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 <span id="projectnumber">2.4</span>
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<div class="title">mathExtra.H</div> </div>
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<div class="contents">
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">/* ----------------------------------------------------------------------</span></div>
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<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment"> CFDEMcoupling - Open Source CFD-DEM coupling</span></div>
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<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment"></span></div>
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<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment"> CFDEMcoupling is part of the CFDEMproject</span></div>
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<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"> www.cfdem.com</span></div>
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<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment"> Christoph Goniva, christoph.goniva@cfdem.com</span></div>
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<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"> Copyright 2009-2012 JKU Linz</span></div>
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<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"> Copyright 2012- DCS Computing GmbH, Linz</span></div>
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<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">-------------------------------------------------------------------------------</span></div>
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<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">License</span></div>
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<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment"> This file is part of CFDEMcoupling.</span></div>
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<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment"></span></div>
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<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment"> CFDEMcoupling is free software; you can redistribute it and/or modify it</span></div>
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<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment"> under the terms of the GNU General Public License as published by the</span></div>
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<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment"> Free Software Foundation; either version 3 of the License, or (at your</span></div>
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<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment"> option) any later version.</span></div>
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<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment"></span></div>
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<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment"> CFDEMcoupling is distributed in the hope that it will be useful, but WITHOUT</span></div>
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<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment"> ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or</span></div>
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<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment"> FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License</span></div>
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<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="comment"> for more details.</span></div>
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<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="comment"></span></div>
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<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="comment"> You should have received a copy of the GNU General Public License</span></div>
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<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment"> along with CFDEMcoupling; if not, write to the Free Software Foundation,</span></div>
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<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment"> Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA</span></div>
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<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment"></span></div>
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<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment">Description</span></div>
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<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment"> This code is designed to realize coupled CFD-DEM simulations using LIGGGHTS</span></div>
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<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment"> and OpenFOAM(R). Note: this code is not part of OpenFOAM(R) (see DISCLAIMER).</span></div>
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<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment"> </span></div>
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<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment"> Copyright of this contribution:</span></div>
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<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment"> Copyright 2014- TU Graz, IPPT</span></div>
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<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment">------------------------------------------------------------------------- */</span></div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> </div>
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<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="preprocessor">#ifndef CFDEM_MATH_EXTRA_H</span></div>
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<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="preprocessor"></span><span class="preprocessor">#define CFDEM_MATH_EXTRA_H</span></div>
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<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="preprocessor"></span></div>
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<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="preprocessor">#include <vector></span></div>
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<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment">//#include "math.h"</span></div>
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<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="preprocessor">#include "stdio.h"</span></div>
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<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="preprocessor">#include "string.h"</span></div>
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<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="preprocessor">#include "error.h"</span></div>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="preprocessor">#include "ctype.h"</span></div>
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<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> </div>
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<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="preprocessor">#define TOLERANCE_ORTHO 1e-10</span></div>
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<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="preprocessor"></span></div>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="keyword">namespace </span>MathExtra </div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> {</div>
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<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> </div>
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<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="comment">// inline void outerProduct(double *vec1, double *vec2, double **m);</span></div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment">// inline double spheroidGeometry(int index, double bi, double ai);</span></div>
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<div class="line"><a name="l00052"></a><span class="lineno"> 52</span> </div>
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<div class="line"><a name="l00053"></a><span class="lineno"> 53</span> </div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span> </div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="comment">//--------------------------------------------------------------------</span></div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="comment">// Outer Product of two vectors</span></div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="keyword">inline</span> <span class="keywordtype">void</span> outerProduct(<span class="keywordtype">double</span> *vec1, <span class="keywordtype">double</span> *vec2, <span class="keywordtype">double</span> **m)</div>
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<div class="line"><a name="l00058"></a><span class="lineno"> 58</span> {</div>
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<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <span class="keywordtype">int</span> i, j;</div>
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<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="comment">//debug output</span></div>
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<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <span class="keywordflow">for</span>( i = 0; i < 3; ++i )</div>
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<div class="line"><a name="l00062"></a><span class="lineno"> 62</span> <span class="comment">// printf("OUTER PRODUCT: Input: vec1 element %d = %g", i, vec1[i]);</span></div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="keywordflow">for</span>( i = 0; i < 3; ++i )</div>
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<div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="comment">// printf("OUTER PRODUCT: Input: vec2 element %d=%g", i, vec2[i]);</span></div>
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<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  </div>
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<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="comment">//calculation</span></div>
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<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="keywordflow">for</span>( i = 0; i < 3; ++i )</div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="keywordflow">for</span>( j = 0; j < 3; ++j )</div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  {</div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  m[i][j] = vec1[i] * vec2[j];</div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  printf(<span class="stringliteral">"OUTER PRODUCT: Result: m[%d][%d]=%g"</span>, i, j, m[i][j]);</div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  }</div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  </div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  </div>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</span> }</div>
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<div class="line"><a name="l00076"></a><span class="lineno"> 76</span> <span class="comment">//--------------------------------------------------------------------</span></div>
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<div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="comment">// Compute the major, minor axis and eccentricity parameters of a prolate spheroid</span></div>
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<div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> spheroidGeometry(<span class="keywordtype">double</span> radius, <span class="keywordtype">double</span> aspectRatio, <span class="comment">//inputs</span></div>
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<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="keywordtype">double</span>& ai, <span class="keywordtype">double</span>& bi, <span class="comment">//outputs</span></div>
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<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <span class="keywordtype">double</span>& ei, <span class="keywordtype">double</span>& Le <span class="comment">//outputs</span></div>
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<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  ) <span class="comment">//</span></div>
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<div class="line"><a name="l00082"></a><span class="lineno"> 82</span> {</div>
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<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="comment">//INPUT</span></div>
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<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="comment">// radius ...volume-equivalent radius of the spheroid</span></div>
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<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="comment">// aspectRatio ...major/minor aspect ratio</span></div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  </div>
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<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="comment">//OUTPUT</span></div>
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<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  <span class="comment">// ai ... </span></div>
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<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  <span class="comment">// bi ... </span></div>
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<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <span class="comment">// ei ... </span></div>
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<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <span class="comment">// Le ... </span></div>
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<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  </div>
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<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="keywordflow">if</span>(radius<=0.0) <span class="comment">//avoid troubles in case radius is 0 or negative</span></div>
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<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00095"></a><span class="lineno"> 95</span> </div>
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<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  ai = radius * std::pow(aspectRatio*aspectRatio,0.33333333333333333333333);</div>
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<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  bi = ai / aspectRatio;</div>
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<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  ei = std::sqrt( </div>
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<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  1.0</div>
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<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  - 1.0 / (aspectRatio*aspectRatio)</div>
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<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  );</div>
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<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  Le = std::log(</div>
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<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  (1.0+ei)</div>
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<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  /(1.0-ei)</div>
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<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  );</div>
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<div class="line"><a name="l00106"></a><span class="lineno"> 106</span> </div>
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<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>; </div>
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<div class="line"><a name="l00108"></a><span class="lineno"> 108</span> }</div>
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<div class="line"><a name="l00109"></a><span class="lineno"> 109</span> </div>
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<div class="line"><a name="l00110"></a><span class="lineno"> 110</span> <span class="comment">//--------------------------------------------------------------------</span></div>
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<div class="line"><a name="l00111"></a><span class="lineno"> 111</span> <span class="comment">// Compute the major, minor axis and eccentricity parameters of a prolate spheroid</span></div>
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<div class="line"><a name="l00112"></a><span class="lineno"> 112</span> <span class="keyword">inline</span> <span class="keywordtype">double</span> Pi()</div>
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<div class="line"><a name="l00113"></a><span class="lineno"> 113</span> {</div>
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<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <span class="keywordflow">return</span> 3.1415926535897932384626433832795;</div>
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<div class="line"><a name="l00115"></a><span class="lineno"> 115</span> }</div>
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<div class="line"><a name="l00116"></a><span class="lineno"> 116</span> </div>
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<div class="line"><a name="l00117"></a><span class="lineno"> 117</span> </div>
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<div class="line"><a name="l00118"></a><span class="lineno"> 118</span> <span class="comment">//--------------------------------------------------------------------</span></div>
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<div class="line"><a name="l00119"></a><span class="lineno"> 119</span> <span class="comment">// Compute the major, minor axis and eccentricity parameters of a prolate spheroid</span></div>
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<div class="line"><a name="l00120"></a><span class="lineno"> 120</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> spheroidGeometry2(<span class="keywordtype">double</span> radius, <span class="keywordtype">double</span> aspectRatio, <span class="comment">//inputs</span></div>
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<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <span class="keywordtype">double</span>& ai, <span class="keywordtype">double</span>& bi, <span class="comment">//outputs</span></div>
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<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  <span class="keywordtype">double</span>& XAe, <span class="keywordtype">double</span>& YAe, <span class="comment">//outputs</span></div>
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<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <span class="keywordtype">double</span>& XCe, <span class="keywordtype">double</span>& YCe, <span class="comment">//outputs</span></div>
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|
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <span class="keywordtype">double</span>& YHe</div>
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<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  ) <span class="comment">//</span></div>
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<div class="line"><a name="l00126"></a><span class="lineno"> 126</span> {</div>
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<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <span class="comment">//INPUT</span></div>
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<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="comment">// radius ...volume-equivalent radius of the spheroid</span></div>
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|
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <span class="comment">// aspectRatio ...major/minor aspect ratio</span></div>
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<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  </div>
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<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <span class="comment">//OUTPUT</span></div>
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<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="comment">// XAe ...Eccentricity dependet parameter</span></div>
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<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <span class="comment">// YAe ...Eccentricity dependet parameter</span></div>
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<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="comment">// XCe ...Eccentricity dependet parameter</span></div>
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<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <span class="comment">// XCe ...Eccentricity dependet parameter</span></div>
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<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  <span class="comment">// YCe ...Eccentricity dependet parameter</span></div>
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<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="comment">// YHe ...Eccentricity dependet parameter</span></div>
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<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  </div>
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<div class="line"><a name="l00139"></a><span class="lineno"> 139</span> </div>
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<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  <span class="keywordtype">double</span> ei(0.0), Le(0.0); </div>
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<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <span class="keywordtype">bool</span> result = </div>
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<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  spheroidGeometry(radius, aspectRatio, <span class="comment">//inputs</span></div>
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<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  ai, bi, <span class="comment">//outputs</span></div>
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<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  ei, Le <span class="comment">//outputs</span></div>
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<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  );</div>
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<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <span class="keywordflow">if</span>(!result)</div>
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<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  </div>
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<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  XAe= 2.6666666666666666666666667</div>
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<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  *ei*ei*ei</div>
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<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  /(-2.0*ei+(1.0+ei*ei)*Le); </div>
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<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  YAe= 5.333333333333333333333333333</div>
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<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  *ei*ei*ei</div>
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<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  /(2.0*ei+(3*ei*ei-1.0)*Le);</div>
|
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<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  XCe= 1.333333333333333333333333333</div>
|
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<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  *ei*ei*ei</div>
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<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  *(1.0-ei*ei)</div>
|
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<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  /(2.0*ei-(1.0-ei*ei)*Le);</div>
|
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<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  YCe= 1.3333333333333333333333</div>
|
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<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  *ei*ei*ei</div>
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<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  *(2.0-ei*ei)</div>
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<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  /(-2.0*ei+(1.0+ei*ei)*Le);</div>
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<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  YHe= 1.3333333333333333333333</div>
|
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<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  *ei*ei*ei*ei*ei</div>
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<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  /(-2.0*ei+(1.0+ei*ei)*Le);</div>
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|
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span> </div>
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<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>; </div>
|
|
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span> </div>
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<div class="line"><a name="l00169"></a><span class="lineno"> 169</span> }</div>
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<div class="line"><a name="l00170"></a><span class="lineno"> 170</span> </div>
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<div class="line"><a name="l00171"></a><span class="lineno"> 171</span> <span class="comment">//--------------------------------------------------------------------</span></div>
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|
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span> <span class="comment">// zeroize a 3x3x3 tensor</span></div>
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|
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span> <span class="keyword">inline</span> <span class="keywordtype">void</span> zeroize333(<span class="keywordtype">double</span> tensor[3][3][3] )</div>
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<div class="line"><a name="l00174"></a><span class="lineno"> 174</span> {</div>
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<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iX=0; iX<3; iX++)</div>
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<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iY=0; iY<3; iY++)</div>
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<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iZ=0; iZ<3; iZ++)</div>
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<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  tensor[iX][iY][iZ] = 0.0;</div>
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<div class="line"><a name="l00179"></a><span class="lineno"> 179</span> }</div>
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<div class="line"><a name="l00180"></a><span class="lineno"> 180</span> </div>
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<div class="line"><a name="l00181"></a><span class="lineno"> 181</span> <span class="comment">//--------------------------------------------------------------------</span></div>
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<div class="line"><a name="l00182"></a><span class="lineno"> 182</span> <span class="comment">// zeroize a 3x3 tensor</span></div>
|
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<div class="line"><a name="l00183"></a><span class="lineno"> 183</span> <span class="keyword">inline</span> <span class="keywordtype">void</span> zeroize33(<span class="keywordtype">double</span> tensor[3][3] )</div>
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<div class="line"><a name="l00184"></a><span class="lineno"> 184</span> {</div>
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<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iX=0; iX<3; iX++)</div>
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|
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iY=0; iY<3; iY++)</div>
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<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  tensor[iX][iY] = 0.0;</div>
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<div class="line"><a name="l00188"></a><span class="lineno"> 188</span> }</div>
|
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<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> <span class="comment">//--------------------------------------------------------------------</span></div>
|
|
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span> <span class="comment">// multiply a 3x3x3 tensor with a scalar</span></div>
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|
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span> <span class="keyword">inline</span> <span class="keywordtype">void</span> multiply333(<span class="keywordtype">double</span> scalar, <span class="keywordtype">double</span> tensor[3][3][3] )</div>
|
|
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span> {</div>
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|
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iX=0; iX<3; iX++)</div>
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|
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iY=0; iY<3; iY++)</div>
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|
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iZ=0; iZ<3; iZ++)</div>
|
|
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  tensor[iX][iY][iZ] *= scalar;</div>
|
|
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span> }</div>
|
|
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span> <span class="comment">//--------------------------------------------------------------------</span></div>
|
|
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span> <span class="comment">// Compute a dot and dyadic product of with a vector</span></div>
|
|
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span> <span class="keyword">inline</span> <span class="keywordtype">void</span> permutationTensor(<span class="keywordtype">double</span> tensor[3][3][3] )</div>
|
|
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span> {</div>
|
|
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  zeroize333(tensor);</div>
|
|
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  tensor[0][1][2] = 1.0; </div>
|
|
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  tensor[1][2][0] = 1.0; </div>
|
|
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  tensor[2][0][1] = 1.0; </div>
|
|
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  tensor[0][2][1] =-1.0; </div>
|
|
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  tensor[2][1][0] =-1.0; </div>
|
|
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  tensor[1][0][2] =-1.0; </div>
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<div class="line"><a name="l00210"></a><span class="lineno"> 210</span> }</div>
|
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<div class="line"><a name="l00211"></a><span class="lineno"> 211</span> </div>
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<div class="line"><a name="l00212"></a><span class="lineno"> 212</span> </div>
|
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<div class="line"><a name="l00213"></a><span class="lineno"> 213</span> </div>
|
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<div class="line"><a name="l00214"></a><span class="lineno"> 214</span> <span class="comment">//--------------------------------------------------------------------</span></div>
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<div class="line"><a name="l00215"></a><span class="lineno"> 215</span> <span class="comment">// Compute a dot product of the permutation tensor and </span></div>
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<div class="line"><a name="l00216"></a><span class="lineno"> 216</span> <span class="comment">// then a dyadic product of with a vector</span></div>
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<div class="line"><a name="l00217"></a><span class="lineno"> 217</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> permutationDotDyadic( </div>
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<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <span class="keywordtype">double</span> vector[3], </div>
|
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<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <span class="keywordtype">double</span> tensor[3][3][3] </div>
|
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<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  )</div>
|
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<div class="line"><a name="l00221"></a><span class="lineno"> 221</span> {</div>
|
|
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  <span class="comment">//Generate permutation tensor</span></div>
|
|
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  <span class="keywordtype">double</span> permutationT[3][3][3];</div>
|
|
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  permutationTensor(permutationT);</div>
|
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<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  </div>
|
|
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  <span class="comment">//Step 1: compute dot prodcut of permutation tensor</span></div>
|
|
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  <span class="keywordtype">double</span> permutationDotProd[3][3];</div>
|
|
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  zeroize33(permutationDotProd);</div>
|
|
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span> </div>
|
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<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iX=0; iX<3; iX++)</div>
|
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<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iY=0; iY<3; iY++)</div>
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<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iZ=0; iZ<3; iZ++)</div>
|
|
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  permutationDotProd[iX][iY] += permutationT[iX][iY][iZ]</div>
|
|
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  * vector[iZ];</div>
|
|
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span> </div>
|
|
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iX=0; iX<3; iX++)</div>
|
|
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iY=0; iY<3; iY++)</div>
|
|
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iZ=0; iZ<3; iZ++)</div>
|
|
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  tensor[iX][iY][iZ] = permutationDotProd[iX][iY]</div>
|
|
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  * vector[iZ]; </div>
|
|
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
|
|
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span> </div>
|
|
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span> }</div>
|
|
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span> </div>
|
|
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span> <span class="comment">//--------------------------------------------------------------------</span></div>
|
|
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span> <span class="comment">// Compute a dot and dyadic product of with a vector</span></div>
|
|
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> doubleDotTensor333Tensor33(<span class="keywordtype">double</span> tensor333[3][3][3], </div>
|
|
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  <span class="keywordtype">double</span> tensor33[3][3],</div>
|
|
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <span class="keywordtype">double</span> result[3]</div>
|
|
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  )</div>
|
|
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span> {</div>
|
|
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  result[0]=0.0;result[1]=0.0;result[2]=0.0;</div>
|
|
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  </div>
|
|
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iX=0; iX<3; iX++)</div>
|
|
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iY=0; iY<3; iY++)</div>
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<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  <span class="keywordflow">for</span>(<span class="keywordtype">int</span> iZ=0; iZ<3; iZ++)</div>
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<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  result[iX] += tensor333[iX][iY][iZ] * tensor33[iY][iZ];</div>
|
|
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span> </div>
|
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<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
|
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<div class="line"><a name="l00260"></a><span class="lineno"> 260</span> }</div>
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<div class="line"><a name="l00261"></a><span class="lineno"> 261</span> </div>
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<div class="line"><a name="l00262"></a><span class="lineno"> 262</span> </div>
|
|
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span> }; <span class="comment">//end of namespace</span></div>
|
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<div class="line"><a name="l00264"></a><span class="lineno"> 264</span> </div>
|
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<div class="line"><a name="l00265"></a><span class="lineno"> 265</span> <span class="preprocessor">#endif</span></div>
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</div><!-- fragment --></div><!-- contents -->
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