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<div class="title">PolynomialSolver.h</div> </div>
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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_POLYNOMIAL_SOLVER_H</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_POLYNOMIAL_SOLVER_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="keyword">namespace </span>Eigen { </div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> </div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="keyword">template</span>< <span class="keyword">typename</span> _Scalar, <span class="keywordtype">int</span> _Deg ></div>
<div class="line"><a name="l00029"></a><span class="lineno"><a class="line" href="classEigen_1_1PolynomialSolverBase.html"> 29</a></span> <span class="keyword">class </span><a class="code" href="classEigen_1_1PolynomialSolverBase.html">PolynomialSolverBase</a></div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> {</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Deg==Dynamic ? Dynamic : _Deg)</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> </div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <span class="keyword">typedef</span> _Scalar Scalar;</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::Real RealScalar;</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <span class="keyword">typedef</span> std::complex<RealScalar> RootType;</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <span class="keyword">typedef</span> Matrix<RootType,_Deg,1> RootsType;</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> </div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  <span class="keyword">typedef</span> DenseIndex Index;</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">protected</span>:</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  <span class="keyword">template</span>< <span class="keyword">typename</span> OtherPolynomial ></div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  <span class="keyword">inline</span> <span class="keywordtype">void</span> setPolynomial( <span class="keyword">const</span> OtherPolynomial& poly ){</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  m_roots.resize(poly.size()); }</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> </div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  <span class="keyword">template</span>< <span class="keyword">typename</span> OtherPolynomial ></div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  <span class="keyword">inline</span> <a class="code" href="classEigen_1_1PolynomialSolverBase.html">PolynomialSolverBase</a>( <span class="keyword">const</span> OtherPolynomial& poly ){</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  setPolynomial( poly() ); }</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> </div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <span class="keyword">inline</span> <a class="code" href="classEigen_1_1PolynomialSolverBase.html">PolynomialSolverBase</a>(){}</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span> </div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00055"></a><span class="lineno"><a class="line" href="classEigen_1_1PolynomialSolverBase.html#a170e917417495c3d536ae6a1b75e9d1e"> 55</a></span>  <span class="keyword">inline</span> <span class="keyword">const</span> RootsType& <a class="code" href="classEigen_1_1PolynomialSolverBase.html#a170e917417495c3d536ae6a1b75e9d1e">roots</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_roots; }</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span> </div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Stl_back_insertion_sequence></div>
<div class="line"><a name="l00069"></a><span class="lineno"><a class="line" href="classEigen_1_1PolynomialSolverBase.html#a152ced5a7f96ba18528e540cd0c7e6ce"> 69</a></span>  <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1PolynomialSolverBase.html#a152ced5a7f96ba18528e540cd0c7e6ce">realRoots</a>( Stl_back_insertion_sequence& bi_seq,</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="keyword">const</span> RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() )<span class="keyword"> const</span></div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  bi_seq.clear();</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="keywordflow">for</span>(Index i=0; i<m_roots.size(); ++i )</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  {</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="keywordflow">if</span>( abs( m_roots[i].imag() ) < absImaginaryThreshold ){</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  bi_seq.push_back( m_roots[i].real() ); }</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  }</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  }</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span> </div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="keyword">template</span><<span class="keyword">typename</span> squaredNormBinaryPredicate></div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="keyword">inline</span> <span class="keyword">const</span> RootType& selectComplexRoot_withRespectToNorm( squaredNormBinaryPredicate& pred )<span class="keyword"> const</span></div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  Index res=0;</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  RealScalar norm2 = numext::abs2( m_roots[0] );</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="keywordflow">for</span>( Index i=1; i<m_roots.size(); ++i )</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  {</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  <span class="keyword">const</span> RealScalar currNorm2 = numext::abs2( m_roots[i] );</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <span class="keywordflow">if</span>( pred( currNorm2, norm2 ) ){</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  res=i; norm2=currNorm2; }</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  }</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="keywordflow">return</span> m_roots[res];</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  }</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span> </div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00100"></a><span class="lineno"><a class="line" href="classEigen_1_1PolynomialSolverBase.html#a1057f89aeacfd843351d5016dda4a047"> 100</a></span>  <span class="keyword">inline</span> <span class="keyword">const</span> RootType& <a class="code" href="classEigen_1_1PolynomialSolverBase.html#a1057f89aeacfd843351d5016dda4a047">greatestRoot</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  std::greater<Scalar> greater;</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="keywordflow">return</span> selectComplexRoot_withRespectToNorm( greater );</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  }</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span> </div>
<div class="line"><a name="l00109"></a><span class="lineno"><a class="line" href="classEigen_1_1PolynomialSolverBase.html#afcc2f9f37f2641d8adc18e6a4be2425b"> 109</a></span>  <span class="keyword">inline</span> <span class="keyword">const</span> RootType& <a class="code" href="classEigen_1_1PolynomialSolverBase.html#afcc2f9f37f2641d8adc18e6a4be2425b">smallestRoot</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  std::less<Scalar> less;</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="keywordflow">return</span> selectComplexRoot_withRespectToNorm( less );</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  }</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span> </div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <span class="keyword">template</span><<span class="keyword">typename</span> squaredRealPartBinaryPredicate></div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="keyword">inline</span> <span class="keyword">const</span> RealScalar& selectRealRoot_withRespectToAbsRealPart(</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  squaredRealPartBinaryPredicate& pred,</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <span class="keywordtype">bool</span>& hasArealRoot,</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="keyword">const</span> RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() )<span class="keyword"> const</span></div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  hasArealRoot = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  Index res=0;</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  RealScalar abs2(0);</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span> </div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <span class="keywordflow">for</span>( Index i=0; i<m_roots.size(); ++i )</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  {</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <span class="keywordflow">if</span>( abs( m_roots[i].imag() ) < absImaginaryThreshold )</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  {</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <span class="keywordflow">if</span>( !hasArealRoot )</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>  hasArealRoot = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  res = i;</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  abs2 = m_roots[i].real() * m_roots[i].real();</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  }</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="keywordflow">else</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>  <span class="keyword">const</span> RealScalar currAbs2 = m_roots[i].real() * m_roots[i].real();</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  <span class="keywordflow">if</span>( pred( currAbs2, abs2 ) )</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  {</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  abs2 = currAbs2;</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  res = i;</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>  }</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  }</div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  {</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  <span class="keywordflow">if</span>( abs( m_roots[i].imag() ) < abs( m_roots[res].imag() ) ){</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  res = i; }</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  }</div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  }</div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  <span class="keywordflow">return</span> numext::real_ref(m_roots[res]);</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  }</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span> </div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span> </div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  <span class="keyword">template</span><<span class="keyword">typename</span> RealPartBinaryPredicate></div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  <span class="keyword">inline</span> <span class="keyword">const</span> RealScalar& selectRealRoot_withRespectToRealPart(</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  RealPartBinaryPredicate& pred,</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  <span class="keywordtype">bool</span>& hasArealRoot,</div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  <span class="keyword">const</span> RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() )<span class="keyword"> const</span></div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  hasArealRoot = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  Index res=0;</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  RealScalar val(0);</div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span> </div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  <span class="keywordflow">for</span>( Index i=0; i<m_roots.size(); ++i )</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>  <span class="keywordflow">if</span>( abs( m_roots[i].imag() ) < absImaginaryThreshold )</div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  {</div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <span class="keywordflow">if</span>( !hasArealRoot )</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>  hasArealRoot = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  res = i;</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  val = m_roots[i].real();</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>  {</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  <span class="keyword">const</span> RealScalar curr = m_roots[i].real();</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  <span class="keywordflow">if</span>( pred( curr, val ) )</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>  val = curr;</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  res = i;</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  }</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  }</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">else</span></div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  {</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  <span class="keywordflow">if</span>( abs( m_roots[i].imag() ) < abs( m_roots[res].imag() ) ){</div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  res = i; }</div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  }</div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  }</div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  <span class="keywordflow">return</span> numext::real_ref(m_roots[res]);</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  }</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span> </div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00212"></a><span class="lineno"><a class="line" href="classEigen_1_1PolynomialSolverBase.html#a39f7bf9d7209ad81023ac260c0c73b95"> 212</a></span>  <span class="keyword">inline</span> <span class="keyword">const</span> RealScalar& <a class="code" href="classEigen_1_1PolynomialSolverBase.html#a39f7bf9d7209ad81023ac260c0c73b95">absGreatestRealRoot</a>(</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  <span class="keywordtype">bool</span>& hasArealRoot,</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  <span class="keyword">const</span> RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() )<span class="keyword"> const</span></div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  std::greater<Scalar> greater;</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  <span class="keywordflow">return</span> selectRealRoot_withRespectToAbsRealPart( greater, hasArealRoot, absImaginaryThreshold );</div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  }</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span> </div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span> </div>
<div class="line"><a name="l00235"></a><span class="lineno"><a class="line" href="classEigen_1_1PolynomialSolverBase.html#a9d126b6ec7d4272a57c2599290eaded8"> 235</a></span>  <span class="keyword">inline</span> <span class="keyword">const</span> RealScalar& <a class="code" href="classEigen_1_1PolynomialSolverBase.html#a9d126b6ec7d4272a57c2599290eaded8">absSmallestRealRoot</a>(</div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  <span class="keywordtype">bool</span>& hasArealRoot,</div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  <span class="keyword">const</span> RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() )<span class="keyword"> const</span></div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  std::less<Scalar> less;</div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  <span class="keywordflow">return</span> selectRealRoot_withRespectToAbsRealPart( less, hasArealRoot, absImaginaryThreshold );</div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  }</div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span> </div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span> </div>
<div class="line"><a name="l00258"></a><span class="lineno"><a class="line" href="classEigen_1_1PolynomialSolverBase.html#a98061536184cd108e00753d4218fbbc1"> 258</a></span>  <span class="keyword">inline</span> <span class="keyword">const</span> RealScalar& <a class="code" href="classEigen_1_1PolynomialSolverBase.html#a98061536184cd108e00753d4218fbbc1">greatestRealRoot</a>(</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  <span class="keywordtype">bool</span>& hasArealRoot,</div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  <span class="keyword">const</span> RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() )<span class="keyword"> const</span></div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  std::greater<Scalar> greater;</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  <span class="keywordflow">return</span> selectRealRoot_withRespectToRealPart( greater, hasArealRoot, absImaginaryThreshold );</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  }</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span> </div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span> </div>
<div class="line"><a name="l00281"></a><span class="lineno"><a class="line" href="classEigen_1_1PolynomialSolverBase.html#a399ac0a070144fdb3b7266be28f47e8b"> 281</a></span>  <span class="keyword">inline</span> <span class="keyword">const</span> RealScalar& <a class="code" href="classEigen_1_1PolynomialSolverBase.html#a399ac0a070144fdb3b7266be28f47e8b">smallestRealRoot</a>(</div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  <span class="keywordtype">bool</span>& hasArealRoot,</div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  <span class="keyword">const</span> RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() )<span class="keyword"> const</span></div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  std::less<Scalar> less;</div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  <span class="keywordflow">return</span> selectRealRoot_withRespectToRealPart( less, hasArealRoot, absImaginaryThreshold );</div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  }</div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span> </div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  RootsType m_roots;</div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span> };</div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span> </div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span> <span class="preprocessor">#define EIGEN_POLYNOMIAL_SOLVER_BASE_INHERITED_TYPES( BASE ) \</span></div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span> <span class="preprocessor"> typedef typename BASE::Scalar Scalar; \</span></div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span> <span class="preprocessor"> typedef typename BASE::RealScalar RealScalar; \</span></div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span> <span class="preprocessor"> typedef typename BASE::RootType RootType; \</span></div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span> <span class="preprocessor"> typedef typename BASE::RootsType RootsType;</span></div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span> </div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span> </div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span> <span class="keyword">template</span>< <span class="keyword">typename</span> _Scalar, <span class="keywordtype">int</span> _Deg ></div>
<div class="line"><a name="l00331"></a><span class="lineno"><a class="line" href="classEigen_1_1PolynomialSolver.html"> 331</a></span> <span class="keyword">class </span><a class="code" href="classEigen_1_1PolynomialSolver.html">PolynomialSolver</a> : <span class="keyword">public</span> <a class="code" href="classEigen_1_1PolynomialSolverBase.html">PolynomialSolverBase</a><_Scalar,_Deg></div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span> {</div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Deg==Dynamic ? Dynamic : _Deg)</div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span> </div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1PolynomialSolverBase.html">PolynomialSolverBase<_Scalar,_Deg></a> <a class="code" href="classEigen_1_1PolynomialSolverBase.html">PS_Base</a>;</div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  EIGEN_POLYNOMIAL_SOLVER_BASE_INHERITED_TYPES( <a class="code" href="classEigen_1_1PolynomialSolverBase.html">PS_Base</a> )</div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span> </div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  <span class="keyword">typedef</span> Matrix<Scalar,_Deg,_Deg> CompanionMatrixType;</div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  <span class="keyword">typedef</span> EigenSolver<CompanionMatrixType> EigenSolverType;</div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span> </div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  <span class="keyword">template</span>< <span class="keyword">typename</span> OtherPolynomial ></div>
<div class="line"><a name="l00345"></a><span class="lineno"><a class="line" href="classEigen_1_1PolynomialSolver.html#a0ebea181d86798f6f44665459bbc0a9b"> 345</a></span>  <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1PolynomialSolver.html#a0ebea181d86798f6f44665459bbc0a9b">compute</a>( <span class="keyword">const</span> OtherPolynomial& poly )</div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  {</div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  eigen_assert( Scalar(0) != poly[poly.size()-1] );</div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  internal::companion<Scalar,_Deg> companion( poly );</div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  companion.balance();</div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  m_eigenSolver.compute( companion.denseMatrix() );</div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  m_roots = m_eigenSolver.eigenvalues();</div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  }</div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span> </div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  <span class="keyword">template</span>< <span class="keyword">typename</span> OtherPolynomial ></div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  <span class="keyword">inline</span> <a class="code" href="classEigen_1_1PolynomialSolver.html">PolynomialSolver</a>( <span class="keyword">const</span> OtherPolynomial& poly ){</div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  <a class="code" href="classEigen_1_1PolynomialSolver.html#a0ebea181d86798f6f44665459bbc0a9b">compute</a>( poly ); }</div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span> </div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  <span class="keyword">inline</span> PolynomialSolver(){}</div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span> </div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  <span class="keyword">using</span> PS_Base::m_roots;</div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  EigenSolverType m_eigenSolver;</div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span> };</div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span> </div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span> </div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span> <span class="keyword">template</span>< <span class="keyword">typename</span> _Scalar ></div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span> <span class="keyword">class </span>PolynomialSolver<_Scalar,1> : <span class="keyword">public</span> PolynomialSolverBase<_Scalar,1></div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span> {</div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  <span class="keyword">typedef</span> PolynomialSolverBase<_Scalar,1> PS_Base;</div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  EIGEN_POLYNOMIAL_SOLVER_BASE_INHERITED_TYPES( PS_Base )</div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span> </div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  public:</div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  template< typename OtherPolynomial ></div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1PolynomialSolver.html#a0ebea181d86798f6f44665459bbc0a9b">compute</a>( const OtherPolynomial& poly )</div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  {</div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  eigen_assert( Scalar(0) != poly[poly.size()-1] );</div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  m_roots[0] = -poly[0]/poly[poly.size()-1];</div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  }</div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span> </div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  <span class="keyword">using</span> PS_Base::m_roots;</div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span> };</div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span> </div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span> } <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span> </div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span> <span class="preprocessor">#endif // EIGEN_POLYNOMIAL_SOLVER_H</span></div>
<div class="ttc" id="classEigen_1_1PolynomialSolver_html_a0ebea181d86798f6f44665459bbc0a9b"><div class="ttname"><a href="classEigen_1_1PolynomialSolver.html#a0ebea181d86798f6f44665459bbc0a9b">Eigen::PolynomialSolver::compute</a></div><div class="ttdeci">void compute(const OtherPolynomial &poly)</div><div class="ttdef"><b>Definition:</b> PolynomialSolver.h:345</div></div>
<div class="ttc" id="classEigen_1_1PolynomialSolverBase_html_a170e917417495c3d536ae6a1b75e9d1e"><div class="ttname"><a href="classEigen_1_1PolynomialSolverBase.html#a170e917417495c3d536ae6a1b75e9d1e">Eigen::PolynomialSolverBase::roots</a></div><div class="ttdeci">const RootsType & roots() const </div><div class="ttdef"><b>Definition:</b> PolynomialSolver.h:55</div></div>
<div class="ttc" id="classEigen_1_1PolynomialSolverBase_html_a9d126b6ec7d4272a57c2599290eaded8"><div class="ttname"><a href="classEigen_1_1PolynomialSolverBase.html#a9d126b6ec7d4272a57c2599290eaded8">Eigen::PolynomialSolverBase::absSmallestRealRoot</a></div><div class="ttdeci">const RealScalar & absSmallestRealRoot(bool &hasArealRoot, const RealScalar &absImaginaryThreshold=NumTraits< Scalar >::dummy_precision()) const </div><div class="ttdef"><b>Definition:</b> PolynomialSolver.h:235</div></div>
<div class="ttc" id="classEigen_1_1PolynomialSolverBase_html_a39f7bf9d7209ad81023ac260c0c73b95"><div class="ttname"><a href="classEigen_1_1PolynomialSolverBase.html#a39f7bf9d7209ad81023ac260c0c73b95">Eigen::PolynomialSolverBase::absGreatestRealRoot</a></div><div class="ttdeci">const RealScalar & absGreatestRealRoot(bool &hasArealRoot, const RealScalar &absImaginaryThreshold=NumTraits< Scalar >::dummy_precision()) const </div><div class="ttdef"><b>Definition:</b> PolynomialSolver.h:212</div></div>
<div class="ttc" id="classEigen_1_1PolynomialSolverBase_html_a98061536184cd108e00753d4218fbbc1"><div class="ttname"><a href="classEigen_1_1PolynomialSolverBase.html#a98061536184cd108e00753d4218fbbc1">Eigen::PolynomialSolverBase::greatestRealRoot</a></div><div class="ttdeci">const RealScalar & greatestRealRoot(bool &hasArealRoot, const RealScalar &absImaginaryThreshold=NumTraits< Scalar >::dummy_precision()) const </div><div class="ttdef"><b>Definition:</b> PolynomialSolver.h:258</div></div>
<div class="ttc" id="classEigen_1_1PolynomialSolverBase_html"><div class="ttname"><a href="classEigen_1_1PolynomialSolverBase.html">Eigen::PolynomialSolverBase</a></div><div class="ttdoc">Defined to be inherited by polynomial solvers: it provides convenient methods such as...</div><div class="ttdef"><b>Definition:</b> PolynomialSolver.h:29</div></div>
<div class="ttc" id="classEigen_1_1PolynomialSolverBase_html_a1057f89aeacfd843351d5016dda4a047"><div class="ttname"><a href="classEigen_1_1PolynomialSolverBase.html#a1057f89aeacfd843351d5016dda4a047">Eigen::PolynomialSolverBase::greatestRoot</a></div><div class="ttdeci">const RootType & greatestRoot() const </div><div class="ttdef"><b>Definition:</b> PolynomialSolver.h:100</div></div>
<div class="ttc" id="classEigen_1_1PolynomialSolverBase_html_afcc2f9f37f2641d8adc18e6a4be2425b"><div class="ttname"><a href="classEigen_1_1PolynomialSolverBase.html#afcc2f9f37f2641d8adc18e6a4be2425b">Eigen::PolynomialSolverBase::smallestRoot</a></div><div class="ttdeci">const RootType & smallestRoot() const </div><div class="ttdef"><b>Definition:</b> PolynomialSolver.h:109</div></div>
<div class="ttc" id="classEigen_1_1PolynomialSolverBase_html_a399ac0a070144fdb3b7266be28f47e8b"><div class="ttname"><a href="classEigen_1_1PolynomialSolverBase.html#a399ac0a070144fdb3b7266be28f47e8b">Eigen::PolynomialSolverBase::smallestRealRoot</a></div><div class="ttdeci">const RealScalar & smallestRealRoot(bool &hasArealRoot, const RealScalar &absImaginaryThreshold=NumTraits< Scalar >::dummy_precision()) const </div><div class="ttdef"><b>Definition:</b> PolynomialSolver.h:281</div></div>
<div class="ttc" id="classEigen_1_1PolynomialSolverBase_html_a152ced5a7f96ba18528e540cd0c7e6ce"><div class="ttname"><a href="classEigen_1_1PolynomialSolverBase.html#a152ced5a7f96ba18528e540cd0c7e6ce">Eigen::PolynomialSolverBase::realRoots</a></div><div class="ttdeci">void realRoots(Stl_back_insertion_sequence &bi_seq, const RealScalar &absImaginaryThreshold=NumTraits< Scalar >::dummy_precision()) const </div><div class="ttdef"><b>Definition:</b> PolynomialSolver.h:69</div></div>
<div class="ttc" id="classEigen_1_1PolynomialSolver_html"><div class="ttname"><a href="classEigen_1_1PolynomialSolver.html">Eigen::PolynomialSolver</a></div><div class="ttdoc">A polynomial solver. </div><div class="ttdef"><b>Definition:</b> PolynomialSolver.h:331</div></div>
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