from_bar.params();</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  }</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  <span class="keywordflow">return</span> <a class="code" href="classsophus_1_1lie_1_1_group.html#ac94b6dfc9087ea289f5a2f3671713e8b">Translation<TScalar, kPointDim>::fromParams</a>(</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a> / TScalar(k_matrix_dim));</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span> }</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  </div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span> <span class="comment">// Mean implementation for Scaling.</span></div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span> <span class="keyword">template</span> <</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <a class="code" href="namespacesophus_1_1concepts.html#afad436533a1ee7ad7cf99d1182765e97">concepts::Range</a> TSequenceContainer,</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  <span class="keywordtype">int</span> kPointDim = TSequenceContainer::value_type::kDof,</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  <span class="keyword">class </span>TScalar = <span class="keyword">typename</span> TSequenceContainer::value_type::Scalar></div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span> <span class="keyword">auto</span> <a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a>(TSequenceContainer <span class="keyword">const</span>& foo_from_bar_transforms)</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  -> std::enable_if_t<</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  std::is_same<</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="keyword">typename</span> TSequenceContainer::value_type,</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  Scaling<TScalar, kPointDim> >::value,</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  std::optional<typename TSequenceContainer::value_type> > {</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="keywordtype">size_t</span> <span class="keyword">const</span> k_matrix_dim = std::distance(</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  std::begin(foo_from_bar_transforms), std::end(foo_from_bar_transforms));</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  SOPHUS_ASSERT(k_matrix_dim >= 1, <span class="stringliteral">"kMatrixDim must be >= 1."</span>);</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  </div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  Eigen::Array<TScalar, kPointDim, 1> <a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a>;</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a>.setZero();</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <span class="keywordflow">for</span> (Scaling<TScalar, kPointDim> <span class="keyword">const</span>& foo_from_bar :</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  foo_from_bar_transforms) {</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a> += foo_from_bar.params().array().log();</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  }</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  <span class="keywordflow">return</span> <a class="code" href="classsophus_1_1lie_1_1_group.html#ac94b6dfc9087ea289f5a2f3671713e8b">Scaling<TScalar, kPointDim>::fromParams</a>(</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  (<a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a> / TScalar(k_matrix_dim)).exp().matrix());</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span> }</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  </div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span> <span class="comment">// Mean implementation for SO(2).</span></div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span> <span class="keyword">template</span> <</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <a class="code" href="namespacesophus_1_1concepts.html#afad436533a1ee7ad7cf99d1182765e97">concepts::Range</a> TSequenceContainer,</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <span class="keyword">class </span>TScalar = <span class="keyword">typename</span> TSequenceContainer::value_type::Scalar></div>
<div class="line"><a name="l00130"></a><span class="lineno"><a class="line" href="namespacesophus.html#a55f68e15a2321fb8945a27579d9fa7fc"> 130</a></span> <span class="keyword">auto</span> <a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a>(TSequenceContainer <span class="keyword">const</span>& foo_from_bar_transforms)</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  -> std::enable_if_t<</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  std::is_same<</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <span class="keyword">typename</span> TSequenceContainer::value_type,</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <a class="code" href="classsophus_1_1_rotation2.html">Rotation2<TScalar></a> >::value,</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  std::optional<typename TSequenceContainer::value_type> > {</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  <span class="comment">// This implements rotational part of Proposition 12 from Sec. 6.2 of</span></div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="comment">// ftp://ftp-sop.inria.fr/epidaure/Publications/Arsigny/arsigny_rr_biinvariant_average.pdf.</span></div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <span class="keywordtype">size_t</span> <span class="keyword">const</span> k_matrix_dim = std::distance(</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  std::begin(foo_from_bar_transforms), std::end(foo_from_bar_transforms));</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  SOPHUS_ASSERT(k_matrix_dim >= 1, <span class="stringliteral">"kMatrixDim must be >= 1."</span>);</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <a class="code" href="classsophus_1_1_rotation2.html">Rotation2<TScalar></a> foo_from_average = *std::begin(foo_from_bar_transforms);</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  TScalar w = TScalar(1. / k_matrix_dim);</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  </div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  Eigen::Vector<TScalar, 1> <a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a>;</div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  <a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a>.setZero();</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <span class="keywordflow">for</span> (<a class="code" href="classsophus_1_1_rotation2.html">Rotation2<TScalar></a> <span class="keyword">const</span>& foo_from_bar : foo_from_bar_transforms) {</div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  <a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a> += w * (foo_from_average.<a class="code" href="classsophus_1_1lie_1_1_group.html#ae70c407d4462a6644721d494af1e1289">inverse</a>() * foo_from_bar).log();</div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  }</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  <span class="keywordflow">return</span> foo_from_average * <a class="code" href="classsophus_1_1lie_1_1_group.html#a20de1a3ff2580023d24b0c7cff45a4cd">Rotation2<TScalar>::exp</a>(<a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a>);</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span> }</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  </div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span> <span class="comment">// Mean implementation for RxSO(2).</span></div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span> <span class="keyword">template</span> <</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  <a class="code" href="namespacesophus_1_1concepts.html#afad436533a1ee7ad7cf99d1182765e97">concepts::Range</a> TSequenceContainer,</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  <span class="keyword">class </span>TScalar = <span class="keyword">typename</span> TSequenceContainer::value_type::Scalar></div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span> <span class="keyword">auto</span> <a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a>(TSequenceContainer <span class="keyword">const</span>& foo_from_bar_transforms)</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  -> std::enable_if_t<</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  std::is_same<</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  <span class="keyword">typename</span> TSequenceContainer::value_type,</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  SpiralSimilarity2<TScalar> >::value,</div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  std::optional<typename TSequenceContainer::value_type> > {</div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  <span class="keywordtype">size_t</span> <span class="keyword">const</span> k_matrix_dim = std::distance(</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  std::begin(foo_from_bar_transforms), std::end(foo_from_bar_transforms));</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  SOPHUS_ASSERT(k_matrix_dim >= 1, <span class="stringliteral">"kMatrixDim must be >= 1."</span>);</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  SpiralSimilarity2<TScalar> foo_from_average =</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  *std::begin(foo_from_bar_transforms);</div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  TScalar w = TScalar(1. / k_matrix_dim);</div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  </div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  Eigen::Vector2<TScalar> <a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a>(TScalar(0), TScalar(0));</div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  <span class="keywordflow">for</span> (SpiralSimilarity2<TScalar> <span class="keyword">const</span>& foo_from_bar :</div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  foo_from_bar_transforms) {</div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a> += w * (foo_from_average.inverse() * foo_from_bar).log();</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  }</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  <span class="keywordflow">return</span> foo_from_average * SpiralSimilarity2<TScalar>::exp(<a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a>);</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span> }</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  </div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span> <span class="keyword">namespace </span>details {</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span> <span class="keyword">template</span> <<span class="keyword">class</span> TScalar></div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span> <span class="keywordtype">void</span> getQuaternion(TScalar <span class="keyword">const</span>&);</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  </div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span> <span class="keyword">template</span> <<span class="keyword">class</span> TScalar></div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span> <span class="keyword">auto</span> getUnitQuaternion(Rotation3<TScalar> <span class="keyword">const</span>& r)</div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  -> Eigen::Vector<TScalar, 4> {</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  <span class="keywordflow">return</span> r.params().template head<4>();</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span> }</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  </div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span> <span class="keyword">template</span> <<span class="keyword">class</span> TScalar></div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span> <span class="keyword">auto</span> getUnitQuaternion(SpiralSimilarity3<TScalar> <span class="keyword">const</span>& s_r)</div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  -> Eigen::Vector<TScalar, 4> {</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  <span class="keywordflow">return</span> s_r.params().template head<4>().normalized();</div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span> }</div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  </div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span> <span class="keyword">template</span> <</div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  <a class="code" href="namespacesophus_1_1concepts.html#afad436533a1ee7ad7cf99d1182765e97">concepts::Range</a> TSequenceContainer,</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  <span class="keyword">class </span>TScalar = <span class="keyword">typename</span> TSequenceContainer::value_type::Scalar></div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span> <span class="keyword">auto</span> averageUnitQuaternion(TSequenceContainer <span class="keyword">const</span>& foo_from_bar_transforms)</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  -> Eigen::Vector<TScalar, 4> {</div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <span class="comment">// This: http://stackoverflow.com/a/27410865/1221742</span></div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <span class="keywordtype">size_t</span> <span class="keyword">const</span> k_matrix_dim = std::distance(</div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  std::begin(foo_from_bar_transforms), std::end(foo_from_bar_transforms));</div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  SOPHUS_ASSERT(k_matrix_dim >= 1, <span class="stringliteral">"kMatrixDim must be >= 1."</span>);</div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  Eigen::Matrix<TScalar, 4, Eigen::Dynamic> q(4, k_matrix_dim);</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  <span class="keywordtype">int</span> i = 0;</div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  TScalar w = TScalar(1. / k_matrix_dim);</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  <span class="keywordflow">for</span> (<span class="keyword">auto</span> <span class="keyword">const</span>& foo_from_bar : foo_from_bar_transforms) {</div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  q.col(i) = w * details::getUnitQuaternion(foo_from_bar);</div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  ++i;</div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  }</div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  </div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  Eigen::Matrix<TScalar, 4, 4> q_qt = q * q.transpose();</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  <span class="comment">// TODO: Figure out why we can't use SelfAdjointEigenSolver here.</span></div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  Eigen::EigenSolver<Eigen::Matrix<TScalar, 4, 4> > es(q_qt);</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  </div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  std::complex<TScalar> max_eigenvalue = es.eigenvalues()[0];</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  Eigen::Matrix<std::complex<TScalar>, 4, 1> max_eigenvector =</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  es.eigenvectors().col(0);</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  </div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i < 4; i++) {</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <span class="keywordflow">if</span> (std::norm(es.eigenvalues()[i]) > std::norm(max_eigenvalue)) {</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  max_eigenvalue = es.eigenvalues()[i];</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  max_eigenvector = es.eigenvectors().col(i);</div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  }</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  }</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  Eigen::Vector<TScalar, 4> quat;</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  quat << <span class="comment">//</span></div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  max_eigenvector[0].real(), <span class="comment">//</span></div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  max_eigenvector[1].real(), <span class="comment">//</span></div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  max_eigenvector[2].real(), <span class="comment">//</span></div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  max_eigenvector[3].real();</div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  <span class="keywordflow">return</span> quat;</div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span> }</div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span> } <span class="comment">// namespace details</span></div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  </div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span> <span class="comment">// Mean implementation for SO(3).</span></div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span> <span class="comment">//</span></div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span> <span class="comment">// TODO: Detect degenerated cases and return nullopt.</span></div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span> <span class="keyword">template</span> <</div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  <a class="code" href="namespacesophus_1_1concepts.html#afad436533a1ee7ad7cf99d1182765e97">concepts::Range</a> TSequenceContainer,</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  <span class="keyword">class </span>TScalar = <span class="keyword">typename</span> TSequenceContainer::value_type::Scalar></div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span> <span class="keyword">auto</span> <a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a>(TSequenceContainer <span class="keyword">const</span>& foo_from_bar_transforms)</div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  -> std::enable_if_t<</div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  std::is_same<</div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  <span class="keyword">typename</span> TSequenceContainer::value_type,</div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  Rotation3<TScalar> >::value,</div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  std::optional<typename TSequenceContainer::value_type> > {</div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  <span class="keywordflow">return</span> <a class="code" href="classsophus_1_1lie_1_1_group.html#ac94b6dfc9087ea289f5a2f3671713e8b">Rotation3<TScalar>::fromParams</a>(</div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  details::averageUnitQuaternion(foo_from_bar_transforms));</div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span> }</div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  </div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span> <span class="comment">// Mean implementation for R x SO(3).</span></div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span> <span class="keyword">template</span> <</div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  <a class="code" href="namespacesophus_1_1concepts.html#afad436533a1ee7ad7cf99d1182765e97">concepts::Range</a> TSequenceContainer,</div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  <span class="keyword">class </span>TScalar = <span class="keyword">typename</span> TSequenceContainer::value_type::Scalar></div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span> <span class="keyword">auto</span> <a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a>(TSequenceContainer <span class="keyword">const</span>& foo_from_bar_transforms)</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  -> std::enable_if_t<</div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  std::is_same<</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  <span class="keyword">typename</span> TSequenceContainer::value_type,</div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  SpiralSimilarity3<TScalar> >::value,</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  std::optional<typename TSequenceContainer::value_type> > {</div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  <span class="keywordtype">size_t</span> k_matrix_dim = std::distance(</div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  std::begin(foo_from_bar_transforms), std::end(foo_from_bar_transforms));</div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  </div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  SOPHUS_ASSERT(k_matrix_dim >= 1, <span class="stringliteral">"kMatrixDim must be >= 1."</span>);</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  TScalar scale_sum = TScalar(0);</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  <span class="keyword">using</span> std::exp;</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  <span class="keyword">using</span> std::log;</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  <span class="keywordflow">for</span> (SpiralSimilarity3<TScalar> <span class="keyword">const</span>& foo_from_bar :</div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  foo_from_bar_transforms) {</div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  scale_sum += log(foo_from_bar.scale());</div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  }</div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  <span class="keywordflow">return</span> SpiralSimilarity3<TScalar>(</div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  <a class="code" href="classsophus_1_1lie_1_1_group.html#ac94b6dfc9087ea289f5a2f3671713e8b">Rotation3<TScalar>::fromParams</a>(</div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  details::averageUnitQuaternion(foo_from_bar_transforms)),</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  exp(scale_sum / TScalar(k_matrix_dim)));</div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span> }</div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  </div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span> <span class="keyword">template</span> <</div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  <a class="code" href="namespacesophus_1_1concepts.html#afad436533a1ee7ad7cf99d1182765e97">concepts::Range</a> TSequenceContainer,</div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  <span class="keyword">class </span>TScalar = <span class="keyword">typename</span> TSequenceContainer::value_type::Scalar></div>
<div class="line"><a name="l00280"></a><span class="lineno"><a class="line" href="namespacesophus.html#a02f3591883d0c7f9de4885bb4ec3fbe6"> 280</a></span> <span class="keyword">auto</span> <a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a>(</div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  TSequenceContainer <span class="keyword">const</span>& foo_from_bar_transforms,</div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  <span class="keywordtype">int</span> max_num_iterations = 20)</div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  -> std::enable_if_t<</div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  std::is_same<</div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  <span class="keyword">typename</span> TSequenceContainer::value_type,</div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  <a class="code" href="classsophus_1_1_isometry2.html">Isometry2<TScalar></a> >::value,</div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  std::optional<typename TSequenceContainer::value_type> > {</div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  <span class="comment">// TODO: Implement Proposition 12 from Sec. 6.2 of</span></div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  <span class="comment">// ftp://ftp-sop.inria.fr/epidaure/Publications/Arsigny/arsigny_rr_biinvariant_average.pdf.</span></div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  <span class="keywordflow">return</span> <a class="code" href="namespacesophus.html#a37dc98a953aee6515a775d7524382874">iterativeMean</a>(foo_from_bar_transforms, max_num_iterations);</div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span> }</div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  </div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span> <span class="keyword">template</span> <</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  <a class="code" href="namespacesophus_1_1concepts.html#afad436533a1ee7ad7cf99d1182765e97">concepts::Range</a> TSequenceContainer,</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  <span class="keyword">class </span>TScalar = <span class="keyword">typename</span> TSequenceContainer::value_type::Scalar></div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span> <span class="keyword">auto</span> <a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a>(</div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  TSequenceContainer <span class="keyword">const</span>& foo_from_bar_transforms,</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  <span class="keywordtype">int</span> max_num_iterations = 20)</div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  -> std::enable_if_t<</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  std::is_same<</div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  <span class="keyword">typename</span> TSequenceContainer::value_type,</div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  Similarity2<TScalar> >::value,</div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  std::optional<typename TSequenceContainer::value_type> > {</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  <span class="keywordflow">return</span> <a class="code" href="namespacesophus.html#a37dc98a953aee6515a775d7524382874">iterativeMean</a>(foo_from_bar_transforms, max_num_iterations);</div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span> }</div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  </div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span> <span class="keyword">template</span> <</div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  <a class="code" href="namespacesophus_1_1concepts.html#afad436533a1ee7ad7cf99d1182765e97">concepts::Range</a> TSequenceContainer,</div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  <span class="keyword">class </span>TScalar = <span class="keyword">typename</span> TSequenceContainer::value_type::Scalar></div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span> <span class="keyword">auto</span> <a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a>(</div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  TSequenceContainer <span class="keyword">const</span>& foo_from_bar_transforms,</div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  <span class="keywordtype">int</span> max_num_iterations = 20)</div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  -> std::enable_if_t<</div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  std::is_same<</div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  <span class="keyword">typename</span> TSequenceContainer::value_type,</div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  Isometry3<TScalar> >::value,</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  std::optional<typename TSequenceContainer::value_type> > {</div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  <span class="keywordflow">return</span> <a class="code" href="namespacesophus.html#a37dc98a953aee6515a775d7524382874">iterativeMean</a>(foo_from_bar_transforms, max_num_iterations);</div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span> }</div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  </div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span> <span class="keyword">template</span> <</div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  <a class="code" href="namespacesophus_1_1concepts.html#afad436533a1ee7ad7cf99d1182765e97">concepts::Range</a> TSequenceContainer,</div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  <span class="keyword">class </span>TScalar = <span class="keyword">typename</span> TSequenceContainer::value_type::Scalar></div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span> <span class="keyword">auto</span> <a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a>(</div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  TSequenceContainer <span class="keyword">const</span>& foo_from_bar_transforms,</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  <span class="keywordtype">int</span> max_num_iterations = 20)</div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  -> std::enable_if_t<</div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  std::is_same<</div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  <span class="keyword">typename</span> TSequenceContainer::value_type,</div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  Similarity3<TScalar> >::value,</div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  std::optional<typename TSequenceContainer::value_type> > {</div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  <span class="keywordflow">return</span> <a class="code" href="namespacesophus.html#a37dc98a953aee6515a775d7524382874">iterativeMean</a>(foo_from_bar_transforms, max_num_iterations);</div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span> }</div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  </div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span> <span class="keyword">template</span> <</div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  <a class="code" href="namespacesophus_1_1concepts.html#afad436533a1ee7ad7cf99d1182765e97">concepts::Range</a> TSequenceContainer,</div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  <span class="keywordtype">int</span> kPointDim = TSequenceContainer::value_type::kPointDim,</div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  <span class="keyword">class </span>TScalar = <span class="keyword">typename</span> TSequenceContainer::value_type::Scalar></div>
<div class="line"><a name="l00339"></a><span class="lineno"><a class="line" href="namespacesophus.html#aa46bfd15e02fa50d5adb6f60ef5a82c1"> 339</a></span> <span class="keyword">auto</span> <a class="code" href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">average</a>(</div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  TSequenceContainer <span class="keyword">const</span>& foo_from_bar_transforms,</div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  <span class="keywordtype">int</span> max_num_iterations = 20)</div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  -> std::enable_if_t<</div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  std::is_same<</div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  <span class="keyword">typename</span> TSequenceContainer::value_type,</div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  <a class="code" href="classsophus_1_1_scaling_translation.html">ScalingTranslation<TScalar, kPointDim></a> >::value,</div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  std::optional<typename TSequenceContainer::value_type> > {</div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  <span class="keywordflow">return</span> <a class="code" href="namespacesophus.html#a37dc98a953aee6515a775d7524382874">iterativeMean</a>(foo_from_bar_transforms, max_num_iterations);</div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span> }</div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  </div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span> <span class="preprocessor">#endif </span><span class="comment">// DOXYGEN_SHOULD_SKIP_THIS</span></div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  </div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span> } <span class="comment">// namespace sophus</span></div>
<div class="ttc" id="aclasssophus_1_1_isometry2_html"><div class="ttname"><a href="classsophus_1_1_isometry2.html">sophus::Isometry2</a></div><div class="ttdef"><b>Definition:</b> isometry2.h:26</div></div>
<div class="ttc" id="aclasssophus_1_1_rotation2_html"><div class="ttname"><a href="classsophus_1_1_rotation2.html">sophus::Rotation2</a></div><div class="ttdef"><b>Definition:</b> rotation2.h:20</div></div>
<div class="ttc" id="aclasssophus_1_1_scaling_translation_html"><div class="ttname"><a href="classsophus_1_1_scaling_translation.html">sophus::ScalingTranslation</a></div><div class="ttdef"><b>Definition:</b> scaling_translation.h:39</div></div>
<div class="ttc" id="aclasssophus_1_1_translation_html"><div class="ttname"><a href="classsophus_1_1_translation.html">sophus::Translation</a></div><div class="ttdef"><b>Definition:</b> translation.h:38</div></div>
<div class="ttc" id="aclasssophus_1_1lie_1_1_group_html_a20de1a3ff2580023d24b0c7cff45a4cd"><div class="ttname"><a href="classsophus_1_1lie_1_1_group.html#a20de1a3ff2580023d24b0c7cff45a4cd">sophus::lie::Group< Rotation2, TScalar, lie::Rotation2Impl >::exp</a></div><div class="ttdeci">static auto exp(Tangent const &tangent) -> Derived</div><div class="ttdef"><b>Definition:</b> lie_group.h:93</div></div>
<div class="ttc" id="aclasssophus_1_1lie_1_1_group_html_ac94b6dfc9087ea289f5a2f3671713e8b"><div class="ttname"><a href="classsophus_1_1lie_1_1_group.html#ac94b6dfc9087ea289f5a2f3671713e8b">sophus::lie::Group< lie::TranslationWithDim< kDim >::template Group, TScalar, lie::WithDimAndSubgroup< kDim, lie::IdentityWithDim< kDim >::template Impl >::template SemiDirectProduct >::fromParams</a></div><div class="ttdeci">static auto fromParams(Params const &params) -> Derived</div><div class="ttdef"><b>Definition:</b> lie_group.h:79</div></div>
<div class="ttc" id="aclasssophus_1_1lie_1_1_group_html_ae70c407d4462a6644721d494af1e1289"><div class="ttname"><a href="classsophus_1_1lie_1_1_group.html#ae70c407d4462a6644721d494af1e1289">sophus::lie::Group::inverse</a></div><div class="ttdeci">auto inverse() const -> Derived</div><div class="ttdef"><b>Definition:</b> lie_group.h:127</div></div>
<div class="ttc" id="aisometry2_8h_html"><div class="ttname"><a href="isometry2_8h.html">isometry2.h</a></div></div>
<div class="ttc" id="aisometry3_8h_html"><div class="ttname"><a href="isometry3_8h.html">isometry3.h</a></div></div>
<div class="ttc" id="anamespacesophus_1_1concepts_html_a4144508616d6bff3e6cca31364bd2026"><div class="ttname"><a href="namespacesophus_1_1concepts.html#a4144508616d6bff3e6cca31364bd2026">sophus::concepts::Tangent</a></div><div class="ttdeci">concept Tangent</div><div class="ttdef"><b>Definition:</b> params.h:34</div></div>
<div class="ttc" id="anamespacesophus_1_1concepts_html_afad436533a1ee7ad7cf99d1182765e97"><div class="ttname"><a href="namespacesophus_1_1concepts.html#afad436533a1ee7ad7cf99d1182765e97">sophus::concepts::Range</a></div><div class="ttdeci">concept Range</div><div class="ttdef"><b>Definition:</b> utils.h:42</div></div>
<div class="ttc" id="anamespacesophus_html"><div class="ttname"><a href="namespacesophus.html">sophus</a></div><div class="ttdoc">Image MutImage, owning images types.</div><div class="ttdef"><b>Definition:</b> num_diff.h:20</div></div>
<div class="ttc" id="anamespacesophus_html_a37dc98a953aee6515a775d7524382874"><div class="ttname"><a href="namespacesophus.html#a37dc98a953aee6515a775d7524382874">sophus::iterativeMean</a></div><div class="ttdeci">auto iterativeMean(TSequenceContainer const &foo_from_bar_transforms, int max_num_iterations) -> std::optional< typename TSequenceContainer::value_type ></div><div class="ttdoc">Calculates mean iteratively.</div><div class="ttdef"><b>Definition:</b> average.h:35</div></div>
<div class="ttc" id="anamespacesophus_html_ae8b45afda85b09978ad78e77cd442274"><div class="ttname"><a href="namespacesophus.html#ae8b45afda85b09978ad78e77cd442274">sophus::average</a></div><div class="ttdeci">auto average(TSequenceContainer const &foo_from_bar_transforms) -> std::enable_if_t< std::is_same< typename TSequenceContainer::value_type, Translation< TScalar, kPointDim > >::value, std::optional< typename TSequenceContainer::value_type > ></div><div class="ttdef"><b>Definition:</b> average.h:81</div></div>
<div class="ttc" id="arotation2_8h_html"><div class="ttname"><a href="rotation2_8h.html">rotation2.h</a></div></div>
<div class="ttc" id="arotation3_8h_html"><div class="ttname"><a href="rotation3_8h.html">rotation3.h</a></div></div>
<div class="ttc" id="ascaling_8h_html"><div class="ttname"><a href="scaling_8h.html">scaling.h</a></div></div>
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