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@@ -4,7 +4,7 @@
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@@ -28,16 +28,16 @@
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<div id="projectname">Templates -- Meow
- &#160;<span id="projectnumber">1.1.2</span>
+ &#160;<span id="projectnumber">1.1.4</span>
</div>
- <div id="projectbrief">不能,也不應該先編譯成obj-file的templates</div>
+ <div id="projectbrief">A C++ template which is unable and also not allowed to compile to obj-file first.</div>
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-<!-- Generated by Doxygen 1.8.3.1 -->
+<!-- Generated by Doxygen 1.8.6 -->
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@@ -71,7 +71,7 @@ $(document).ready(function(){initNavTree('methods_8h_source.html','');});
<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="code" 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" title="Run the RANSAC method to approach the best solution.">ransac</a>(std::vector&lt;Data&gt; <span class="keyword">const</span>&amp; data,</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>
@@ -108,26 +108,154 @@ $(document).ready(function(){initNavTree('methods_8h_source.html','');});
<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="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> F, <span class="keyword">class</span> J, <span class="keyword">class</span> I, <span class="keyword">class</span> Stop&gt;</div>
-<div class="line"><a name="l00163"></a><span class="lineno"><a class="code" href="namespacemeow.html#a8e4a4baed7fb497f170075648ac95077"> 163</a></span>&#160;<span class="keyword">inline</span> <a class="code" href="classmeow_1_1Vector.html" title="vector ">Vector&lt;Scalar&gt;</a> <a class="code" href="namespacemeow.html#a8e4a4baed7fb497f170075648ac95077" title="Run the Levenberg-Marquardt method to solve a non-linear least squares problem.">levenbergMarquardt</a>(F <span class="keyword">const</span>&amp; func,</div>
-<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>&#160; J <span class="keyword">const</span>&amp; jaco,</div>
-<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>&#160; I <span class="keyword">const</span>&amp; iden,</div>
-<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>&#160; <a class="code" href="classmeow_1_1Vector.html" title="vector ">Vector&lt;Scalar&gt;</a> <span class="keyword">const</span>&amp; init,</div>
-<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>&#160; Stop <span class="keyword">const</span>&amp; stop,</div>
-<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>&#160; <span class="keywordtype">int</span> counter = -1) {</div>
-<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>&#160; <a class="code" href="classmeow_1_1Vector.html" title="vector ">Vector&lt;Scalar&gt;</a> ans(init);</div>
-<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>&#160; <span class="keywordflow">for</span>(<a class="code" href="classmeow_1_1Vector.html" title="vector ">Vector&lt;Scalar&gt;</a> rv;</div>
-<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>&#160; !stop((rv = func(ans)).length2()) &amp;&amp; counter != 0; counter--) {</div>
-<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>&#160; <a class="code" href="classmeow_1_1Matrix.html">Matrix&lt;Scalar&gt;</a> j(jaco(ans)), jt(j.transpose());</div>
-<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>&#160; <a class="code" href="classmeow_1_1Matrix.html">Matrix&lt;Scalar&gt;</a> i(iden(ans));</div>
-<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>&#160; ans = ans - <a class="code" href="classmeow_1_1Vector.html" title="vector ">Vector&lt;Scalar&gt;</a>((jt * j + i).inverse() * jt * rv.matrix());</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;}</div>
-<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>&#160;</div>
-<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>&#160;<span class="preprocessor">#endif // math_methods_H__</span></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#l00115">Matrix.h:115</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#l00051">utility.h:51</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#l00416">Matrix.h:416</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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