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 <span id="projectnumber">3.4.90 (git rev 21cd3fe20990a5ac1d683806f605110962aac3f1)</span>
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<div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">// for linear algebra.</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment">//</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment">// Copyright (C) 2006-2008, 2010 Benoit Jacob <[email protected]></span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">//</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span> </div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="preprocessor">#ifndef EIGEN_DOT_H</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="preprocessor">#define EIGEN_DOT_H</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span> </div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="preprocessor">#include "./InternalHeaderCheck.h"</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span> </div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceEigen.html">Eigen</a> { </div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span> </div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="keyword">namespace </span>internal {</div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span> </div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="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 id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="comment">// with mismatched types, the compiler emits errors about failing to instantiate cwiseProduct BEFORE</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</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 id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="keyword">template</span><<span class="keyword">typename</span> T, <span class="keyword">typename</span> U,</div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> <span class="keywordtype">bool</span> NeedToTranspose = T::IsVectorAtCompileTime && U::IsVectorAtCompileTime &&</div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> ((int(T::RowsAtCompileTime) == 1 && int(U::ColsAtCompileTime) == 1) ||</div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> (<span class="keywordtype">int</span>(T::ColsAtCompileTime) == 1 && int(U::RowsAtCompileTime) == 1))></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="keyword">struct </span>dot_nocheck</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span>{</div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> <span class="keyword">typedef</span> scalar_conj_product_op<typename traits<T>::Scalar,<span class="keyword">typename</span> traits<U>::Scalar> conj_prod;</div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> conj_prod::result_type ResScalar;</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> EIGEN_DEVICE_FUNC</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> EIGEN_STRONG_INLINE</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> <span class="keyword">static</span> ResScalar run(<span class="keyword">const</span> MatrixBase<T>& a, <span class="keyword">const</span> MatrixBase<U>& b)</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> {</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <span class="keywordflow">return</span> a.template binaryExpr<conj_prod>(b).sum();</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> }</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span>};</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> </div>
<div class="line"><a id="l00038" 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 id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="keyword">struct </span>dot_nocheck<T, U, true></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span>{</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="keyword">typedef</span> scalar_conj_product_op<typename traits<T>::Scalar,<span class="keyword">typename</span> traits<U>::Scalar> conj_prod;</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> conj_prod::result_type ResScalar;</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> EIGEN_DEVICE_FUNC</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> EIGEN_STRONG_INLINE</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="keyword">static</span> ResScalar run(<span class="keyword">const</span> MatrixBase<T>& a, <span class="keyword">const</span> MatrixBase<U>& b)</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> {</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <span class="keywordflow">return</span> a.transpose().template binaryExpr<conj_prod>(b).sum();</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> }</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span>};</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> </div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span>} <span class="comment">// end namespace internal</span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> </div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span><span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span><span class="keyword">template</span><<span class="keyword">typename</span> OtherDerived></div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span>EIGEN_DEVICE_FUNC</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span>EIGEN_STRONG_INLINE</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span><span class="keyword">typename</span> ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,<span class="keyword">typename</span> internal::traits<OtherDerived>::Scalar>::ReturnType</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a7b43194239d11dd6579517098303e08b"> 69</a></span><a class="code hl_class" href="classEigen_1_1MatrixBase.html">MatrixBase<Derived>::dot</a>(<span class="keyword">const</span> <a class="code hl_class" href="classEigen_1_1MatrixBase.html">MatrixBase<OtherDerived></a>& other)<span class="keyword"> const</span></div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span><span class="keyword"></span>{</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span><span class="preprocessor">#if !(defined(EIGEN_NO_STATIC_ASSERT) && defined(EIGEN_NO_DEBUG))</span></div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> EIGEN_CHECK_BINARY_COMPATIBILIY(</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> Eigen::internal::scalar_conj_product_op<Scalar EIGEN_COMMA typename OtherDerived::Scalar>, </div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <a class="code hl_typedef" href="classEigen_1_1DenseBase.html#a5feed465b3a8e60c47e73ecce83e39a2">Scalar</a>, <span class="keyword">typename</span> OtherDerived::Scalar);</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> </div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> eigen_assert(size() == other.<a class="code hl_function" href="classEigen_1_1DenseCoeffsBase_3_01Derived_00_01DirectWriteAccessors_01_4.html#ae106171b6fefd3f7af108a8283de36c9">size</a>());</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> </div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="keywordflow">return</span> internal::dot_nocheck<Derived,OtherDerived>::run(*<span class="keyword">this</span>, other);</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span>}</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> </div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span><span class="comment">//---------- implementation of L2 norm and related functions ----------</span></div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> </div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span><span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#ac66416bebcaf89bf2c65ee5ebc1cd203"> 94</a></span>EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keyword">typename</span> <a class="code hl_class" href="structEigen_1_1NumTraits.html">NumTraits<typename internal::traits<Derived>::Scalar</a>>::Real <a class="code hl_class" href="classEigen_1_1MatrixBase.html">MatrixBase<Derived>::squaredNorm</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span><span class="keyword"></span>{</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="keywordflow">return</span> numext::real((*this).cwiseAbs2().sum());</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span>}</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> </div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span><span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#ad95753dd5cd59db78bfcef8c422ad383"> 106</a></span>EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keyword">typename</span> <a class="code hl_class" href="structEigen_1_1NumTraits.html">NumTraits<typename internal::traits<Derived>::Scalar</a>>::Real <a class="code hl_class" href="classEigen_1_1MatrixBase.html">MatrixBase<Derived>::norm</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span><span class="keyword"></span>{</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> <span class="keywordflow">return</span> numext::sqrt(squaredNorm());</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span>}</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> </div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span><span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span>EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keyword">const</span> <span class="keyword">typename</span> MatrixBase<Derived>::PlainObject</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a5cf2fd4c57e59604fd4116158fd34308"> 122</a></span><a class="code hl_class" href="classEigen_1_1MatrixBase.html">MatrixBase<Derived>::normalized</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span><span class="keyword"></span>{</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::nested_eval<Derived,2>::type Nested_;</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> Nested_ n(derived());</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> RealScalar z = n.squaredNorm();</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <span class="comment">// NOTE: after extensive benchmarking, this conditional does not impact performance, at least on recent x86 CPU</span></div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> <span class="keywordflow">if</span>(z>RealScalar(0))</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> <span class="keywordflow">return</span> n / numext::sqrt(z);</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> <span class="keywordflow">return</span> n;</div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span>}</div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> </div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span><span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#ad16303c47ba36f7a41ea264cb26bceb6"> 143</a></span>EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keywordtype">void</span> <a class="code hl_class" href="classEigen_1_1MatrixBase.html">MatrixBase<Derived>::normalize</a>()</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span>{</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> RealScalar z = squaredNorm();</div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <span class="comment">// NOTE: after extensive benchmarking, this conditional does not impact performance, at least on recent x86 CPU</span></div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> <span class="keywordflow">if</span>(z>RealScalar(0))</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> derived() /= numext::sqrt(z);</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span>}</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> </div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span><span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span>EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keyword">const</span> <span class="keyword">typename</span> MatrixBase<Derived>::PlainObject</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a399dca938633b9f8df5ec4beefeccec0"> 165</a></span><a class="code hl_class" href="classEigen_1_1MatrixBase.html">MatrixBase<Derived>::stableNormalized</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span><span class="keyword"></span>{</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::nested_eval<Derived,3>::type Nested_;</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> Nested_ n(derived());</div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> RealScalar w = n.cwiseAbs().maxCoeff();</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> RealScalar z = (n/w).squaredNorm();</div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> <span class="keywordflow">if</span>(z>RealScalar(0))</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> <span class="keywordflow">return</span> n / (numext::sqrt(z)*w);</div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> <span class="keywordflow">return</span> n;</div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span>}</div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> </div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span><span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a0b1443fa322615379557ade3399a3c3c"> 189</a></span>EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keywordtype">void</span> <a class="code hl_class" href="classEigen_1_1MatrixBase.html">MatrixBase<Derived>::stableNormalize</a>()</div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span>{</div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> RealScalar w = cwiseAbs().maxCoeff();</div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> RealScalar z = (derived()/w).squaredNorm();</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> <span class="keywordflow">if</span>(z>RealScalar(0))</div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> derived() /= numext::sqrt(z)*w;</div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span>}</div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> </div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a7b43194239d11dd6579517098303e08b"> 197</a></span><span class="comment">//---------- implementation of other norms ----------</span></div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> </div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#ac66416bebcaf89bf2c65ee5ebc1cd203"> 199</a></span><span class="keyword">namespace </span>internal {</div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#ad95753dd5cd59db78bfcef8c422ad383"> 200</a></span> </div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span><span class="keyword">template</span><<span class="keyword">typename</span> Derived, <span class="keywordtype">int</span> p></div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span><span class="keyword">struct </span>lpNorm_selector</div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span>{</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a5cf2fd4c57e59604fd4116158fd34308"> 204</a></span> <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code hl_class" href="structEigen_1_1NumTraits.html">NumTraits<typename traits<Derived>::Scalar</a>>::Real RealScalar;</div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a399dca938633b9f8df5ec4beefeccec0"> 205</a></span> EIGEN_DEVICE_FUNC</div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#ad16303c47ba36f7a41ea264cb26bceb6"> 206</a></span> <span class="keyword">static</span> <span class="keyword">inline</span> RealScalar run(<span class="keyword">const</span> <a class="code hl_class" href="classEigen_1_1MatrixBase.html">MatrixBase<Derived></a>& m)</div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a0b1443fa322615379557ade3399a3c3c"> 207</a></span> {</div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> EIGEN_USING_STD(pow)</div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> <span class="keywordflow">return</span> pow(m.cwiseAbs().<a class="code hl_function" href="classEigen_1_1MatrixBase.html#a6d285ea9b37cbd80209e70543d10fd67">array</a>().pow(p).sum(), RealScalar(1)/p);</div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> }</div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span>};</div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> </div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span><span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span><span class="keyword">struct </span>lpNorm_selector<Derived, 1></div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span>{</div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> EIGEN_DEVICE_FUNC</div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</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 id="l00218" name="l00218"></a><span class="lineno"> 218</span> {</div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> <span class="keywordflow">return</span> m.cwiseAbs().sum();</div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> }</div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span>};</div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> </div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span><span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span><span class="keyword">struct </span>lpNorm_selector<Derived, 2></div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span>{</div>
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> EIGEN_DEVICE_FUNC</div>
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</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 id="l00228" name="l00228"></a><span class="lineno"> 228</span> {</div>
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> <span class="keywordflow">return</span> m.norm();</div>
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> }</div>
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span>};</div>
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> </div>
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span><span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span><span class="keyword">struct </span>lpNorm_selector<Derived, <a class="code hl_variable" href="namespaceEigen.html#a7951593b031e13d90223c83d022ce99e">Infinity</a>></div>
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span>{</div>
<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<typename traits<Derived>::Scalar>::Real RealScalar;</div>
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span> EIGEN_DEVICE_FUNC</div>
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span> <span class="keyword">static</span> <span class="keyword">inline</span> RealScalar run(<span class="keyword">const</span> MatrixBase<Derived>& m)</div>
<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> {</div>
<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span> <span class="keywordflow">if</span>(Derived::SizeAtCompileTime==0 || (Derived::SizeAtCompileTime==<a class="code hl_variable" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> && m.size()==0))</div>
<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> <span class="keywordflow">return</span> RealScalar(0);</div>
<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span> <span class="keywordflow">return</span> m.cwiseAbs().maxCoeff();</div>
<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span> }</div>
<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span>};</div>
<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> </div>
<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span>} <span class="comment">// end namespace internal</span></div>
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> </div>
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span><span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span><span class="keyword">template</span><<span class="keywordtype">int</span> p></div>
<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span><span class="preprocessor">#ifndef EIGEN_PARSED_BY_DOXYGEN</span></div>
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span>EIGEN_DEVICE_FUNC <span class="keyword">inline</span> <span class="keyword">typename</span> NumTraits<typename internal::traits<Derived>::Scalar>::Real</div>
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span><span class="preprocessor">#else</span></div>
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span>EIGEN_DEVICE_FUNC MatrixBase<Derived>::RealScalar</div>
<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a72586ab059e889e7d2894ff227747e35"> 265</a></span><a class="code hl_class" href="classEigen_1_1MatrixBase.html">MatrixBase<Derived>::lpNorm</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span><span class="keyword"></span>{</div>
<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span> <span class="keywordflow">return</span> internal::lpNorm_selector<Derived, p>::run(*<span class="keyword">this</span>);</div>
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span>}</div>
<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span> </div>
<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span><span class="comment">//---------- implementation of isOrthogonal / isUnitary ----------</span></div>
<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> </div>
<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span><span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"> 279</span><span class="keyword">template</span><<span class="keyword">typename</span> OtherDerived></div>
<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#aefdc8e4e4c156fdd79a21479e75dcd8a"> 280</a></span><span class="keywordtype">bool</span> <a class="code hl_class" href="classEigen_1_1MatrixBase.html">MatrixBase<Derived>::isOrthogonal</a></div>
<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</span>(<span class="keyword">const</span> <a class="code hl_class" 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 id="l00282" name="l00282"></a><span class="lineno"> 282</span><span class="keyword"></span>{</div>
<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span> <span class="keyword">typename</span> internal::nested_eval<Derived,2>::type nested(derived());</div>
<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span> <span class="keyword">typename</span> internal::nested_eval<OtherDerived,2>::type otherNested(other.<a class="code hl_function" href="classEigen_1_1DenseCoeffsBase_3_01Derived_00_01DirectWriteAccessors_01_4.html#a749b057c52245e486a101868d2578a24">derived</a>());</div>
<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span> <span class="keywordflow">return</span> numext::abs2(nested.dot(otherNested)) <= prec * prec * nested.squaredNorm() * otherNested.squaredNorm();</div>
<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#aefdc8e4e4c156fdd79a21479e75dcd8a"> 286</a></span>}</div>
<div class="line"><a id="l00287" name="l00287"></a><span class="lineno"> 287</span> </div>
<div class="line"><a id="l00299" name="l00299"></a><span class="lineno"> 299</span><span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a id="l00300" name="l00300"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a8a7ee34ce202cac3eeea9cf20c9e4833"> 300</a></span><span class="keywordtype">bool</span> <a class="code hl_class" href="classEigen_1_1MatrixBase.html">MatrixBase<Derived>::isUnitary</a>(<span class="keyword">const</span> RealScalar& prec)<span class="keyword"> const</span></div>
<div class="line"><a id="l00301" name="l00301"></a><span class="lineno"> 301</span><span class="keyword"></span>{</div>
<div class="line"><a id="l00302" name="l00302"></a><span class="lineno"> 302</span> <span class="keyword">typename</span> internal::nested_eval<Derived,1>::type self(derived());</div>
<div class="line"><a id="l00303" name="l00303"></a><span class="lineno"> 303</span> <span class="keywordflow">for</span>(<a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = 0; i < cols(); ++i)</div>
<div class="line"><a id="l00304" name="l00304"></a><span class="lineno"> 304</span> {</div>
<div class="line"><a id="l00305" name="l00305"></a><span class="lineno"> 305</span> <span class="keywordflow">if</span>(!internal::isApprox(self.col(i).squaredNorm(), <span class="keyword">static_cast<</span>RealScalar<span class="keyword">></span>(1), prec))</div>
<div class="line"><a id="l00306" name="l00306"></a><span class="lineno"> 306</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00307" name="l00307"></a><span class="lineno"> 307</span> <span class="keywordflow">for</span>(<a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> j = 0; j < i; ++j)</div>
<div class="line"><a id="l00308" name="l00308"></a><span class="lineno"> 308</span> <span class="keywordflow">if</span>(!internal::isMuchSmallerThan(self.col(i).dot(self.col(j)), <span class="keyword">static_cast<</span><a class="code hl_typedef" href="classEigen_1_1DenseBase.html#a5feed465b3a8e60c47e73ecce83e39a2">Scalar</a><span class="keyword">></span>(1), prec))</div>
<div class="line"><a id="l00309" name="l00309"></a><span class="lineno"> 309</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00310" name="l00310"></a><span class="lineno"> 310</span> }</div>
<div class="line"><a id="l00311" name="l00311"></a><span class="lineno"> 311</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a id="l00312" name="l00312"></a><span class="lineno"> 312</span>}</div>
<div class="line"><a id="l00313" name="l00313"></a><span class="lineno"> 313</span> </div>
<div class="line"><a id="l00314" name="l00314"></a><span class="lineno"> 314</span>} <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a id="l00315" name="l00315"></a><span class="lineno"> 315</span> </div>
<div class="line"><a id="l00316" name="l00316"></a><span class="lineno"> 316</span><span class="preprocessor">#endif </span><span class="comment">// EIGEN_DOT_H</span></div>
<div class="ttc" id="aclassEigen_1_1DenseBase_html_a5feed465b3a8e60c47e73ecce83e39a2"><div class="ttname"><a href="classEigen_1_1DenseBase.html#a5feed465b3a8e60c47e73ecce83e39a2">Eigen::DenseBase::Scalar</a></div><div class="ttdeci">internal::traits< Derived >::Scalar Scalar</div><div class="ttdef"><b>Definition</b> DenseBase.h:61</div></div>
<div class="ttc" id="aclassEigen_1_1DenseCoeffsBase_3_01Derived_00_01DirectWriteAccessors_01_4_html_a749b057c52245e486a101868d2578a24"><div class="ttname"><a href="classEigen_1_1DenseCoeffsBase_3_01Derived_00_01DirectWriteAccessors_01_4.html#a749b057c52245e486a101868d2578a24">Eigen::DenseCoeffsBase< Derived, DirectWriteAccessors >::derived</a></div><div class="ttdeci">Derived & derived()</div><div class="ttdef"><b>Definition</b> EigenBase.h:48</div></div>
<div class="ttc" id="aclassEigen_1_1DenseCoeffsBase_3_01Derived_00_01DirectWriteAccessors_01_4_html_ae106171b6fefd3f7af108a8283de36c9"><div class="ttname"><a href="classEigen_1_1DenseCoeffsBase_3_01Derived_00_01DirectWriteAccessors_01_4.html#ae106171b6fefd3f7af108a8283de36c9">Eigen::DenseCoeffsBase< Derived, DirectWriteAccessors >::size</a></div><div class="ttdeci">EIGEN_CONSTEXPR Index size() const EIGEN_NOEXCEPT</div><div class="ttdef"><b>Definition</b> EigenBase.h:69</div></div>
<div class="ttc" id="aclassEigen_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:52</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixBase_html_a6d285ea9b37cbd80209e70543d10fd67"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#a6d285ea9b37cbd80209e70543d10fd67">Eigen::MatrixBase::array</a></div><div class="ttdeci">ArrayWrapper< Derived > array()</div><div class="ttdef"><b>Definition</b> MatrixBase.h:324</div></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition</b> Core:139</div></div>
<div class="ttc" id="anamespaceEigen_html_a62e77e0933482dafde8fe197d9a2cfde"><div class="ttname"><a href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a></div><div class="ttdeci">EIGEN_DEFAULT_DENSE_INDEX_TYPE Index</div><div class="ttdoc">The Index type as used for the API.</div><div class="ttdef"><b>Definition</b> Meta.h:82</div></div>
<div class="ttc" id="anamespaceEigen_html_a7951593b031e13d90223c83d022ce99e"><div class="ttname"><a href="namespaceEigen.html#a7951593b031e13d90223c83d022ce99e">Eigen::Infinity</a></div><div class="ttdeci">const int Infinity</div><div class="ttdef"><b>Definition</b> Constants.h:38</div></div>
<div class="ttc" id="anamespaceEigen_html_ad81fa7195215a0ce30017dfac309f0b2"><div class="ttname"><a href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Eigen::Dynamic</a></div><div class="ttdeci">const int Dynamic</div><div class="ttdef"><b>Definition</b> Constants.h:24</div></div>
<div class="ttc" id="astructEigen_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:231</div></div>
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