<!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-unsupported: LevenbergMarquardt.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-unsupported</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('NonLinearOptimization_2LevenbergMarquardt_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>Enumerator</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(7)"><span class="SelectionMark"> </span>Groups</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(8)"><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">NonLinearOptimization/LevenbergMarquardt.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">// -*- coding: utf-8</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// vim: set fileencoding=utf-8</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> </div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">//</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org></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">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</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="l00011"></a><span class="lineno"> 11</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="l00012"></a><span class="lineno"> 12</span> </div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="preprocessor">#ifndef EIGEN_LEVENBERGMARQUARDT__H</span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_LEVENBERGMARQUARDT__H</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="keyword">namespace </span>Eigen { </div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> </div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="keyword">namespace </span>LevenbergMarquardtSpace {</div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span>  <span class="keyword">enum</span> Status {</div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span>  NotStarted = -2,</div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>  Running = -1,</div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>  ImproperInputParameters = 0,</div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>  RelativeReductionTooSmall = 1,</div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>  RelativeErrorTooSmall = 2,</div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  RelativeErrorAndReductionTooSmall = 3,</div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  CosinusTooSmall = 4,</div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  TooManyFunctionEvaluation = 5,</div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  FtolTooSmall = 6,</div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  XtolTooSmall = 7,</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  GtolTooSmall = 8,</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  UserAsked = 9</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  };</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> </div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> </div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> </div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="keyword">template</span><<span class="keyword">typename</span> FunctorType, <span class="keyword">typename</span> Scalar=<span class="keywordtype">double</span>></div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="keyword">class </span>LevenbergMarquardt</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> {</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="keyword">public</span>:</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  LevenbergMarquardt(FunctorType &_functor)</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  : functor(_functor) { <a class="code" href="classEigen_1_1LevenbergMarquardt.html#ad39de8ec664e09b12b528b4d8cdffc8c">nfev</a> = <a class="code" href="classEigen_1_1LevenbergMarquardt.html#a4ec1e17c7206359b96335f2c0744a783">njev</a> = iter = 0; <a class="code" href="classEigen_1_1LevenbergMarquardt.html#a09f0a7a9fefa463f4415e386922b3b48">fnorm</a> = <a class="code" href="classEigen_1_1LevenbergMarquardt.html#ac4b9a92a37e8f656a9bc7f222d3f1d3b">gnorm</a> = 0.; useExternalScaling=<span class="keyword">false</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>  <span class="keyword">typedef</span> DenseIndex Index;</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span> </div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="keyword">struct </span>Parameters {</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  Parameters()</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  : factor(Scalar(100.))</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  , maxfev(400)</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  , ftol(std::sqrt(NumTraits<Scalar>::epsilon()))</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  , xtol(std::sqrt(NumTraits<Scalar>::epsilon()))</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  , gtol(Scalar(0.))</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  , epsfcn(Scalar(0.)) {}</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  Scalar factor;</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  Index maxfev; <span class="comment">// maximum number of function evaluation</span></div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  Scalar ftol;</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  Scalar xtol;</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  Scalar gtol;</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  Scalar epsfcn;</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> </div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="keyword">typedef</span> Matrix< Scalar, Dynamic, 1 > FVectorType;</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="keyword">typedef</span> Matrix< Scalar, Dynamic, Dynamic > JacobianType;</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span> </div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  LevenbergMarquardtSpace::Status lmder1(</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  FVectorType &x,</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="keyword">const</span> Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  );</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span> </div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  LevenbergMarquardtSpace::Status minimize(FVectorType &x);</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  LevenbergMarquardtSpace::Status minimizeInit(FVectorType &x);</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  LevenbergMarquardtSpace::Status minimizeOneStep(FVectorType &x);</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span> </div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="keyword">static</span> LevenbergMarquardtSpace::Status lmdif1(</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  FunctorType &functor,</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  FVectorType &x,</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  Index *<a class="code" href="classEigen_1_1LevenbergMarquardt.html#ad39de8ec664e09b12b528b4d8cdffc8c">nfev</a>,</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keyword">const</span> Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  );</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span> </div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  LevenbergMarquardtSpace::Status lmstr1(</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  FVectorType &x,</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <span class="keyword">const</span> Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  );</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span> </div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  LevenbergMarquardtSpace::Status minimizeOptimumStorage(FVectorType &x);</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  LevenbergMarquardtSpace::Status minimizeOptimumStorageInit(FVectorType &x);</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  LevenbergMarquardtSpace::Status minimizeOptimumStorageOneStep(FVectorType &x);</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span> </div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1LevenbergMarquardt.html#af52cd5af951ff74e784deeadecf73552">resetParameters</a>(<span class="keywordtype">void</span>) { parameters = Parameters(); }</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>  Parameters parameters;</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  FVectorType <a class="code" href="classEigen_1_1LevenbergMarquardt.html#a8407d07d45184a84310dfaa297ca9425">fvec</a>, qtf, <a class="code" href="classEigen_1_1LevenbergMarquardt.html#a937987337a0875eee70a181a02cb9122">diag</a>;</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  JacobianType fjac;</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  PermutationMatrix<Dynamic,Dynamic> <a class="code" href="classEigen_1_1LevenbergMarquardt.html#afb981cc5d4a68f39d4ffd8a681f4ed81">permutation</a>;</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  Index <a class="code" href="classEigen_1_1LevenbergMarquardt.html#ad39de8ec664e09b12b528b4d8cdffc8c">nfev</a>;</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  Index <a class="code" href="classEigen_1_1LevenbergMarquardt.html#a4ec1e17c7206359b96335f2c0744a783">njev</a>;</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  Index iter;</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  Scalar <a class="code" href="classEigen_1_1LevenbergMarquardt.html#a09f0a7a9fefa463f4415e386922b3b48">fnorm</a>, <a class="code" href="classEigen_1_1LevenbergMarquardt.html#ac4b9a92a37e8f656a9bc7f222d3f1d3b">gnorm</a>;</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="keywordtype">bool</span> useExternalScaling; </div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span> </div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  Scalar <a class="code" href="classEigen_1_1LevenbergMarquardt.html#aa6d934df3d16027df0d0100cca3841fe">lm_param</a>(<span class="keywordtype">void</span>) { <span class="keywordflow">return</span> par; }</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span> <span class="keyword">private</span>:</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  FunctorType &functor;</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  Index n;</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  Index m;</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  FVectorType wa1, wa2, wa3, wa4;</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span> </div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  Scalar par, sum;</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  Scalar temp, temp1, temp2;</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  Scalar delta;</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  Scalar ratio;</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  Scalar pnorm, xnorm, fnorm1, actred, dirder, prered;</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span> </div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  LevenbergMarquardt& operator=(<span class="keyword">const</span> LevenbergMarquardt&);</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="keyword">template</span><<span class="keyword">typename</span> FunctorType, <span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span> LevenbergMarquardtSpace::Status</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span> LevenbergMarquardt<FunctorType,Scalar>::lmder1(</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  FVectorType &x,</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="keyword">const</span> Scalar tol</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> {</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  n = x.size();</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  m = functor.values();</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span> </div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  <span class="comment">/* check the input parameters for errors. */</span></div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="keywordflow">if</span> (n <= 0 || m < n || tol < 0.)</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::ImproperInputParameters;</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span> </div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  resetParameters();</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  parameters.ftol = tol;</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  parameters.xtol = tol;</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  parameters.maxfev = 100*(n+1);</div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span> </div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  <span class="keywordflow">return</span> minimize(x);</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span> }</div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span> </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="keyword">template</span><<span class="keyword">typename</span> FunctorType, <span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span> LevenbergMarquardtSpace::Status</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span> LevenbergMarquardt<FunctorType,Scalar>::minimize(FVectorType &x)</div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span> {</div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  LevenbergMarquardtSpace::Status status = minimizeInit(x);</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  <span class="keywordflow">if</span> (status==LevenbergMarquardtSpace::ImproperInputParameters)</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  <span class="keywordflow">return</span> status;</div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  <span class="keywordflow">do</span> {</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  status = minimizeOneStep(x);</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  } <span class="keywordflow">while</span> (status==LevenbergMarquardtSpace::Running);</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  <span class="keywordflow">return</span> status;</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> </div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span> <span class="keyword">template</span><<span class="keyword">typename</span> FunctorType, <span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span> LevenbergMarquardtSpace::Status</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span> LevenbergMarquardt<FunctorType,Scalar>::minimizeInit(FVectorType &x)</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>  n = x.size();</div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  m = functor.values();</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>  wa1.resize(n); wa2.resize(n); wa3.resize(n);</div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  wa4.resize(m);</div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  fvec.resize(m);</div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  fjac.resize(m, n);</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  <span class="keywordflow">if</span> (!useExternalScaling)</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  diag.resize(n);</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  eigen_assert( (!useExternalScaling || diag.size()==n) || <span class="stringliteral">"When useExternalScaling is set, the caller must provide a valid 'diag'"</span>);</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  qtf.resize(n);</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span> </div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  <span class="comment">/* Function Body */</span></div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  nfev = 0;</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  njev = 0;</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span> </div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  <span class="comment">/* check the input parameters for errors. */</span></div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  <span class="keywordflow">if</span> (n <= 0 || m < n || parameters.ftol < 0. || parameters.xtol < 0. || parameters.gtol < 0. || parameters.maxfev <= 0 || parameters.factor <= 0.)</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::ImproperInputParameters;</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>  <span class="keywordflow">if</span> (useExternalScaling)</div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  <span class="keywordflow">for</span> (Index j = 0; j < n; ++j)</div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  <span class="keywordflow">if</span> (diag[j] <= 0.)</div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::ImproperInputParameters;</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span> </div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  <span class="comment">/* evaluate the function at the starting point */</span></div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  <span class="comment">/* and calculate its norm. */</span></div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  nfev = 1;</div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  <span class="keywordflow">if</span> ( functor(x, fvec) < 0)</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::UserAsked;</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  fnorm = fvec.stableNorm();</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span> </div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <span class="comment">/* initialize levenberg-marquardt parameter and iteration counter. */</span></div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  par = 0.;</div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  iter = 1;</div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span> </div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::NotStarted;</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span> }</div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span> </div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span> <span class="keyword">template</span><<span class="keyword">typename</span> FunctorType, <span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span> LevenbergMarquardtSpace::Status</div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span> LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(FVectorType &x)</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>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  </div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  eigen_assert(x.size()==n); <span class="comment">// check the caller is not cheating us</span></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>  <span class="comment">/* calculate the jacobian matrix. */</span></div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  Index df_ret = functor.df(x, fjac);</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  <span class="keywordflow">if</span> (df_ret<0)</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::UserAsked;</div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <span class="keywordflow">if</span> (df_ret>0)</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <span class="comment">// numerical diff, we evaluated the function df_ret times</span></div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  nfev += df_ret;</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  <span class="keywordflow">else</span> njev++;</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>  <span class="comment">/* compute the qr factorization of the jacobian. */</span></div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  wa2 = fjac.colwise().blueNorm();</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  ColPivHouseholderQR<JacobianType> qrfac(fjac);</div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  fjac = qrfac.matrixQR();</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  permutation = qrfac.colsPermutation();</div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span> </div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  <span class="comment">/* on the first iteration and if external scaling is not used, scale according */</span></div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  <span class="comment">/* to the norms of the columns of the initial jacobian. */</span></div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  <span class="keywordflow">if</span> (iter == 1) {</div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  <span class="keywordflow">if</span> (!useExternalScaling)</div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  <span class="keywordflow">for</span> (Index j = 0; j < n; ++j)</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  diag[j] = (wa2[j]==0.)? 1. : wa2[j];</div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span> </div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  <span class="comment">/* on the first iteration, calculate the norm of the scaled x */</span></div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  <span class="comment">/* and initialize the step bound delta. */</span></div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  xnorm = diag.cwiseProduct(x).stableNorm();</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  delta = parameters.factor * xnorm;</div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  <span class="keywordflow">if</span> (delta == 0.)</div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  delta = parameters.factor;</div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  }</div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span> </div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  <span class="comment">/* form (q transpose)*fvec and store the first n components in */</span></div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  <span class="comment">/* qtf. */</span></div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  wa4 = fvec;</div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  wa4.applyOnTheLeft(qrfac.householderQ().adjoint());</div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  qtf = wa4.head(n);</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">/* compute the norm of the scaled gradient. */</span></div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  gnorm = 0.;</div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  <span class="keywordflow">if</span> (fnorm != 0.)</div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  <span class="keywordflow">for</span> (Index j = 0; j < n; ++j)</div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  <span class="keywordflow">if</span> (wa2[permutation.indices()[j]] != 0.)</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  gnorm = (std::max)(gnorm, abs( fjac.col(j).head(j+1).dot(qtf.head(j+1)/fnorm) / wa2[permutation.indices()[j]]));</div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span> </div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  <span class="comment">/* test for convergence of the gradient norm. */</span></div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  <span class="keywordflow">if</span> (gnorm <= parameters.gtol)</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::CosinusTooSmall;</div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span> </div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  <span class="comment">/* rescale if necessary. */</span></div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  <span class="keywordflow">if</span> (!useExternalScaling)</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  diag = diag.cwiseMax(wa2);</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span> </div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  <span class="keywordflow">do</span> {</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span> </div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  <span class="comment">/* determine the levenberg-marquardt parameter. */</span></div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  internal::lmpar2<Scalar>(qrfac, diag, qtf, delta, par, wa1);</div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span> </div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  <span class="comment">/* store the direction p and x + p. calculate the norm of p. */</span></div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  wa1 = -wa1;</div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  wa2 = x + wa1;</div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  pnorm = diag.cwiseProduct(wa1).stableNorm();</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span> </div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  <span class="comment">/* on the first iteration, adjust the initial step bound. */</span></div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  <span class="keywordflow">if</span> (iter == 1)</div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  delta = (std::min)(delta,pnorm);</div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span> </div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  <span class="comment">/* evaluate the function at x + p and calculate its norm. */</span></div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  <span class="keywordflow">if</span> ( functor(wa2, wa4) < 0)</div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::UserAsked;</div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  ++nfev;</div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  fnorm1 = wa4.stableNorm();</div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span> </div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  <span class="comment">/* compute the scaled actual reduction. */</span></div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  actred = -1.;</div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  <span class="keywordflow">if</span> (Scalar(.1) * fnorm1 < fnorm)</div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  actred = 1. - numext::abs2(fnorm1 / fnorm);</div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span> </div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  <span class="comment">/* compute the scaled predicted reduction and */</span></div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  <span class="comment">/* the scaled directional derivative. */</span></div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  wa3 = fjac.template triangularView<Upper>() * (qrfac.colsPermutation().inverse() *wa1);</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  temp1 = numext::abs2(wa3.stableNorm() / fnorm);</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  temp2 = numext::abs2(sqrt(par) * pnorm / fnorm);</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  prered = temp1 + temp2 / Scalar(.5);</div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  dirder = -(temp1 + temp2);</div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span> </div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  <span class="comment">/* compute the ratio of the actual to the predicted */</span></div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  <span class="comment">/* reduction. */</span></div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  ratio = 0.;</div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  <span class="keywordflow">if</span> (prered != 0.)</div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  ratio = actred / prered;</div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span> </div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  <span class="comment">/* update the step bound. */</span></div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  <span class="keywordflow">if</span> (ratio <= Scalar(.25)) {</div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  <span class="keywordflow">if</span> (actred >= 0.)</div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  temp = Scalar(.5);</div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  <span class="keywordflow">if</span> (actred < 0.)</div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  temp = Scalar(.5) * dirder / (dirder + Scalar(.5) * actred);</div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  <span class="keywordflow">if</span> (Scalar(.1) * fnorm1 >= fnorm || temp < Scalar(.1))</div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  temp = Scalar(.1);</div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  <span class="comment">/* Computing MIN */</span></div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  delta = temp * (std::min)(delta, pnorm / Scalar(.1));</div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  par /= temp;</div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (!(par != 0. && ratio < Scalar(.75))) {</div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  delta = pnorm / Scalar(.5);</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  par = Scalar(.5) * par;</div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  }</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>  <span class="comment">/* test for successful iteration. */</span></div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  <span class="keywordflow">if</span> (ratio >= Scalar(1e-4)) {</div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  <span class="comment">/* successful iteration. update x, fvec, and their norms. */</span></div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  x = wa2;</div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  wa2 = diag.cwiseProduct(x);</div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  fvec = wa4;</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  xnorm = wa2.stableNorm();</div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  fnorm = fnorm1;</div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  ++iter;</div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  }</div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span> </div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  <span class="comment">/* tests for convergence. */</span></div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  <span class="keywordflow">if</span> (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm)</div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::RelativeErrorAndReductionTooSmall;</div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  <span class="keywordflow">if</span> (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.)</div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::RelativeReductionTooSmall;</div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  <span class="keywordflow">if</span> (delta <= parameters.xtol * xnorm)</div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::RelativeErrorTooSmall;</div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span> </div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  <span class="comment">/* tests for termination and stringent tolerances. */</span></div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  <span class="keywordflow">if</span> (nfev >= parameters.maxfev)</div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::TooManyFunctionEvaluation;</div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  <span class="keywordflow">if</span> (abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.)</div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::FtolTooSmall;</div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  <span class="keywordflow">if</span> (delta <= NumTraits<Scalar>::epsilon() * xnorm)</div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::XtolTooSmall;</div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  <span class="keywordflow">if</span> (gnorm <= NumTraits<Scalar>::epsilon())</div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::GtolTooSmall;</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>  } <span class="keywordflow">while</span> (ratio < Scalar(1e-4));</div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span> </div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::Running;</div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span> }</div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span> </div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span> <span class="keyword">template</span><<span class="keyword">typename</span> FunctorType, <span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span> LevenbergMarquardtSpace::Status</div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span> LevenbergMarquardt<FunctorType,Scalar>::lmstr1(</div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  FVectorType &x,</div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  <span class="keyword">const</span> Scalar tol</div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  )</div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span> {</div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  n = x.size();</div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  m = functor.values();</div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span> </div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  <span class="comment">/* check the input parameters for errors. */</span></div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  <span class="keywordflow">if</span> (n <= 0 || m < n || tol < 0.)</div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::ImproperInputParameters;</div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span> </div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  resetParameters();</div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  parameters.ftol = tol;</div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  parameters.xtol = tol;</div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  parameters.maxfev = 100*(n+1);</div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span> </div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  <span class="keywordflow">return</span> minimizeOptimumStorage(x);</div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span> }</div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span> </div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span> <span class="keyword">template</span><<span class="keyword">typename</span> FunctorType, <span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span> LevenbergMarquardtSpace::Status</div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span> LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageInit(FVectorType &x)</div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span> {</div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  n = x.size();</div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  m = functor.values();</div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span> </div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  wa1.resize(n); wa2.resize(n); wa3.resize(n);</div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  wa4.resize(m);</div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  fvec.resize(m);</div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  <span class="comment">// Only R is stored in fjac. Q is only used to compute 'qtf', which is</span></div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  <span class="comment">// Q.transpose()*rhs. qtf will be updated using givens rotation,</span></div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  <span class="comment">// instead of storing them in Q.</span></div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  <span class="comment">// The purpose it to only use a nxn matrix, instead of mxn here, so</span></div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  <span class="comment">// that we can handle cases where m>>n :</span></div>
<div class="line"><a name="l00391"></a><span class="lineno"> 391</span>  fjac.resize(n, n);</div>
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span>  <span class="keywordflow">if</span> (!useExternalScaling)</div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  diag.resize(n);</div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  eigen_assert( (!useExternalScaling || diag.size()==n) || <span class="stringliteral">"When useExternalScaling is set, the caller must provide a valid 'diag'"</span>);</div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  qtf.resize(n);</div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span> </div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  <span class="comment">/* Function Body */</span></div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span>  nfev = 0;</div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span>  njev = 0;</div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span> </div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  <span class="comment">/* check the input parameters for errors. */</span></div>
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span>  <span class="keywordflow">if</span> (n <= 0 || m < n || parameters.ftol < 0. || parameters.xtol < 0. || parameters.gtol < 0. || parameters.maxfev <= 0 || parameters.factor <= 0.)</div>
<div class="line"><a name="l00403"></a><span class="lineno"> 403</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::ImproperInputParameters;</div>
<div class="line"><a name="l00404"></a><span class="lineno"> 404</span> </div>
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span>  <span class="keywordflow">if</span> (useExternalScaling)</div>
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span>  <span class="keywordflow">for</span> (Index j = 0; j < n; ++j)</div>
<div class="line"><a name="l00407"></a><span class="lineno"> 407</span>  <span class="keywordflow">if</span> (diag[j] <= 0.)</div>
<div class="line"><a name="l00408"></a><span class="lineno"> 408</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::ImproperInputParameters;</div>
<div class="line"><a name="l00409"></a><span class="lineno"> 409</span> </div>
<div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  <span class="comment">/* evaluate the function at the starting point */</span></div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span>  <span class="comment">/* and calculate its norm. */</span></div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  nfev = 1;</div>
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span>  <span class="keywordflow">if</span> ( functor(x, fvec) < 0)</div>
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::UserAsked;</div>
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  fnorm = fvec.stableNorm();</div>
<div class="line"><a name="l00416"></a><span class="lineno"> 416</span> </div>
<div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  <span class="comment">/* initialize levenberg-marquardt parameter and iteration counter. */</span></div>
<div class="line"><a name="l00418"></a><span class="lineno"> 418</span>  par = 0.;</div>
<div class="line"><a name="l00419"></a><span class="lineno"> 419</span>  iter = 1;</div>
<div class="line"><a name="l00420"></a><span class="lineno"> 420</span> </div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::NotStarted;</div>
<div class="line"><a name="l00422"></a><span class="lineno"> 422</span> }</div>
<div class="line"><a name="l00423"></a><span class="lineno"> 423</span> </div>
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span> </div>
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span> <span class="keyword">template</span><<span class="keyword">typename</span> FunctorType, <span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span> LevenbergMarquardtSpace::Status</div>
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span> LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(FVectorType &x)</div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span> {</div>
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00431"></a><span class="lineno"> 431</span>  </div>
<div class="line"><a name="l00432"></a><span class="lineno"> 432</span>  eigen_assert(x.size()==n); <span class="comment">// check the caller is not cheating us</span></div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span> </div>
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  Index i, j;</div>
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span>  <span class="keywordtype">bool</span> sing;</div>
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span> </div>
<div class="line"><a name="l00437"></a><span class="lineno"> 437</span>  <span class="comment">/* compute the qr factorization of the jacobian matrix */</span></div>
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span>  <span class="comment">/* calculated one row at a time, while simultaneously */</span></div>
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  <span class="comment">/* forming (q transpose)*fvec and storing the first */</span></div>
<div class="line"><a name="l00440"></a><span class="lineno"> 440</span>  <span class="comment">/* n components in qtf. */</span></div>
<div class="line"><a name="l00441"></a><span class="lineno"> 441</span>  qtf.fill(0.);</div>
<div class="line"><a name="l00442"></a><span class="lineno"> 442</span>  fjac.fill(0.);</div>
<div class="line"><a name="l00443"></a><span class="lineno"> 443</span>  Index rownb = 2;</div>
<div class="line"><a name="l00444"></a><span class="lineno"> 444</span>  <span class="keywordflow">for</span> (i = 0; i < m; ++i) {</div>
<div class="line"><a name="l00445"></a><span class="lineno"> 445</span>  <span class="keywordflow">if</span> (functor.df(x, wa3, rownb) < 0) <span class="keywordflow">return</span> LevenbergMarquardtSpace::UserAsked;</div>
<div class="line"><a name="l00446"></a><span class="lineno"> 446</span>  internal::rwupdt<Scalar>(fjac, wa3, qtf, fvec[i]);</div>
<div class="line"><a name="l00447"></a><span class="lineno"> 447</span>  ++rownb;</div>
<div class="line"><a name="l00448"></a><span class="lineno"> 448</span>  }</div>
<div class="line"><a name="l00449"></a><span class="lineno"> 449</span>  ++njev;</div>
<div class="line"><a name="l00450"></a><span class="lineno"> 450</span> </div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span>  <span class="comment">/* if the jacobian is rank deficient, call qrfac to */</span></div>
<div class="line"><a name="l00452"></a><span class="lineno"> 452</span>  <span class="comment">/* reorder its columns and update the components of qtf. */</span></div>
<div class="line"><a name="l00453"></a><span class="lineno"> 453</span>  sing = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00454"></a><span class="lineno"> 454</span>  <span class="keywordflow">for</span> (j = 0; j < n; ++j) {</div>
<div class="line"><a name="l00455"></a><span class="lineno"> 455</span>  <span class="keywordflow">if</span> (fjac(j,j) == 0.)</div>
<div class="line"><a name="l00456"></a><span class="lineno"> 456</span>  sing = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00457"></a><span class="lineno"> 457</span>  wa2[j] = fjac.col(j).head(j).stableNorm();</div>
<div class="line"><a name="l00458"></a><span class="lineno"> 458</span>  }</div>
<div class="line"><a name="l00459"></a><span class="lineno"> 459</span>  permutation.setIdentity(n);</div>
<div class="line"><a name="l00460"></a><span class="lineno"> 460</span>  <span class="keywordflow">if</span> (sing) {</div>
<div class="line"><a name="l00461"></a><span class="lineno"> 461</span>  wa2 = fjac.colwise().blueNorm();</div>
<div class="line"><a name="l00462"></a><span class="lineno"> 462</span>  <span class="comment">// TODO We have no unit test covering this code path, do not modify</span></div>
<div class="line"><a name="l00463"></a><span class="lineno"> 463</span>  <span class="comment">// until it is carefully tested</span></div>
<div class="line"><a name="l00464"></a><span class="lineno"> 464</span>  ColPivHouseholderQR<JacobianType> qrfac(fjac);</div>
<div class="line"><a name="l00465"></a><span class="lineno"> 465</span>  fjac = qrfac.matrixQR();</div>
<div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  wa1 = fjac.diagonal();</div>
<div class="line"><a name="l00467"></a><span class="lineno"> 467</span>  fjac.diagonal() = qrfac.hCoeffs();</div>
<div class="line"><a name="l00468"></a><span class="lineno"> 468</span>  permutation = qrfac.colsPermutation();</div>
<div class="line"><a name="l00469"></a><span class="lineno"> 469</span>  <span class="comment">// TODO : avoid this:</span></div>
<div class="line"><a name="l00470"></a><span class="lineno"> 470</span>  <span class="keywordflow">for</span>(Index ii=0; ii< fjac.cols(); ii++) fjac.col(ii).segment(ii+1, fjac.rows()-ii-1) *= fjac(ii,ii); <span class="comment">// rescale vectors</span></div>
<div class="line"><a name="l00471"></a><span class="lineno"> 471</span> </div>
<div class="line"><a name="l00472"></a><span class="lineno"> 472</span>  <span class="keywordflow">for</span> (j = 0; j < n; ++j) {</div>
<div class="line"><a name="l00473"></a><span class="lineno"> 473</span>  <span class="keywordflow">if</span> (fjac(j,j) != 0.) {</div>
<div class="line"><a name="l00474"></a><span class="lineno"> 474</span>  sum = 0.;</div>
<div class="line"><a name="l00475"></a><span class="lineno"> 475</span>  <span class="keywordflow">for</span> (i = j; i < n; ++i)</div>
<div class="line"><a name="l00476"></a><span class="lineno"> 476</span>  sum += fjac(i,j) * qtf[i];</div>
<div class="line"><a name="l00477"></a><span class="lineno"> 477</span>  temp = -sum / fjac(j,j);</div>
<div class="line"><a name="l00478"></a><span class="lineno"> 478</span>  <span class="keywordflow">for</span> (i = j; i < n; ++i)</div>
<div class="line"><a name="l00479"></a><span class="lineno"> 479</span>  qtf[i] += fjac(i,j) * temp;</div>
<div class="line"><a name="l00480"></a><span class="lineno"> 480</span>  }</div>
<div class="line"><a name="l00481"></a><span class="lineno"> 481</span>  fjac(j,j) = wa1[j];</div>
<div class="line"><a name="l00482"></a><span class="lineno"> 482</span>  }</div>
<div class="line"><a name="l00483"></a><span class="lineno"> 483</span>  }</div>
<div class="line"><a name="l00484"></a><span class="lineno"> 484</span> </div>
<div class="line"><a name="l00485"></a><span class="lineno"> 485</span>  <span class="comment">/* on the first iteration and if external scaling is not used, scale according */</span></div>
<div class="line"><a name="l00486"></a><span class="lineno"> 486</span>  <span class="comment">/* to the norms of the columns of the initial jacobian. */</span></div>
<div class="line"><a name="l00487"></a><span class="lineno"> 487</span>  <span class="keywordflow">if</span> (iter == 1) {</div>
<div class="line"><a name="l00488"></a><span class="lineno"> 488</span>  <span class="keywordflow">if</span> (!useExternalScaling)</div>
<div class="line"><a name="l00489"></a><span class="lineno"> 489</span>  <span class="keywordflow">for</span> (j = 0; j < n; ++j)</div>
<div class="line"><a name="l00490"></a><span class="lineno"> 490</span>  diag[j] = (wa2[j]==0.)? 1. : wa2[j];</div>
<div class="line"><a name="l00491"></a><span class="lineno"> 491</span> </div>
<div class="line"><a name="l00492"></a><span class="lineno"> 492</span>  <span class="comment">/* on the first iteration, calculate the norm of the scaled x */</span></div>
<div class="line"><a name="l00493"></a><span class="lineno"> 493</span>  <span class="comment">/* and initialize the step bound delta. */</span></div>
<div class="line"><a name="l00494"></a><span class="lineno"> 494</span>  xnorm = diag.cwiseProduct(x).stableNorm();</div>
<div class="line"><a name="l00495"></a><span class="lineno"> 495</span>  delta = parameters.factor * xnorm;</div>
<div class="line"><a name="l00496"></a><span class="lineno"> 496</span>  <span class="keywordflow">if</span> (delta == 0.)</div>
<div class="line"><a name="l00497"></a><span class="lineno"> 497</span>  delta = parameters.factor;</div>
<div class="line"><a name="l00498"></a><span class="lineno"> 498</span>  }</div>
<div class="line"><a name="l00499"></a><span class="lineno"> 499</span> </div>
<div class="line"><a name="l00500"></a><span class="lineno"> 500</span>  <span class="comment">/* compute the norm of the scaled gradient. */</span></div>
<div class="line"><a name="l00501"></a><span class="lineno"> 501</span>  gnorm = 0.;</div>
<div class="line"><a name="l00502"></a><span class="lineno"> 502</span>  <span class="keywordflow">if</span> (fnorm != 0.)</div>
<div class="line"><a name="l00503"></a><span class="lineno"> 503</span>  <span class="keywordflow">for</span> (j = 0; j < n; ++j)</div>
<div class="line"><a name="l00504"></a><span class="lineno"> 504</span>  <span class="keywordflow">if</span> (wa2[permutation.indices()[j]] != 0.)</div>
<div class="line"><a name="l00505"></a><span class="lineno"> 505</span>  gnorm = (std::max)(gnorm, abs( fjac.col(j).head(j+1).dot(qtf.head(j+1)/fnorm) / wa2[permutation.indices()[j]]));</div>
<div class="line"><a name="l00506"></a><span class="lineno"> 506</span> </div>
<div class="line"><a name="l00507"></a><span class="lineno"> 507</span>  <span class="comment">/* test for convergence of the gradient norm. */</span></div>
<div class="line"><a name="l00508"></a><span class="lineno"> 508</span>  <span class="keywordflow">if</span> (gnorm <= parameters.gtol)</div>
<div class="line"><a name="l00509"></a><span class="lineno"> 509</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::CosinusTooSmall;</div>
<div class="line"><a name="l00510"></a><span class="lineno"> 510</span> </div>
<div class="line"><a name="l00511"></a><span class="lineno"> 511</span>  <span class="comment">/* rescale if necessary. */</span></div>
<div class="line"><a name="l00512"></a><span class="lineno"> 512</span>  <span class="keywordflow">if</span> (!useExternalScaling)</div>
<div class="line"><a name="l00513"></a><span class="lineno"> 513</span>  diag = diag.cwiseMax(wa2);</div>
<div class="line"><a name="l00514"></a><span class="lineno"> 514</span> </div>
<div class="line"><a name="l00515"></a><span class="lineno"> 515</span>  <span class="keywordflow">do</span> {</div>
<div class="line"><a name="l00516"></a><span class="lineno"> 516</span> </div>
<div class="line"><a name="l00517"></a><span class="lineno"> 517</span>  <span class="comment">/* determine the levenberg-marquardt parameter. */</span></div>
<div class="line"><a name="l00518"></a><span class="lineno"> 518</span>  internal::lmpar<Scalar>(fjac, permutation.indices(), diag, qtf, delta, par, wa1);</div>
<div class="line"><a name="l00519"></a><span class="lineno"> 519</span> </div>
<div class="line"><a name="l00520"></a><span class="lineno"> 520</span>  <span class="comment">/* store the direction p and x + p. calculate the norm of p. */</span></div>
<div class="line"><a name="l00521"></a><span class="lineno"> 521</span>  wa1 = -wa1;</div>
<div class="line"><a name="l00522"></a><span class="lineno"> 522</span>  wa2 = x + wa1;</div>
<div class="line"><a name="l00523"></a><span class="lineno"> 523</span>  pnorm = diag.cwiseProduct(wa1).stableNorm();</div>
<div class="line"><a name="l00524"></a><span class="lineno"> 524</span> </div>
<div class="line"><a name="l00525"></a><span class="lineno"> 525</span>  <span class="comment">/* on the first iteration, adjust the initial step bound. */</span></div>
<div class="line"><a name="l00526"></a><span class="lineno"> 526</span>  <span class="keywordflow">if</span> (iter == 1)</div>
<div class="line"><a name="l00527"></a><span class="lineno"> 527</span>  delta = (std::min)(delta,pnorm);</div>
<div class="line"><a name="l00528"></a><span class="lineno"> 528</span> </div>
<div class="line"><a name="l00529"></a><span class="lineno"> 529</span>  <span class="comment">/* evaluate the function at x + p and calculate its norm. */</span></div>
<div class="line"><a name="l00530"></a><span class="lineno"> 530</span>  <span class="keywordflow">if</span> ( functor(wa2, wa4) < 0)</div>
<div class="line"><a name="l00531"></a><span class="lineno"> 531</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::UserAsked;</div>
<div class="line"><a name="l00532"></a><span class="lineno"> 532</span>  ++nfev;</div>
<div class="line"><a name="l00533"></a><span class="lineno"> 533</span>  fnorm1 = wa4.stableNorm();</div>
<div class="line"><a name="l00534"></a><span class="lineno"> 534</span> </div>
<div class="line"><a name="l00535"></a><span class="lineno"> 535</span>  <span class="comment">/* compute the scaled actual reduction. */</span></div>
<div class="line"><a name="l00536"></a><span class="lineno"> 536</span>  actred = -1.;</div>
<div class="line"><a name="l00537"></a><span class="lineno"> 537</span>  <span class="keywordflow">if</span> (Scalar(.1) * fnorm1 < fnorm)</div>
<div class="line"><a name="l00538"></a><span class="lineno"> 538</span>  actred = 1. - numext::abs2(fnorm1 / fnorm);</div>
<div class="line"><a name="l00539"></a><span class="lineno"> 539</span> </div>
<div class="line"><a name="l00540"></a><span class="lineno"> 540</span>  <span class="comment">/* compute the scaled predicted reduction and */</span></div>
<div class="line"><a name="l00541"></a><span class="lineno"> 541</span>  <span class="comment">/* the scaled directional derivative. */</span></div>
<div class="line"><a name="l00542"></a><span class="lineno"> 542</span>  wa3 = fjac.topLeftCorner(n,n).template triangularView<Upper>() * (permutation.inverse() * wa1);</div>
<div class="line"><a name="l00543"></a><span class="lineno"> 543</span>  temp1 = numext::abs2(wa3.stableNorm() / fnorm);</div>
<div class="line"><a name="l00544"></a><span class="lineno"> 544</span>  temp2 = numext::abs2(sqrt(par) * pnorm / fnorm);</div>
<div class="line"><a name="l00545"></a><span class="lineno"> 545</span>  prered = temp1 + temp2 / Scalar(.5);</div>
<div class="line"><a name="l00546"></a><span class="lineno"> 546</span>  dirder = -(temp1 + temp2);</div>
<div class="line"><a name="l00547"></a><span class="lineno"> 547</span> </div>
<div class="line"><a name="l00548"></a><span class="lineno"> 548</span>  <span class="comment">/* compute the ratio of the actual to the predicted */</span></div>
<div class="line"><a name="l00549"></a><span class="lineno"> 549</span>  <span class="comment">/* reduction. */</span></div>
<div class="line"><a name="l00550"></a><span class="lineno"> 550</span>  ratio = 0.;</div>
<div class="line"><a name="l00551"></a><span class="lineno"> 551</span>  <span class="keywordflow">if</span> (prered != 0.)</div>
<div class="line"><a name="l00552"></a><span class="lineno"> 552</span>  ratio = actred / prered;</div>
<div class="line"><a name="l00553"></a><span class="lineno"> 553</span> </div>
<div class="line"><a name="l00554"></a><span class="lineno"> 554</span>  <span class="comment">/* update the step bound. */</span></div>
<div class="line"><a name="l00555"></a><span class="lineno"> 555</span>  <span class="keywordflow">if</span> (ratio <= Scalar(.25)) {</div>
<div class="line"><a name="l00556"></a><span class="lineno"> 556</span>  <span class="keywordflow">if</span> (actred >= 0.)</div>
<div class="line"><a name="l00557"></a><span class="lineno"> 557</span>  temp = Scalar(.5);</div>
<div class="line"><a name="l00558"></a><span class="lineno"> 558</span>  <span class="keywordflow">if</span> (actred < 0.)</div>
<div class="line"><a name="l00559"></a><span class="lineno"> 559</span>  temp = Scalar(.5) * dirder / (dirder + Scalar(.5) * actred);</div>
<div class="line"><a name="l00560"></a><span class="lineno"> 560</span>  <span class="keywordflow">if</span> (Scalar(.1) * fnorm1 >= fnorm || temp < Scalar(.1))</div>
<div class="line"><a name="l00561"></a><span class="lineno"> 561</span>  temp = Scalar(.1);</div>
<div class="line"><a name="l00562"></a><span class="lineno"> 562</span>  <span class="comment">/* Computing MIN */</span></div>
<div class="line"><a name="l00563"></a><span class="lineno"> 563</span>  delta = temp * (std::min)(delta, pnorm / Scalar(.1));</div>
<div class="line"><a name="l00564"></a><span class="lineno"> 564</span>  par /= temp;</div>
<div class="line"><a name="l00565"></a><span class="lineno"> 565</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (!(par != 0. && ratio < Scalar(.75))) {</div>
<div class="line"><a name="l00566"></a><span class="lineno"> 566</span>  delta = pnorm / Scalar(.5);</div>
<div class="line"><a name="l00567"></a><span class="lineno"> 567</span>  par = Scalar(.5) * par;</div>
<div class="line"><a name="l00568"></a><span class="lineno"> 568</span>  }</div>
<div class="line"><a name="l00569"></a><span class="lineno"> 569</span> </div>
<div class="line"><a name="l00570"></a><span class="lineno"> 570</span>  <span class="comment">/* test for successful iteration. */</span></div>
<div class="line"><a name="l00571"></a><span class="lineno"> 571</span>  <span class="keywordflow">if</span> (ratio >= Scalar(1e-4)) {</div>
<div class="line"><a name="l00572"></a><span class="lineno"> 572</span>  <span class="comment">/* successful iteration. update x, fvec, and their norms. */</span></div>
<div class="line"><a name="l00573"></a><span class="lineno"> 573</span>  x = wa2;</div>
<div class="line"><a name="l00574"></a><span class="lineno"> 574</span>  wa2 = diag.cwiseProduct(x);</div>
<div class="line"><a name="l00575"></a><span class="lineno"> 575</span>  fvec = wa4;</div>
<div class="line"><a name="l00576"></a><span class="lineno"> 576</span>  xnorm = wa2.stableNorm();</div>
<div class="line"><a name="l00577"></a><span class="lineno"> 577</span>  fnorm = fnorm1;</div>
<div class="line"><a name="l00578"></a><span class="lineno"> 578</span>  ++iter;</div>
<div class="line"><a name="l00579"></a><span class="lineno"> 579</span>  }</div>
<div class="line"><a name="l00580"></a><span class="lineno"> 580</span> </div>
<div class="line"><a name="l00581"></a><span class="lineno"> 581</span>  <span class="comment">/* tests for convergence. */</span></div>
<div class="line"><a name="l00582"></a><span class="lineno"> 582</span>  <span class="keywordflow">if</span> (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm)</div>
<div class="line"><a name="l00583"></a><span class="lineno"> 583</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::RelativeErrorAndReductionTooSmall;</div>
<div class="line"><a name="l00584"></a><span class="lineno"> 584</span>  <span class="keywordflow">if</span> (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.)</div>
<div class="line"><a name="l00585"></a><span class="lineno"> 585</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::RelativeReductionTooSmall;</div>
<div class="line"><a name="l00586"></a><span class="lineno"> 586</span>  <span class="keywordflow">if</span> (delta <= parameters.xtol * xnorm)</div>
<div class="line"><a name="l00587"></a><span class="lineno"> 587</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::RelativeErrorTooSmall;</div>
<div class="line"><a name="l00588"></a><span class="lineno"> 588</span> </div>
<div class="line"><a name="l00589"></a><span class="lineno"> 589</span>  <span class="comment">/* tests for termination and stringent tolerances. */</span></div>
<div class="line"><a name="l00590"></a><span class="lineno"> 590</span>  <span class="keywordflow">if</span> (nfev >= parameters.maxfev)</div>
<div class="line"><a name="l00591"></a><span class="lineno"> 591</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::TooManyFunctionEvaluation;</div>
<div class="line"><a name="l00592"></a><span class="lineno"> 592</span>  <span class="keywordflow">if</span> (abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.)</div>
<div class="line"><a name="l00593"></a><span class="lineno"> 593</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::FtolTooSmall;</div>
<div class="line"><a name="l00594"></a><span class="lineno"> 594</span>  <span class="keywordflow">if</span> (delta <= NumTraits<Scalar>::epsilon() * xnorm)</div>
<div class="line"><a name="l00595"></a><span class="lineno"> 595</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::XtolTooSmall;</div>
<div class="line"><a name="l00596"></a><span class="lineno"> 596</span>  <span class="keywordflow">if</span> (gnorm <= NumTraits<Scalar>::epsilon())</div>
<div class="line"><a name="l00597"></a><span class="lineno"> 597</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::GtolTooSmall;</div>
<div class="line"><a name="l00598"></a><span class="lineno"> 598</span> </div>
<div class="line"><a name="l00599"></a><span class="lineno"> 599</span>  } <span class="keywordflow">while</span> (ratio < Scalar(1e-4));</div>
<div class="line"><a name="l00600"></a><span class="lineno"> 600</span> </div>
<div class="line"><a name="l00601"></a><span class="lineno"> 601</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::Running;</div>
<div class="line"><a name="l00602"></a><span class="lineno"> 602</span> }</div>
<div class="line"><a name="l00603"></a><span class="lineno"> 603</span> </div>
<div class="line"><a name="l00604"></a><span class="lineno"> 604</span> <span class="keyword">template</span><<span class="keyword">typename</span> FunctorType, <span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00605"></a><span class="lineno"> 605</span> LevenbergMarquardtSpace::Status</div>
<div class="line"><a name="l00606"></a><span class="lineno"> 606</span> LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorage(FVectorType &x)</div>
<div class="line"><a name="l00607"></a><span class="lineno"> 607</span> {</div>
<div class="line"><a name="l00608"></a><span class="lineno"> 608</span>  LevenbergMarquardtSpace::Status status = minimizeOptimumStorageInit(x);</div>
<div class="line"><a name="l00609"></a><span class="lineno"> 609</span>  <span class="keywordflow">if</span> (status==LevenbergMarquardtSpace::ImproperInputParameters)</div>
<div class="line"><a name="l00610"></a><span class="lineno"> 610</span>  <span class="keywordflow">return</span> status;</div>
<div class="line"><a name="l00611"></a><span class="lineno"> 611</span>  <span class="keywordflow">do</span> {</div>
<div class="line"><a name="l00612"></a><span class="lineno"> 612</span>  status = minimizeOptimumStorageOneStep(x);</div>
<div class="line"><a name="l00613"></a><span class="lineno"> 613</span>  } <span class="keywordflow">while</span> (status==LevenbergMarquardtSpace::Running);</div>
<div class="line"><a name="l00614"></a><span class="lineno"> 614</span>  <span class="keywordflow">return</span> status;</div>
<div class="line"><a name="l00615"></a><span class="lineno"> 615</span> }</div>
<div class="line"><a name="l00616"></a><span class="lineno"> 616</span> </div>
<div class="line"><a name="l00617"></a><span class="lineno"> 617</span> <span class="keyword">template</span><<span class="keyword">typename</span> FunctorType, <span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00618"></a><span class="lineno"> 618</span> LevenbergMarquardtSpace::Status</div>
<div class="line"><a name="l00619"></a><span class="lineno"> 619</span> LevenbergMarquardt<FunctorType,Scalar>::lmdif1(</div>
<div class="line"><a name="l00620"></a><span class="lineno"> 620</span>  FunctorType &functor,</div>
<div class="line"><a name="l00621"></a><span class="lineno"> 621</span>  FVectorType &x,</div>
<div class="line"><a name="l00622"></a><span class="lineno"> 622</span>  Index *nfev,</div>
<div class="line"><a name="l00623"></a><span class="lineno"> 623</span>  <span class="keyword">const</span> Scalar tol</div>
<div class="line"><a name="l00624"></a><span class="lineno"> 624</span>  )</div>
<div class="line"><a name="l00625"></a><span class="lineno"> 625</span> {</div>
<div class="line"><a name="l00626"></a><span class="lineno"> 626</span>  Index n = x.size();</div>
<div class="line"><a name="l00627"></a><span class="lineno"> 627</span>  Index m = functor.values();</div>
<div class="line"><a name="l00628"></a><span class="lineno"> 628</span> </div>
<div class="line"><a name="l00629"></a><span class="lineno"> 629</span>  <span class="comment">/* check the input parameters for errors. */</span></div>
<div class="line"><a name="l00630"></a><span class="lineno"> 630</span>  <span class="keywordflow">if</span> (n <= 0 || m < n || tol < 0.)</div>
<div class="line"><a name="l00631"></a><span class="lineno"> 631</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::ImproperInputParameters;</div>
<div class="line"><a name="l00632"></a><span class="lineno"> 632</span> </div>
<div class="line"><a name="l00633"></a><span class="lineno"> 633</span>  NumericalDiff<FunctorType> numDiff(functor);</div>
<div class="line"><a name="l00634"></a><span class="lineno"> 634</span>  <span class="comment">// embedded LevenbergMarquardt</span></div>
<div class="line"><a name="l00635"></a><span class="lineno"> 635</span>  LevenbergMarquardt<NumericalDiff<FunctorType>, Scalar > lm(numDiff);</div>
<div class="line"><a name="l00636"></a><span class="lineno"> 636</span>  lm.parameters.ftol = tol;</div>
<div class="line"><a name="l00637"></a><span class="lineno"> 637</span>  lm.parameters.xtol = tol;</div>
<div class="line"><a name="l00638"></a><span class="lineno"> 638</span>  lm.parameters.maxfev = 200*(n+1);</div>
<div class="line"><a name="l00639"></a><span class="lineno"> 639</span> </div>
<div class="line"><a name="l00640"></a><span class="lineno"> 640</span>  LevenbergMarquardtSpace::Status info = LevenbergMarquardtSpace::Status(lm.minimize(x));</div>
<div class="line"><a name="l00641"></a><span class="lineno"> 641</span>  <span class="keywordflow">if</span> (nfev)</div>
<div class="line"><a name="l00642"></a><span class="lineno"> 642</span>  * nfev = lm.nfev;</div>
<div class="line"><a name="l00643"></a><span class="lineno"> 643</span>  <span class="keywordflow">return</span> info;</div>
<div class="line"><a name="l00644"></a><span class="lineno"> 644</span> }</div>
<div class="line"><a name="l00645"></a><span class="lineno"> 645</span> </div>
<div class="line"><a name="l00646"></a><span class="lineno"> 646</span> } <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00647"></a><span class="lineno"> 647</span> </div>
<div class="line"><a name="l00648"></a><span class="lineno"> 648</span> <span class="preprocessor">#endif // EIGEN_LEVENBERGMARQUARDT__H</span></div>
<div class="line"><a name="l00649"></a><span class="lineno"> 649</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00650"></a><span class="lineno"> 650</span> <span class="comment">//vim: ai ts=4 sts=4 et sw=4</span></div>
<div class="ttc" id="classEigen_1_1LevenbergMarquardt_html_a8407d07d45184a84310dfaa297ca9425"><div class="ttname"><a href="classEigen_1_1LevenbergMarquardt.html#a8407d07d45184a84310dfaa297ca9425">Eigen::LevenbergMarquardt::fvec</a></div><div class="ttdeci">FVectorType & fvec()</div><div class="ttdef"><b>Definition:</b> LevenbergMarquardt/LevenbergMarquardt.h:200</div></div>
<div class="ttc" id="classEigen_1_1LevenbergMarquardt_html_ad39de8ec664e09b12b528b4d8cdffc8c"><div class="ttname"><a href="classEigen_1_1LevenbergMarquardt.html#ad39de8ec664e09b12b528b4d8cdffc8c">Eigen::LevenbergMarquardt::nfev</a></div><div class="ttdeci">Index nfev()</div><div class="ttdef"><b>Definition:</b> LevenbergMarquardt/LevenbergMarquardt.h:184</div></div>
<div class="ttc" id="classEigen_1_1LevenbergMarquardt_html_a937987337a0875eee70a181a02cb9122"><div class="ttname"><a href="classEigen_1_1LevenbergMarquardt.html#a937987337a0875eee70a181a02cb9122">Eigen::LevenbergMarquardt::diag</a></div><div class="ttdeci">FVectorType & diag()</div><div class="ttdef"><b>Definition:</b> LevenbergMarquardt/LevenbergMarquardt.h:178</div></div>
<div class="ttc" id="classEigen_1_1LevenbergMarquardt_html_aa6d934df3d16027df0d0100cca3841fe"><div class="ttname"><a href="classEigen_1_1LevenbergMarquardt.html#aa6d934df3d16027df0d0100cca3841fe">Eigen::LevenbergMarquardt::lm_param</a></div><div class="ttdeci">RealScalar lm_param(void)</div><div class="ttdef"><b>Definition:</b> LevenbergMarquardt/LevenbergMarquardt.h:196</div></div>
<div class="ttc" id="classEigen_1_1LevenbergMarquardt_html_af52cd5af951ff74e784deeadecf73552"><div class="ttname"><a href="classEigen_1_1LevenbergMarquardt.html#af52cd5af951ff74e784deeadecf73552">Eigen::LevenbergMarquardt::resetParameters</a></div><div class="ttdeci">void resetParameters()</div><div class="ttdef"><b>Definition:</b> LevenbergMarquardt/LevenbergMarquardt.h:146</div></div>
<div class="ttc" id="classEigen_1_1LevenbergMarquardt_html_a09f0a7a9fefa463f4415e386922b3b48"><div class="ttname"><a href="classEigen_1_1LevenbergMarquardt.html#a09f0a7a9fefa463f4415e386922b3b48">Eigen::LevenbergMarquardt::fnorm</a></div><div class="ttdeci">RealScalar fnorm()</div><div class="ttdef"><b>Definition:</b> LevenbergMarquardt/LevenbergMarquardt.h:190</div></div>
<div class="ttc" id="classEigen_1_1LevenbergMarquardt_html_ac4b9a92a37e8f656a9bc7f222d3f1d3b"><div class="ttname"><a href="classEigen_1_1LevenbergMarquardt.html#ac4b9a92a37e8f656a9bc7f222d3f1d3b">Eigen::LevenbergMarquardt::gnorm</a></div><div class="ttdeci">RealScalar gnorm()</div><div class="ttdef"><b>Definition:</b> LevenbergMarquardt/LevenbergMarquardt.h:193</div></div>
<div class="ttc" id="classEigen_1_1LevenbergMarquardt_html_a4ec1e17c7206359b96335f2c0744a783"><div class="ttname"><a href="classEigen_1_1LevenbergMarquardt.html#a4ec1e17c7206359b96335f2c0744a783">Eigen::LevenbergMarquardt::njev</a></div><div class="ttdeci">Index njev()</div><div class="ttdef"><b>Definition:</b> LevenbergMarquardt/LevenbergMarquardt.h:187</div></div>
<div class="ttc" id="classEigen_1_1LevenbergMarquardt_html_afb981cc5d4a68f39d4ffd8a681f4ed81"><div class="ttname"><a href="classEigen_1_1LevenbergMarquardt.html#afb981cc5d4a68f39d4ffd8a681f4ed81">Eigen::LevenbergMarquardt::permutation</a></div><div class="ttdeci">PermutationType permutation()</div><div class="ttdef"><b>Definition:</b> LevenbergMarquardt/LevenbergMarquardt.h:213</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_70b2be79c95c9d5bfaa4c2dafa46bf10.html">unsupported</a></li><li class="navelem"><a class="el" href="dir_f12b092121fb86d54df52b635b2d8129.html">Eigen</a></li><li class="navelem"><a class="el" href="dir_756fd3610c3abb5994ea9c814224d188.html">src</a></li><li class="navelem"><a class="el" href="dir_ae2b96a00306ba646bcffb5f70dcaf92.html">NonLinearOptimization</a></li><li class="navelem"><b>LevenbergMarquardt.h</b></li>
<li class="footer">Generated on Mon Oct 28 2013 11:05:27 for Eigen-unsupported 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>
