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<div class="title">Jacobi.h</div> </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com></span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr></span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">//</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <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> <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> <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> </div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="preprocessor">#ifndef EIGEN_JACOBI_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_JACOBI_H</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="keyword">namespace </span>Eigen { </div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> </div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar> <span class="keyword">class </span>JacobiRotation</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> {</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::Real RealScalar;</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> </div>
<div class="line"><a name="l00040"></a><span class="lineno"><a class="line" href="classEigen_1_1JacobiRotation.html#a5700212c7e79eccd3cde8b07d6816e9d"> 40</a></span>  <a class="code" href="classEigen_1_1JacobiRotation.html#a5700212c7e79eccd3cde8b07d6816e9d">JacobiRotation</a>() {}</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> </div>
<div class="line"><a name="l00043"></a><span class="lineno"><a class="line" href="classEigen_1_1JacobiRotation.html#a7999227436ed5e6bbe679fd40564abf1"> 43</a></span>  <a class="code" href="classEigen_1_1JacobiRotation.html#a7999227436ed5e6bbe679fd40564abf1">JacobiRotation</a>(<span class="keyword">const</span> Scalar& c, <span class="keyword">const</span> Scalar& s) : m_c(c), m_s(s) {}</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> </div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  Scalar& c() { <span class="keywordflow">return</span> m_c; }</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  Scalar c()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_c; }</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  Scalar& s() { <span class="keywordflow">return</span> m_s; }</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  Scalar s()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_s; }</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> </div>
<div class="line"><a name="l00051"></a><span class="lineno"><a class="line" href="classEigen_1_1JacobiRotation.html#a693f65729440b5c31feb6d86d1b075d1"> 51</a></span>  <a class="code" href="classEigen_1_1JacobiRotation.html">JacobiRotation</a> <a class="code" href="classEigen_1_1JacobiRotation.html#a693f65729440b5c31feb6d86d1b075d1">operator*</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1JacobiRotation.html">JacobiRotation</a>& other)</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  {</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="keyword">using</span> numext::conj;</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1JacobiRotation.html#a5700212c7e79eccd3cde8b07d6816e9d">JacobiRotation</a>(m_c * other.m_c - conj(m_s) * other.m_s,</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  conj(m_c * conj(other.m_s) + conj(m_s) * conj(other.m_c)));</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  }</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span> </div>
<div class="line"><a name="l00059"></a><span class="lineno"><a class="line" href="classEigen_1_1JacobiRotation.html#a535dd93be32736dbe23a201c33c279d7"> 59</a></span>  <a class="code" href="classEigen_1_1JacobiRotation.html">JacobiRotation</a> <a class="code" href="classEigen_1_1JacobiRotation.html#a535dd93be32736dbe23a201c33c279d7">transpose</a>()<span class="keyword"> const </span>{ <span class="keyword">using</span> numext::conj; <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1JacobiRotation.html#a5700212c7e79eccd3cde8b07d6816e9d">JacobiRotation</a>(m_c, -conj(m_s)); }</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span> </div>
<div class="line"><a name="l00062"></a><span class="lineno"><a class="line" href="classEigen_1_1JacobiRotation.html#acf21a38021bf2100bb50268a166317f1"> 62</a></span>  <a class="code" href="classEigen_1_1JacobiRotation.html">JacobiRotation</a> <a class="code" href="classEigen_1_1JacobiRotation.html#acf21a38021bf2100bb50268a166317f1">adjoint</a>()<span class="keyword"> const </span>{ <span class="keyword">using</span> numext::conj; <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1JacobiRotation.html#a5700212c7e79eccd3cde8b07d6816e9d">JacobiRotation</a>(conj(m_c), -m_s); }</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span> </div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="keywordtype">bool</span> <a class="code" href="classEigen_1_1JacobiRotation.html#a7349f180eaab3d2b4c654b32a41f8932">makeJacobi</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase<Derived></a>&, <span class="keyword">typename</span> Derived::Index p, <span class="keyword">typename</span> Derived::Index q);</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="keywordtype">bool</span> <a class="code" href="classEigen_1_1JacobiRotation.html#a7349f180eaab3d2b4c654b32a41f8932">makeJacobi</a>(<span class="keyword">const</span> RealScalar& x, <span class="keyword">const</span> Scalar& y, <span class="keyword">const</span> RealScalar& z);</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span> </div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1JacobiRotation.html#a459c7bb56a9862bc2b66d03070b4a3e0">makeGivens</a>(<span class="keyword">const</span> Scalar& p, <span class="keyword">const</span> Scalar& q, Scalar* z=0);</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span> </div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1JacobiRotation.html#a459c7bb56a9862bc2b66d03070b4a3e0">makeGivens</a>(<span class="keyword">const</span> Scalar& p, <span class="keyword">const</span> Scalar& q, Scalar* z, internal::true_type);</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1JacobiRotation.html#a459c7bb56a9862bc2b66d03070b4a3e0">makeGivens</a>(<span class="keyword">const</span> Scalar& p, <span class="keyword">const</span> Scalar& q, Scalar* z, internal::false_type);</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span> </div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  Scalar m_c, m_s;</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span> };</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span> </div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00083"></a><span class="lineno"><a class="line" href="classEigen_1_1JacobiRotation.html#aa44fbe850470b9f08adceff2655decdf"> 83</a></span> <span class="keywordtype">bool</span> <a class="code" href="classEigen_1_1JacobiRotation.html#a7349f180eaab3d2b4c654b32a41f8932">JacobiRotation<Scalar>::makeJacobi</a>(<span class="keyword">const</span> RealScalar& x, <span class="keyword">const</span> Scalar& y, <span class="keyword">const</span> RealScalar& z)</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span> {</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="structEigen_1_1NumTraits.html">NumTraits<Scalar>::Real</a> RealScalar;</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  <span class="keywordflow">if</span>(y == Scalar(0))</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  {</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  m_c = Scalar(1);</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  m_s = Scalar(0);</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  }</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  {</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  RealScalar tau = (x-z)/(RealScalar(2)*abs(y));</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  RealScalar w = sqrt(numext::abs2(tau) + RealScalar(1));</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  RealScalar t;</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <span class="keywordflow">if</span>(tau>RealScalar(0))</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  {</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  t = RealScalar(1) / (tau + w);</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  }</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  {</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  t = RealScalar(1) / (tau - w);</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  }</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  RealScalar sign_t = t > RealScalar(0) ? RealScalar(1) : RealScalar(-1);</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  RealScalar n = RealScalar(1) / sqrt(numext::abs2(t)+RealScalar(1));</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  m_s = - sign_t * (numext::conj(y) / abs(y)) * abs(t) * n;</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  m_c = n;</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  }</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span> }</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span> </div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00126"></a><span class="lineno"><a class="line" href="classEigen_1_1JacobiRotation.html#a7349f180eaab3d2b4c654b32a41f8932"> 126</a></span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="classEigen_1_1JacobiRotation.html#a7349f180eaab3d2b4c654b32a41f8932">JacobiRotation<Scalar>::makeJacobi</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase<Derived></a>& m, <span class="keyword">typename</span> Derived::Index p, <span class="keyword">typename</span> Derived::Index q)</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span> {</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="keywordflow">return</span> makeJacobi(numext::real(m.coeff(p,p)), m.coeff(p,q), numext::real(m.coeff(q,q)));</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span> }</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span> </div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00148"></a><span class="lineno"><a class="line" href="classEigen_1_1JacobiRotation.html#a459c7bb56a9862bc2b66d03070b4a3e0"> 148</a></span> <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1JacobiRotation.html#a459c7bb56a9862bc2b66d03070b4a3e0">JacobiRotation<Scalar>::makeGivens</a>(<span class="keyword">const</span> Scalar& p, <span class="keyword">const</span> Scalar& q, Scalar* z)</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span> {</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  makeGivens(p, q, z, <span class="keyword">typename</span> internal::conditional<<a class="code" href="structEigen_1_1NumTraits.html">NumTraits<Scalar>::IsComplex</a>, internal::true_type, internal::false_type>::type());</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span> }</div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span> </div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span> </div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span> <span class="comment">// specialization for complexes</span></div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span> <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1JacobiRotation.html#a459c7bb56a9862bc2b66d03070b4a3e0">JacobiRotation<Scalar>::makeGivens</a>(<span class="keyword">const</span> Scalar& p, <span class="keyword">const</span> Scalar& q, Scalar* r, internal::true_type)</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span> {</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  <span class="keyword">using</span> numext::conj;</div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  </div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  <span class="keywordflow">if</span>(q==Scalar(0))</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  {</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  m_c = numext::real(p)<0 ? Scalar(-1) : Scalar(1);</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  m_s = 0;</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  <span class="keywordflow">if</span>(r) *r = m_c * p;</div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  }</div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span>(p==Scalar(0))</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  {</div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  m_c = 0;</div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  m_s = -q/abs(q);</div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <span class="keywordflow">if</span>(r) *r = abs(q);</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  }</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  {</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  RealScalar p1 = numext::norm1(p);</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  RealScalar q1 = numext::norm1(q);</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  <span class="keywordflow">if</span>(p1>=q1)</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  {</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  Scalar ps = p / p1;</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  RealScalar p2 = numext::abs2(ps);</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  Scalar qs = q / p1;</div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  RealScalar q2 = numext::abs2(qs);</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span> </div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  RealScalar u = sqrt(RealScalar(1) + q2/p2);</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  <span class="keywordflow">if</span>(numext::real(p)<RealScalar(0))</div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  u = -u;</div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span> </div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  m_c = Scalar(1)/u;</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  m_s = -qs*conj(ps)*(m_c/p2);</div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  <span class="keywordflow">if</span>(r) *r = p * u;</div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  }</div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  {</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  Scalar ps = p / q1;</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  RealScalar p2 = numext::abs2(ps);</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  Scalar qs = q / q1;</div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  RealScalar q2 = numext::abs2(qs);</div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span> </div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  RealScalar u = q1 * sqrt(p2 + q2);</div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <span class="keywordflow">if</span>(numext::real(p)<RealScalar(0))</div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  u = -u;</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span> </div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  p1 = abs(p);</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  ps = p/p1;</div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  m_c = p1/u;</div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  m_s = -conj(ps) * (q/u);</div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  <span class="keywordflow">if</span>(r) *r = ps * u;</div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  }</div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  }</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span> }</div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span> </div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span> <span class="comment">// specialization for reals</span></div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span> <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1JacobiRotation.html#a459c7bb56a9862bc2b66d03070b4a3e0">JacobiRotation<Scalar>::makeGivens</a>(<span class="keyword">const</span> Scalar& p, <span class="keyword">const</span> Scalar& q, Scalar* r, internal::false_type)</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span> {</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <span class="keywordflow">if</span>(q==Scalar(0))</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  {</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  m_c = p<Scalar(0) ? Scalar(-1) : Scalar(1);</div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  m_s = Scalar(0);</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  <span class="keywordflow">if</span>(r) *r = abs(p);</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  }</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span>(p==Scalar(0))</div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  {</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  m_c = Scalar(0);</div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  m_s = q<Scalar(0) ? Scalar(1) : Scalar(-1);</div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  <span class="keywordflow">if</span>(r) *r = abs(q);</div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  }</div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span>(abs(p) > abs(q))</div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  {</div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  Scalar t = q/p;</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  Scalar u = sqrt(Scalar(1) + numext::abs2(t));</div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  <span class="keywordflow">if</span>(p<Scalar(0))</div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  u = -u;</div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  m_c = Scalar(1)/u;</div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  m_s = -t * m_c;</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  <span class="keywordflow">if</span>(r) *r = p * u;</div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  }</div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  {</div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  Scalar t = p/q;</div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  Scalar u = sqrt(Scalar(1) + numext::abs2(t));</div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  <span class="keywordflow">if</span>(q<Scalar(0))</div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  u = -u;</div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  m_s = -Scalar(1)/u;</div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  m_c = -t * m_s;</div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <span class="keywordflow">if</span>(r) *r = q * u;</div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  }</div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span> </div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span> }</div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span> </div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span> <span class="comment">/****************************************************************************************</span></div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span> <span class="comment">* Implementation of MatrixBase methods</span></div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span> <span class="comment">****************************************************************************************/</span></div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span> </div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span> <span class="keyword">template</span><<span class="keyword">typename</span> VectorX, <span class="keyword">typename</span> VectorY, <span class="keyword">typename</span> OtherScalar></div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span> <span class="keywordtype">void</span> apply_rotation_in_the_plane(VectorX& _x, VectorY& _y, <span class="keyword">const</span> JacobiRotation<OtherScalar>& j);</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span> }</div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span> </div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span> <span class="keyword">template</span><<span class="keyword">typename</span> OtherScalar></div>
<div class="line"><a name="l00277"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a68c6383c506e63a2250be4433c73b519"> 277</a></span> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1MatrixBase.html#a9aaee4fba54baa7d0ca508e094f2d6f9">MatrixBase<Derived>::applyOnTheLeft</a>(<a class="code" href="classEigen_1_1DenseBase.html#a4d4873e91be950c079f067fa97fd5c40">Index</a> p, <a class="code" href="classEigen_1_1DenseBase.html#a4d4873e91be950c079f067fa97fd5c40">Index</a> q, <span class="keyword">const</span> <a class="code" href="classEigen_1_1JacobiRotation.html">JacobiRotation<OtherScalar></a>& j)</div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span> {</div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  RowXpr x(this->row(p));</div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  RowXpr y(this->row(q));</div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  internal::apply_rotation_in_the_plane(x, y, j);</div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span> }</div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span> </div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span> <span class="keyword">template</span><<span class="keyword">typename</span> OtherScalar></div>
<div class="line"><a name="l00292"></a><span class="lineno"><a class="line" href="group__Jacobi__Module.html#ga794a90a8b3f30366546f93c5b9b77b18"> 292</a></span> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1MatrixBase.html#a6e5b1e71a1916ddd01e7c324831c40dc">MatrixBase<Derived>::applyOnTheRight</a>(<a class="code" href="classEigen_1_1DenseBase.html#a4d4873e91be950c079f067fa97fd5c40">Index</a> p, <a class="code" href="classEigen_1_1DenseBase.html#a4d4873e91be950c079f067fa97fd5c40">Index</a> q, <span class="keyword">const</span> <a class="code" href="classEigen_1_1JacobiRotation.html">JacobiRotation<OtherScalar></a>& j)</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span> {</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  ColXpr x(this->col(p));</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  ColXpr y(this->col(q));</div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  internal::apply_rotation_in_the_plane(x, y, j.transpose());</div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span> }</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span> </div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span> <span class="keyword">template</span><<span class="keyword">typename</span> VectorX, <span class="keyword">typename</span> VectorY, <span class="keyword">typename</span> OtherScalar></div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span> <span class="keywordtype">void</span> <span class="comment">/*EIGEN_DONT_INLINE*/</span> apply_rotation_in_the_plane(VectorX& _x, VectorY& _y, <span class="keyword">const</span> <a class="code" href="classEigen_1_1JacobiRotation.html">JacobiRotation<OtherScalar></a>& j)</div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span> {</div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> VectorX::Index Index;</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> VectorX::Scalar Scalar;</div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  <span class="keyword">enum</span> { PacketSize = packet_traits<Scalar>::size };</div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> packet_traits<Scalar>::type Packet;</div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  eigen_assert(_x.size() == _y.size());</div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  Index size = _x.size();</div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  Index incrx = _x.innerStride();</div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  Index incry = _y.innerStride();</div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span> </div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  Scalar* EIGEN_RESTRICT x = &_x.coeffRef(0);</div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  Scalar* EIGEN_RESTRICT y = &_y.coeffRef(0);</div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  </div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  OtherScalar c = j.c();</div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  OtherScalar s = j.s();</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  <span class="keywordflow">if</span> (c==OtherScalar(1) && s==OtherScalar(0))</div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span> </div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  <span class="comment">/*** dynamic-size vectorized paths ***/</span></div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span> </div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  <span class="keywordflow">if</span>(VectorX::SizeAtCompileTime == <a class="code" href="namespaceEigen.html#adc9da5be31bdce40c25a92c27999c0e3">Dynamic</a> &&</div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  (VectorX::Flags & VectorY::Flags & <a class="code" href="group__flags.html#gaa780614dc11271c147db56e9c1524e76">PacketAccessBit</a>) &&</div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  ((incrx==1 && incry==1) || PacketSize == 1))</div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  {</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  <span class="comment">// both vectors are sequentially stored in memory => vectorization</span></div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  <span class="keyword">enum</span> { Peeling = 2 };</div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span> </div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  Index alignedStart = internal::first_aligned(y, size);</div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  Index alignedEnd = alignedStart + ((size-alignedStart)/PacketSize)*PacketSize;</div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span> </div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  <span class="keyword">const</span> Packet pc = pset1<Packet>(c);</div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  <span class="keyword">const</span> Packet ps = pset1<Packet>(s);</div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  conj_helper<Packet,Packet,NumTraits<Scalar>::IsComplex,<span class="keyword">false</span>> pcj;</div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span> </div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  <span class="keywordflow">for</span>(Index i=0; i<alignedStart; ++i)</div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  {</div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  Scalar xi = x[i];</div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  Scalar yi = y[i];</div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  x[i] = c * xi + numext::conj(s) * yi;</div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  y[i] = -s * xi + numext::conj(c) * yi;</div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  }</div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span> </div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  Scalar* EIGEN_RESTRICT px = x + alignedStart;</div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  Scalar* EIGEN_RESTRICT py = y + alignedStart;</div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span> </div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  <span class="keywordflow">if</span>(internal::first_aligned(x, size)==alignedStart)</div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  {</div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  <span class="keywordflow">for</span>(Index i=alignedStart; i<alignedEnd; i+=PacketSize)</div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  {</div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  Packet xi = pload<Packet>(px);</div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  Packet yi = pload<Packet>(py);</div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  pstore(px, padd(pmul(pc,xi),pcj.pmul(ps,yi)));</div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  pstore(py, psub(pcj.pmul(pc,yi),pmul(ps,xi)));</div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  px += PacketSize;</div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  py += PacketSize;</div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  }</div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  }</div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  {</div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  Index peelingEnd = alignedStart + ((size-alignedStart)/(Peeling*PacketSize))*(Peeling*PacketSize);</div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  <span class="keywordflow">for</span>(Index i=alignedStart; i<peelingEnd; i+=Peeling*PacketSize)</div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  {</div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  Packet xi = ploadu<Packet>(px);</div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  Packet xi1 = ploadu<Packet>(px+PacketSize);</div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  Packet yi = pload <Packet>(py);</div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  Packet yi1 = pload <Packet>(py+PacketSize);</div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  pstoreu(px, padd(pmul(pc,xi),pcj.pmul(ps,yi)));</div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  pstoreu(px+PacketSize, padd(pmul(pc,xi1),pcj.pmul(ps,yi1)));</div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  pstore (py, psub(pcj.pmul(pc,yi),pmul(ps,xi)));</div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  pstore (py+PacketSize, psub(pcj.pmul(pc,yi1),pmul(ps,xi1)));</div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  px += Peeling*PacketSize;</div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  py += Peeling*PacketSize;</div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  }</div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  <span class="keywordflow">if</span>(alignedEnd!=peelingEnd)</div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  {</div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  Packet xi = ploadu<Packet>(x+peelingEnd);</div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  Packet yi = pload <Packet>(y+peelingEnd);</div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  pstoreu(x+peelingEnd, padd(pmul(pc,xi),pcj.pmul(ps,yi)));</div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  pstore (y+peelingEnd, psub(pcj.pmul(pc,yi),pmul(ps,xi)));</div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  }</div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  }</div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span> </div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  <span class="keywordflow">for</span>(Index i=alignedEnd; i<size; ++i)</div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  {</div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  Scalar xi = x[i];</div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  Scalar yi = y[i];</div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  x[i] = c * xi + numext::conj(s) * yi;</div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  y[i] = -s * xi + numext::conj(c) * yi;</div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  }</div>
<div class="line"><a name="l00391"></a><span class="lineno"> 391</span>  }</div>
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span> </div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  <span class="comment">/*** fixed-size vectorized path ***/</span></div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span>(VectorX::SizeAtCompileTime != <a class="code" href="namespaceEigen.html#adc9da5be31bdce40c25a92c27999c0e3">Dynamic</a> &&</div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  (VectorX::Flags & VectorY::Flags & PacketAccessBit) &&</div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  (VectorX::Flags & VectorY::Flags & <a class="code" href="group__flags.html#ga972a2dcb6603215fa53e0b9e82051426">AlignedBit</a>))</div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  {</div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span>  <span class="keyword">const</span> Packet pc = pset1<Packet>(c);</div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span>  <span class="keyword">const</span> Packet ps = pset1<Packet>(s);</div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span>  conj_helper<Packet,Packet,NumTraits<Scalar>::IsComplex,<span class="keyword">false</span>> pcj;</div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  Scalar* EIGEN_RESTRICT px = x;</div>
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span>  Scalar* EIGEN_RESTRICT py = y;</div>
<div class="line"><a name="l00403"></a><span class="lineno"> 403</span>  <span class="keywordflow">for</span>(Index i=0; i<size; i+=PacketSize)</div>
<div class="line"><a name="l00404"></a><span class="lineno"> 404</span>  {</div>
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span>  Packet xi = pload<Packet>(px);</div>
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span>  Packet yi = pload<Packet>(py);</div>
<div class="line"><a name="l00407"></a><span class="lineno"> 407</span>  pstore(px, padd(pmul(pc,xi),pcj.pmul(ps,yi)));</div>
<div class="line"><a name="l00408"></a><span class="lineno"> 408</span>  pstore(py, psub(pcj.pmul(pc,yi),pmul(ps,xi)));</div>
<div class="line"><a name="l00409"></a><span class="lineno"> 409</span>  px += PacketSize;</div>
<div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  py += PacketSize;</div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span>  }</div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  }</div>
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span> </div>
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  <span class="comment">/*** non-vectorized path ***/</span></div>
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00416"></a><span class="lineno"> 416</span>  {</div>
<div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  <span class="keywordflow">for</span>(Index i=0; i<size; ++i)</div>
<div class="line"><a name="l00418"></a><span class="lineno"> 418</span>  {</div>
<div class="line"><a name="l00419"></a><span class="lineno"> 419</span>  Scalar xi = *x;</div>
<div class="line"><a name="l00420"></a><span class="lineno"> 420</span>  Scalar yi = *y;</div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  *x = c * xi + numext::conj(s) * yi;</div>
<div class="line"><a name="l00422"></a><span class="lineno"> 422</span>  *y = -s * xi + numext::conj(c) * yi;</div>
<div class="line"><a name="l00423"></a><span class="lineno"> 423</span>  x += incrx;</div>
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span>  y += incry;</div>
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span>  }</div>
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span>  }</div>
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span> }</div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span> </div>
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span> } <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span> </div>
<div class="line"><a name="l00431"></a><span class="lineno"> 431</span> } <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00432"></a><span class="lineno"> 432</span> </div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span> <span class="preprocessor">#endif // EIGEN_JACOBI_H</span></div>
<div class="ttc" id="classEigen_1_1JacobiRotation_html_a5700212c7e79eccd3cde8b07d6816e9d"><div class="ttname"><a href="classEigen_1_1JacobiRotation.html#a5700212c7e79eccd3cde8b07d6816e9d">Eigen::JacobiRotation::JacobiRotation</a></div><div class="ttdeci">JacobiRotation()</div><div class="ttdef"><b>Definition:</b> Jacobi.h:40</div></div>
<div class="ttc" id="classEigen_1_1JacobiRotation_html"><div class="ttname"><a href="classEigen_1_1JacobiRotation.html">Eigen::JacobiRotation</a></div><div class="ttdoc">Rotation given by a cosine-sine pair. </div><div class="ttdef"><b>Definition:</b> ForwardDeclarations.h:228</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="namespaceEigen_html_adc9da5be31bdce40c25a92c27999c0e3"><div class="ttname"><a href="namespaceEigen.html#adc9da5be31bdce40c25a92c27999c0e3">Eigen::Dynamic</a></div><div class="ttdeci">const int Dynamic</div><div class="ttdef"><b>Definition:</b> Constants.h:21</div></div>
<div class="ttc" id="group__flags_html_gaa780614dc11271c147db56e9c1524e76"><div class="ttname"><a href="group__flags.html#gaa780614dc11271c147db56e9c1524e76">Eigen::PacketAccessBit</a></div><div class="ttdeci">const unsigned int PacketAccessBit</div><div class="ttdef"><b>Definition:</b> Constants.h:81</div></div>
<div class="ttc" id="classEigen_1_1MatrixBase_html_a9aaee4fba54baa7d0ca508e094f2d6f9"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#a9aaee4fba54baa7d0ca508e094f2d6f9">Eigen::MatrixBase::applyOnTheLeft</a></div><div class="ttdeci">void applyOnTheLeft(const EigenBase< OtherDerived > &other)</div><div class="ttdef"><b>Definition:</b> EigenBase.h:154</div></div>
<div class="ttc" id="classEigen_1_1MatrixBase_html_a6e5b1e71a1916ddd01e7c324831c40dc"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#a6e5b1e71a1916ddd01e7c324831c40dc">Eigen::MatrixBase::applyOnTheRight</a></div><div class="ttdeci">void applyOnTheRight(const EigenBase< OtherDerived > &other)</div><div class="ttdef"><b>Definition:</b> EigenBase.h:146</div></div>
<div class="ttc" id="classEigen_1_1JacobiRotation_html_a535dd93be32736dbe23a201c33c279d7"><div class="ttname"><a href="classEigen_1_1JacobiRotation.html#a535dd93be32736dbe23a201c33c279d7">Eigen::JacobiRotation::transpose</a></div><div class="ttdeci">JacobiRotation transpose() const </div><div class="ttdef"><b>Definition:</b> Jacobi.h:59</div></div>
<div class="ttc" id="classEigen_1_1JacobiRotation_html_a459c7bb56a9862bc2b66d03070b4a3e0"><div class="ttname"><a href="classEigen_1_1JacobiRotation.html#a459c7bb56a9862bc2b66d03070b4a3e0">Eigen::JacobiRotation::makeGivens</a></div><div class="ttdeci">void makeGivens(const Scalar &p, const Scalar &q, Scalar *z=0)</div><div class="ttdef"><b>Definition:</b> Jacobi.h:148</div></div>
<div class="ttc" id="classEigen_1_1JacobiRotation_html_a7999227436ed5e6bbe679fd40564abf1"><div class="ttname"><a href="classEigen_1_1JacobiRotation.html#a7999227436ed5e6bbe679fd40564abf1">Eigen::JacobiRotation::JacobiRotation</a></div><div class="ttdeci">JacobiRotation(const Scalar &c, const Scalar &s)</div><div class="ttdef"><b>Definition:</b> Jacobi.h:43</div></div>
<div class="ttc" id="classEigen_1_1DenseBase_html_a4d4873e91be950c079f067fa97fd5c40"><div class="ttname"><a href="classEigen_1_1DenseBase.html#a4d4873e91be950c079f067fa97fd5c40">Eigen::DenseBase::Index</a></div><div class="ttdeci">internal::traits< Derived >::Index Index</div><div class="ttdoc">The type of indices. </div><div class="ttdef"><b>Definition:</b> DenseBase.h:61</div></div>
<div class="ttc" id="classEigen_1_1JacobiRotation_html_a693f65729440b5c31feb6d86d1b075d1"><div class="ttname"><a href="classEigen_1_1JacobiRotation.html#a693f65729440b5c31feb6d86d1b075d1">Eigen::JacobiRotation::operator*</a></div><div class="ttdeci">JacobiRotation operator*(const JacobiRotation &other)</div><div class="ttdef"><b>Definition:</b> Jacobi.h:51</div></div>
<div class="ttc" id="classEigen_1_1JacobiRotation_html_acf21a38021bf2100bb50268a166317f1"><div class="ttname"><a href="classEigen_1_1JacobiRotation.html#acf21a38021bf2100bb50268a166317f1">Eigen::JacobiRotation::adjoint</a></div><div class="ttdeci">JacobiRotation adjoint() const </div><div class="ttdef"><b>Definition:</b> Jacobi.h:62</div></div>
<div class="ttc" id="group__flags_html_ga972a2dcb6603215fa53e0b9e82051426"><div class="ttname"><a href="group__flags.html#ga972a2dcb6603215fa53e0b9e82051426">Eigen::AlignedBit</a></div><div class="ttdeci">const unsigned int AlignedBit</div><div class="ttdef"><b>Definition:</b> Constants.h:147</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_1JacobiRotation_html_a7349f180eaab3d2b4c654b32a41f8932"><div class="ttname"><a href="classEigen_1_1JacobiRotation.html#a7349f180eaab3d2b4c654b32a41f8932">Eigen::JacobiRotation::makeJacobi</a></div><div class="ttdeci">bool makeJacobi(const MatrixBase< Derived > &, typename Derived::Index p, typename Derived::Index q)</div><div class="ttdef"><b>Definition:</b> Jacobi.h:126</div></div>
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