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<div class="title">PolynomialUtils.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_UTILS_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_UTILS_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="l00026"></a><span class="lineno"> 26</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Polynomials, <span class="keyword">typename</span> T></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="keyword">inline</span></div>
<div class="line"><a name="l00028"></a><span class="lineno"><a class="line" href="group__Polynomials__Module.html#gaadbf059bc28ce1cf94c57c1454633d40"> 28</a></span> T <a class="code" href="group__Polynomials__Module.html#gaadbf059bc28ce1cf94c57c1454633d40">poly_eval_horner</a>( <span class="keyword">const</span> Polynomials& poly, <span class="keyword">const</span> T& x )</div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> {</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  T val=poly[poly.size()-1];</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  <span class="keywordflow">for</span>(DenseIndex i=poly.size()-2; i>=0; --i ){</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  val = val*x + poly[i]; }</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  <span class="keywordflow">return</span> val;</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="l00044"></a><span class="lineno"> 44</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Polynomials, <span class="keyword">typename</span> T></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="keyword">inline</span></div>
<div class="line"><a name="l00046"></a><span class="lineno"><a class="line" href="group__Polynomials__Module.html#gadb64ffddaa9e83634e3ab0e3fd3664f5"> 46</a></span> T <a class="code" href="group__Polynomials__Module.html#gadb64ffddaa9e83634e3ab0e3fd3664f5">poly_eval</a>( <span class="keyword">const</span> Polynomials& poly, <span class="keyword">const</span> T& x )</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> {</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<T>::Real Real;</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> </div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <span class="keywordflow">if</span>( numext::abs2( x ) <= Real(1) ){</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <span class="keywordflow">return</span> <a class="code" href="group__Polynomials__Module.html#gaadbf059bc28ce1cf94c57c1454633d40">poly_eval_horner</a>( poly, x ); }</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  {</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  T val=poly[0];</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  T inv_x = T(1)/x;</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="keywordflow">for</span>( DenseIndex i=1; i<poly.size(); ++i ){</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  val = val*inv_x + poly[i]; }</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span> </div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <span class="keywordflow">return</span> std::pow(x,(T)(poly.size()-1)) * val;</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  }</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> </div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Polynomial></div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="keyword">inline</span></div>
<div class="line"><a name="l00075"></a><span class="lineno"><a class="line" href="group__Polynomials__Module.html#ga375e3ea1f370fb76dfe0f43a89b95926"> 75</a></span> <span class="keyword">typename</span> NumTraits<typename Polynomial::Scalar>::Real <a class="code" href="group__Polynomials__Module.html#ga375e3ea1f370fb76dfe0f43a89b95926">cauchy_max_bound</a>( <span class="keyword">const</span> Polynomial& 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">using</span> std::abs;</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Polynomial::Scalar Scalar;</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::Real Real;</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>  eigen_assert( Scalar(0) != poly[poly.size()-1] );</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="keyword">const</span> Scalar inv_leading_coeff = Scalar(1)/poly[poly.size()-1];</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  Real cb(0);</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span> </div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="keywordflow">for</span>( DenseIndex i=0; i<poly.size()-1; ++i ){</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  cb += abs(poly[i]*inv_leading_coeff); }</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="keywordflow">return</span> cb + Real(1);</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> </div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Polynomial></div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span> <span class="keyword">inline</span></div>
<div class="line"><a name="l00098"></a><span class="lineno"><a class="line" href="group__Polynomials__Module.html#gab076afbdba0e9298a541cc4e8cc7506b"> 98</a></span> <span class="keyword">typename</span> NumTraits<typename Polynomial::Scalar>::Real <a class="code" href="group__Polynomials__Module.html#gab076afbdba0e9298a541cc4e8cc7506b">cauchy_min_bound</a>( <span class="keyword">const</span> Polynomial& poly )</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>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Polynomial::Scalar Scalar;</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::Real Real;</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span> </div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  DenseIndex i=0;</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  <span class="keywordflow">while</span>( i<poly.size()-1 && Scalar(0) == poly(i) ){ ++i; }</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="keywordflow">if</span>( poly.size()-1 == i ){</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  <span class="keywordflow">return</span> Real(1); }</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span> </div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="keyword">const</span> Scalar inv_min_coeff = Scalar(1)/poly[i];</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  Real cb(1);</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <span class="keywordflow">for</span>( DenseIndex j=i+1; j<poly.size(); ++j ){</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  cb += abs(poly[j]*inv_min_coeff); }</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="keywordflow">return</span> Real(1)/cb;</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> </div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span> <span class="keyword">template</span> <<span class="keyword">typename</span> RootVector, <span class="keyword">typename</span> Polynomial></div>
<div class="line"><a name="l00127"></a><span class="lineno"><a class="line" href="group__Polynomials__Module.html#gafbc3648f7ef67db3d5d04454fc1257fd"> 127</a></span> <span class="keywordtype">void</span> <a class="code" href="group__Polynomials__Module.html#gafbc3648f7ef67db3d5d04454fc1257fd">roots_to_monicPolynomial</a>( <span class="keyword">const</span> RootVector& rv, Polynomial& poly )</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> </div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Polynomial::Scalar Scalar;</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span> </div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  poly.setZero( rv.size()+1 );</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  poly[0] = -rv[0]; poly[1] = Scalar(1);</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="keywordflow">for</span>( DenseIndex i=1; i< rv.size(); ++i )</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  {</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  <span class="keywordflow">for</span>( DenseIndex j=i+1; j>0; --j ){ poly[j] = poly[j-1] - rv[i]*poly[j]; }</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  poly[0] = -rv[i]*poly[0];</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> </div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span> } <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span> </div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span> <span class="preprocessor">#endif // EIGEN_POLYNOMIAL_UTILS_H</span></div>
<div class="ttc" id="group__Polynomials__Module_html_ga375e3ea1f370fb76dfe0f43a89b95926"><div class="ttname"><a href="group__Polynomials__Module.html#ga375e3ea1f370fb76dfe0f43a89b95926">Eigen::cauchy_max_bound</a></div><div class="ttdeci">NumTraits< typename Polynomial::Scalar >::Real cauchy_max_bound(const Polynomial &poly)</div><div class="ttdef"><b>Definition:</b> PolynomialUtils.h:75</div></div>
<div class="ttc" id="group__Polynomials__Module_html_gafbc3648f7ef67db3d5d04454fc1257fd"><div class="ttname"><a href="group__Polynomials__Module.html#gafbc3648f7ef67db3d5d04454fc1257fd">Eigen::roots_to_monicPolynomial</a></div><div class="ttdeci">void roots_to_monicPolynomial(const RootVector &rv, Polynomial &poly)</div><div class="ttdef"><b>Definition:</b> PolynomialUtils.h:127</div></div>
<div class="ttc" id="group__Polynomials__Module_html_gab076afbdba0e9298a541cc4e8cc7506b"><div class="ttname"><a href="group__Polynomials__Module.html#gab076afbdba0e9298a541cc4e8cc7506b">Eigen::cauchy_min_bound</a></div><div class="ttdeci">NumTraits< typename Polynomial::Scalar >::Real cauchy_min_bound(const Polynomial &poly)</div><div class="ttdef"><b>Definition:</b> PolynomialUtils.h:98</div></div>
<div class="ttc" id="group__Polynomials__Module_html_gadb64ffddaa9e83634e3ab0e3fd3664f5"><div class="ttname"><a href="group__Polynomials__Module.html#gadb64ffddaa9e83634e3ab0e3fd3664f5">Eigen::poly_eval</a></div><div class="ttdeci">T poly_eval(const Polynomials &poly, const T &x)</div><div class="ttdef"><b>Definition:</b> PolynomialUtils.h:46</div></div>
<div class="ttc" id="group__Polynomials__Module_html_gaadbf059bc28ce1cf94c57c1454633d40"><div class="ttname"><a href="group__Polynomials__Module.html#gaadbf059bc28ce1cf94c57c1454633d40">Eigen::poly_eval_horner</a></div><div class="ttdeci">T poly_eval_horner(const Polynomials &poly, const T &x)</div><div class="ttdef"><b>Definition:</b> PolynomialUtils.h:28</div></div>
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