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<div class="title">ColPivHouseholderQR.h</div>  </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<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>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2008-2009 Gael Guennebaud &lt;gael.guennebaud@inria.fr&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">// Copyright (C) 2009 Benoit Jacob &lt;jacob.benoit.1@gmail.com&gt;</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;</div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#ifndef EIGEN_COLPIVOTINGHOUSEHOLDERQR_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="preprocessor"></span><span class="preprocessor">#define EIGEN_COLPIVOTINGHOUSEHOLDERQR_H</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="preprocessor"></span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="keyword">namespace </span>Eigen { </div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> _MatrixType&gt; <span class="keyword">class </span>ColPivHouseholderQR</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;{</div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;    <span class="keyword">typedef</span> _MatrixType MatrixType;</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;    <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;      RowsAtCompileTime = MatrixType::RowsAtCompileTime,</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;      ColsAtCompileTime = MatrixType::ColsAtCompileTime,</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;      Options = MatrixType::Options,</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;      MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;    };</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::RealScalar RealScalar;</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;    <span class="keyword">typedef</span> Matrix&lt;Scalar, RowsAtCompileTime, RowsAtCompileTime, Options, MaxRowsAtCompileTime, MaxRowsAtCompileTime&gt; MatrixQType;</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_diag_type&lt;MatrixType&gt;::type HCoeffsType;</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;    <span class="keyword">typedef</span> PermutationMatrix&lt;ColsAtCompileTime, MaxColsAtCompileTime&gt; PermutationType;</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_row_type&lt;MatrixType, Index&gt;::type IntRowVectorType;</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_row_type&lt;MatrixType&gt;::type RowVectorType;</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_row_type&lt;MatrixType, RealScalar&gt;::type RealRowVectorType;</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;    <span class="keyword">typedef</span> HouseholderSequence&lt;MatrixType,typename internal::remove_all&lt;typename HCoeffsType::ConjugateReturnType&gt;::type&gt; HouseholderSequenceType;</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;    </div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;  <span class="keyword">private</span>:</div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;    </div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> PermutationType::Index PermIndexType;</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;    </div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;</div>
<div class="line"><a name="l00072"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a72f7fb8c1359fa8d9743068e5699228e">   72</a></span>&#160;    <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a72f7fb8c1359fa8d9743068e5699228e">ColPivHouseholderQR</a>()</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;      : m_qr(),</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;        m_hCoeffs(),</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;        m_colsPermutation(),</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;        m_colsTranspositions(),</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;        m_temp(),</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;        m_colSqNorms(),</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;        m_isInitialized(false) {}</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;</div>
<div class="line"><a name="l00087"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a4a15f3e5e33478b9969d8c71aabd09ea">   87</a></span>&#160;    <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a4a15f3e5e33478b9969d8c71aabd09ea">ColPivHouseholderQR</a>(Index rows, Index cols)</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;      : m_qr(rows, cols),</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;        m_hCoeffs((std::min)(rows,cols)),</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;        m_colsPermutation(PermIndexType(cols)),</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;        m_colsTranspositions(cols),</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;        m_temp(cols),</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;        m_colSqNorms(cols),</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;        m_isInitialized(false),</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;        m_usePrescribedThreshold(false) {}</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;</div>
<div class="line"><a name="l00109"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#ac93cc6a4fd4247486c2c8eab79b4c0ad">  109</a></span>&#160;    <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#ac93cc6a4fd4247486c2c8eab79b4c0ad">ColPivHouseholderQR</a>(<span class="keyword">const</span> MatrixType&amp; matrix)</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;      : m_qr(matrix.rows(), matrix.cols()),</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;        m_hCoeffs((std::min)(matrix.rows(),matrix.cols())),</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;        m_colsPermutation(PermIndexType(matrix.cols())),</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;        m_colsTranspositions(matrix.cols()),</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;        m_temp(matrix.cols()),</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;        m_colSqNorms(matrix.cols()),</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;        m_isInitialized(false),</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;        m_usePrescribedThreshold(false)</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;    {</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;      <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a812205d31cae2005b7779c7a3a442f1b">compute</a>(matrix);</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;    }</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> Rhs&gt;</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;    <span class="keyword">inline</span> <span class="keyword">const</span> internal::solve_retval&lt;ColPivHouseholderQR, Rhs&gt;</div>
<div class="line"><a name="l00141"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#afbe1cd1202964011ae7e7411577749a0">  141</a></span>&#160;    <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#afbe1cd1202964011ae7e7411577749a0">solve</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase&lt;Rhs&gt;</a>&amp; b)<span class="keyword"> const</span></div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;ColPivHouseholderQR is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;      <span class="keywordflow">return</span> internal::solve_retval&lt;ColPivHouseholderQR, Rhs&gt;(*<span class="keyword">this</span>, b.derived());</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;    }</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;</div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;    HouseholderSequenceType <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a97150efba7e2da32f48a7f823f047a89">householderQ</a>(<span class="keywordtype">void</span>) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;    HouseholderSequenceType matrixQ(<span class="keywordtype">void</span>)<span class="keyword"> const</span></div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;      <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a97150efba7e2da32f48a7f823f047a89">householderQ</a>(); </div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;    }</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;</div>
<div class="line"><a name="l00155"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a7b142db8924dd7fad99acbdd0ff4bdd1">  155</a></span>&#160;    <span class="keyword">const</span> MatrixType&amp; <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a7b142db8924dd7fad99acbdd0ff4bdd1">matrixQR</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;ColPivHouseholderQR is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;      <span class="keywordflow">return</span> m_qr;</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;    }</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;    </div>
<div class="line"><a name="l00170"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a84cd3aba44220008bdbd81506703de37">  170</a></span>&#160;    <span class="keyword">const</span> MatrixType&amp; <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a84cd3aba44220008bdbd81506703de37">matrixR</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;ColPivHouseholderQR is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;      <span class="keywordflow">return</span> m_qr;</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;    }</div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;    </div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;    <a class="code" href="classEigen_1_1ColPivHouseholderQR.html">ColPivHouseholderQR</a>&amp; <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a812205d31cae2005b7779c7a3a442f1b">compute</a>(<span class="keyword">const</span> MatrixType&amp; matrix);</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;</div>
<div class="line"><a name="l00179"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a1229744f4e8554ca6e96fe32ac359924">  179</a></span>&#160;    <span class="keyword">const</span> <a class="code" href="classEigen_1_1PermutationMatrix.html">PermutationType</a>&amp; <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a1229744f4e8554ca6e96fe32ac359924">colsPermutation</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;ColPivHouseholderQR is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;      <span class="keywordflow">return</span> m_colsPermutation;</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;    }</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;    <span class="keyword">typename</span> MatrixType::RealScalar <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a2bb8fa5593d2f447c16ba2e3cfb9c432">absDeterminant</a>() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;    <span class="keyword">typename</span> MatrixType::RealScalar <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a82a3f15f0cda1f4f874d50951344b5a9">logAbsDeterminant</a>() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;</div>
<div class="line"><a name="l00220"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a363d1c09d77f09d6ea2d2789776e7be3">  220</a></span>&#160;    <span class="keyword">inline</span> Index <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a363d1c09d77f09d6ea2d2789776e7be3">rank</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;      <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;ColPivHouseholderQR is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;      RealScalar premultiplied_threshold = abs(m_maxpivot) * <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#aa5a87faaa92a3081045d1f934e292ef0">threshold</a>();</div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;      Index result = 0;</div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;      <span class="keywordflow">for</span>(Index i = 0; i &lt; m_nonzero_pivots; ++i)</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;        result += (abs(m_qr.coeff(i,i)) &gt; premultiplied_threshold);</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;      <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;    }</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;</div>
<div class="line"><a name="l00237"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a7c6323871c4f080fc6e2d3ad7fc607fc">  237</a></span>&#160;    <span class="keyword">inline</span> Index <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a7c6323871c4f080fc6e2d3ad7fc607fc">dimensionOfKernel</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;ColPivHouseholderQR is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;      <span class="keywordflow">return</span> cols() - <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a363d1c09d77f09d6ea2d2789776e7be3">rank</a>();</div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;    }</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;</div>
<div class="line"><a name="l00250"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a1e119085e53eca65e9ba15451c102d40">  250</a></span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a1e119085e53eca65e9ba15451c102d40">isInjective</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;ColPivHouseholderQR is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;      <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a363d1c09d77f09d6ea2d2789776e7be3">rank</a>() == cols();</div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;    }</div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;</div>
<div class="line"><a name="l00263"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a5968b9ca46303b3cc7250e7b120ab7e6">  263</a></span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a5968b9ca46303b3cc7250e7b120ab7e6">isSurjective</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;ColPivHouseholderQR is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;      <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a363d1c09d77f09d6ea2d2789776e7be3">rank</a>() == rows();</div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;    }</div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;</div>
<div class="line"><a name="l00275"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#ab60c7d993c9eba31668fb8886d621094">  275</a></span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#ab60c7d993c9eba31668fb8886d621094">isInvertible</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;ColPivHouseholderQR is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;      <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a1e119085e53eca65e9ba15451c102d40">isInjective</a>() &amp;&amp; <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a5968b9ca46303b3cc7250e7b120ab7e6">isSurjective</a>();</div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;    }</div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;</div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;    <span class="keyword">inline</span> <span class="keyword">const</span></div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;    internal::solve_retval&lt;ColPivHouseholderQR, typename MatrixType::IdentityReturnType&gt;</div>
<div class="line"><a name="l00288"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a3021b1285c868ef94b26f387766bdf92">  288</a></span>&#160;    <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a3021b1285c868ef94b26f387766bdf92">inverse</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;ColPivHouseholderQR is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;      <span class="keywordflow">return</span> internal::solve_retval&lt;ColPivHouseholderQR,typename MatrixType::IdentityReturnType&gt;</div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;               (*<span class="keyword">this</span>, MatrixType::Identity(m_qr.rows(), m_qr.cols()));</div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;    }</div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;</div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;    <span class="keyword">inline</span> Index rows()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_qr.rows(); }</div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;    <span class="keyword">inline</span> Index cols()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_qr.cols(); }</div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;    </div>
<div class="line"><a name="l00302"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a321e96844544eacde2272c3a487048e9">  302</a></span>&#160;    <span class="keyword">const</span> HCoeffsType&amp; <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a321e96844544eacde2272c3a487048e9">hCoeffs</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_hCoeffs; }</div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;</div>
<div class="line"><a name="l00321"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a5631914aef48f4f719789c823edacb2c">  321</a></span>&#160;    <a class="code" href="classEigen_1_1ColPivHouseholderQR.html">ColPivHouseholderQR</a>&amp; <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a5631914aef48f4f719789c823edacb2c">setThreshold</a>(<span class="keyword">const</span> RealScalar&amp; <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#aa5a87faaa92a3081045d1f934e292ef0">threshold</a>)</div>
<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;    {</div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;      m_usePrescribedThreshold = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;      m_prescribedThreshold = <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#aa5a87faaa92a3081045d1f934e292ef0">threshold</a>;</div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;      <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;    }</div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;</div>
<div class="line"><a name="l00336"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a446f775405186b238f20bd092fd107a6">  336</a></span>&#160;    <a class="code" href="classEigen_1_1ColPivHouseholderQR.html">ColPivHouseholderQR</a>&amp; <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a446f775405186b238f20bd092fd107a6">setThreshold</a>(Default_t)</div>
<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;    {</div>
<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;      m_usePrescribedThreshold = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;      <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;    }</div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;</div>
<div class="line"><a name="l00346"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#aa5a87faaa92a3081045d1f934e292ef0">  346</a></span>&#160;    RealScalar <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#aa5a87faaa92a3081045d1f934e292ef0">threshold</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;      eigen_assert(m_isInitialized || m_usePrescribedThreshold);</div>
<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;      <span class="keywordflow">return</span> m_usePrescribedThreshold ? m_prescribedThreshold</div>
<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;      <span class="comment">// this formula comes from experimenting (see &quot;LU precision tuning&quot; thread on the list)</span></div>
<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;      <span class="comment">// and turns out to be identical to Higham&#39;s formula used already in LDLt.</span></div>
<div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;                                      : <a class="code" href="structEigen_1_1NumTraits.html">NumTraits&lt;Scalar&gt;::epsilon</a>() * m_qr.diagonalSize();</div>
<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;    }</div>
<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;</div>
<div class="line"><a name="l00362"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a6dda9285f13dec9f49e9c17229a89988">  362</a></span>&#160;    <span class="keyword">inline</span> Index <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a6dda9285f13dec9f49e9c17229a89988">nonzeroPivots</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;ColPivHouseholderQR is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;      <span class="keywordflow">return</span> m_nonzero_pivots;</div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;    }</div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;</div>
<div class="line"><a name="l00371"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a067e9d4143ce0558fc684b736128a4ed">  371</a></span>&#160;    RealScalar <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a067e9d4143ce0558fc684b736128a4ed">maxPivot</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_maxpivot; }</div>
<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;    </div>
<div class="line"><a name="l00379"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a0c06d5c2034ebb329c54235369643ad2">  379</a></span>&#160;    <a class="code" href="group__enums.html#ga51bc1ac16f26ebe51eae1abb77bd037b">ComputationInfo</a> <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a0c06d5c2034ebb329c54235369643ad2">info</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;Decomposition is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;      <span class="keywordflow">return</span> <a class="code" href="group__enums.html#gga51bc1ac16f26ebe51eae1abb77bd037bafdfbdf3247bd36a1f17270d5cec74c9c">Success</a>;</div>
<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;    }</div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;</div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;    MatrixType m_qr;</div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;    HCoeffsType m_hCoeffs;</div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;    PermutationType m_colsPermutation;</div>
<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;    IntRowVectorType m_colsTranspositions;</div>
<div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160;    RowVectorType m_temp;</div>
<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160;    RealRowVectorType m_colSqNorms;</div>
<div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160;    <span class="keywordtype">bool</span> m_isInitialized, m_usePrescribedThreshold;</div>
<div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160;    RealScalar m_prescribedThreshold, m_maxpivot;</div>
<div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160;    Index m_nonzero_pivots;</div>
<div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160;    Index m_det_pq;</div>
<div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;};</div>
<div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;</div>
<div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00399"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a2bb8fa5593d2f447c16ba2e3cfb9c432">  399</a></span>&#160;<span class="keyword">typename</span> MatrixType::RealScalar <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a2bb8fa5593d2f447c16ba2e3cfb9c432">ColPivHouseholderQR&lt;MatrixType&gt;::absDeterminant</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;  eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;ColPivHouseholderQR is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;  eigen_assert(m_qr.rows() == m_qr.cols() &amp;&amp; <span class="stringliteral">&quot;You can&#39;t take the determinant of a non-square matrix!&quot;</span>);</div>
<div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;  <span class="keywordflow">return</span> abs(m_qr.diagonal().prod());</div>
<div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;}</div>
<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;</div>
<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00408"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a82a3f15f0cda1f4f874d50951344b5a9">  408</a></span>&#160;<span class="keyword">typename</span> MatrixType::RealScalar <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a82a3f15f0cda1f4f874d50951344b5a9">ColPivHouseholderQR&lt;MatrixType&gt;::logAbsDeterminant</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;  eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;ColPivHouseholderQR is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;  eigen_assert(m_qr.rows() == m_qr.cols() &amp;&amp; <span class="stringliteral">&quot;You can&#39;t take the determinant of a non-square matrix!&quot;</span>);</div>
<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;  <span class="keywordflow">return</span> m_qr.diagonal().cwiseAbs().array().log().sum();</div>
<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;}</div>
<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;</div>
<div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00422"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a812205d31cae2005b7779c7a3a442f1b">  422</a></span>&#160;<a class="code" href="classEigen_1_1ColPivHouseholderQR.html">ColPivHouseholderQR&lt;MatrixType&gt;</a>&amp; <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a812205d31cae2005b7779c7a3a442f1b">ColPivHouseholderQR&lt;MatrixType&gt;::compute</a>(<span class="keyword">const</span> MatrixType&amp; matrix)</div>
<div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160;{</div>
<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;  Index rows = matrix.rows();</div>
<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;  Index cols = matrix.cols();</div>
<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;  Index size = matrix.diagonalSize();</div>
<div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160;  </div>
<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160;  <span class="comment">// the column permutation is stored as int indices, so just to be sure:</span></div>
<div class="line"><a name="l00430"></a><span class="lineno">  430</span>&#160;  eigen_assert(cols&lt;=<a class="code" href="structEigen_1_1NumTraits.html">NumTraits&lt;int&gt;::highest</a>());</div>
<div class="line"><a name="l00431"></a><span class="lineno">  431</span>&#160;</div>
<div class="line"><a name="l00432"></a><span class="lineno">  432</span>&#160;  m_qr = matrix;</div>
<div class="line"><a name="l00433"></a><span class="lineno">  433</span>&#160;  m_hCoeffs.resize(size);</div>
<div class="line"><a name="l00434"></a><span class="lineno">  434</span>&#160;</div>
<div class="line"><a name="l00435"></a><span class="lineno">  435</span>&#160;  m_temp.resize(cols);</div>
<div class="line"><a name="l00436"></a><span class="lineno">  436</span>&#160;</div>
<div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;  m_colsTranspositions.resize(matrix.cols());</div>
<div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160;  Index number_of_transpositions = 0;</div>
<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160;</div>
<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160;  m_colSqNorms.resize(cols);</div>
<div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160;  <span class="keywordflow">for</span>(Index k = 0; k &lt; cols; ++k)</div>
<div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160;    m_colSqNorms.coeffRef(k) = m_qr.col(k).squaredNorm();</div>
<div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;</div>
<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;  RealScalar threshold_helper = m_colSqNorms.maxCoeff() * numext::abs2(<a class="code" href="structEigen_1_1NumTraits.html">NumTraits&lt;Scalar&gt;::epsilon</a>()) / RealScalar(rows);</div>
<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160;</div>
<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160;  m_nonzero_pivots = size; <span class="comment">// the generic case is that in which all pivots are nonzero (invertible case)</span></div>
<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160;  m_maxpivot = RealScalar(0);</div>
<div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160;</div>
<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160;  <span class="keywordflow">for</span>(Index k = 0; k &lt; size; ++k)</div>
<div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;  {</div>
<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160;    <span class="comment">// first, we look up in our table m_colSqNorms which column has the biggest squared norm</span></div>
<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;    Index biggest_col_index;</div>
<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;    RealScalar biggest_col_sq_norm = m_colSqNorms.tail(cols-k).maxCoeff(&amp;biggest_col_index);</div>
<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160;    biggest_col_index += k;</div>
<div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160;</div>
<div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;    <span class="comment">// since our table m_colSqNorms accumulates imprecision at every step, we must now recompute</span></div>
<div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160;    <span class="comment">// the actual squared norm of the selected column.</span></div>
<div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160;    <span class="comment">// Note that not doing so does result in solve() sometimes returning inf/nan values</span></div>
<div class="line"><a name="l00459"></a><span class="lineno">  459</span>&#160;    <span class="comment">// when running the unit test with 1000 repetitions.</span></div>
<div class="line"><a name="l00460"></a><span class="lineno">  460</span>&#160;    biggest_col_sq_norm = m_qr.col(biggest_col_index).tail(rows-k).squaredNorm();</div>
<div class="line"><a name="l00461"></a><span class="lineno">  461</span>&#160;</div>
<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;    <span class="comment">// we store that back into our table: it can&#39;t hurt to correct our table.</span></div>
<div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160;    m_colSqNorms.coeffRef(biggest_col_index) = biggest_col_sq_norm;</div>
<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;</div>
<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160;    <span class="comment">// if the current biggest column is smaller than epsilon times the initial biggest column,</span></div>
<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;    <span class="comment">// terminate to avoid generating nan/inf values.</span></div>
<div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160;    <span class="comment">// Note that here, if we test instead for &quot;biggest == 0&quot;, we get a failure every 1000 (or so)</span></div>
<div class="line"><a name="l00468"></a><span class="lineno">  468</span>&#160;    <span class="comment">// repetitions of the unit test, with the result of solve() filled with large values of the order</span></div>
<div class="line"><a name="l00469"></a><span class="lineno">  469</span>&#160;    <span class="comment">// of 1/(size*epsilon).</span></div>
<div class="line"><a name="l00470"></a><span class="lineno">  470</span>&#160;    <span class="keywordflow">if</span>(biggest_col_sq_norm &lt; threshold_helper * RealScalar(rows-k))</div>
<div class="line"><a name="l00471"></a><span class="lineno">  471</span>&#160;    {</div>
<div class="line"><a name="l00472"></a><span class="lineno">  472</span>&#160;      m_nonzero_pivots = k;</div>
<div class="line"><a name="l00473"></a><span class="lineno">  473</span>&#160;      m_hCoeffs.tail(size-k).setZero();</div>
<div class="line"><a name="l00474"></a><span class="lineno">  474</span>&#160;      m_qr.bottomRightCorner(rows-k,cols-k)</div>
<div class="line"><a name="l00475"></a><span class="lineno">  475</span>&#160;          .template triangularView&lt;StrictlyLower&gt;()</div>
<div class="line"><a name="l00476"></a><span class="lineno">  476</span>&#160;          .setZero();</div>
<div class="line"><a name="l00477"></a><span class="lineno">  477</span>&#160;      <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00478"></a><span class="lineno">  478</span>&#160;    }</div>
<div class="line"><a name="l00479"></a><span class="lineno">  479</span>&#160;</div>
<div class="line"><a name="l00480"></a><span class="lineno">  480</span>&#160;    <span class="comment">// apply the transposition to the columns</span></div>
<div class="line"><a name="l00481"></a><span class="lineno">  481</span>&#160;    m_colsTranspositions.coeffRef(k) = biggest_col_index;</div>
<div class="line"><a name="l00482"></a><span class="lineno">  482</span>&#160;    <span class="keywordflow">if</span>(k != biggest_col_index) {</div>
<div class="line"><a name="l00483"></a><span class="lineno">  483</span>&#160;      m_qr.col(k).swap(m_qr.col(biggest_col_index));</div>
<div class="line"><a name="l00484"></a><span class="lineno">  484</span>&#160;      std::swap(m_colSqNorms.coeffRef(k), m_colSqNorms.coeffRef(biggest_col_index));</div>
<div class="line"><a name="l00485"></a><span class="lineno">  485</span>&#160;      ++number_of_transpositions;</div>
<div class="line"><a name="l00486"></a><span class="lineno">  486</span>&#160;    }</div>
<div class="line"><a name="l00487"></a><span class="lineno">  487</span>&#160;</div>
<div class="line"><a name="l00488"></a><span class="lineno">  488</span>&#160;    <span class="comment">// generate the householder vector, store it below the diagonal</span></div>
<div class="line"><a name="l00489"></a><span class="lineno">  489</span>&#160;    RealScalar beta;</div>
<div class="line"><a name="l00490"></a><span class="lineno">  490</span>&#160;    m_qr.col(k).tail(rows-k).makeHouseholderInPlace(m_hCoeffs.coeffRef(k), beta);</div>
<div class="line"><a name="l00491"></a><span class="lineno">  491</span>&#160;</div>
<div class="line"><a name="l00492"></a><span class="lineno">  492</span>&#160;    <span class="comment">// apply the householder transformation to the diagonal coefficient</span></div>
<div class="line"><a name="l00493"></a><span class="lineno">  493</span>&#160;    m_qr.coeffRef(k,k) = beta;</div>
<div class="line"><a name="l00494"></a><span class="lineno">  494</span>&#160;</div>
<div class="line"><a name="l00495"></a><span class="lineno">  495</span>&#160;    <span class="comment">// remember the maximum absolute value of diagonal coefficients</span></div>
<div class="line"><a name="l00496"></a><span class="lineno">  496</span>&#160;    <span class="keywordflow">if</span>(abs(beta) &gt; m_maxpivot) m_maxpivot = abs(beta);</div>
<div class="line"><a name="l00497"></a><span class="lineno">  497</span>&#160;</div>
<div class="line"><a name="l00498"></a><span class="lineno">  498</span>&#160;    <span class="comment">// apply the householder transformation</span></div>
<div class="line"><a name="l00499"></a><span class="lineno">  499</span>&#160;    m_qr.bottomRightCorner(rows-k, cols-k-1)</div>
<div class="line"><a name="l00500"></a><span class="lineno">  500</span>&#160;        .applyHouseholderOnTheLeft(m_qr.col(k).tail(rows-k-1), m_hCoeffs.coeffRef(k), &amp;m_temp.coeffRef(k+1));</div>
<div class="line"><a name="l00501"></a><span class="lineno">  501</span>&#160;</div>
<div class="line"><a name="l00502"></a><span class="lineno">  502</span>&#160;    <span class="comment">// update our table of squared norms of the columns</span></div>
<div class="line"><a name="l00503"></a><span class="lineno">  503</span>&#160;    m_colSqNorms.tail(cols-k-1) -= m_qr.row(k).tail(cols-k-1).cwiseAbs2();</div>
<div class="line"><a name="l00504"></a><span class="lineno">  504</span>&#160;  }</div>
<div class="line"><a name="l00505"></a><span class="lineno">  505</span>&#160;</div>
<div class="line"><a name="l00506"></a><span class="lineno">  506</span>&#160;  m_colsPermutation.setIdentity(PermIndexType(cols));</div>
<div class="line"><a name="l00507"></a><span class="lineno">  507</span>&#160;  <span class="keywordflow">for</span>(PermIndexType k = 0; k &lt; m_nonzero_pivots; ++k)</div>
<div class="line"><a name="l00508"></a><span class="lineno">  508</span>&#160;    m_colsPermutation.applyTranspositionOnTheRight(k, PermIndexType(m_colsTranspositions.coeff(k)));</div>
<div class="line"><a name="l00509"></a><span class="lineno">  509</span>&#160;</div>
<div class="line"><a name="l00510"></a><span class="lineno">  510</span>&#160;  m_det_pq = (number_of_transpositions%2) ? -1 : 1;</div>
<div class="line"><a name="l00511"></a><span class="lineno">  511</span>&#160;  m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00512"></a><span class="lineno">  512</span>&#160;</div>
<div class="line"><a name="l00513"></a><span class="lineno">  513</span>&#160;  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00514"></a><span class="lineno">  514</span>&#160;}</div>
<div class="line"><a name="l00515"></a><span class="lineno">  515</span>&#160;</div>
<div class="line"><a name="l00516"></a><span class="lineno">  516</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00517"></a><span class="lineno">  517</span>&#160;</div>
<div class="line"><a name="l00518"></a><span class="lineno">  518</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> _MatrixType, <span class="keyword">typename</span> Rhs&gt;</div>
<div class="line"><a name="l00519"></a><span class="lineno">  519</span>&#160;<span class="keyword">struct </span>solve_retval&lt;<a class="code" href="classEigen_1_1ColPivHouseholderQR.html">ColPivHouseholderQR</a>&lt;_MatrixType&gt;, Rhs&gt;</div>
<div class="line"><a name="l00520"></a><span class="lineno">  520</span>&#160;  : solve_retval_base&lt;ColPivHouseholderQR&lt;_MatrixType&gt;, Rhs&gt;</div>
<div class="line"><a name="l00521"></a><span class="lineno">  521</span>&#160;{</div>
<div class="line"><a name="l00522"></a><span class="lineno">  522</span>&#160;  EIGEN_MAKE_SOLVE_HELPERS(<a class="code" href="classEigen_1_1ColPivHouseholderQR.html">ColPivHouseholderQR&lt;_MatrixType&gt;</a>,Rhs)</div>
<div class="line"><a name="l00523"></a><span class="lineno">  523</span>&#160;</div>
<div class="line"><a name="l00524"></a><span class="lineno">  524</span>&#160;  template&lt;typename Dest&gt; <span class="keywordtype">void</span> evalTo(Dest&amp; dst)<span class="keyword"> const</span></div>
<div class="line"><a name="l00525"></a><span class="lineno">  525</span>&#160;<span class="keyword">  </span>{</div>
<div class="line"><a name="l00526"></a><span class="lineno">  526</span>&#160;    eigen_assert(rhs().rows() == dec().rows());</div>
<div class="line"><a name="l00527"></a><span class="lineno">  527</span>&#160;</div>
<div class="line"><a name="l00528"></a><span class="lineno">  528</span>&#160;    <span class="keyword">const</span> Index cols = dec().cols(),</div>
<div class="line"><a name="l00529"></a><span class="lineno">  529</span>&#160;                                nonzero_pivots = dec().nonzeroPivots();</div>
<div class="line"><a name="l00530"></a><span class="lineno">  530</span>&#160;</div>
<div class="line"><a name="l00531"></a><span class="lineno">  531</span>&#160;    <span class="keywordflow">if</span>(nonzero_pivots == 0)</div>
<div class="line"><a name="l00532"></a><span class="lineno">  532</span>&#160;    {</div>
<div class="line"><a name="l00533"></a><span class="lineno">  533</span>&#160;      dst.setZero();</div>
<div class="line"><a name="l00534"></a><span class="lineno">  534</span>&#160;      <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00535"></a><span class="lineno">  535</span>&#160;    }</div>
<div class="line"><a name="l00536"></a><span class="lineno">  536</span>&#160;</div>
<div class="line"><a name="l00537"></a><span class="lineno">  537</span>&#160;    <span class="keyword">typename</span> Rhs::PlainObject c(rhs());</div>
<div class="line"><a name="l00538"></a><span class="lineno">  538</span>&#160;</div>
<div class="line"><a name="l00539"></a><span class="lineno">  539</span>&#160;    <span class="comment">// Note that the matrix Q = H_0^* H_1^*... so its inverse is Q^* = (H_0 H_1 ...)^T</span></div>
<div class="line"><a name="l00540"></a><span class="lineno">  540</span>&#160;    c.applyOnTheLeft(<a class="code" href="group__Householder__Module.html#ga5f2b3f80cdf7ae96609e4a8d2e55e371">householderSequence</a>(dec().matrixQR(), dec().hCoeffs())</div>
<div class="line"><a name="l00541"></a><span class="lineno">  541</span>&#160;                     .setLength(dec().nonzeroPivots())</div>
<div class="line"><a name="l00542"></a><span class="lineno">  542</span>&#160;                     .transpose()</div>
<div class="line"><a name="l00543"></a><span class="lineno">  543</span>&#160;      );</div>
<div class="line"><a name="l00544"></a><span class="lineno">  544</span>&#160;</div>
<div class="line"><a name="l00545"></a><span class="lineno">  545</span>&#160;    dec().matrixR()</div>
<div class="line"><a name="l00546"></a><span class="lineno">  546</span>&#160;       .topLeftCorner(nonzero_pivots, nonzero_pivots)</div>
<div class="line"><a name="l00547"></a><span class="lineno">  547</span>&#160;       .template triangularView&lt;Upper&gt;()</div>
<div class="line"><a name="l00548"></a><span class="lineno">  548</span>&#160;       .solveInPlace(c.topRows(nonzero_pivots));</div>
<div class="line"><a name="l00549"></a><span class="lineno">  549</span>&#160;</div>
<div class="line"><a name="l00550"></a><span class="lineno">  550</span>&#160;    <span class="keywordflow">for</span>(Index i = 0; i &lt; nonzero_pivots; ++i) dst.row(dec().colsPermutation().indices().coeff(i)) = c.row(i);</div>
<div class="line"><a name="l00551"></a><span class="lineno">  551</span>&#160;    <span class="keywordflow">for</span>(Index i = nonzero_pivots; i &lt; cols; ++i) dst.row(dec().colsPermutation().indices().coeff(i)).setZero();</div>
<div class="line"><a name="l00552"></a><span class="lineno">  552</span>&#160;  }</div>
<div class="line"><a name="l00553"></a><span class="lineno">  553</span>&#160;};</div>
<div class="line"><a name="l00554"></a><span class="lineno">  554</span>&#160;</div>
<div class="line"><a name="l00555"></a><span class="lineno">  555</span>&#160;} <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00556"></a><span class="lineno">  556</span>&#160;</div>
<div class="line"><a name="l00558"></a><span class="lineno">  558</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00559"></a><span class="lineno">  559</span>&#160;<span class="keyword">typename</span> ColPivHouseholderQR&lt;MatrixType&gt;::HouseholderSequenceType <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a97150efba7e2da32f48a7f823f047a89">ColPivHouseholderQR&lt;MatrixType&gt;</a></div>
<div class="line"><a name="l00560"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a97150efba7e2da32f48a7f823f047a89">  560</a></span>&#160;<a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a97150efba7e2da32f48a7f823f047a89">  ::householderQ</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00561"></a><span class="lineno">  561</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00562"></a><span class="lineno">  562</span>&#160;  eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;ColPivHouseholderQR is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00563"></a><span class="lineno">  563</span>&#160;  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1HouseholderSequence.html">HouseholderSequenceType</a>(m_qr, m_hCoeffs.conjugate()).setLength(m_nonzero_pivots);</div>
<div class="line"><a name="l00564"></a><span class="lineno">  564</span>&#160;}</div>
<div class="line"><a name="l00565"></a><span class="lineno">  565</span>&#160;</div>
<div class="line"><a name="l00570"></a><span class="lineno">  570</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l00571"></a><span class="lineno">  571</span>&#160;<span class="keyword">const</span> <a class="code" href="classEigen_1_1ColPivHouseholderQR.html">ColPivHouseholderQR&lt;typename MatrixBase&lt;Derived&gt;::PlainObject</a>&gt;</div>
<div class="line"><a name="l00572"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a05afed751d3a7277951d1918468e0872">  572</a></span>&#160;<a class="code" href="classEigen_1_1MatrixBase.html#a05afed751d3a7277951d1918468e0872">MatrixBase&lt;Derived&gt;::colPivHouseholderQr</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00573"></a><span class="lineno">  573</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00574"></a><span class="lineno">  574</span>&#160;  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1ColPivHouseholderQR.html">ColPivHouseholderQR&lt;PlainObject&gt;</a>(eval());</div>
<div class="line"><a name="l00575"></a><span class="lineno">  575</span>&#160;}</div>
<div class="line"><a name="l00576"></a><span class="lineno">  576</span>&#160;</div>
<div class="line"><a name="l00577"></a><span class="lineno">  577</span>&#160;} <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00578"></a><span class="lineno">  578</span>&#160;</div>
<div class="line"><a name="l00579"></a><span class="lineno">  579</span>&#160;<span class="preprocessor">#endif // EIGEN_COLPIVOTINGHOUSEHOLDERQR_H</span></div>
<div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a2bb8fa5593d2f447c16ba2e3cfb9c432"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a2bb8fa5593d2f447c16ba2e3cfb9c432">Eigen::ColPivHouseholderQR::absDeterminant</a></div><div class="ttdeci">MatrixType::RealScalar absDeterminant() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:399</div></div>
<div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a82a3f15f0cda1f4f874d50951344b5a9"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a82a3f15f0cda1f4f874d50951344b5a9">Eigen::ColPivHouseholderQR::logAbsDeterminant</a></div><div class="ttdeci">MatrixType::RealScalar logAbsDeterminant() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:408</div></div>
<div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a067e9d4143ce0558fc684b736128a4ed"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a067e9d4143ce0558fc684b736128a4ed">Eigen::ColPivHouseholderQR::maxPivot</a></div><div class="ttdeci">RealScalar maxPivot() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:371</div></div>
<div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_aa5a87faaa92a3081045d1f934e292ef0"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#aa5a87faaa92a3081045d1f934e292ef0">Eigen::ColPivHouseholderQR::threshold</a></div><div class="ttdeci">RealScalar threshold() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:346</div></div>
<div class="ttc" id="structEigen_1_1NumTraits_html"><div class="ttname"><a href="structEigen_1_1NumTraits.html">Eigen::NumTraits</a></div><div class="ttdoc">Holds information about the various numeric (i.e. scalar) types allowed by Eigen. ...</div><div class="ttdef"><b>Definition:</b> NumTraits.h:88</div></div>
<div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a321e96844544eacde2272c3a487048e9"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a321e96844544eacde2272c3a487048e9">Eigen::ColPivHouseholderQR::hCoeffs</a></div><div class="ttdeci">const HCoeffsType &amp; hCoeffs() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:302</div></div>
<div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a7b142db8924dd7fad99acbdd0ff4bdd1"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a7b142db8924dd7fad99acbdd0ff4bdd1">Eigen::ColPivHouseholderQR::matrixQR</a></div><div class="ttdeci">const MatrixType &amp; matrixQR() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:155</div></div>
<div class="ttc" id="group__Householder__Module_html_ga5f2b3f80cdf7ae96609e4a8d2e55e371"><div class="ttname"><a href="group__Householder__Module.html#ga5f2b3f80cdf7ae96609e4a8d2e55e371">Eigen::householderSequence</a></div><div class="ttdeci">HouseholderSequence&lt; VectorsType, CoeffsType &gt; householderSequence(const VectorsType &amp;v, const CoeffsType &amp;h)</div><div class="ttdoc">Convenience function for constructing a Householder sequence. </div><div class="ttdef"><b>Definition:</b> HouseholderSequence.h:422</div></div>
<div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a72f7fb8c1359fa8d9743068e5699228e"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a72f7fb8c1359fa8d9743068e5699228e">Eigen::ColPivHouseholderQR::ColPivHouseholderQR</a></div><div class="ttdeci">ColPivHouseholderQR()</div><div class="ttdoc">Default Constructor. </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:72</div></div>
<div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a0c06d5c2034ebb329c54235369643ad2"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a0c06d5c2034ebb329c54235369643ad2">Eigen::ColPivHouseholderQR::info</a></div><div class="ttdeci">ComputationInfo info() const </div><div class="ttdoc">Reports whether the QR factorization was succesful. </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:379</div></div>
<div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a97150efba7e2da32f48a7f823f047a89"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a97150efba7e2da32f48a7f823f047a89">Eigen::ColPivHouseholderQR::householderQ</a></div><div class="ttdeci">HouseholderSequenceType householderQ(void) const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:560</div></div>
<div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_ac93cc6a4fd4247486c2c8eab79b4c0ad"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#ac93cc6a4fd4247486c2c8eab79b4c0ad">Eigen::ColPivHouseholderQR::ColPivHouseholderQR</a></div><div class="ttdeci">ColPivHouseholderQR(const MatrixType &amp;matrix)</div><div class="ttdoc">Constructs a QR factorization from a given matrix. </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:109</div></div>
<div class="ttc" id="classEigen_1_1HouseholderSequence_html"><div class="ttname"><a href="classEigen_1_1HouseholderSequence.html">Eigen::HouseholderSequence</a></div><div class="ttdoc">Sequence of Householder reflections acting on subspaces with decreasing size. </div><div class="ttdef"><b>Definition:</b> ForwardDeclarations.h:227</div></div>
<div class="ttc" id="classEigen_1_1PermutationMatrix_html"><div class="ttname"><a href="classEigen_1_1PermutationMatrix.html">Eigen::PermutationMatrix&lt; ColsAtCompileTime, MaxColsAtCompileTime &gt;</a></div></div>
<div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a812205d31cae2005b7779c7a3a442f1b"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a812205d31cae2005b7779c7a3a442f1b">Eigen::ColPivHouseholderQR::compute</a></div><div class="ttdeci">ColPivHouseholderQR &amp; compute(const MatrixType &amp;matrix)</div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:422</div></div>
<div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a1229744f4e8554ca6e96fe32ac359924"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a1229744f4e8554ca6e96fe32ac359924">Eigen::ColPivHouseholderQR::colsPermutation</a></div><div class="ttdeci">const PermutationType &amp; colsPermutation() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:179</div></div>
<div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a5968b9ca46303b3cc7250e7b120ab7e6"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a5968b9ca46303b3cc7250e7b120ab7e6">Eigen::ColPivHouseholderQR::isSurjective</a></div><div class="ttdeci">bool isSurjective() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:263</div></div>
<div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html">Eigen::ColPivHouseholderQR</a></div><div class="ttdoc">Householder rank-revealing QR decomposition of a matrix with column-pivoting. </div><div class="ttdef"><b>Definition:</b> ForwardDeclarations.h:222</div></div>
<div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a1e119085e53eca65e9ba15451c102d40"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a1e119085e53eca65e9ba15451c102d40">Eigen::ColPivHouseholderQR::isInjective</a></div><div class="ttdeci">bool isInjective() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:250</div></div>
<div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_ab60c7d993c9eba31668fb8886d621094"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#ab60c7d993c9eba31668fb8886d621094">Eigen::ColPivHouseholderQR::isInvertible</a></div><div class="ttdeci">bool isInvertible() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:275</div></div>
<div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a446f775405186b238f20bd092fd107a6"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a446f775405186b238f20bd092fd107a6">Eigen::ColPivHouseholderQR::setThreshold</a></div><div class="ttdeci">ColPivHouseholderQR &amp; setThreshold(Default_t)</div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:336</div></div>
<div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a5631914aef48f4f719789c823edacb2c"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a5631914aef48f4f719789c823edacb2c">Eigen::ColPivHouseholderQR::setThreshold</a></div><div class="ttdeci">ColPivHouseholderQR &amp; setThreshold(const RealScalar &amp;threshold)</div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:321</div></div>
<div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_afbe1cd1202964011ae7e7411577749a0"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#afbe1cd1202964011ae7e7411577749a0">Eigen::ColPivHouseholderQR::solve</a></div><div class="ttdeci">const internal::solve_retval&lt; ColPivHouseholderQR, Rhs &gt; solve(const MatrixBase&lt; Rhs &gt; &amp;b) const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:141</div></div>
<div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a84cd3aba44220008bdbd81506703de37"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a84cd3aba44220008bdbd81506703de37">Eigen::ColPivHouseholderQR::matrixR</a></div><div class="ttdeci">const MatrixType &amp; matrixR() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:170</div></div>
<div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a6dda9285f13dec9f49e9c17229a89988"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a6dda9285f13dec9f49e9c17229a89988">Eigen::ColPivHouseholderQR::nonzeroPivots</a></div><div class="ttdeci">Index nonzeroPivots() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:362</div></div>
<div class="ttc" id="group__enums_html_gga51bc1ac16f26ebe51eae1abb77bd037bafdfbdf3247bd36a1f17270d5cec74c9c"><div class="ttname"><a href="group__enums.html#gga51bc1ac16f26ebe51eae1abb77bd037bafdfbdf3247bd36a1f17270d5cec74c9c">Eigen::Success</a></div><div class="ttdef"><b>Definition:</b> Constants.h:376</div></div>
<div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a3021b1285c868ef94b26f387766bdf92"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a3021b1285c868ef94b26f387766bdf92">Eigen::ColPivHouseholderQR::inverse</a></div><div class="ttdeci">const internal::solve_retval&lt; ColPivHouseholderQR, typename MatrixType::IdentityReturnType &gt; inverse() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:288</div></div>
<div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a7c6323871c4f080fc6e2d3ad7fc607fc"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a7c6323871c4f080fc6e2d3ad7fc607fc">Eigen::ColPivHouseholderQR::dimensionOfKernel</a></div><div class="ttdeci">Index dimensionOfKernel() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:237</div></div>
<div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a4a15f3e5e33478b9969d8c71aabd09ea"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a4a15f3e5e33478b9969d8c71aabd09ea">Eigen::ColPivHouseholderQR::ColPivHouseholderQR</a></div><div class="ttdeci">ColPivHouseholderQR(Index rows, Index cols)</div><div class="ttdoc">Default Constructor with memory preallocation. </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:87</div></div>
<div class="ttc" id="group__enums_html_ga51bc1ac16f26ebe51eae1abb77bd037b"><div class="ttname"><a href="group__enums.html#ga51bc1ac16f26ebe51eae1abb77bd037b">Eigen::ComputationInfo</a></div><div class="ttdeci">ComputationInfo</div><div class="ttdef"><b>Definition:</b> Constants.h:374</div></div>
<div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a363d1c09d77f09d6ea2d2789776e7be3"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a363d1c09d77f09d6ea2d2789776e7be3">Eigen::ColPivHouseholderQR::rank</a></div><div class="ttdeci">Index rank() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:220</div></div>
<div class="ttc" id="classEigen_1_1MatrixBase_html"><div class="ttname"><a href="classEigen_1_1MatrixBase.html">Eigen::MatrixBase</a></div><div class="ttdoc">Base class for all dense matrices, vectors, and expressions. </div><div class="ttdef"><b>Definition:</b> MatrixBase.h:48</div></div>
<div class="ttc" id="classEigen_1_1MatrixBase_html_a05afed751d3a7277951d1918468e0872"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#a05afed751d3a7277951d1918468e0872">Eigen::MatrixBase::colPivHouseholderQr</a></div><div class="ttdeci">const ColPivHouseholderQR&lt; PlainObject &gt; colPivHouseholderQr() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:572</div></div>
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