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<div class="title">al_Complex.hpp</div> </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="preprocessor">#ifndef INCLUDE_AL_COMPLEX_HPP</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="preprocessor">#define INCLUDE_AL_COMPLEX_HPP</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span>  </div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">/* Allocore --</span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"> Multimedia / virtual environment application class library</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"> Copyright (C) 2009. AlloSphere Research Group, Media Arts & Technology, UCSB.</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"> Copyright (C) 2012. The Regents of the University of California.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment"> All rights reserved.</span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment"></span> </div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment"> Redistribution and use in source and binary forms, with or without</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment"> modification, are permitted provided that the following conditions are met:</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment"></span> </div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment"> Redistributions of source code must retain the above copyright notice,</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment"> this list of conditions and the following disclaimer.</span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment"></span> </div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment"> Redistributions in binary form must reproduce the above copyright</span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment"> notice, this list of conditions and the following disclaimer in the</span></div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment"> documentation and/or other materials provided with the distribution.</span></div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment"></span> </div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="comment"> Neither the name of the University of California nor the names of its</span></div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="comment"> contributors may be used to endorse or promote products derived from</span></div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="comment"> this software without specific prior written permission.</span></div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment"></span> </div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment"> THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"</span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment"> AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE</span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment"> IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE</span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment"> ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE</span></div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment"> LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR</span></div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment"> CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF</span></div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment"> SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS</span></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment"> INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN</span></div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment"> CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)</span></div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment"> ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE</span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment"> POSSIBILITY OF SUCH DAMAGE.</span></div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment"></span> </div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment"></span> </div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment"> File description:</span></div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment"> Complex number class</span></div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment"></span> </div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment"> File author(s):</span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment"> Lance Putnam, 2006, [email protected]</span></div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment">*/</span></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> <span class="preprocessor">#include <cmath></span></div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="preprocessor">#include "al/math/al_Constants.hpp"</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="keyword">namespace </span><a class="code" href="namespaceal.html">al</a> {</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  </div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="keyword">class </span>Complex;</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="keyword">class </span>Polar;</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  </div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="keyword">typedef</span> Polar<float> Polarf;</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="keyword">typedef</span> Polar<double> Polard;</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="keyword">typedef</span> Complex<float> Complexf;</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="keyword">typedef</span> Complex<double> Complexd;</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  </div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00064"></a><span class="lineno"><a class="line" href="classal_1_1_polar.html"> 64</a></span> <span class="keyword">class </span><a class="code" href="classal_1_1_polar.html">Polar</a> {</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="keyword">union </span>{</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="keyword">struct </span>{</div>
<div class="line"><a name="l00068"></a><span class="lineno"><a class="line" href="classal_1_1_polar.html#ae25abb3fc29203774c54bdbd594a9ce8"> 68</a></span>  T <a class="code" href="classal_1_1_polar.html#ae25abb3fc29203774c54bdbd594a9ce8">m</a>; </div>
<div class="line"><a name="l00069"></a><span class="lineno"><a class="line" href="classal_1_1_polar.html#a85d8571636ceafe81c716c3bbe12dbb6"> 69</a></span>  T <a class="code" href="classal_1_1_polar.html#a85d8571636ceafe81c716c3bbe12dbb6">p</a>; </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>  T elems[2];</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>  </div>
<div class="line"><a name="l00075"></a><span class="lineno"><a class="line" href="classal_1_1_polar.html#acd11bf2c5563a45fe0b7b2c40ef4ad5f"> 75</a></span>  <a class="code" href="classal_1_1_polar.html#acd11bf2c5563a45fe0b7b2c40ef4ad5f">Polar</a>(<span class="keyword">const</span> T& phs = T(0)) : <a class="code" href="classal_1_1_polar.html#ae25abb3fc29203774c54bdbd594a9ce8">m</a>(T(1)), <a class="code" href="classal_1_1_polar.html#a85d8571636ceafe81c716c3bbe12dbb6">p</a>(phs) {}</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  </div>
<div class="line"><a name="l00079"></a><span class="lineno"><a class="line" href="classal_1_1_polar.html#a0456e71fb0abd22aea58758011005ea7"> 79</a></span>  <a class="code" href="classal_1_1_polar.html#a0456e71fb0abd22aea58758011005ea7">Polar</a>(<span class="keyword">const</span> T& mag, <span class="keyword">const</span> T& phs) : <a class="code" href="classal_1_1_polar.html#ae25abb3fc29203774c54bdbd594a9ce8">m</a>(mag), <a class="code" href="classal_1_1_polar.html#a85d8571636ceafe81c716c3bbe12dbb6">p</a>(phs) {}</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  </div>
<div class="line"><a name="l00082"></a><span class="lineno"><a class="line" href="classal_1_1_polar.html#a84160608a4bd926a5af693cd1acc61ff"> 82</a></span>  <a class="code" href="classal_1_1_polar.html#a84160608a4bd926a5af693cd1acc61ff">Polar</a>(<span class="keyword">const</span> <a class="code" href="classal_1_1_complex.html">Complex<T></a>& v) { *<span class="keyword">this</span> = v; }</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  </div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <a class="code" href="classal_1_1_polar.html">Polar</a>& operator=(<span class="keyword">const</span> <a class="code" href="classal_1_1_complex.html">Complex<T></a>& v) {</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <a class="code" href="classal_1_1_polar.html#ae25abb3fc29203774c54bdbd594a9ce8">m</a> = v.<a class="code" href="classal_1_1_complex.html#a9016f65e0e7e01045fb034736cc246ea">norm</a>();</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <a class="code" href="classal_1_1_polar.html#a85d8571636ceafe81c716c3bbe12dbb6">p</a> = v.<a class="code" href="classal_1_1_complex.html#a98871e41ebbf098d5a37c33848e4bd22">arg</a>();</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  }</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>  </div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00095"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html"> 95</a></span> <span class="keyword">class </span><a class="code" href="classal_1_1_complex.html">Complex</a> {</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  <span class="keyword">typedef</span> <a class="code" href="classal_1_1_complex.html">Complex<T></a> <a class="code" href="classal_1_1_complex.html">C</a>;</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>  <span class="keyword">union </span>{</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <span class="keyword">struct </span>{</div>
<div class="line"><a name="l00101"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11"> 101</a></span>  T <a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a>; </div>
<div class="line"><a name="l00102"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb"> 102</a></span>  T <a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a>; </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>  T elems[2];</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  };</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>  Complex(<span class="keyword">const</span> Complex& v) : <a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a>(v.<a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a>), <a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a>(v.<a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a>) {}</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  Complex(<span class="keyword">const</span> Polar<T>& v) { *<span class="keyword">this</span> = v; }</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  Complex(<span class="keyword">const</span> T& <a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a> = T(0), <span class="keyword">const</span> T& <a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a> = T(0)) : <a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a>(<a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a>), <a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a>(<a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a>) {}</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  Complex(<span class="keyword">const</span> T& m, <span class="keyword">const</span> T& p, <span class="keywordtype">int</span> <a class="code" href="classal_1_1_complex.html#aba0d1d398bac0071b0ca1d712765e171">fromPolar</a>) { (*this) = Polar<T>(m, p); }</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  </div>
<div class="line"><a name="l00112"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#a98871e41ebbf098d5a37c33848e4bd22"> 112</a></span>  <a class="code" href="classal_1_1_complex.html">C</a>& <a class="code" href="classal_1_1_complex.html#a98871e41ebbf098d5a37c33848e4bd22">arg</a>(T v) {</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_complex.html#aba0d1d398bac0071b0ca1d712765e171">fromPolar</a>(<a class="code" href="classal_1_1_complex.html#a218390dfa649ea62be730c60e78d2401">norm</a>(), v);</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  } </div>
<div class="line"><a name="l00115"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#a9016f65e0e7e01045fb034736cc246ea"> 115</a></span>  <a class="code" href="classal_1_1_complex.html">C</a>& <a class="code" href="classal_1_1_complex.html#a9016f65e0e7e01045fb034736cc246ea">norm</a>(T v) {</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_complex.html#aba0d1d398bac0071b0ca1d712765e171">fromPolar</a>(v, <a class="code" href="classal_1_1_complex.html#a0b7363c5cd016a1d5d66d27d1993ae4f">arg</a>());</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  } </div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  </div>
<div class="line"><a name="l00119"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#aba0d1d398bac0071b0ca1d712765e171"> 119</a></span>  <a class="code" href="classal_1_1_complex.html">C</a>& <a class="code" href="classal_1_1_complex.html#aba0d1d398bac0071b0ca1d712765e171">fromPolar</a>(T <a class="code" href="classal_1_1_complex.html#a05e4fe79178bd58f1a80436049832a77">phase</a>) {</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a> = <a class="code" href="classal_1_1_complex.html#a82ddb2cdefd7e442080093b72e4aaa1d">::cos</a>(<a class="code" href="classal_1_1_complex.html#a05e4fe79178bd58f1a80436049832a77">phase</a>);</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a> = <a class="code" href="classal_1_1_complex.html#a128d504a4a0266687c44c5aabae7b32b">::sin</a>(<a class="code" href="classal_1_1_complex.html#a05e4fe79178bd58f1a80436049832a77">phase</a>);</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  } </div>
<div class="line"><a name="l00124"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#a1c8914fa162173c62841b41af0e94871"> 124</a></span>  <a class="code" href="classal_1_1_complex.html">C</a>& <a class="code" href="classal_1_1_complex.html#a1c8914fa162173c62841b41af0e94871">fromPolar</a>(T m, T p) {</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_complex.html#a1b590169ff1416df978b55bce8e84036">set</a>(<a class="code" href="classal_1_1_polar.html">Polar<T></a>(m, p));</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  } </div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  </div>
<div class="line"><a name="l00129"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#a1b590169ff1416df978b55bce8e84036"> 129</a></span>  <a class="code" href="classal_1_1_complex.html">C</a>& <a class="code" href="classal_1_1_complex.html#a1b590169ff1416df978b55bce8e84036">set</a>(T vr, T vi) {</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a> = vr;</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a> = vi;</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  }</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  C& <a class="code" href="classal_1_1_complex.html#a1b590169ff1416df978b55bce8e84036">set</a>(<span class="keyword">const</span> <a class="code" href="classal_1_1_polar.html">Polar<T></a>& p) { <span class="keywordflow">return</span> *<span class="keyword">this</span> = p; }</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  </div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  T& operator[](<span class="keywordtype">int</span> <a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a>) { <span class="keywordflow">return</span> elems[<a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a>]; }</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="keyword">const</span> T& operator[](<span class="keywordtype">int</span> <a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a>)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> elems[<a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a>]; }</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  </div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  <span class="comment">// Accessors compatible with std::complex</span></div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  T& real() { <span class="keywordflow">return</span> <a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a>; }</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <span class="keyword">const</span> T& real()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a>; }</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  T& imag() { <span class="keywordflow">return</span> <a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a>; }</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <span class="keyword">const</span> T& imag()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a>; }</div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  </div>
<div class="line"><a name="l00145"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#aac1c97ec0dec260b29a18f2c40158ad7"> 145</a></span>  <span class="keywordtype">bool</span> <a class="code" href="classal_1_1_complex.html#aac1c97ec0dec260b29a18f2c40158ad7">operator==</a>(<span class="keyword">const</span> <a class="code" href="classal_1_1_complex.html">C</a>& v)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <span class="keywordflow">return</span> (<a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a> == v.<a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a>) && (<a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a> == v.<a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a>);</div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  } </div>
<div class="line"><a name="l00148"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#a333639a5b9aa942f7128f4af847da8d7"> 148</a></span>  <span class="keywordtype">bool</span> <a class="code" href="classal_1_1_complex.html#a333639a5b9aa942f7128f4af847da8d7">operator==</a>(<span class="keyword">const</span> T& v)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  <span class="keywordflow">return</span> (<a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a> == v) && (<a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a> == T(0));</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  } </div>
<div class="line"><a name="l00151"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#a91987a3fff79caad88328096a337069c"> 151</a></span>  <span class="keywordtype">bool</span> <a class="code" href="classal_1_1_complex.html#a91987a3fff79caad88328096a337069c">operator!=</a>(<span class="keyword">const</span> <a class="code" href="classal_1_1_complex.html">C</a>& v)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  <span class="keywordflow">return</span> (<a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a> != v.<a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a>) || (<a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a> != v.<a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a>);</div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  } </div>
<div class="line"><a name="l00154"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#a432bc36e09f8552e9bebd2b72541d07f"> 154</a></span>  <span class="keywordtype">bool</span> <a class="code" href="classal_1_1_complex.html#a432bc36e09f8552e9bebd2b72541d07f">operator></a>(<span class="keyword">const</span> <a class="code" href="classal_1_1_complex.html">C</a>& v)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_complex.html#a65094cc454a57f98d00164d776c8d088">normSqr</a>() > v.<a class="code" href="classal_1_1_complex.html#a65094cc454a57f98d00164d776c8d088">normSqr</a>();</div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  } </div>
<div class="line"><a name="l00157"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#a2ea31ad12b3b1e4e5e797823f5090589"> 157</a></span>  <span class="keywordtype">bool</span> <a class="code" href="classal_1_1_complex.html#a2ea31ad12b3b1e4e5e797823f5090589">operator<</a>(<span class="keyword">const</span> <a class="code" href="classal_1_1_complex.html">C</a>& c)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_complex.html#a65094cc454a57f98d00164d776c8d088">normSqr</a>() < c.<a class="code" href="classal_1_1_complex.html#a65094cc454a57f98d00164d776c8d088">normSqr</a>();</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</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>  C& operator=(<span class="keyword">const</span> <a class="code" href="classal_1_1_polar.html">Polar<T></a>& v) {</div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  <a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a> = v.<a class="code" href="classal_1_1_polar.html#ae25abb3fc29203774c54bdbd594a9ce8">m</a> * <a class="code" href="classal_1_1_complex.html#a82ddb2cdefd7e442080093b72e4aaa1d">::cos</a>(v.<a class="code" href="classal_1_1_polar.html#a85d8571636ceafe81c716c3bbe12dbb6">p</a>);</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  <a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a> = v.<a class="code" href="classal_1_1_polar.html#ae25abb3fc29203774c54bdbd594a9ce8">m</a> * <a class="code" href="classal_1_1_complex.html#a128d504a4a0266687c44c5aabae7b32b">::sin</a>(v.<a class="code" href="classal_1_1_polar.html#a85d8571636ceafe81c716c3bbe12dbb6">p</a>);</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</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>  C& operator=(<span class="keyword">const</span> C& v) {</div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  <a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a> = v.r;</div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  <a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a> = v.i;</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  }</div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  C& operator=(T v) {</div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a> = v;</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  <a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a> = T(0);</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  <span class="keywordflow">return</span> *<span class="keyword">this</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>  C& operator-=(<span class="keyword">const</span> C& v) {</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  <a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a> -= v.r;</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  <a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a> -= v.i;</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</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>  C& operator-=(T v) {</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  <a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a> -= v;</div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</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>  C& operator+=(<span class="keyword">const</span> C& v) {</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  <a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a> += v.r;</div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  <a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a> += v.i;</div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</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>  C& operator+=(T v) {</div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  <a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a> += v;</div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  }</div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  C& operator*=(<span class="keyword">const</span> C& v) {</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_complex.html#a1b590169ff1416df978b55bce8e84036">set</a>(<a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a> * v.r - <a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a> * v.i, <a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a> * v.r + <a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a> * v.i);</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>  C& operator*=(T v) {</div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a> *= v;</div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a> *= v;</div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  }</div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  C& operator/=(<span class="keyword">const</span> C& v) { <span class="keywordflow">return</span> (*<span class="keyword">this</span>) *= v.recip(); }</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  C& operator/=(T v) {</div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  <a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a> /= v;</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  <a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a> /= v;</div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  }</div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  </div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  C operator-()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> C(-<a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a>, -<a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a>); }</div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  C operator-(<span class="keyword">const</span> C& v)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> C(*<span class="keyword">this</span>) -= v; }</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  C operator-(T v)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> C(*<span class="keyword">this</span>) -= v; }</div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  C operator+(<span class="keyword">const</span> C& v)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> C(*<span class="keyword">this</span>) += v; }</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  C operator+(T v)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> C(*<span class="keyword">this</span>) += v; }</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  C operator*(<span class="keyword">const</span> C& v)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> C(*<span class="keyword">this</span>) *= v; }</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  C operator*(T v)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> C(*<span class="keyword">this</span>) *= v; }</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  C operator/(<span class="keyword">const</span> C& v)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> C(*<span class="keyword">this</span>) /= v; }</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  C operator/(T v)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> C(*<span class="keyword">this</span>) /= v; }</div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  </div>
<div class="line"><a name="l00219"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#a0b7363c5cd016a1d5d66d27d1993ae4f"> 219</a></span>  T <a class="code" href="classal_1_1_complex.html#a0b7363c5cd016a1d5d66d27d1993ae4f">arg</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> atan2(<a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a>, <a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a>); } </div>
<div class="line"><a name="l00220"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#ad92f6978e926fab08c0513feb72c73c2"> 220</a></span>  T <a class="code" href="classal_1_1_complex.html#ad92f6978e926fab08c0513feb72c73c2">argUnit</a>()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  T <a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a> = <a class="code" href="classal_1_1_complex.html#a0b7363c5cd016a1d5d66d27d1993ae4f">arg</a>() / (2 * M_PI);</div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a> > 0 ? <a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a> : <a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a> + 1;</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  } </div>
<div class="line"><a name="l00224"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#aae3db9206b2214430fe63ad4b552a1d8"> 224</a></span>  <a class="code" href="classal_1_1_complex.html">C</a> <a class="code" href="classal_1_1_complex.html#aae3db9206b2214430fe63ad4b552a1d8">conj</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="classal_1_1_complex.html">C</a>(<a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a>, -<a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a>); } </div>
<div class="line"><a name="l00225"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#a5c9850751a3a5d3e8fff254cebc1d10f"> 225</a></span>  T <a class="code" href="classal_1_1_complex.html#a5c9850751a3a5d3e8fff254cebc1d10f">dot</a>(<span class="keyword">const</span> <a class="code" href="classal_1_1_complex.html">C</a>& v)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a> * v.<a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a> + <a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a> * v.<a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a>;</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  } </div>
<div class="line"><a name="l00228"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#a23298e630346b3a13105030c515c565f"> 228</a></span>  <a class="code" href="classal_1_1_complex.html">C</a> <a class="code" href="classal_1_1_complex.html#a23298e630346b3a13105030c515c565f">exp</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="classal_1_1_polar.html">Polar<T></a>(::<a class="code" href="classal_1_1_complex.html#a23298e630346b3a13105030c515c565f">exp</a>(<a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a>), <a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a>); } </div>
<div class="line"><a name="l00229"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#ae71470089b14cb4e8802382df03ec47a"> 229</a></span>  <a class="code" href="classal_1_1_complex.html">C</a> <a class="code" href="classal_1_1_complex.html#ae71470089b14cb4e8802382df03ec47a">log</a>()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_complex.html">Complex<T></a>(T(0.5) * ::<a class="code" href="classal_1_1_complex.html#ae71470089b14cb4e8802382df03ec47a">log</a>(<a class="code" href="classal_1_1_complex.html#a65094cc454a57f98d00164d776c8d088">normSqr</a>()), <a class="code" href="classal_1_1_complex.html#a0b7363c5cd016a1d5d66d27d1993ae4f">arg</a>());</div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  } </div>
<div class="line"><a name="l00232"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#a218390dfa649ea62be730c60e78d2401"> 232</a></span>  T <a class="code" href="classal_1_1_complex.html#a218390dfa649ea62be730c60e78d2401">norm</a>()<span class="keyword"> const </span>{ return ::sqrt(<a class="code" href="classal_1_1_complex.html#a65094cc454a57f98d00164d776c8d088">normSqr</a>()); } </div>
<div class="line"><a name="l00233"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#a65094cc454a57f98d00164d776c8d088"> 233</a></span>  T <a class="code" href="classal_1_1_complex.html#a65094cc454a57f98d00164d776c8d088">normSqr</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="classal_1_1_complex.html#a5c9850751a3a5d3e8fff254cebc1d10f">dot</a>(*<span class="keyword">this</span>); } </div>
<div class="line"><a name="l00234"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#aaec1ff9bf630d55df12b96a347a2ac3a"> 234</a></span>  <a class="code" href="classal_1_1_complex.html">C</a>& <a class="code" href="classal_1_1_complex.html#aaec1ff9bf630d55df12b96a347a2ac3a">normalize</a>(T m = T(1)) {</div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span> *= (m / <a class="code" href="classal_1_1_complex.html#a218390dfa649ea62be730c60e78d2401">norm</a>());</div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  } </div>
<div class="line"><a name="l00237"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#a1e929197114c0e2e909e487c0a340f4b"> 237</a></span>  <a class="code" href="classal_1_1_complex.html">C</a> <a class="code" href="classal_1_1_complex.html#a1e929197114c0e2e909e487c0a340f4b">pow</a>(<span class="keyword">const</span> <a class="code" href="classal_1_1_complex.html">C</a>& v)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  <span class="keywordflow">return</span> ((*this).log() * v).<a class="code" href="classal_1_1_complex.html#a23298e630346b3a13105030c515c565f">exp</a>();</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  } </div>
<div class="line"><a name="l00240"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#ae6cb8396f8159ab3894a5b25c297c5e3"> 240</a></span>  <a class="code" href="classal_1_1_complex.html">C</a> <a class="code" href="classal_1_1_complex.html#ae6cb8396f8159ab3894a5b25c297c5e3">pow</a>(T v)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> ((*this).log() * v).<a class="code" href="classal_1_1_complex.html#a23298e630346b3a13105030c515c565f">exp</a>(); } </div>
<div class="line"><a name="l00241"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#a6e90e28116a65f4abc295125d8f437a6"> 241</a></span>  <a class="code" href="classal_1_1_complex.html">C</a> <a class="code" href="classal_1_1_complex.html#a6e90e28116a65f4abc295125d8f437a6">recip</a>()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_complex.html#aae3db9206b2214430fe63ad4b552a1d8">conj</a>() / <a class="code" href="classal_1_1_complex.html#a65094cc454a57f98d00164d776c8d088">normSqr</a>();</div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  } </div>
<div class="line"><a name="l00244"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#abb762ec4a1dd5119c5d275f97ea9ac5a"> 244</a></span>  <a class="code" href="classal_1_1_complex.html">C</a> <a class="code" href="classal_1_1_complex.html#abb762ec4a1dd5119c5d275f97ea9ac5a">sgn</a>(T m = T(1))<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_complex.html">C</a>(*this).<a class="code" href="classal_1_1_complex.html#aaec1ff9bf630d55df12b96a347a2ac3a">normalize</a>(m);</div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  } </div>
<div class="line"><a name="l00247"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#a9ab5476fe6d7d22b3bc78fd4fa7a008d"> 247</a></span>  <a class="code" href="classal_1_1_complex.html">C</a> <a class="code" href="classal_1_1_complex.html#a9ab5476fe6d7d22b3bc78fd4fa7a008d">sqr</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="classal_1_1_complex.html">C</a>(<a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a> * <a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a> - <a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a> * <a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a>, T(2) * <a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a> * <a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a>); } </div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  </div>
<div class="line"><a name="l00250"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#a152d44956efad66d475d9f777276634e"> 250</a></span>  <a class="code" href="classal_1_1_complex.html">C</a> <a class="code" href="classal_1_1_complex.html#a152d44956efad66d475d9f777276634e">sqrt</a>()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  <span class="keyword">static</span> <span class="keyword">const</span> T c = T(1) / <a class="code" href="classal_1_1_complex.html#a152d44956efad66d475d9f777276634e">::sqrt</a>(T(2));</div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  T n = <a class="code" href="classal_1_1_complex.html#a218390dfa649ea62be730c60e78d2401">norm</a>();</div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  T a = <a class="code" href="classal_1_1_complex.html#a152d44956efad66d475d9f777276634e">::sqrt</a>(n + <a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a>) * c;</div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  T b = <a class="code" href="classal_1_1_complex.html#a152d44956efad66d475d9f777276634e">::sqrt</a>(n - <a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a>) * (<a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a> < T(0) ? -c : c);</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_complex.html">C</a>(a, b);</div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</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"><a class="line" href="classal_1_1_complex.html#a82ddb2cdefd7e442080093b72e4aaa1d"> 258</a></span>  <a class="code" href="classal_1_1_complex.html">C</a> <a class="code" href="classal_1_1_complex.html#a82ddb2cdefd7e442080093b72e4aaa1d">cos</a>()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_complex.html">C</a>(::<a class="code" href="classal_1_1_complex.html#a82ddb2cdefd7e442080093b72e4aaa1d">cos</a>(<a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a>) * ::<a class="code" href="classal_1_1_complex.html#a426b58bf50eea320f1e3bef94f54fa8a">cosh</a>(<a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a>), -::<a class="code" href="classal_1_1_complex.html#a128d504a4a0266687c44c5aabae7b32b">sin</a>(<a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a>) * ::<a class="code" href="classal_1_1_complex.html#a305a9b5c70c4d8769bb8b5bfb6fdc8d3">sinh</a>(<a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a>));</div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  } </div>
<div class="line"><a name="l00261"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#a128d504a4a0266687c44c5aabae7b32b"> 261</a></span>  <a class="code" href="classal_1_1_complex.html">C</a> <a class="code" href="classal_1_1_complex.html#a128d504a4a0266687c44c5aabae7b32b">sin</a>()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_complex.html">C</a>(::<a class="code" href="classal_1_1_complex.html#a128d504a4a0266687c44c5aabae7b32b">sin</a>(<a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a>) * ::<a class="code" href="classal_1_1_complex.html#a426b58bf50eea320f1e3bef94f54fa8a">cosh</a>(<a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a>), ::<a class="code" href="classal_1_1_complex.html#a82ddb2cdefd7e442080093b72e4aaa1d">cos</a>(<a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a>) * ::<a class="code" href="classal_1_1_complex.html#a305a9b5c70c4d8769bb8b5bfb6fdc8d3">sinh</a>(<a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a>));</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  } </div>
<div class="line"><a name="l00264"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#a426b58bf50eea320f1e3bef94f54fa8a"> 264</a></span>  <a class="code" href="classal_1_1_complex.html">C</a> <a class="code" href="classal_1_1_complex.html#a426b58bf50eea320f1e3bef94f54fa8a">cosh</a>()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_complex.html">C</a>(::<a class="code" href="classal_1_1_complex.html#a82ddb2cdefd7e442080093b72e4aaa1d">cos</a>(<a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a>) * ::<a class="code" href="classal_1_1_complex.html#a305a9b5c70c4d8769bb8b5bfb6fdc8d3">sinh</a>(<a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a>), ::<a class="code" href="classal_1_1_complex.html#a128d504a4a0266687c44c5aabae7b32b">sin</a>(<a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a>) * ::<a class="code" href="classal_1_1_complex.html#a426b58bf50eea320f1e3bef94f54fa8a">cosh</a>(<a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a>));</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  } </div>
<div class="line"><a name="l00267"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#a305a9b5c70c4d8769bb8b5bfb6fdc8d3"> 267</a></span>  <a class="code" href="classal_1_1_complex.html">C</a> <a class="code" href="classal_1_1_complex.html#a305a9b5c70c4d8769bb8b5bfb6fdc8d3">sinh</a>()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  <span class="keywordflow">return</span> <a class="code" href="classal_1_1_complex.html">C</a>(::<a class="code" href="classal_1_1_complex.html#a82ddb2cdefd7e442080093b72e4aaa1d">cos</a>(<a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a>) * ::<a class="code" href="classal_1_1_complex.html#a426b58bf50eea320f1e3bef94f54fa8a">cosh</a>(<a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a>), ::<a class="code" href="classal_1_1_complex.html#a128d504a4a0266687c44c5aabae7b32b">sin</a>(<a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a>) * ::<a class="code" href="classal_1_1_complex.html#a305a9b5c70c4d8769bb8b5bfb6fdc8d3">sinh</a>(<a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a>));</div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  } </div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  </div>
<div class="line"><a name="l00271"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#a203cb47683c065ebffbc2609734ca98a"> 271</a></span>  T <a class="code" href="classal_1_1_complex.html#a203cb47683c065ebffbc2609734ca98a">abs</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="classal_1_1_complex.html#a218390dfa649ea62be730c60e78d2401">norm</a>(); } </div>
<div class="line"><a name="l00272"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#a8339362123dd31ac0baab888037524a0"> 272</a></span>  T <a class="code" href="classal_1_1_complex.html#a8339362123dd31ac0baab888037524a0">mag</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="classal_1_1_complex.html#a218390dfa649ea62be730c60e78d2401">norm</a>(); } </div>
<div class="line"><a name="l00273"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#aec8ec88787c25cc14a489528706bcfa4"> 273</a></span>  T <a class="code" href="classal_1_1_complex.html#aec8ec88787c25cc14a489528706bcfa4">magSqr</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="classal_1_1_complex.html#a65094cc454a57f98d00164d776c8d088">normSqr</a>(); } </div>
<div class="line"><a name="l00274"></a><span class="lineno"><a class="line" href="classal_1_1_complex.html#a05e4fe79178bd58f1a80436049832a77"> 274</a></span>  T <a class="code" href="classal_1_1_complex.html#a05e4fe79178bd58f1a80436049832a77">phase</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="classal_1_1_complex.html#a0b7363c5cd016a1d5d66d27d1993ae4f">arg</a>(); } </div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span> };</div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  </div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span> <span class="preprocessor">#define TEM \</span></div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span> <span class="preprocessor"> template <class T> \</span></div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span> <span class="preprocessor"> inline</span></div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span> TEM T abs(<span class="keyword">const</span> Complex<T>& c) { <span class="keywordflow">return</span> c.mag(); }</div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span> TEM Complex<T> exp(<span class="keyword">const</span> Complex<T>& c) { <span class="keywordflow">return</span> c.exp(); }</div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span> TEM Complex<T> log(<span class="keyword">const</span> Complex<T>& c) { <span class="keywordflow">return</span> c.log(); }</div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span> TEM Complex<T> pow(<span class="keyword">const</span> Complex<T>& b, <span class="keyword">const</span> Complex<T>& e) {</div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  <span class="keywordflow">return</span> b.pow(e);</div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span> }</div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span> TEM Complex<T> pow(<span class="keyword">const</span> Complex<T>& b, <span class="keyword">const</span> T& e) { <span class="keywordflow">return</span> b.pow(e); }</div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span> <span class="comment">// TEM Complex<T> sqrt(const Complex<T>& v){ return v.sqrt(); } // TODO: these</span></div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span> <span class="comment">// ambiguate other functions TEM Complex<T> cos(const Complex<T>& v){ return</span></div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span> <span class="comment">// v.cos(); } TEM Complex<T> sin(const Complex<T>& v){ return v.sin(); }</span></div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span> <span class="preprocessor">#undef TEM</span></div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  </div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span> <span class="keyword">inline</span> Complex<T> operator+(T r, <span class="keyword">const</span> Complex<T>& c) {</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  <span class="keywordflow">return</span> c + r;</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span> }</div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  </div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span> <span class="keyword">inline</span> Complex<T> operator-(T r, <span class="keyword">const</span> Complex<T>& c) {</div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  <span class="keywordflow">return</span> -c + r;</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span> }</div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  </div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span> <span class="keyword">inline</span> Complex<T> operator*(T r, <span class="keyword">const</span> Complex<T>& c) {</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  <span class="keywordflow">return</span> c * r;</div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span> }</div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  </div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span> <span class="keyword">inline</span> Complex<T> operator/(T r, <span class="keyword">const</span> Complex<T>& c) {</div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  <span class="keywordflow">return</span> c.conj() * (r / c.normSqr());</div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span> }</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> <span class="keyword">template</span> <<span class="keyword">class</span> VecN, <span class="keyword">class</span> T></div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span> VecN rotate(<span class="keyword">const</span> VecN& v, <span class="keyword">const</span> VecN& p, <span class="keyword">const</span> Complex<T>& a) {</div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  <span class="keywordflow">return</span> v * a.r + p * a.i;</div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span> }</div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  </div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span> <span class="keyword">template</span> <<span class="keyword">class</span> VecN, <span class="keyword">class</span> T></div>
<div class="line"><a name="l00321"></a><span class="lineno"><a class="line" href="group___math.html#gafc0b72e9edcefe5f8d173e9ae75e15bd"> 321</a></span> <span class="keywordtype">void</span> <a class="code" href="group___math.html#gafc0b72e9edcefe5f8d173e9ae75e15bd">rotatePlane</a>(VecN& v1, VecN& v2, <span class="keyword">const</span> <a class="code" href="classal_1_1_complex.html">Complex<T></a>& a) {</div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  VecN t = al::rotate(v1, v2, a);</div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  v2 = al::rotate(v2, VecN(-v1), a);</div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  v1 = t;</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>  </div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span> <span class="keyword">template</span> <<span class="keyword">class</span> Vec3, <span class="keyword">class</span> T></div>
<div class="line"><a name="l00331"></a><span class="lineno"><a class="line" href="group___math.html#ga223da6b1f51d3a7e8515ae723de3681f"> 331</a></span> Vec3 <a class="code" href="group___math.html#ga223da6b1f51d3a7e8515ae723de3681f">sterProj</a>(<span class="keyword">const</span> <a class="code" href="classal_1_1_complex.html">al::Complex<T></a>& c) {</div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  T magSqr = c.<a class="code" href="classal_1_1_complex.html#aec8ec88787c25cc14a489528706bcfa4">magSqr</a>();</div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  T mul = T(2) / (magSqr + T(1));</div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  <span class="keywordflow">return</span> Vec3(c.<a class="code" href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">r</a> * mul, c.<a class="code" href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">i</a> * mul, (magSqr - T(1)) * mul * T(0.5));</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>  </div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span> } <span class="comment">// namespace al</span></div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  </div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span> <span class="preprocessor">#endif</span></div>
<div class="ttc" id="aclassal_1_1_complex_html"><div class="ttname"><a href="classal_1_1_complex.html">al::Complex</a></div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00095">al_Complex.hpp:95</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_a05e4fe79178bd58f1a80436049832a77"><div class="ttname"><a href="classal_1_1_complex.html#a05e4fe79178bd58f1a80436049832a77">al::Complex::phase</a></div><div class="ttdeci">T phase() const</div><div class="ttdoc">Returns argument (angle)</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00274">al_Complex.hpp:274</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_a0b7363c5cd016a1d5d66d27d1993ae4f"><div class="ttname"><a href="classal_1_1_complex.html#a0b7363c5cd016a1d5d66d27d1993ae4f">al::Complex::arg</a></div><div class="ttdeci">T arg() const</div><div class="ttdoc">Returns argument in [-pi, pi].</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00219">al_Complex.hpp:219</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_a128d504a4a0266687c44c5aabae7b32b"><div class="ttname"><a href="classal_1_1_complex.html#a128d504a4a0266687c44c5aabae7b32b">al::Complex::sin</a></div><div class="ttdeci">C sin() const</div><div class="ttdoc">Returns sin(z)</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00261">al_Complex.hpp:261</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_a152d44956efad66d475d9f777276634e"><div class="ttname"><a href="classal_1_1_complex.html#a152d44956efad66d475d9f777276634e">al::Complex::sqrt</a></div><div class="ttdeci">C sqrt() const</div><div class="ttdoc">Returns square root.</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00250">al_Complex.hpp:250</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_a1b590169ff1416df978b55bce8e84036"><div class="ttname"><a href="classal_1_1_complex.html#a1b590169ff1416df978b55bce8e84036">al::Complex::set</a></div><div class="ttdeci">C & set(T vr, T vi)</div><div class="ttdoc">Set real and imaginary components.</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00129">al_Complex.hpp:129</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_a1c8914fa162173c62841b41af0e94871"><div class="ttname"><a href="classal_1_1_complex.html#a1c8914fa162173c62841b41af0e94871">al::Complex::fromPolar</a></div><div class="ttdeci">C & fromPolar(T m, T p)</div><div class="ttdoc">Set magnitude and phase.</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00124">al_Complex.hpp:124</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_a1e929197114c0e2e909e487c0a340f4b"><div class="ttname"><a href="classal_1_1_complex.html#a1e929197114c0e2e909e487c0a340f4b">al::Complex::pow</a></div><div class="ttdeci">C pow(const C &v) const</div><div class="ttdoc">Returns z^v.</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00237">al_Complex.hpp:237</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_a203cb47683c065ebffbc2609734ca98a"><div class="ttname"><a href="classal_1_1_complex.html#a203cb47683c065ebffbc2609734ca98a">al::Complex::abs</a></div><div class="ttdeci">T abs() const</div><div class="ttdoc">Returns norm (radius), |z|.</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00271">al_Complex.hpp:271</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_a218390dfa649ea62be730c60e78d2401"><div class="ttname"><a href="classal_1_1_complex.html#a218390dfa649ea62be730c60e78d2401">al::Complex::norm</a></div><div class="ttdeci">T norm() const</div><div class="ttdoc">Returns norm (radius), |z|.</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00232">al_Complex.hpp:232</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_a23298e630346b3a13105030c515c565f"><div class="ttname"><a href="classal_1_1_complex.html#a23298e630346b3a13105030c515c565f">al::Complex::exp</a></div><div class="ttdeci">C exp() const</div><div class="ttdoc">Returns e^z.</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00228">al_Complex.hpp:228</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_a236bdec18e7fc6e2a535568d17e0f8cb"><div class="ttname"><a href="classal_1_1_complex.html#a236bdec18e7fc6e2a535568d17e0f8cb">al::Complex::i</a></div><div class="ttdeci">T i</div><div class="ttdoc">Imaginary component.</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00102">al_Complex.hpp:102</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_a2b012f87713033e13acf07ba220f6e11"><div class="ttname"><a href="classal_1_1_complex.html#a2b012f87713033e13acf07ba220f6e11">al::Complex::r</a></div><div class="ttdeci">T r</div><div class="ttdoc">Real component.</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00101">al_Complex.hpp:101</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_a2ea31ad12b3b1e4e5e797823f5090589"><div class="ttname"><a href="classal_1_1_complex.html#a2ea31ad12b3b1e4e5e797823f5090589">al::Complex::operator<</a></div><div class="ttdeci">bool operator<(const C &c) const</div><div class="ttdoc">Returns true if norm is less than argument's norm.</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00157">al_Complex.hpp:157</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_a305a9b5c70c4d8769bb8b5bfb6fdc8d3"><div class="ttname"><a href="classal_1_1_complex.html#a305a9b5c70c4d8769bb8b5bfb6fdc8d3">al::Complex::sinh</a></div><div class="ttdeci">C sinh() const</div><div class="ttdoc">Returns sinh(z)</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00267">al_Complex.hpp:267</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_a333639a5b9aa942f7128f4af847da8d7"><div class="ttname"><a href="classal_1_1_complex.html#a333639a5b9aa942f7128f4af847da8d7">al::Complex::operator==</a></div><div class="ttdeci">bool operator==(const T &v) const</div><div class="ttdoc">Returns true if real and equals value.</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00148">al_Complex.hpp:148</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_a426b58bf50eea320f1e3bef94f54fa8a"><div class="ttname"><a href="classal_1_1_complex.html#a426b58bf50eea320f1e3bef94f54fa8a">al::Complex::cosh</a></div><div class="ttdeci">C cosh() const</div><div class="ttdoc">Returns cosh(z)</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00264">al_Complex.hpp:264</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_a432bc36e09f8552e9bebd2b72541d07f"><div class="ttname"><a href="classal_1_1_complex.html#a432bc36e09f8552e9bebd2b72541d07f">al::Complex::operator></a></div><div class="ttdeci">bool operator>(const C &v) const</div><div class="ttdoc">Returns true if norm is greater than argument's norm.</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00154">al_Complex.hpp:154</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_a5c9850751a3a5d3e8fff254cebc1d10f"><div class="ttname"><a href="classal_1_1_complex.html#a5c9850751a3a5d3e8fff254cebc1d10f">al::Complex::dot</a></div><div class="ttdeci">T dot(const C &v) const</div><div class="ttdoc">Returns vector dot product.</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00225">al_Complex.hpp:225</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_a65094cc454a57f98d00164d776c8d088"><div class="ttname"><a href="classal_1_1_complex.html#a65094cc454a57f98d00164d776c8d088">al::Complex::normSqr</a></div><div class="ttdeci">T normSqr() const</div><div class="ttdoc">Returns square of norm, |z|^2.</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00233">al_Complex.hpp:233</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_a6e90e28116a65f4abc295125d8f437a6"><div class="ttname"><a href="classal_1_1_complex.html#a6e90e28116a65f4abc295125d8f437a6">al::Complex::recip</a></div><div class="ttdeci">C recip() const</div><div class="ttdoc">Return multiplicative inverse, 1/z.</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00241">al_Complex.hpp:241</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_a82ddb2cdefd7e442080093b72e4aaa1d"><div class="ttname"><a href="classal_1_1_complex.html#a82ddb2cdefd7e442080093b72e4aaa1d">al::Complex::cos</a></div><div class="ttdeci">C cos() const</div><div class="ttdoc">Returns cos(z)</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00258">al_Complex.hpp:258</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_a8339362123dd31ac0baab888037524a0"><div class="ttname"><a href="classal_1_1_complex.html#a8339362123dd31ac0baab888037524a0">al::Complex::mag</a></div><div class="ttdeci">T mag() const</div><div class="ttdoc">Returns norm (radius), |z|.</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00272">al_Complex.hpp:272</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_a9016f65e0e7e01045fb034736cc246ea"><div class="ttname"><a href="classal_1_1_complex.html#a9016f65e0e7e01045fb034736cc246ea">al::Complex::norm</a></div><div class="ttdeci">C & norm(T v)</div><div class="ttdoc">Set norm leaving argument the same.</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00115">al_Complex.hpp:115</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_a91987a3fff79caad88328096a337069c"><div class="ttname"><a href="classal_1_1_complex.html#a91987a3fff79caad88328096a337069c">al::Complex::operator!=</a></div><div class="ttdeci">bool operator!=(const C &v) const</div><div class="ttdoc">Returns true if any components are not equal.</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00151">al_Complex.hpp:151</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_a98871e41ebbf098d5a37c33848e4bd22"><div class="ttname"><a href="classal_1_1_complex.html#a98871e41ebbf098d5a37c33848e4bd22">al::Complex::arg</a></div><div class="ttdeci">C & arg(T v)</div><div class="ttdoc">Set argument leaving norm the same.</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00112">al_Complex.hpp:112</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_a9ab5476fe6d7d22b3bc78fd4fa7a008d"><div class="ttname"><a href="classal_1_1_complex.html#a9ab5476fe6d7d22b3bc78fd4fa7a008d">al::Complex::sqr</a></div><div class="ttdeci">C sqr() const</div><div class="ttdoc">Returns square.</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00247">al_Complex.hpp:247</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_aac1c97ec0dec260b29a18f2c40158ad7"><div class="ttname"><a href="classal_1_1_complex.html#aac1c97ec0dec260b29a18f2c40158ad7">al::Complex::operator==</a></div><div class="ttdeci">bool operator==(const C &v) const</div><div class="ttdoc">Returns true if all components are equal.</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00145">al_Complex.hpp:145</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_aae3db9206b2214430fe63ad4b552a1d8"><div class="ttname"><a href="classal_1_1_complex.html#aae3db9206b2214430fe63ad4b552a1d8">al::Complex::conj</a></div><div class="ttdeci">C conj() const</div><div class="ttdoc">Returns conjugate, z*.</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00224">al_Complex.hpp:224</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_aaec1ff9bf630d55df12b96a347a2ac3a"><div class="ttname"><a href="classal_1_1_complex.html#aaec1ff9bf630d55df12b96a347a2ac3a">al::Complex::normalize</a></div><div class="ttdeci">C & normalize(T m=T(1))</div><div class="ttdoc">Sets magnitude to 1, |z|=1.</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00234">al_Complex.hpp:234</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_aba0d1d398bac0071b0ca1d712765e171"><div class="ttname"><a href="classal_1_1_complex.html#aba0d1d398bac0071b0ca1d712765e171">al::Complex::fromPolar</a></div><div class="ttdeci">C & fromPolar(T phase)</div><div class="ttdoc">Set phase and normalize.</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00119">al_Complex.hpp:119</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_abb762ec4a1dd5119c5d275f97ea9ac5a"><div class="ttname"><a href="classal_1_1_complex.html#abb762ec4a1dd5119c5d275f97ea9ac5a">al::Complex::sgn</a></div><div class="ttdeci">C sgn(T m=T(1)) const</div><div class="ttdoc">Returns signum, z/|z|, the closest point on unit circle.</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00244">al_Complex.hpp:244</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_ad92f6978e926fab08c0513feb72c73c2"><div class="ttname"><a href="classal_1_1_complex.html#ad92f6978e926fab08c0513feb72c73c2">al::Complex::argUnit</a></div><div class="ttdeci">T argUnit() const</div><div class="ttdoc">Return argument in unit interval [0, 1)</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00220">al_Complex.hpp:220</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_ae6cb8396f8159ab3894a5b25c297c5e3"><div class="ttname"><a href="classal_1_1_complex.html#ae6cb8396f8159ab3894a5b25c297c5e3">al::Complex::pow</a></div><div class="ttdeci">C pow(T v) const</div><div class="ttdoc">Returns z^v.</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00240">al_Complex.hpp:240</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_ae71470089b14cb4e8802382df03ec47a"><div class="ttname"><a href="classal_1_1_complex.html#ae71470089b14cb4e8802382df03ec47a">al::Complex::log</a></div><div class="ttdeci">C log() const</div><div class="ttdoc">Returns log(z)</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00229">al_Complex.hpp:229</a></div></div>
<div class="ttc" id="aclassal_1_1_complex_html_aec8ec88787c25cc14a489528706bcfa4"><div class="ttname"><a href="classal_1_1_complex.html#aec8ec88787c25cc14a489528706bcfa4">al::Complex::magSqr</a></div><div class="ttdeci">T magSqr() const</div><div class="ttdoc">Returns square of norm, |z|^2.</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00273">al_Complex.hpp:273</a></div></div>
<div class="ttc" id="aclassal_1_1_polar_html"><div class="ttname"><a href="classal_1_1_polar.html">al::Polar</a></div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00064">al_Complex.hpp:64</a></div></div>
<div class="ttc" id="aclassal_1_1_polar_html_a0456e71fb0abd22aea58758011005ea7"><div class="ttname"><a href="classal_1_1_polar.html#a0456e71fb0abd22aea58758011005ea7">al::Polar::Polar</a></div><div class="ttdeci">Polar(const T &mag, const T &phs)</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00079">al_Complex.hpp:79</a></div></div>
<div class="ttc" id="aclassal_1_1_polar_html_a84160608a4bd926a5af693cd1acc61ff"><div class="ttname"><a href="classal_1_1_polar.html#a84160608a4bd926a5af693cd1acc61ff">al::Polar::Polar</a></div><div class="ttdeci">Polar(const Complex< T > &v)</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00082">al_Complex.hpp:82</a></div></div>
<div class="ttc" id="aclassal_1_1_polar_html_a85d8571636ceafe81c716c3bbe12dbb6"><div class="ttname"><a href="classal_1_1_polar.html#a85d8571636ceafe81c716c3bbe12dbb6">al::Polar::p</a></div><div class="ttdeci">T p</div><div class="ttdoc">Phase, in radians.</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00069">al_Complex.hpp:69</a></div></div>
<div class="ttc" id="aclassal_1_1_polar_html_acd11bf2c5563a45fe0b7b2c40ef4ad5f"><div class="ttname"><a href="classal_1_1_polar.html#acd11bf2c5563a45fe0b7b2c40ef4ad5f">al::Polar::Polar</a></div><div class="ttdeci">Polar(const T &phs=T(0))</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00075">al_Complex.hpp:75</a></div></div>
<div class="ttc" id="aclassal_1_1_polar_html_ae25abb3fc29203774c54bdbd594a9ce8"><div class="ttname"><a href="classal_1_1_polar.html#ae25abb3fc29203774c54bdbd594a9ce8">al::Polar::m</a></div><div class="ttdeci">T m</div><div class="ttdoc">Magnitude.</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00068">al_Complex.hpp:68</a></div></div>
<div class="ttc" id="agroup___math_html_ga223da6b1f51d3a7e8515ae723de3681f"><div class="ttname"><a href="group___math.html#ga223da6b1f51d3a7e8515ae723de3681f">al::sterProj</a></div><div class="ttdeci">Vec3 sterProj(const al::Complex< T > &c)</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00331">al_Complex.hpp:331</a></div></div>
<div class="ttc" id="agroup___math_html_gafc0b72e9edcefe5f8d173e9ae75e15bd"><div class="ttname"><a href="group___math.html#gafc0b72e9edcefe5f8d173e9ae75e15bd">al::rotatePlane</a></div><div class="ttdeci">void rotatePlane(VecN &v1, VecN &v2, const Complex< T > &a)</div><div class="ttdef"><b>Definition:</b> <a href="al___complex_8hpp_source.html#l00321">al_Complex.hpp:321</a></div></div>
<div class="ttc" id="anamespaceal_html"><div class="ttname"><a href="namespaceal.html">al</a></div><div class="ttdef"><b>Definition:</b> <a href="al___app_8hpp_source.html#l00023">al_App.hpp:23</a></div></div>
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