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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// Copyright (C) 2010 Manuel Yguel <manuel.yguel@gmail.com></span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> </div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="preprocessor">#ifndef EIGEN_COMPANION_H</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_COMPANION_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment">// This file requires the user to include</span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment">// * Eigen/Core</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment">// * Eigen/src/PolynomialSolver.h</span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> </div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="keyword">namespace </span>Eigen { </div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> </div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> </div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="preprocessor">#ifndef EIGEN_PARSED_BY_DOXYGEN</span></div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="keyword">template</span> <<span class="keyword">typename</span> T></div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> T radix(){ <span class="keywordflow">return</span> 2; }</div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> </div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="keyword">template</span> <<span class="keyword">typename</span> T></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> T radix2(){ <span class="keywordflow">return</span> radix<T>()*radix<T>(); }</div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> </div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="keyword">template</span><<span class="keywordtype">int</span> Size></div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="keyword">struct </span>decrement_if_fixed_size</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> {</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  ret = (Size == Dynamic) ? Dynamic : Size-1 };</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> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="keyword">template</span>< <span class="keyword">typename</span> _Scalar, <span class="keywordtype">int</span> _Deg ></div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="keyword">class </span>companion</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> {</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Deg==Dynamic ? Dynamic : _Deg)</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> </div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  Deg = _Deg,</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  Deg_1=decrement_if_fixed_size<Deg>::ret</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> </div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  <span class="keyword">typedef</span> _Scalar Scalar;</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::Real RealScalar;</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <span class="keyword">typedef</span> Matrix<Scalar, Deg, 1> RightColumn;</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="comment">//typedef DiagonalMatrix< Scalar, Deg_1, Deg_1 > BottomLeftDiagonal;</span></div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="keyword">typedef</span> Matrix<Scalar, Deg_1, 1> BottomLeftDiagonal;</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span> </div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="keyword">typedef</span> Matrix<Scalar, Deg, Deg> DenseCompanionMatrixType;</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="keyword">typedef</span> Matrix< Scalar, _Deg, Deg_1 > LeftBlock;</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <span class="keyword">typedef</span> Matrix< Scalar, Deg_1, Deg_1 > BottomLeftBlock;</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="keyword">typedef</span> Matrix< Scalar, 1, Deg_1 > LeftBlockFirstRow;</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span> </div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="keyword">typedef</span> DenseIndex Index;</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span> </div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  EIGEN_STRONG_INLINE <span class="keyword">const</span> _Scalar operator()(Index row, Index col )<span class="keyword"> const</span></div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="keywordflow">if</span>( m_bl_diag.rows() > col )</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  {</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="keywordflow">if</span>( 0 < row ){ <span class="keywordflow">return</span> m_bl_diag[col]; }</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="keywordflow">else</span>{ <span class="keywordflow">return</span> 0; }</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="keywordflow">else</span>{ <span class="keywordflow">return</span> m_monic[row]; }</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  }</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>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="keyword">template</span><<span class="keyword">typename</span> VectorType></div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="keywordtype">void</span> setPolynomial( <span class="keyword">const</span> VectorType& poly )</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>  <span class="keyword">const</span> Index deg = poly.size()-1;</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  m_monic = -1/poly[deg] * poly.head(deg);</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="comment">//m_bl_diag.setIdentity( deg-1 );</span></div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  m_bl_diag.setOnes(deg-1);</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> </div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="keyword">template</span><<span class="keyword">typename</span> VectorType></div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  companion( <span class="keyword">const</span> VectorType& poly ){</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  setPolynomial( poly ); }</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span> </div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  DenseCompanionMatrixType denseMatrix()<span class="keyword"> const</span></div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <span class="keyword">const</span> Index deg = m_monic.size();</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <span class="keyword">const</span> Index deg_1 = deg-1;</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  DenseCompanionMatrixType companion(deg,deg);</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  companion <<</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  ( LeftBlock(deg,deg_1)</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  << LeftBlockFirstRow::Zero(1,deg_1),</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  BottomLeftBlock::Identity(deg-1,deg-1)*m_bl_diag.asDiagonal() ).finished()</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  , m_monic;</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="keywordflow">return</span> companion;</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  }</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span> </div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span> </div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span> </div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="keywordtype">bool</span> balanced( Scalar colNorm, Scalar rowNorm,</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <span class="keywordtype">bool</span>& isBalanced, Scalar& colB, Scalar& rowB );</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span> </div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <span class="keywordtype">bool</span> balancedR( Scalar colNorm, Scalar rowNorm,</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="keywordtype">bool</span>& isBalanced, Scalar& colB, Scalar& rowB );</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span> </div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <span class="keywordtype">void</span> balance();</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>  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  RightColumn m_monic;</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  BottomLeftDiagonal m_bl_diag;</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span> };</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span> </div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span> </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> <span class="keyword">template</span>< <span class="keyword">typename</span> _Scalar, <span class="keywordtype">int</span> _Deg ></div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span> <span class="keyword">inline</span></div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span> <span class="keywordtype">bool</span> companion<_Scalar,_Deg>::balanced( Scalar colNorm, Scalar rowNorm,</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <span class="keywordtype">bool</span>& isBalanced, Scalar& colB, Scalar& rowB )</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">if</span>( Scalar(0) == colNorm || Scalar(0) == rowNorm ){ <span class="keywordflow">return</span> <span class="keyword">true</span>; }</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <span class="keywordflow">else</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>  <span class="comment">//To find the balancing coefficients, if the radix is 2,</span></div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  <span class="comment">//one finds \f$ \sigma \f$ such that</span></div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="comment">// \f$ 2^{2\sigma-1} < rowNorm / colNorm \le 2^{2\sigma+1} \f$</span></div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  <span class="comment">// then the balancing coefficient for the row is \f$ 1/2^{\sigma} \f$</span></div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  <span class="comment">// and the balancing coefficient for the column is \f$ 2^{\sigma} \f$</span></div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  rowB = rowNorm / radix<Scalar>();</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  colB = Scalar(1);</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  <span class="keyword">const</span> Scalar s = colNorm + rowNorm;</div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span> </div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  <span class="keywordflow">while</span> (colNorm < rowB)</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  {</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  colB *= radix<Scalar>();</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  colNorm *= radix2<Scalar>();</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> </div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  rowB = rowNorm * radix<Scalar>();</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span> </div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  <span class="keywordflow">while</span> (colNorm >= rowB)</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  {</div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  colB /= radix<Scalar>();</div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  colNorm /= radix2<Scalar>();</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  }</div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span> </div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  <span class="comment">//This line is used to avoid insubstantial balancing</span></div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <span class="keywordflow">if</span> ((rowNorm + colNorm) < Scalar(0.95) * s * colB)</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  {</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  isBalanced = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  rowB = Scalar(1) / colB;</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</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="keywordflow">else</span>{</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>; }</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  }</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span> }</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span> </div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span> <span class="keyword">template</span>< <span class="keyword">typename</span> _Scalar, <span class="keywordtype">int</span> _Deg ></div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span> <span class="keyword">inline</span></div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span> <span class="keywordtype">bool</span> companion<_Scalar,_Deg>::balancedR( Scalar colNorm, Scalar rowNorm,</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  <span class="keywordtype">bool</span>& isBalanced, Scalar& colB, Scalar& rowB )</div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span> {</div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  <span class="keywordflow">if</span>( Scalar(0) == colNorm || Scalar(0) == rowNorm ){ <span class="keywordflow">return</span> <span class="keyword">true</span>; }</div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  {</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  <span class="keyword">const</span> _Scalar q = colNorm/rowNorm;</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  <span class="keywordflow">if</span>( !isApprox( q, _Scalar(1) ) )</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>  rowB = sqrt( colNorm/rowNorm );</div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  colB = Scalar(1)/rowB;</div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span> </div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  isBalanced = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</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>  <span class="keywordflow">else</span>{</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>; }</div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  }</div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span> }</div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span> </div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span> </div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span> <span class="keyword">template</span>< <span class="keyword">typename</span> _Scalar, <span class="keywordtype">int</span> _Deg ></div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span> <span class="keywordtype">void</span> companion<_Scalar,_Deg>::balance()</div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span> {</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  EIGEN_STATIC_ASSERT( Deg == Dynamic || 1 < Deg, YOU_MADE_A_PROGRAMMING_MISTAKE );</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  <span class="keyword">const</span> Index deg = m_monic.size();</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  <span class="keyword">const</span> Index deg_1 = deg-1;</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span> </div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <span class="keywordtype">bool</span> hasConverged=<span class="keyword">false</span>;</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <span class="keywordflow">while</span>( !hasConverged )</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  {</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  hasConverged = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  Scalar colNorm,rowNorm;</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  Scalar colB,rowB;</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span> </div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  <span class="comment">//First row, first column excluding the diagonal</span></div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  <span class="comment">//==============================================</span></div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  colNorm = abs(m_bl_diag[0]);</div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  rowNorm = abs(m_monic[0]);</div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span> </div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  <span class="comment">//Compute balancing of the row and the column</span></div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  <span class="keywordflow">if</span>( !balanced( colNorm, rowNorm, hasConverged, colB, rowB ) )</div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  {</div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  m_bl_diag[0] *= colB;</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  m_monic[0] *= rowB;</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> </div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  <span class="comment">//Middle rows and columns excluding the diagonal</span></div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  <span class="comment">//==============================================</span></div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  <span class="keywordflow">for</span>( Index i=1; i<deg_1; ++i )</div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  {</div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  <span class="comment">// column norm, excluding the diagonal</span></div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  colNorm = abs(m_bl_diag[i]);</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">// row norm, excluding the diagonal</span></div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  rowNorm = abs(m_bl_diag[i-1]) + abs(m_monic[i]);</div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span> </div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  <span class="comment">//Compute balancing of the row and the column</span></div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  <span class="keywordflow">if</span>( !balanced( colNorm, rowNorm, hasConverged, colB, rowB ) )</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>  m_bl_diag[i] *= colB;</div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  m_bl_diag[i-1] *= rowB;</div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  m_monic[i] *= rowB;</div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  }</div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  }</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span> </div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  <span class="comment">//Last row, last column excluding the diagonal</span></div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  <span class="comment">//============================================</span></div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  <span class="keyword">const</span> Index ebl = m_bl_diag.size()-1;</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  VectorBlock<RightColumn,Deg_1> headMonic( m_monic, 0, deg_1 );</div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  colNorm = headMonic.array().abs().sum();</div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  rowNorm = abs( m_bl_diag[ebl] );</div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span> </div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  <span class="comment">//Compute balancing of the row and the column</span></div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  <span class="keywordflow">if</span>( !balanced( colNorm, rowNorm, hasConverged, colB, rowB ) )</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  {</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  headMonic *= colB;</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  m_bl_diag[ebl] *= rowB;</div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  }</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> }</div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span> </div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span> } <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span> </div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span> } <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span> </div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span> <span class="preprocessor">#endif // EIGEN_COMPANION_H</span></div>
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