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<div class="fragment"><div class="line"><a id="l00001" 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 id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">// for linear algebra.</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment">//</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment">// Copyright (C) 2016 Rasmus Munk Larsen (rmlarsen@google.com)</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">//</span></div>
<div class="line"><a id="l00006" 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 id="l00007" 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 id="l00008" 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 id="l00009" name="l00009"></a><span class="lineno"> 9</span> </div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="preprocessor">#ifndef EIGEN_CONDITIONESTIMATOR_H</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="preprocessor">#define EIGEN_CONDITIONESTIMATOR_H</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span> </div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="preprocessor">#include "./InternalHeaderCheck.h"</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span> </div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span> </div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="keyword">namespace </span>internal {</div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span> </div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="keyword">template</span> <<span class="keyword">typename</span> Vector, <span class="keyword">typename</span> RealVector, <span class="keywordtype">bool</span> IsComplex></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="keyword">struct </span>rcond_compute_sign {</div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span> <span class="keyword">static</span> <span class="keyword">inline</span> <a class="code hl_typedef" href="group__matrixtypedefs.html#ga2623c0d4641dda067fbdb9a009ef0c91">Vector</a> run(<span class="keyword">const</span> <a class="code hl_typedef" href="group__matrixtypedefs.html#ga2623c0d4641dda067fbdb9a009ef0c91">Vector</a>& v) {</div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span> <span class="keyword">const</span> RealVector v_abs = v.cwiseAbs();</div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> <span class="keywordflow">return</span> (v_abs.array() == <span class="keyword">static_cast<</span>typename Vector::RealScalar<span class="keyword">></span>(0))</div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> .select(Vector::Ones(v.size()), v.cwiseQuotient(v_abs));</div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> }</div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span>};</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> </div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="comment">// Partial specialization to avoid elementwise division for real vectors.</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="keyword">template</span> <<span class="keyword">typename</span> Vector></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="keyword">struct </span>rcond_compute_sign<<a class="code hl_typedef" href="group__matrixtypedefs.html#ga2623c0d4641dda067fbdb9a009ef0c91">Vector</a>, <a class="code hl_typedef" href="group__matrixtypedefs.html#ga2623c0d4641dda067fbdb9a009ef0c91">Vector</a>, false> {</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> <span class="keyword">static</span> <span class="keyword">inline</span> <a class="code hl_typedef" href="group__matrixtypedefs.html#ga2623c0d4641dda067fbdb9a009ef0c91">Vector</a> run(<span class="keyword">const</span> <a class="code hl_typedef" href="group__matrixtypedefs.html#ga2623c0d4641dda067fbdb9a009ef0c91">Vector</a>& v) {</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> <span class="keywordflow">return</span> (v.array() < <span class="keyword">static_cast<</span>typename Vector::RealScalar<span class="keyword">></span>(0))</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> .select(-Vector::Ones(v.size()), Vector::Ones(v.size()));</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> }</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span>};</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> </div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span><span class="keyword">template</span> <<span class="keyword">typename</span> Decomposition></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span><span class="keyword">typename</span> Decomposition::RealScalar rcond_invmatrix_L1_norm_estimate(<span class="keyword">const</span> Decomposition& dec)</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span>{</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> Decomposition::MatrixType MatrixType;</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> Decomposition::Scalar Scalar;</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> Decomposition::RealScalar RealScalar;</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_col_type<MatrixType>::type <a class="code hl_typedef" href="group__matrixtypedefs.html#ga2623c0d4641dda067fbdb9a009ef0c91">Vector</a>;</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_col_type<MatrixType, RealScalar>::type RealVector;</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="keyword">const</span> <span class="keywordtype">bool</span> is_complex = (NumTraits<Scalar>::IsComplex != 0);</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> </div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> eigen_assert(dec.rows() == dec.cols());</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n = dec.rows();</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="keywordflow">if</span> (n == 0)</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> </div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="comment">// Disable Index to float conversion warning</span></div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span><span class="preprocessor">#ifdef __INTEL_COMPILER</span></div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span><span class="preprocessor"> #pragma warning push</span></div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span><span class="preprocessor"> #pragma warning ( disable : 2259 )</span></div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <a class="code hl_typedef" href="group__matrixtypedefs.html#ga2623c0d4641dda067fbdb9a009ef0c91">Vector</a> v = dec.solve(Vector::Ones(n) / Scalar(n));</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span><span class="preprocessor">#ifdef __INTEL_COMPILER</span></div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span><span class="preprocessor"> #pragma warning pop</span></div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> </div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="comment">// lower_bound is a lower bound on</span></div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="comment">// ||inv(matrix)||_1 = sup_v ||inv(matrix) v||_1 / ||v||_1</span></div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <span class="comment">// and is the objective maximized by the ("super-") gradient ascent</span></div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <span class="comment">// algorithm below.</span></div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> RealScalar lower_bound = v.template lpNorm<1>();</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="keywordflow">if</span> (n == 1)</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <span class="keywordflow">return</span> lower_bound;</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> </div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="comment">// Gradient ascent algorithm follows: We know that the optimum is achieved at</span></div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="comment">// one of the simplices v = e_i, so in each iteration we follow a</span></div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="comment">// super-gradient to move towards the optimal one.</span></div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> RealScalar old_lower_bound = lower_bound;</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <a class="code hl_typedef" href="group__matrixtypedefs.html#ga2623c0d4641dda067fbdb9a009ef0c91">Vector</a> sign_vector(n);</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <a class="code hl_typedef" href="group__matrixtypedefs.html#ga2623c0d4641dda067fbdb9a009ef0c91">Vector</a> old_sign_vector;</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> v_max_abs_index = -1;</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> old_v_max_abs_index = v_max_abs_index;</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k < 4; ++k)</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> {</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> sign_vector = internal::rcond_compute_sign<Vector, RealVector, is_complex>::run(v);</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="keywordflow">if</span> (k > 0 && !is_complex && sign_vector == old_sign_vector) {</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="comment">// Break if the solution stagnated.</span></div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> }</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <span class="comment">// v_max_abs_index = argmax |real( inv(matrix)^T * sign_vector )|</span></div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> v = dec.adjoint().solve(sign_vector);</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> v.real().cwiseAbs().maxCoeff(&v_max_abs_index);</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> <span class="keywordflow">if</span> (v_max_abs_index == old_v_max_abs_index) {</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <span class="comment">// Break if the solution stagnated.</span></div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> }</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> <span class="comment">// Move to the new simplex e_j, where j = v_max_abs_index.</span></div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> v = dec.solve(Vector::Unit(n, v_max_abs_index)); <span class="comment">// v = inv(matrix) * e_j.</span></div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> lower_bound = v.template lpNorm<1>();</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="keywordflow">if</span> (lower_bound <= old_lower_bound) {</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <span class="comment">// Break if the gradient step did not increase the lower_bound.</span></div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> }</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <span class="keywordflow">if</span> (!is_complex) {</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> old_sign_vector = sign_vector;</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> }</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> old_v_max_abs_index = v_max_abs_index;</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> old_lower_bound = lower_bound;</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> }</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> <span class="comment">// The following calculates an independent estimate of ||matrix||_1 by</span></div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <span class="comment">// multiplying matrix by a vector with entries of slowly increasing</span></div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <span class="comment">// magnitude and alternating sign:</span></div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> <span class="comment">// v_i = (-1)^{i} (1 + (i / (dim-1))), i = 0,...,dim-1.</span></div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> <span class="comment">// This improvement to Hager's algorithm above is due to Higham. It was</span></div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> <span class="comment">// added to make the algorithm more robust in certain corner cases where</span></div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> <span class="comment">// large elements in the matrix might otherwise escape detection due to</span></div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> <span class="comment">// exact cancellation (especially when op and op_adjoint correspond to a</span></div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> <span class="comment">// sequence of backsubstitutions and permutations), which could cause</span></div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <span class="comment">// Hager's algorithm to vastly underestimate ||matrix||_1.</span></div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> Scalar alternating_sign(RealScalar(1));</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> <span class="keywordflow">for</span> (<a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = 0; i < n; ++i) {</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> <span class="comment">// The static_cast is needed when Scalar is a complex and RealScalar implements expression templates</span></div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> v[i] = alternating_sign * <span class="keyword">static_cast<</span>RealScalar<span class="keyword">></span>(RealScalar(1) + (RealScalar(i) / (RealScalar(n - 1))));</div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> alternating_sign = -alternating_sign;</div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> }</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> v = dec.solve(v);</div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> <span class="keyword">const</span> RealScalar alternate_lower_bound = (2 * v.template lpNorm<1>()) / (3 * RealScalar(n));</div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> <span class="keywordflow">return</span> numext::maxi(lower_bound, alternate_lower_bound);</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span>}</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> </div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span><span class="keyword">template</span> <<span class="keyword">typename</span> Decomposition></div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span><span class="keyword">typename</span> Decomposition::RealScalar</div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span>rcond_estimate_helper(<span class="keyword">typename</span> Decomposition::RealScalar matrix_norm, <span class="keyword">const</span> Decomposition& dec)</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span>{</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> Decomposition::RealScalar RealScalar;</div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> eigen_assert(dec.rows() == dec.cols());</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> <span class="keywordflow">if</span> (dec.rows() == 0) <span class="keywordflow">return</span> NumTraits<RealScalar>::infinity();</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> <span class="keywordflow">if</span> (numext::is_exactly_zero(matrix_norm)) <span class="keywordflow">return</span> RealScalar(0);</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> <span class="keywordflow">if</span> (dec.rows() == 1) <span class="keywordflow">return</span> RealScalar(1);</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> <span class="keyword">const</span> RealScalar inverse_matrix_norm = rcond_invmatrix_L1_norm_estimate(dec);</div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> <span class="keywordflow">return</span> (numext::is_exactly_zero(inverse_matrix_norm) ? RealScalar(0)</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> : (RealScalar(1) / inverse_matrix_norm) / matrix_norm);</div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span>}</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> </div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span>} <span class="comment">// namespace internal</span></div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> </div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span>} <span class="comment">// namespace Eigen</span></div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> </div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span><span class="preprocessor">#endif</span></div>
<div class="ttc" id="agroup__matrixtypedefs_html_ga2623c0d4641dda067fbdb9a009ef0c91"><div class="ttname"><a href="group__matrixtypedefs.html#ga2623c0d4641dda067fbdb9a009ef0c91">Eigen::Vector</a></div><div class="ttdeci">Matrix< Type, Size, 1 > Vector</div><div class="ttdoc">[c++11] Size×1 vector of type Type.</div><div class="ttdef"><b>Definition</b> Matrix.h:545</div></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition</b> Core:139</div></div>
<div class="ttc" id="anamespaceEigen_html_a62e77e0933482dafde8fe197d9a2cfde"><div class="ttname"><a href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a></div><div class="ttdeci">EIGEN_DEFAULT_DENSE_INDEX_TYPE Index</div><div class="ttdoc">The Index type as used for the API.</div><div class="ttdef"><b>Definition</b> Meta.h:82</div></div>
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