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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) 2006-2008, 2010 Benoit Jacob <jacob.benoit.1@gmail.com></span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> </div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="preprocessor">#ifndef EIGEN_DOT_H</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_DOT_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="keyword">namespace </span>Eigen { </div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> </div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> </div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment">// helper function for dot(). The problem is that if we put that in the body of dot(), then upon calling dot</span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment">// with mismatched types, the compiler emits errors about failing to instantiate cwiseProduct BEFORE</span></div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment">// looking at the static assertions. Thus this is a trick to get better compile errors.</span></div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="keyword">template</span><<span class="keyword">typename</span> T, <span class="keyword">typename</span> U,</div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="comment">// the NeedToTranspose condition here is taken straight from Assign.h</span></div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>  <span class="keywordtype">bool</span> NeedToTranspose = T::IsVectorAtCompileTime</div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>  && U::IsVectorAtCompileTime</div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>  && ((int(T::RowsAtCompileTime) == 1 && int(U::ColsAtCompileTime) == 1)</div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  | <span class="comment">// FIXME | instead of || to please GCC 4.4.0 stupid warning "suggest parentheses around &&".</span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  <span class="comment">// revert to || as soon as not needed anymore.</span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  (<span class="keywordtype">int</span>(T::ColsAtCompileTime) == 1 && int(U::RowsAtCompileTime) == 1))</div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> ></div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="keyword">struct </span>dot_nocheck</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> {</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> scalar_product_traits<typename traits<T>::Scalar,<span class="keyword">typename</span> traits<U>::Scalar>::ReturnType ResScalar;</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  <span class="keyword">static</span> <span class="keyword">inline</span> ResScalar run(<span class="keyword">const</span> MatrixBase<T>& a, <span class="keyword">const</span> MatrixBase<U>& b)</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  {</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <span class="keywordflow">return</span> a.template binaryExpr<scalar_conj_product_op<typename traits<T>::Scalar,<span class="keyword">typename</span> traits<U>::Scalar> >(b).sum();</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> };</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> </div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="keyword">template</span><<span class="keyword">typename</span> T, <span class="keyword">typename</span> U></div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="keyword">struct </span>dot_nocheck<T, U, true></div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> {</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> scalar_product_traits<typename traits<T>::Scalar,<span class="keyword">typename</span> traits<U>::Scalar>::ReturnType ResScalar;</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  <span class="keyword">static</span> <span class="keyword">inline</span> ResScalar run(<span class="keyword">const</span> MatrixBase<T>& a, <span class="keyword">const</span> MatrixBase<U>& b)</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  {</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <span class="keywordflow">return</span> a.transpose().template binaryExpr<scalar_conj_product_op<typename traits<T>::Scalar,<span class="keyword">typename</span> traits<U>::Scalar> >(b).sum();</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  }</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> };</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> </div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> } <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> </div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="keyword">template</span><<span class="keyword">typename</span> OtherDerived></div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span> <span class="keyword">typename</span> internal::scalar_product_traits<typename internal::traits<Derived>::Scalar,<span class="keyword">typename</span> internal::traits<OtherDerived>::Scalar>::ReturnType</div>
<div class="line"><a name="l00063"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#adb71ddef4955ae7d353df12d05665191"> 63</a></span> <a class="code" href="classEigen_1_1MatrixBase.html#adb71ddef4955ae7d353df12d05665191">MatrixBase<Derived>::dot</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase<OtherDerived></a>& other)<span class="keyword"> const</span></div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="keyword">typedef</span> internal::scalar_conj_product_op<Scalar,typename OtherDerived::Scalar> func;</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  EIGEN_CHECK_BINARY_COMPATIBILIY(func,Scalar,<span class="keyword">typename</span> OtherDerived::Scalar);</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span> </div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  eigen_assert(size() == other.size());</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span> </div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  <span class="keywordflow">return</span> internal::dot_nocheck<Derived,OtherDerived>::run(*<span class="keyword">this</span>, other);</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span> }</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span> </div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span> <span class="preprocessor">#ifdef EIGEN2_SUPPORT</span></div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span> <span class="keyword">template</span><<span class="keyword">typename</span> OtherDerived></div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span> <span class="keyword">typename</span> internal::traits<Derived>::Scalar</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span> <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase<Derived>::eigen2_dot</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase<OtherDerived></a>& other)<span class="keyword"> const</span></div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span> </div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  eigen_assert(size() == other.size());</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span> </div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  return internal::dot_nocheck<OtherDerived,Derived>::run(other,*this);</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> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span> </div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span> <span class="comment">//---------- implementation of L2 norm and related functions ----------</span></div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span> </div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00113"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a229bd5cc6237359a1d85401743476ede"> 113</a></span> EIGEN_STRONG_INLINE <span class="keyword">typename</span> <a class="code" href="structEigen_1_1NumTraits.html">NumTraits<typename internal::traits<Derived>::Scalar</a>>::Real <a class="code" href="classEigen_1_1MatrixBase.html#a229bd5cc6237359a1d85401743476ede">MatrixBase<Derived>::squaredNorm</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <span class="keywordflow">return</span> numext::real((*this).cwiseAbs2().sum());</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span> }</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span> </div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00125"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a0be1b433c65ce9d92c81a4718daf54e5"> 125</a></span> <span class="keyword">inline</span> <span class="keyword">typename</span> <a class="code" href="structEigen_1_1NumTraits.html">NumTraits<typename internal::traits<Derived>::Scalar</a>>::Real <a class="code" href="classEigen_1_1MatrixBase.html#a0be1b433c65ce9d92c81a4718daf54e5">MatrixBase<Derived>::norm</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="keywordflow">return</span> sqrt(squaredNorm());</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="l00137"></a><span class="lineno"> 137</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span> <span class="keyword">inline</span> <span class="keyword">const</span> <span class="keyword">typename</span> <a class="code" href="classEigen_1_1Matrix.html">MatrixBase<Derived>::PlainObject</a></div>
<div class="line"><a name="l00139"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a8ed1fb2e792b1079639a74e3581fbc74"> 139</a></span> <a class="code" href="classEigen_1_1MatrixBase.html#a8ed1fb2e792b1079639a74e3581fbc74">MatrixBase<Derived>::normalized</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::nested<Derived>::type Nested;</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::remove_reference<Nested>::type _Nested;</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  _Nested n(derived());</div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  <span class="keywordflow">return</span> n / n.norm();</div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span> }</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span> </div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00154"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#acd0de676568888d848beb97dcc53ae47"> 154</a></span> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1MatrixBase.html#acd0de676568888d848beb97dcc53ae47">MatrixBase<Derived>::normalize</a>()</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span> {</div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  *<span class="keyword">this</span> /= norm();</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> </div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span> <span class="comment">//---------- implementation of other norms ----------</span></div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span> </div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span> </div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived, <span class="keywordtype">int</span> p></div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span> <span class="keyword">struct </span>lpNorm_selector</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span> {</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="structEigen_1_1NumTraits.html">NumTraits<typename traits<Derived>::Scalar</a>>::Real RealScalar;</div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  <span class="keyword">static</span> <span class="keyword">inline</span> RealScalar run(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase<Derived></a>& m)</div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  {</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  <span class="keyword">using</span> std::pow;</div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  <span class="keywordflow">return</span> pow(m.<a class="code" href="classEigen_1_1MatrixBase.html#ab4d8398a4497e4a888cfc11c51c14a81">cwiseAbs</a>().array().pow(p).sum(), RealScalar(1)/p);</div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  }</div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span> };</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="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span> <span class="keyword">struct </span>lpNorm_selector<Derived, 1></div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span> {</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keyword">typename</span> NumTraits<typename traits<Derived>::Scalar>::Real run(<span class="keyword">const</span> MatrixBase<Derived>& m)</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  {</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  <span class="keywordflow">return</span> m.cwiseAbs().sum();</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  }</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span> };</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span> </div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span> <span class="keyword">struct </span>lpNorm_selector<Derived, 2></div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span> {</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keyword">typename</span> NumTraits<typename traits<Derived>::Scalar>::Real run(<span class="keyword">const</span> MatrixBase<Derived>& m)</div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  {</div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  <span class="keywordflow">return</span> m.norm();</div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  }</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span> };</div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span> </div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span> <span class="keyword">struct </span>lpNorm_selector<Derived, <a class="code" href="namespaceEigen.html#a6cff718ef6bce746aa5e100036226625">Infinity</a>></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>  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keyword">typename</span> NumTraits<typename traits<Derived>::Scalar>::Real run(<span class="keyword">const</span> MatrixBase<Derived>& m)</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  {</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  <span class="keywordflow">return</span> m.cwiseAbs().maxCoeff();</div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  }</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> </div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span> } <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span> </div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span> <span class="keyword">template</span><<span class="keywordtype">int</span> p></div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span> <span class="keyword">inline</span> <span class="keyword">typename</span> NumTraits<typename internal::traits<Derived>::Scalar>::Real</div>
<div class="line"><a name="l00212"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a88da415114cc113e5795b67a6a5328ab"> 212</a></span> <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase<Derived>::lpNorm</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  <span class="keywordflow">return</span> internal::lpNorm_selector<Derived, p>::run(*<span class="keyword">this</span>);</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span> }</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="comment">//---------- implementation of isOrthogonal / isUnitary ----------</span></div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span> </div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span> <span class="keyword">template</span><<span class="keyword">typename</span> OtherDerived></div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span> <span class="keywordtype">bool</span> <a class="code" href="classEigen_1_1MatrixBase.html#a0eb573c751ea82273a4dac71e851c1b5">MatrixBase<Derived>::isOrthogonal</a></div>
<div class="line"><a name="l00228"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a0eb573c751ea82273a4dac71e851c1b5"> 228</a></span> (<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase<OtherDerived></a>& other, <span class="keyword">const</span> RealScalar& prec) <span class="keyword">const</span></div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span> {</div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  <span class="keyword">typename</span> internal::nested<Derived,2>::type nested(derived());</div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  <span class="keyword">typename</span> internal::nested<OtherDerived,2>::type otherNested(other.derived());</div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  <span class="keywordflow">return</span> numext::abs2(nested.dot(otherNested)) <= prec * prec * nested.squaredNorm() * otherNested.squaredNorm();</div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span> }</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span> </div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00247"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a1230d9a9fa9557a46047abac659e8ed4"> 247</a></span> <span class="keywordtype">bool</span> <a class="code" href="classEigen_1_1MatrixBase.html#a1230d9a9fa9557a46047abac659e8ed4">MatrixBase<Derived>::isUnitary</a>(<span class="keyword">const</span> RealScalar& prec)<span class="keyword"> const</span></div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <span class="keyword">typename</span> Derived::Nested nested(derived());</div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  <span class="keywordflow">for</span>(<a class="code" href="classEigen_1_1DenseBase.html#a4d4873e91be950c079f067fa97fd5c40">Index</a> i = 0; i < cols(); ++i)</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>  <span class="keywordflow">if</span>(!internal::isApprox(nested.col(i).squaredNorm(), <span class="keyword">static_cast<</span>RealScalar<span class="keyword">></span>(1), prec))</div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  <span class="keywordflow">for</span>(<a class="code" href="classEigen_1_1DenseBase.html#a4d4873e91be950c079f067fa97fd5c40">Index</a> j = 0; j < i; ++j)</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  <span class="keywordflow">if</span>(!internal::isMuchSmallerThan(nested.col(i).dot(nested.col(j)), static_cast<Scalar>(1), prec))</div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  }</div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span> }</div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span> </div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span> } <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span> </div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span> <span class="preprocessor">#endif // EIGEN_DOT_H</span></div>
<div class="ttc" id="classEigen_1_1MatrixBase_html_a229bd5cc6237359a1d85401743476ede"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#a229bd5cc6237359a1d85401743476ede">Eigen::MatrixBase::squaredNorm</a></div><div class="ttdeci">RealScalar squaredNorm() const </div><div class="ttdef"><b>Definition:</b> Dot.h:113</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_1MatrixBase_html_a8ed1fb2e792b1079639a74e3581fbc74"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#a8ed1fb2e792b1079639a74e3581fbc74">Eigen::MatrixBase::normalized</a></div><div class="ttdeci">const PlainObject normalized() const </div><div class="ttdef"><b>Definition:</b> Dot.h:139</div></div>
<div class="ttc" id="classEigen_1_1MatrixBase_html_a0eb573c751ea82273a4dac71e851c1b5"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#a0eb573c751ea82273a4dac71e851c1b5">Eigen::MatrixBase::isOrthogonal</a></div><div class="ttdeci">bool isOrthogonal(const MatrixBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const </div><div class="ttdef"><b>Definition:</b> Dot.h:228</div></div>
<div class="ttc" id="classEigen_1_1MatrixBase_html_a0be1b433c65ce9d92c81a4718daf54e5"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#a0be1b433c65ce9d92c81a4718daf54e5">Eigen::MatrixBase::norm</a></div><div class="ttdeci">RealScalar norm() const </div><div class="ttdef"><b>Definition:</b> Dot.h:125</div></div>
<div class="ttc" id="classEigen_1_1MatrixBase_html_acd0de676568888d848beb97dcc53ae47"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#acd0de676568888d848beb97dcc53ae47">Eigen::MatrixBase::normalize</a></div><div class="ttdeci">void normalize()</div><div class="ttdef"><b>Definition:</b> Dot.h:154</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_1MatrixBase_html_adb71ddef4955ae7d353df12d05665191"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#adb71ddef4955ae7d353df12d05665191">Eigen::MatrixBase::dot</a></div><div class="ttdeci">internal::scalar_product_traits< typename internal::traits< Derived >::Scalar, typename internal::traits< OtherDerived >::Scalar >::ReturnType dot(const MatrixBase< OtherDerived > &other) const </div><div class="ttdef"><b>Definition:</b> Dot.h:63</div></div>
<div class="ttc" id="classEigen_1_1Matrix_html"><div class="ttname"><a href="classEigen_1_1Matrix.html">Eigen::Matrix</a></div><div class="ttdoc">The matrix class, also used for vectors and row-vectors. </div><div class="ttdef"><b>Definition:</b> Matrix.h:127</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="namespaceEigen_html_a6cff718ef6bce746aa5e100036226625"><div class="ttname"><a href="namespaceEigen.html#a6cff718ef6bce746aa5e100036226625">Eigen::Infinity</a></div><div class="ttdeci">const int Infinity</div><div class="ttdef"><b>Definition:</b> Constants.h:31</div></div>
<div class="ttc" id="classEigen_1_1MatrixBase_html_ab4d8398a4497e4a888cfc11c51c14a81"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#ab4d8398a4497e4a888cfc11c51c14a81">Eigen::MatrixBase::cwiseAbs</a></div><div class="ttdeci">const CwiseUnaryOp< internal::scalar_abs_op< Scalar >, const Derived > cwiseAbs() const </div><div class="ttdef"><b>Definition:</b> MatrixBase.h:22</div></div>
<div class="ttc" id="classEigen_1_1MatrixBase_html_a1230d9a9fa9557a46047abac659e8ed4"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#a1230d9a9fa9557a46047abac659e8ed4">Eigen::MatrixBase::isUnitary</a></div><div class="ttdeci">bool isUnitary(const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const </div><div class="ttdef"><b>Definition:</b> Dot.h:247</div></div>
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