<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
<meta http-equiv="X-UA-Compatible" content="IE=9"/>
<meta name="generator" content="Doxygen 1.8.5"/>
<title>Eigen: Umeyama.h Source File</title>
<link href="tabs.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="jquery.js"></script>
<script type="text/javascript" src="dynsections.js"></script>
<link href="navtree.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="resize.js"></script>
<script type="text/javascript" src="navtree.js"></script>
<script type="text/javascript">
$(document).ready(initResizable);
$(window).load(resizeHeight);
</script>
<link href="search/search.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="search/search.js"></script>
<script type="text/javascript">
$(document).ready(function() { searchBox.OnSelectItem(0); });
</script>
<link href="doxygen.css" rel="stylesheet" type="text/css" />
<link href="eigendoxy.css" rel="stylesheet" type="text/css">
<!-- -->
<script type="text/javascript" src="eigen_navtree_hacks.js"></script>
<!-- <script type="text/javascript"> -->
<!-- </script> -->
</head>
<body>
<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
<!-- <a name="top"></a> -->
<div id="titlearea">
<table cellspacing="0" cellpadding="0">
<tbody>
<tr style="height: 56px;">
<td id="projectlogo"><img alt="Logo" src="Eigen_Silly_Professor_64x64.png"/></td>
<td style="padding-left: 0.5em;">
<div id="projectname"><a href="http://eigen.tuxfamily.org">Eigen</a>
 <span id="projectnumber">3.2.0</span>
</div>
</td>
<td> <div id="MSearchBox" class="MSearchBoxInactive">
<span class="left">
<img id="MSearchSelect" src="search/mag_sel.png"
onmouseover="return searchBox.OnSearchSelectShow()"
onmouseout="return searchBox.OnSearchSelectHide()"
alt=""/>
<input type="text" id="MSearchField" value="Search" accesskey="S"
onfocus="searchBox.OnSearchFieldFocus(true)"
onblur="searchBox.OnSearchFieldFocus(false)"
onkeyup="searchBox.OnSearchFieldChange(event)"/>
</span><span class="right">
<a id="MSearchClose" href="javascript:searchBox.CloseResultsWindow()"><img id="MSearchCloseImg" border="0" src="search/close.png" alt=""/></a>
</span>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<!-- end header part -->
<!-- Generated by Doxygen 1.8.5 -->
<script type="text/javascript">
var searchBox = new SearchBox("searchBox", "search",false,'Search');
</script>
</div><!-- top -->
<div id="side-nav" class="ui-resizable side-nav-resizable">
<div id="nav-tree">
<div id="nav-tree-contents">
<div id="nav-sync" class="sync"></div>
</div>
</div>
<div id="splitbar" style="-moz-user-select:none;"
class="ui-resizable-handle">
</div>
</div>
<script type="text/javascript">
$(document).ready(function(){initNavTree('Umeyama_8h_source.html','');});
</script>
<div id="doc-content">
<!-- window showing the filter options -->
<div id="MSearchSelectWindow"
onmouseover="return searchBox.OnSearchSelectShow()"
onmouseout="return searchBox.OnSearchSelectHide()"
onkeydown="return searchBox.OnSearchSelectKey(event)">
<a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(0)"><span class="SelectionMark"> </span>All</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(1)"><span class="SelectionMark"> </span>Classes</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(2)"><span class="SelectionMark"> </span>Namespaces</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(3)"><span class="SelectionMark"> </span>Functions</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(4)"><span class="SelectionMark"> </span>Variables</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(5)"><span class="SelectionMark"> </span>Typedefs</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(6)"><span class="SelectionMark"> </span>Enumerations</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(7)"><span class="SelectionMark"> </span>Enumerator</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(8)"><span class="SelectionMark"> </span>Friends</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(9)"><span class="SelectionMark"> </span>Groups</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(10)"><span class="SelectionMark"> </span>Pages</a></div>
<!-- iframe showing the search results (closed by default) -->
<div id="MSearchResultsWindow">
<iframe src="javascript:void(0)" frameborder="0"
name="MSearchResults" id="MSearchResults">
</iframe>
</div>
<div class="header">
<div class="headertitle">
<div class="title">Umeyama.h</div> </div>
</div><!--header-->
<div class="contents">
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// Copyright (C) 2009 Hauke Heibel <hauke.heibel@gmail.com></span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> </div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="preprocessor">#ifndef EIGEN_UMEYAMA_H</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_UMEYAMA_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment">// This file requires the user to include </span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment">// * Eigen/Core</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment">// * Eigen/LU </span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment">// * Eigen/SVD</span></div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment">// * Eigen/Array</span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> </div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="keyword">namespace </span>Eigen { </div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> </div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="preprocessor">#ifndef EIGEN_PARSED_BY_DOXYGEN</span></div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="comment">// These helpers are required since it allows to use mixed types as parameters</span></div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment">// for the Umeyama. The problem with mixed parameters is that the return type</span></div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment">// cannot trivially be deduced when float and double types are mixed.</span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="keyword">namespace </span>internal {</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="comment">// Compile time return type deduction for different MatrixBase types.</span></div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment">// Different means here different alignment and parameters but the same underlying</span></div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment">// real scalar type.</span></div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> OtherMatrixType></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="keyword">struct </span>umeyama_transform_matrix_type</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> {</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  MinRowsAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(MatrixType::RowsAtCompileTime, OtherMatrixType::RowsAtCompileTime),</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> </div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <span class="comment">// When possible we want to choose some small fixed size value since the result</span></div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  <span class="comment">// is likely to fit on the stack. So here, EIGEN_SIZE_MIN_PREFER_DYNAMIC is not what we want.</span></div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  HomogeneousDimension = int(MinRowsAtCompileTime) == <a class="code" href="namespaceEigen.html#adc9da5be31bdce40c25a92c27999c0e3">Dynamic</a> ? <a class="code" href="namespaceEigen.html#adc9da5be31bdce40c25a92c27999c0e3">Dynamic</a> : int(MinRowsAtCompileTime)+1</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</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">typedef</span> Matrix<typename traits<MatrixType>::Scalar,</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  HomogeneousDimension,</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  HomogeneousDimension,</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <a class="code" href="group__enums.html#gga0c5bde183ecefe103f70b49ad9740bcda02a97bb4792f98916a1156a521fa9813">AutoAlign</a> | (traits<MatrixType>::Flags & <a class="code" href="group__flags.html#ga7bd49e7b260e869e10fb9dc4fd081a85">RowMajorBit</a> ? <a class="code" href="group__enums.html#gga0c5bde183ecefe103f70b49ad9740bcda1e16fa1b92ed7a058cd4ce7a9a0db044">RowMajor</a> : <a class="code" href="group__enums.html#gga0c5bde183ecefe103f70b49ad9740bcdac86184b0e3be936fbfd20249a057a0bf">ColMajor</a>),</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  HomogeneousDimension,</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  HomogeneousDimension</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  > type;</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> };</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> </div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> }</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span> </div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Derived, <span class="keyword">typename</span> OtherDerived></div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span> <span class="keyword">typename</span> internal::umeyama_transform_matrix_type<Derived, OtherDerived>::type</div>
<div class="line"><a name="l00095"></a><span class="lineno"><a class="line" href="group__Geometry__Module.html#gab3f5a82a24490b936f8694cf8fef8e60"> 95</a></span> <a class="code" href="group__Geometry__Module.html#gab3f5a82a24490b936f8694cf8fef8e60">umeyama</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase<Derived></a>& src, <span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase<OtherDerived></a>& dst, <span class="keywordtype">bool</span> with_scaling = <span class="keyword">true</span>)</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="keyword">typedef</span> <span class="keyword">typename</span> internal::umeyama_transform_matrix_type<Derived, OtherDerived>::type TransformationMatrixType;</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::traits<TransformationMatrixType>::Scalar Scalar;</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="structEigen_1_1NumTraits.html">NumTraits<Scalar>::Real</a> RealScalar;</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Derived::Index Index;</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span> </div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  EIGEN_STATIC_ASSERT(!<a class="code" href="structEigen_1_1NumTraits.html">NumTraits<Scalar>::IsComplex</a>, NUMERIC_TYPE_MUST_BE_REAL)</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  EIGEN_STATIC_ASSERT((internal::is_same<Scalar, <span class="keyword">typename</span> internal::traits<OtherDerived>::Scalar>::value),</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span> </div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="keyword">enum</span> { Dimension = EIGEN_SIZE_MIN_PREFER_DYNAMIC(Derived::RowsAtCompileTime, OtherDerived::RowsAtCompileTime) };</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span> </div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix<Scalar, Dimension, 1></a> VectorType;</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix<Scalar, Dimension, Dimension></a> MatrixType;</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classEigen_1_1Matrix.html">internal::plain_matrix_type_row_major<Derived>::type</a> RowMajorMatrixType;</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span> </div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="keyword">const</span> Index m = src.rows(); <span class="comment">// dimension</span></div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="keyword">const</span> Index n = src.cols(); <span class="comment">// number of measurements</span></div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span> </div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <span class="comment">// required for demeaning ...</span></div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <span class="keyword">const</span> RealScalar one_over_n = 1 / <span class="keyword">static_cast<</span>RealScalar<span class="keyword">></span>(n);</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span> </div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <span class="comment">// computation of mean</span></div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <span class="keyword">const</span> VectorType src_mean = src.<a class="code" href="classEigen_1_1DenseBase.html#a3af2f03b1d2affcec24e0748edf892cd">rowwise</a>().sum() * one_over_n;</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="keyword">const</span> VectorType dst_mean = dst.<a class="code" href="classEigen_1_1DenseBase.html#a3af2f03b1d2affcec24e0748edf892cd">rowwise</a>().sum() * one_over_n;</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="comment">// demeaning of src and dst points</span></div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <span class="keyword">const</span> RowMajorMatrixType src_demean = src.<a class="code" href="classEigen_1_1DenseBase.html#a49a617f24129ca31a27fe8a67ec20370">colwise</a>() - src_mean;</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <span class="keyword">const</span> RowMajorMatrixType dst_demean = dst.<a class="code" href="classEigen_1_1DenseBase.html#a49a617f24129ca31a27fe8a67ec20370">colwise</a>() - dst_mean;</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">// Eq. (36)-(37)</span></div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <span class="keyword">const</span> Scalar src_var = src_demean.rowwise().squaredNorm().sum() * one_over_n;</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span> </div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <span class="comment">// Eq. (38)</span></div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="keyword">const</span> MatrixType sigma = one_over_n * dst_demean * src_demean.transpose();</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span> </div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <a class="code" href="classEigen_1_1JacobiSVD.html">JacobiSVD<MatrixType></a> svd(sigma, <a class="code" href="group__enums.html#gga2d78499b99ddc29b9494f7ea33864d52a75953ad8f5837a79d6fbd3c116e7d462">ComputeFullU</a> | <a class="code" href="group__enums.html#gga2d78499b99ddc29b9494f7ea33864d52a1785ac1174dab733556ac572448984c7">ComputeFullV</a>);</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span> </div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="comment">// Initialize the resulting transformation with an identity matrix...</span></div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  TransformationMatrixType Rt = TransformationMatrixType::Identity(m+1,m+1);</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span> </div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="comment">// Eq. (39)</span></div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  VectorType S = VectorType::Ones(m);</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  <span class="keywordflow">if</span> (sigma.determinant()<0) S(m-1) = -1;</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span> </div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <span class="comment">// Eq. (40) and (43)</span></div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  <span class="keyword">const</span> VectorType& d = svd.<a class="code" href="classEigen_1_1JacobiSVD.html#a48d4068b97dfbb83d62599e56e26797a">singularValues</a>();</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  Index rank = 0; <span class="keywordflow">for</span> (Index i=0; i<m; ++i) <span class="keywordflow">if</span> (!internal::isMuchSmallerThan(d.coeff(i),d.coeff(0))) ++rank;</div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  <span class="keywordflow">if</span> (rank == m-1) {</div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  <span class="keywordflow">if</span> ( svd.<a class="code" href="classEigen_1_1JacobiSVD.html#a49e16a4adf4fe58a2d65a5e5a31e7654">matrixU</a>().determinant() * svd.<a class="code" href="classEigen_1_1JacobiSVD.html#ae5158ab7ca44a705c2a3b56ec926b42a">matrixV</a>().determinant() > 0 ) {</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  Rt.block(0,0,m,m).noalias() = svd.<a class="code" href="classEigen_1_1JacobiSVD.html#a49e16a4adf4fe58a2d65a5e5a31e7654">matrixU</a>()*svd.<a class="code" href="classEigen_1_1JacobiSVD.html#ae5158ab7ca44a705c2a3b56ec926b42a">matrixV</a>().transpose();</div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  <span class="keyword">const</span> Scalar s = S(m-1); S(m-1) = -1;</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  Rt.block(0,0,m,m).noalias() = svd.<a class="code" href="classEigen_1_1JacobiSVD.html#a49e16a4adf4fe58a2d65a5e5a31e7654">matrixU</a>() * S.asDiagonal() * svd.<a class="code" href="classEigen_1_1JacobiSVD.html#ae5158ab7ca44a705c2a3b56ec926b42a">matrixV</a>().transpose();</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  S(m-1) = s;</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="keywordflow">else</span> {</div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  Rt.block(0,0,m,m).noalias() = svd.<a class="code" href="classEigen_1_1JacobiSVD.html#a49e16a4adf4fe58a2d65a5e5a31e7654">matrixU</a>() * S.asDiagonal() * svd.<a class="code" href="classEigen_1_1JacobiSVD.html#ae5158ab7ca44a705c2a3b56ec926b42a">matrixV</a>().transpose();</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  }</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span> </div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  <span class="keywordflow">if</span> (with_scaling)</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  {</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  <span class="comment">// Eq. (42)</span></div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  <span class="keyword">const</span> Scalar c = 1/src_var * svd.<a class="code" href="classEigen_1_1JacobiSVD.html#a48d4068b97dfbb83d62599e56e26797a">singularValues</a>().dot(S);</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span> </div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  <span class="comment">// Eq. (41)</span></div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  Rt.col(m).head(m) = dst_mean;</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  Rt.col(m).head(m).noalias() -= c*Rt.topLeftCorner(m,m)*src_mean;</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  Rt.block(0,0,m,m) *= c;</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  }</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  {</div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  Rt.col(m).head(m) = dst_mean;</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  Rt.col(m).head(m).noalias() -= Rt.topLeftCorner(m,m)*src_mean;</div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  }</div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span> </div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <span class="keywordflow">return</span> Rt;</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> </div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span> } <span class="comment">// end namespace Eigen</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="preprocessor">#endif // EIGEN_UMEYAMA_H</span></div>
<div class="ttc" id="group__enums_html_gga0c5bde183ecefe103f70b49ad9740bcda1e16fa1b92ed7a058cd4ce7a9a0db044"><div class="ttname"><a href="group__enums.html#gga0c5bde183ecefe103f70b49ad9740bcda1e16fa1b92ed7a058cd4ce7a9a0db044">Eigen::RowMajor</a></div><div class="ttdef"><b>Definition:</b> Constants.h:266</div></div>
<div class="ttc" id="structEigen_1_1NumTraits_html"><div class="ttname"><a href="structEigen_1_1NumTraits.html">Eigen::NumTraits</a></div><div class="ttdoc">Holds information about the various numeric (i.e. scalar) types allowed by Eigen. ...</div><div class="ttdef"><b>Definition:</b> NumTraits.h:88</div></div>
<div class="ttc" id="namespaceEigen_html_adc9da5be31bdce40c25a92c27999c0e3"><div class="ttname"><a href="namespaceEigen.html#adc9da5be31bdce40c25a92c27999c0e3">Eigen::Dynamic</a></div><div class="ttdeci">const int Dynamic</div><div class="ttdef"><b>Definition:</b> Constants.h:21</div></div>
<div class="ttc" id="group__enums_html_gga2d78499b99ddc29b9494f7ea33864d52a1785ac1174dab733556ac572448984c7"><div class="ttname"><a href="group__enums.html#gga2d78499b99ddc29b9494f7ea33864d52a1785ac1174dab733556ac572448984c7">Eigen::ComputeFullV</a></div><div class="ttdef"><b>Definition:</b> Constants.h:331</div></div>
<div class="ttc" id="classEigen_1_1JacobiSVD_html_a48d4068b97dfbb83d62599e56e26797a"><div class="ttname"><a href="classEigen_1_1JacobiSVD.html#a48d4068b97dfbb83d62599e56e26797a">Eigen::JacobiSVD::singularValues</a></div><div class="ttdeci">const SingularValuesType & singularValues() const </div><div class="ttdef"><b>Definition:</b> JacobiSVD.h:630</div></div>
<div class="ttc" id="group__enums_html_gga0c5bde183ecefe103f70b49ad9740bcdac86184b0e3be936fbfd20249a057a0bf"><div class="ttname"><a href="group__enums.html#gga0c5bde183ecefe103f70b49ad9740bcdac86184b0e3be936fbfd20249a057a0bf">Eigen::ColMajor</a></div><div class="ttdef"><b>Definition:</b> Constants.h:264</div></div>
<div class="ttc" id="group__enums_html_gga0c5bde183ecefe103f70b49ad9740bcda02a97bb4792f98916a1156a521fa9813"><div class="ttname"><a href="group__enums.html#gga0c5bde183ecefe103f70b49ad9740bcda02a97bb4792f98916a1156a521fa9813">Eigen::AutoAlign</a></div><div class="ttdef"><b>Definition:</b> Constants.h:268</div></div>
<div class="ttc" id="classEigen_1_1JacobiSVD_html_a49e16a4adf4fe58a2d65a5e5a31e7654"><div class="ttname"><a href="classEigen_1_1JacobiSVD.html#a49e16a4adf4fe58a2d65a5e5a31e7654">Eigen::JacobiSVD::matrixU</a></div><div class="ttdeci">const MatrixUType & matrixU() const </div><div class="ttdef"><b>Definition:</b> JacobiSVD.h:602</div></div>
<div class="ttc" id="group__Geometry__Module_html_gab3f5a82a24490b936f8694cf8fef8e60"><div class="ttname"><a href="group__Geometry__Module.html#gab3f5a82a24490b936f8694cf8fef8e60">Eigen::umeyama</a></div><div class="ttdeci">internal::umeyama_transform_matrix_type< Derived, OtherDerived >::type umeyama(const MatrixBase< Derived > &src, const MatrixBase< OtherDerived > &dst, bool with_scaling=true)</div><div class="ttdoc">Returns the transformation between two point sets. </div><div class="ttdef"><b>Definition:</b> Umeyama.h:95</div></div>
<div class="ttc" id="classEigen_1_1JacobiSVD_html_ae5158ab7ca44a705c2a3b56ec926b42a"><div class="ttname"><a href="classEigen_1_1JacobiSVD.html#ae5158ab7ca44a705c2a3b56ec926b42a">Eigen::JacobiSVD::matrixV</a></div><div class="ttdeci">const MatrixVType & matrixV() const </div><div class="ttdef"><b>Definition:</b> JacobiSVD.h:618</div></div>
<div class="ttc" id="classEigen_1_1JacobiSVD_html"><div class="ttname"><a href="classEigen_1_1JacobiSVD.html">Eigen::JacobiSVD</a></div><div class="ttdoc">Two-sided Jacobi SVD decomposition of a rectangular matrix. </div><div class="ttdef"><b>Definition:</b> ForwardDeclarations.h:224</div></div>
<div class="ttc" id="group__flags_html_ga7bd49e7b260e869e10fb9dc4fd081a85"><div class="ttname"><a href="group__flags.html#ga7bd49e7b260e869e10fb9dc4fd081a85">Eigen::RowMajorBit</a></div><div class="ttdeci">const unsigned int RowMajorBit</div><div class="ttdef"><b>Definition:</b> Constants.h:53</div></div>
<div class="ttc" id="classEigen_1_1Matrix_html"><div class="ttname"><a href="classEigen_1_1Matrix.html">Eigen::Matrix</a></div><div class="ttdoc">The matrix class, also used for vectors and row-vectors. </div><div class="ttdef"><b>Definition:</b> Matrix.h:127</div></div>
<div class="ttc" id="group__enums_html_gga2d78499b99ddc29b9494f7ea33864d52a75953ad8f5837a79d6fbd3c116e7d462"><div class="ttname"><a href="group__enums.html#gga2d78499b99ddc29b9494f7ea33864d52a75953ad8f5837a79d6fbd3c116e7d462">Eigen::ComputeFullU</a></div><div class="ttdef"><b>Definition:</b> Constants.h:327</div></div>
<div class="ttc" id="classEigen_1_1DenseBase_html_a49a617f24129ca31a27fe8a67ec20370"><div class="ttname"><a href="classEigen_1_1DenseBase.html#a49a617f24129ca31a27fe8a67ec20370">Eigen::DenseBase::colwise</a></div><div class="ttdeci">ConstColwiseReturnType colwise() const </div><div class="ttdef"><b>Definition:</b> VectorwiseOp.h:598</div></div>
<div class="ttc" id="classEigen_1_1MatrixBase_html"><div class="ttname"><a href="classEigen_1_1MatrixBase.html">Eigen::MatrixBase</a></div><div class="ttdoc">Base class for all dense matrices, vectors, and expressions. </div><div class="ttdef"><b>Definition:</b> MatrixBase.h:48</div></div>
<div class="ttc" id="classEigen_1_1DenseBase_html_a3af2f03b1d2affcec24e0748edf892cd"><div class="ttname"><a href="classEigen_1_1DenseBase.html#a3af2f03b1d2affcec24e0748edf892cd">Eigen::DenseBase::rowwise</a></div><div class="ttdeci">ConstRowwiseReturnType rowwise() const </div><div class="ttdef"><b>Definition:</b> VectorwiseOp.h:623</div></div>
</div><!-- fragment --></div><!-- contents -->
</div><!-- doc-content -->
<!-- start footer part -->
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><a class="el" href="dir_e49d68e3078f12dfcf157021597ad168.html">Eigen</a></li><li class="navelem"><a class="el" href="dir_64b228556dc7f9fe757d43bb57fbfc24.html">src</a></li><li class="navelem"><a class="el" href="dir_d3830aef5e02ff83b0a743a58bf9d99e.html">Geometry</a></li><li class="navelem"><b>Umeyama.h</b></li>
<li class="footer">Generated on Mon Oct 28 2013 11:04:26 for Eigen by
<a href="http://www.doxygen.org/index.html">
<img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.5 </li>
</ul>
</div>
<!-- Piwik -->
<!--
<script type="text/javascript">
var pkBaseURL = (("https:" == document.location.protocol) ? "https://stats.sylphide-consulting.com/piwik/" : "http://stats.sylphide-consulting.com/piwik/");
document.write(unescape("%3Cscript src='" + pkBaseURL + "piwik.js' type='text/javascript'%3E%3C/script%3E"));
</script><script type="text/javascript">
try {
var piwikTracker = Piwik.getTracker(pkBaseURL + "piwik.php", 20);
piwikTracker.trackPageView();
piwikTracker.enableLinkTracking();
} catch( err ) {}
</script><noscript><p><img src="http://stats.sylphide-consulting.com/piwik/piwik.php?idsite=20" style="border:0" alt="" /></p></noscript>
-->
<!-- End Piwik Tracking Code -->
</body>
</html>
