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   <div id="projectname">Templates -- Meow
   &#160;<span id="projectnumber">1.2.11</span>
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   <div id="projectbrief">A C++ template contains kinds of interesting classes and functions</div>
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<div class="title">methods.h</div>  </div>
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<a href="methods_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="preprocessor">#ifndef   math_methods_H__</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="preprocessor"></span><span class="preprocessor">#define   math_methods_H__</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="preprocessor"></span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="Matrix_8h.html">Matrix.h</a>&quot;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="Vector_8h.html">Vector.h</a>&quot;</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="math_2utility_8h.html">utility.h</a>&quot;</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;</div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="preprocessor">#include &lt;cstdlib&gt;</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="preprocessor">#include &lt;vector&gt;</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;</div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="keyword">namespace </span>meow {</div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">class</span> Data, <span class="keyword">class</span> WeightingClass&gt;</div>
<div class="line"><a name="l00058"></a><span class="lineno"><a class="line" href="namespacemeow.html#a43a73b75f2e23c8172d2098d57eaf75a">   58</a></span>&#160;<span class="keyword">inline</span> std::vector&lt;Data&gt; <a class="code" href="namespacemeow.html#a43a73b75f2e23c8172d2098d57eaf75a">ransac</a>(std::vector&lt;Data&gt; <span class="keyword">const</span>&amp; data,</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;                                WeightingClass <span class="keyword">const</span>&amp;    w,</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;                                <span class="keywordtype">size_t</span>                   N,</div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;                                <span class="keywordtype">double</span> p0, <span class="keywordtype">double</span> P) {</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;  <span class="keywordflow">if</span> (data.size() &lt; N) {</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;    <span class="keywordflow">return</span> std::vector&lt;Data&gt;();</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;  }</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;  <span class="keywordtype">double</span> ww = -1.0;</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;  std::vector&lt;Data&gt; ret;</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">double</span> count = ceil(log(1.0 - P) / log(1.0 - pow(p0, N)));</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;       count &gt; 0.0; count -= 1.0) {</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;    std::vector&lt;Data&gt; sample;</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;    std::vector&lt;int&gt;  index(N);</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; N; i++) {</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">bool</span> ok = <span class="keyword">false</span>; !ok; ) {</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;        index[i] = rand() % data.size();</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;        ok = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> j = 0; ok &amp;&amp; j &lt; i; j++)</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;          <span class="keywordflow">if</span> (index[i] == index[j])</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;            ok = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;      }</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;      sample.push_back(data[index[i]]);</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;    }</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;    <span class="keywordtype">double</span> w_now = w(sample, data);</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;    <span class="keywordflow">if</span> (w_now &lt; 0) {</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;      count += 0.5;</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;      <span class="keywordflow">continue</span>;</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;    }</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;    <span class="keywordflow">if</span> (ww &lt; w_now) {</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;      ret = sample;</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;      ww = w_now;</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;    }</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;  }</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;  <span class="keywordflow">return</span> ret;</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;}</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;<span class="comment">/*</span></div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;<span class="comment"> * @brief Run the \b Levenberg-Marquardt method to solve a non-linear</span></div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;<span class="comment"> *        least squares problem.</span></div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;<span class="comment"> * Assume:</span></div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;<span class="comment"> *  - The function we want to optimize is</span></div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;<span class="comment"> *    \f$ F: \mathbb{R}  ^N \mapsto \mathbb{R}^M \f$</span></div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;<span class="comment"> *  - We want to find the best solution \f$ v \f$ such that</span></div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;<span class="comment"> *    \f$ F(v)^T F(v) = 0\f$.  But there is a gived threshold</span></div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;<span class="comment"> *    \f$ \epsilon \f$, we can just find a \f$ v \f$ such that</span></div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;<span class="comment"> *    \f$ F(v)^T F(v) &lt; \epsilon \f$, which is mush easier.</span></div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;<span class="comment"> *  - User gived a initiial vector \f$ v_0 \f$</span></div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;<span class="comment"> *  .</span></div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;<span class="comment"> * Then we just iteratilly find \f$ v_1, v_2, v_3, v_4... \f$ until a</span></div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;<span class="comment"> * vector \f$ v_k \f$ satisified that \f$ F(v_k)^TF(v_k)&lt;\epsilon \f$ .</span></div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;<span class="comment"> * And each iterator we have:</span></div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;<span class="comment"> * \f[</span></div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;<span class="comment"> *   v_{i+1} = v_i + (J(v_i)^TJ(v_i)+\lambda I_{N\times N})^{-1} J(v_i)^T F(v_i)</span></div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;<span class="comment"> * \f]</span></div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;<span class="comment"> * Where \f$ J(v) \f$ is a jacobian matrix defined below:</span></div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;<span class="comment"> * \f[</span></div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;<span class="comment"> *   J(v) = \frac{d}{dv}F(v) =</span></div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;<span class="comment"> *   \left[ \begin{array}{ccccc}</span></div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;<span class="comment"> *     \frac{\partial F_1(v)}{\partial v_1} &amp;</span></div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;<span class="comment"> *     \frac{\partial F_1(v)}{\partial v_2} &amp;</span></div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;<span class="comment"> *     \frac{\partial F_1(v)}{\partial v_3} &amp;</span></div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;<span class="comment"> *     ...                                  &amp;</span></div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;<span class="comment"> *     \frac{\partial F_1(v)}{\partial v_N} \\</span></div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;<span class="comment"> *     \frac{\partial F_2(v)}{\partial v_1} &amp;</span></div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;<span class="comment"> *     \frac{\partial F_2(v)}{\partial v_2} &amp;</span></div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;<span class="comment"> *     \frac{\partial F_2(v)}{\partial v_3} &amp;</span></div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;<span class="comment"> *     ...                                  &amp;</span></div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;<span class="comment"> *     \frac{\partial F_2(v)}{\partial v_N} \\</span></div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;<span class="comment"> *     \frac{\partial F_3(v)}{\partial v_1} &amp;</span></div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;<span class="comment"> *     \frac{\partial F_3(v)}{\partial v_2} &amp;</span></div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;<span class="comment"> *     \frac{\partial F_3(v)}{\partial v_3} &amp;</span></div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;<span class="comment"> *     ...                                  &amp;</span></div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;<span class="comment"> *     \frac{\partial F_3(v)}{\partial v_N} \\</span></div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;<span class="comment"> *     . &amp; . &amp; . &amp; &amp; . \\</span></div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;<span class="comment"> *     . &amp; . &amp; . &amp; &amp; . \\</span></div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;<span class="comment"> *     . &amp; . &amp; . &amp; &amp; . \\</span></div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;<span class="comment"> *     \frac{\partial F_M(v)}{\partial v_1} &amp;</span></div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;<span class="comment"> *     \frac{\partial F_M(v)}{\partial v_2} &amp;</span></div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;<span class="comment"> *     \frac{\partial F_M(v)}{\partial v_3} &amp;</span></div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;<span class="comment"> *     ...                                  &amp;</span></div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;<span class="comment"> *     \frac{\partial F_M(v)}{\partial v_N} \\</span></div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;<span class="comment"> *   \end{array} \right]</span></div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;<span class="comment"> * \f]</span></div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;<span class="comment"> * And \f$ \lambda \f$ is a magic number....</span></div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;<span class="comment"> * @param [in] func    \f$ F \f$,  a function(class with \c operator() )</span></div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;<span class="comment"> *                     which input a vector and the output the squares errors.</span></div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;<span class="comment"> * @param [in] jaco    \f$ J \f$, a function which input a vector</span></div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;<span class="comment"> *                     and then output \b func derivate by the vector</span></div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;<span class="comment"> * @param [in] iden    \f$ \lambda I_{N \times N} \f$, defined above</span></div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;<span class="comment"> * @param [in] init    \f$ v_0 \f$Initial vector</span></div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;<span class="comment"> * @param [in] stop    A function return a boolean which means the error is</span></div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;<span class="comment"> *                     acceptable or not, so \f[</span></div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;<span class="comment"> *                       S_{top}(v) = \begin{cases}</span></div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;<span class="comment"> *                         true  &amp; if~F(v)&lt;\epsilon \\</span></div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;<span class="comment"> *                         false &amp; else</span></div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;<span class="comment"> *                       \end{cases}</span></div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;<span class="comment"> *                     \f]</span></div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;<span class="comment"> * @param [in] counter To prevent infinit loop.</span></div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;<span class="comment"> * @return a vector which means the best solution this function found.</span></div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;<span class="comment"> * @author cat_leopard</span></div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">class</span> Scalar, <span class="keyword">class</span> Function&gt;</div>
<div class="line"><a name="l00163"></a><span class="lineno"><a class="line" href="namespacemeow.html#a37b8a0148b872c4533f37dde9bbb9ae4">  163</a></span>&#160;<span class="keyword">inline</span> <a class="code" href="classmeow_1_1Vector.html">Vector&lt;Scalar&gt;</a> <a class="code" href="namespacemeow.html#a37b8a0148b872c4533f37dde9bbb9ae4">levenbergMarquardt</a>(Function       <span class="keyword">const</span>&amp; f,</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;                                         <a class="code" href="classmeow_1_1Vector.html">Vector&lt;Scalar&gt;</a> <span class="keyword">const</span>&amp; init,</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;                                         <span class="keywordtype">int</span>                   counter = -1) {</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;  <a class="code" href="classmeow_1_1Vector.html">Vector&lt;Scalar&gt;</a> ans(init), residure_v;</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;  <span class="keywordflow">for</span> ( ; counter != 0 &amp;&amp; !f.accept(residure_v = f.residure(ans)); --counter) {</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;    <a class="code" href="classmeow_1_1Matrix.html">Matrix&lt;Scalar&gt;</a> m_j (f.jacobian(ans));</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;    <a class="code" href="classmeow_1_1Matrix.html">Matrix&lt;Scalar&gt;</a> m_jt(m_j.transpose());</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;    <a class="code" href="classmeow_1_1Matrix.html">Matrix&lt;Scalar&gt;</a> m(m_j * m_jt), M;</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; M.<a class="code" href="classmeow_1_1Matrix.html#a030758e4938c4d56a0b665e6a51d1405">valid</a>() == <span class="keyword">false</span>; i++) {</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;      M = (m + f.diagonal(ans, i)).inverse();</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;    }</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;    ans = ans - M * m_jt * residure_v;</div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;  }</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;  <span class="keywordflow">return</span> ans;</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;}</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;<span class="comment">// residure</span></div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;<span class="comment">// jacobian</span></div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;<span class="comment">// identity</span></div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">class</span> Scalar, <span class="keyword">class</span> Function&gt;</div>
<div class="line"><a name="l00183"></a><span class="lineno"><a class="line" href="namespacemeow.html#adbd82702daf1e569c4a72176aa799c6d">  183</a></span>&#160;<span class="keyword">inline</span> <a class="code" href="classmeow_1_1Vector.html">Vector&lt;Scalar&gt;</a> <a class="code" href="namespacemeow.html#adbd82702daf1e569c4a72176aa799c6d">levenbergMarquardtTraining</a>(Function            &amp; f,</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;                                                 <a class="code" href="classmeow_1_1Vector.html">Vector&lt;Scalar&gt;</a> <span class="keyword">const</span>&amp; init,</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;                                                 Scalar         <span class="keyword">const</span>&amp; init_mu,</div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;                                                 Scalar         <span class="keyword">const</span>&amp; mu_pow,</div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;                                                 Scalar         <span class="keyword">const</span>&amp; er_max,</div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;                                                 <span class="keywordtype">int</span> retry_number,</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;                                                 <span class="keywordtype">int</span> counter) {</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;  <span class="keywordflow">if</span> (retry_number == 0) retry_number = 1;</div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;  <a class="code" href="classmeow_1_1Vector.html">Vector&lt;Scalar&gt;</a> ans_now(init), rv_now(f.residure(ans_now));</div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;  <a class="code" href="classmeow_1_1Vector.html">Vector&lt;Scalar&gt;</a> ans_nxt      , rv_nxt;</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;  Scalar         er_now(rv_now.length2());</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;  Scalar         er_nxt;</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;  <a class="code" href="classmeow_1_1Vector.html">Vector&lt;Scalar&gt;</a> ans_best(ans_now);</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;  Scalar         er_best ( er_now);</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;  <a class="code" href="classmeow_1_1Matrix.html">Matrix&lt;Scalar&gt;</a> m_ja, m_jt, m, iden(f.identity());</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;  Scalar mu(init_mu);</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;  <span class="keywordflow">for</span> ( ; counter != 0 &amp;&amp; er_now &gt; er_max; --counter) {</div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;    m_ja = f.jacobian();</div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;    m_jt = m_ja.<a class="code" href="classmeow_1_1Matrix.html#a869be60b593d7ce7101ee7ac788b0dd0">transpose</a>();</div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;    m    = m_jt * m_ja;</div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;    <span class="keywordtype">bool</span> good = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;    <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i != retry_number; ++i, mu = mu * mu_pow) {</div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;      ans_nxt = ans_now + (m + iden * mu).inverse() * m_jt * rv_now.matrix();</div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;      rv_nxt  = f.residure(ans_nxt);</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;      er_nxt  = rv_nxt.<a class="code" href="classmeow_1_1Vector.html#a71b56938e01de730490e722824f4b53e">length2</a>();</div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;      <span class="keywordflow">if</span> (er_nxt &lt;= er_now) {</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;        good = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;        <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;      }</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;    }</div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;    <span class="keywordflow">if</span> (good) {</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;      mu = mu / mu_pow;</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;    }</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;    mu = <a class="code" href="namespacemeow.html#a98d838d338a3e6f3c57e94562fab3fa7">inRange</a>(0.0000001, 100.0, mu);</div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;    ans_now = ans_nxt;</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;    rv_now  = rv_nxt;</div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;    er_now  = er_nxt;</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;    <span class="keywordflow">if</span> (er_now &lt; er_best) {</div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;      ans_best = ans_now;</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;      er_best  = er_now;</div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;    }</div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;  }</div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;  <span class="keywordflow">return</span> ans_best;</div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;}</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;} <span class="comment">// meow</span></div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;<span class="preprocessor">#endif // math_methods_H__</span></div>
<div class="ttc" id="namespacemeow_html_adbd82702daf1e569c4a72176aa799c6d"><div class="ttname"><a href="namespacemeow.html#adbd82702daf1e569c4a72176aa799c6d">meow::levenbergMarquardtTraining</a></div><div class="ttdeci">Vector&lt; Scalar &gt; levenbergMarquardtTraining(Function &amp;f, Vector&lt; Scalar &gt; const &amp;init, Scalar const &amp;init_mu, Scalar const &amp;mu_pow, Scalar const &amp;er_max, int retry_number, int counter)</div><div class="ttdef"><b>Definition:</b> <a href="methods_8h_source.html#l00183">methods.h:183</a></div></div>
<div class="ttc" id="classmeow_1_1Vector_html_a71b56938e01de730490e722824f4b53e"><div class="ttname"><a href="classmeow_1_1Vector.html#a71b56938e01de730490e722824f4b53e">meow::Vector::length2</a></div><div class="ttdeci">Scalar length2() const </div><div class="ttdoc">same as (*this).dot(*this) </div><div class="ttdef"><b>Definition:</b> <a href="Vector_8h_source.html#l00204">Vector.h:204</a></div></div>
<div class="ttc" id="namespacemeow_html_a37b8a0148b872c4533f37dde9bbb9ae4"><div class="ttname"><a href="namespacemeow.html#a37b8a0148b872c4533f37dde9bbb9ae4">meow::levenbergMarquardt</a></div><div class="ttdeci">Vector&lt; Scalar &gt; levenbergMarquardt(Function const &amp;f, Vector&lt; Scalar &gt; const &amp;init, int counter=-1)</div><div class="ttdef"><b>Definition:</b> <a href="methods_8h_source.html#l00163">methods.h:163</a></div></div>
<div class="ttc" id="classmeow_1_1Matrix_html_a030758e4938c4d56a0b665e6a51d1405"><div class="ttname"><a href="classmeow_1_1Matrix.html#a030758e4938c4d56a0b665e6a51d1405">meow::Matrix::valid</a></div><div class="ttdeci">bool valid() const </div><div class="ttdoc">Return whether it is a valid matrix. </div><div class="ttdef"><b>Definition:</b> <a href="Matrix_8h_source.html#l00124">Matrix.h:124</a></div></div>
<div class="ttc" id="math_2utility_8h_html"><div class="ttname"><a href="math_2utility_8h.html">utility.h</a></div></div>
<div class="ttc" id="classmeow_1_1Vector_html"><div class="ttname"><a href="classmeow_1_1Vector.html">meow::Vector</a></div><div class="ttdoc">vector </div><div class="ttdef"><b>Definition:</b> <a href="Vector_8h_source.html#l00019">Vector.h:19</a></div></div>
<div class="ttc" id="namespacemeow_html_a98d838d338a3e6f3c57e94562fab3fa7"><div class="ttname"><a href="namespacemeow.html#a98d838d338a3e6f3c57e94562fab3fa7">meow::inRange</a></div><div class="ttdeci">T inRange(T const &amp;mn, T const &amp;mx, T const &amp;v)</div><div class="ttdoc">std::min(mx,std::max(mn,v)) </div><div class="ttdef"><b>Definition:</b> <a href="math_2utility_8h_source.html#l00061">utility.h:61</a></div></div>
<div class="ttc" id="namespacemeow_html_a43a73b75f2e23c8172d2098d57eaf75a"><div class="ttname"><a href="namespacemeow.html#a43a73b75f2e23c8172d2098d57eaf75a">meow::ransac</a></div><div class="ttdeci">std::vector&lt; Data &gt; ransac(std::vector&lt; Data &gt; const &amp;data, WeightingClass const &amp;w, size_t N, double p0, double P)</div><div class="ttdoc">Run the RANSAC method to approach the best solution. </div><div class="ttdef"><b>Definition:</b> <a href="methods_8h_source.html#l00058">methods.h:58</a></div></div>
<div class="ttc" id="classmeow_1_1Matrix_html_a869be60b593d7ce7101ee7ac788b0dd0"><div class="ttname"><a href="classmeow_1_1Matrix.html#a869be60b593d7ce7101ee7ac788b0dd0">meow::Matrix::transpose</a></div><div class="ttdeci">Matrix transpose() const </div><div class="ttdoc">return itself&#39;s transpose matrix </div><div class="ttdef"><b>Definition:</b> <a href="Matrix_8h_source.html#l00435">Matrix.h:435</a></div></div>
<div class="ttc" id="Matrix_8h_html"><div class="ttname"><a href="Matrix_8h.html">Matrix.h</a></div></div>
<div class="ttc" id="Vector_8h_html"><div class="ttname"><a href="Vector_8h.html">Vector.h</a></div></div>
<div class="ttc" id="classmeow_1_1Matrix_html"><div class="ttname"><a href="classmeow_1_1Matrix.html">meow::Matrix&lt; Scalar &gt;</a></div></div>
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