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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">/*</span></div><div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment"> * Copyright (c) 2002, 2016 Jens Keiner, Stefan Kunis, Daniel Potts</span></div><div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment"> *</span></div><div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment"> * This program is free software; you can redistribute it and/or modify it under</span></div><div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"> * the terms of the GNU General Public License as published by the Free Software</span></div><div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment"> * Foundation; either version 2 of the License, or (at your option) any later</span></div><div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"> * version.</span></div><div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"> *</span></div><div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment"> * This program is distributed in the hope that it will be useful, but WITHOUT</span></div><div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment"> * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS</span></div><div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment"> * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more</span></div><div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment"> * details.</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"> * You should have received a copy of the GNU General Public License along with</span></div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment"> * this program; if not, write to the Free Software Foundation, Inc., 51</span></div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment"> * Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.</span></div><div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment"> */</span></div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span> </div><div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="preprocessor">#include <math.h></span></div><div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="preprocessor">#include <stdio.h></span></div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="preprocessor">#include "infft.h"</span></div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="preprocessor">#include "<a class="code" href="wigner_8h.html">wigner.h</a>"</span></div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="preprocessor">#include "infft.h"</span></div><div class="line"><a name="l00024"></a><span class="lineno"> 24</span> </div><div class="line"><a name="l00025"></a><span class="lineno"><a class="line" href="wigner_8h.html#ab67e240f23c39daa7283fee9025a8f03"> 25</a></span> <span class="keywordtype">double</span> <a class="code" href="wigner_8h.html#ab67e240f23c39daa7283fee9025a8f03">SO3_alpha</a>(<span class="keyword">const</span> <span class="keywordtype">int</span> m1, <span class="keyword">const</span> <span class="keywordtype">int</span> m2, <span class="keyword">const</span> <span class="keywordtype">int</span> j)</div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span> {</div><div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> M = MAX(ABS(m1),ABS(m2)), mini = MIN(ABS(m1),ABS(m2));</div><div class="line"><a name="l00028"></a><span class="lineno"> 28</span> </div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  <span class="keywordflow">if</span> (j < 0)</div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  <span class="keywordflow">return</span> K(0.0);</div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (j == 0)</div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  {</div><div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  <span class="keywordflow">if</span> (m1 == 0 && m2 == 0)</div><div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <span class="keywordflow">return</span> K(1.0);</div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <span class="keywordflow">if</span> (m1 == m2)</div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <span class="keywordflow">return</span> K(0.5);</div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  <span class="keywordflow">return</span> IF((m1+m2)%2,K(0.0),K(-0.5));</div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  }</div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (j < M - mini)</div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="keywordflow">return</span> IF(j%2,K(0.5),K(-0.5));</div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (j < M)</div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  <span class="keywordflow">return</span> K(0.5) * SIGNF((R)m1)*SIGNF((R)m2);</div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <span class="keywordflow">return</span></div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  SQRT(((R)(j+1))/((R)(j+1-m1)))</div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  * SQRT(((R)(2*j+1))/((R)(j+1+m1)))</div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  * SQRT(((R)(j+1))/((R)(j+1-m2)))</div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  * SQRT(((R)(2*j+1))/((R)(j+1+m2)));</div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span> }</div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span> </div><div class="line"><a name="l00052"></a><span class="lineno"><a class="line" href="wigner_8h.html#a6722aa3212be1361b531751a850056f6"> 52</a></span> <span class="keywordtype">double</span> <a class="code" href="wigner_8h.html#a6722aa3212be1361b531751a850056f6">SO3_beta</a>(<span class="keyword">const</span> <span class="keywordtype">int</span> m1, <span class="keyword">const</span> <span class="keywordtype">int</span> m2, <span class="keyword">const</span> <span class="keywordtype">int</span> j)</div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span> {</div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="keywordflow">if</span> (j < 0)</div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="keywordflow">return</span> K(0.0);</div><div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (j < MAX(ABS(m1),ABS(m2)))</div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <span class="keywordflow">return</span> K(0.5);</div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (m1 == 0 || m2 == 0)</div><div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <span class="keywordflow">return</span> K(0.0);</div><div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  {</div><div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="keyword">const</span> R m1a = FABS((R)m1), m2a = FABS((R)m2);</div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="keywordflow">return</span> -COPYSIGN(</div><div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  ((SQRT(m1a)*SQRT(m2a))/((R)j))</div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  * SQRT(m1a/((R)(j+1-m1)))</div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  * SQRT(((R)(2*j+1))/((R)(j+1+m1)))</div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  * SQRT(m2a/((R)(j+1-m2)))</div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  * SQRT(((R)(2*j+1))/((R)(j+1+m2))),</div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  SIGNF((R)m1)*SIGNF((R)m2));</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> }</div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span> </div><div class="line"><a name="l00073"></a><span class="lineno"><a class="line" href="wigner_8h.html#a6b13b24d727910800b9f1c0da29f5f73"> 73</a></span> <span class="keywordtype">double</span> <a class="code" href="wigner_8h.html#a6b13b24d727910800b9f1c0da29f5f73">SO3_gamma</a>(<span class="keyword">const</span> <span class="keywordtype">int</span> m1, <span class="keyword">const</span> <span class="keywordtype">int</span> m2, <span class="keyword">const</span> <span class="keywordtype">int</span> j)</div><div class="line"><a name="l00074"></a><span class="lineno"> 74</span> {</div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="keywordflow">if</span> (MAX(ABS(m1),ABS(m2)) < j)</div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="keywordflow">return</span> -(((R)(j+1))/((R)j)) * SQRT((((R)(j-m1))/((R)(j+1-m1)))</div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  *(((R)(j+m1))/((R)(j+1+m1)))*(((R)(j-m2))/((R)(j+1-m2)))</div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  *(((R)(j+m2))/((R)(j+1+m2))));</div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (j == -1)</div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <span class="keywordflow">return</span> IF(m1 > m2 || !((m1 + m2) % 2), K(1.0), K(-1.0))</div><div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  * nfft_lambda2((R)ABS(m2 - m1),(R)ABS(m2 + m1));</div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="keywordflow">return</span> K(0.0);</div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span> }</div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span> </div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span> <span class="comment">/*compute the coefficients for all degrees*/</span></div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span> </div><div class="line"><a name="l00088"></a><span class="lineno"><a class="line" href="wigner_8h.html#ae9c3c9a11f1da35bb0cfbed1fb828ad2"> 88</a></span> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="wigner_8h.html#ae9c3c9a11f1da35bb0cfbed1fb828ad2">SO3_alpha_row</a>(<span class="keywordtype">double</span> *alpha, <span class="keywordtype">int</span> N, <span class="keywordtype">int</span> k, <span class="keywordtype">int</span> m)</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>  <span class="keywordtype">int</span> j;</div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <span class="keywordtype">double</span> *alpha_act = alpha;</div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  <span class="keywordflow">for</span> (j = -1; j <= N; j++)</div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  *alpha_act++ = <a class="code" href="wigner_8h.html#ab67e240f23c39daa7283fee9025a8f03">SO3_alpha</a>(k, m, j);</div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span> }</div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span> </div><div class="line"><a name="l00096"></a><span class="lineno"><a class="line" href="wigner_8h.html#a1b82e072be0c3e0d45426ed56e4e6a9d"> 96</a></span> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="wigner_8h.html#a1b82e072be0c3e0d45426ed56e4e6a9d">SO3_beta_row</a>(<span class="keywordtype">double</span> *beta, <span class="keywordtype">int</span> N, <span class="keywordtype">int</span> k, <span class="keywordtype">int</span> m)</div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span> {</div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="keywordtype">int</span> j;</div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <span class="keywordtype">double</span> *beta_act = beta;</div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <span class="keywordflow">for</span> (j = -1; j <= N; j++)</div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  *beta_act++ = <a class="code" href="wigner_8h.html#a6722aa3212be1361b531751a850056f6">SO3_beta</a>(k, m, j);</div><div class="line"><a name="l00102"></a><span class="lineno"> 102</span> }</div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span> </div><div class="line"><a name="l00104"></a><span class="lineno"><a class="line" href="wigner_8h.html#a46516d6ec71efab3c80eecd459ad20ee"> 104</a></span> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="wigner_8h.html#a46516d6ec71efab3c80eecd459ad20ee">SO3_gamma_row</a>(<span class="keywordtype">double</span> *gamma, <span class="keywordtype">int</span> N, <span class="keywordtype">int</span> k, <span class="keywordtype">int</span> m)</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>  <span class="keywordtype">int</span> j;</div><div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  <span class="keywordtype">double</span> *gamma_act = gamma;</div><div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="keywordflow">for</span> (j = -1; j <= N; j++)</div><div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  *gamma_act++ = <a class="code" href="wigner_8h.html#a6b13b24d727910800b9f1c0da29f5f73">SO3_gamma</a>(k, m, j);</div><div class="line"><a name="l00110"></a><span class="lineno"> 110</span> }</div><div class="line"><a name="l00111"></a><span class="lineno"> 111</span> </div><div class="line"><a name="l00112"></a><span class="lineno"> 112</span> <span class="comment">/*compute for all degrees l and orders k*/</span></div><div class="line"><a name="l00113"></a><span class="lineno"> 113</span> </div><div class="line"><a name="l00114"></a><span class="lineno"><a class="line" href="wigner_8h.html#a9ab913c454dd078bed0db8b4aa9365e1"> 114</a></span> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="wigner_8h.html#a9ab913c454dd078bed0db8b4aa9365e1">SO3_alpha_matrix</a>(<span class="keywordtype">double</span> *alpha, <span class="keywordtype">int</span> N, <span class="keywordtype">int</span> m)</div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span> {</div><div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <span class="keywordtype">int</span> i, j;</div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="keywordtype">double</span> *alpha_act = alpha;</div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <span class="keywordflow">for</span> (i = -N; i <= N; i++)</div><div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  {</div><div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="keywordflow">for</span> (j = -1; j <= N; j++)</div><div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  {</div><div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  *alpha_act = <a class="code" href="wigner_8h.html#ab67e240f23c39daa7283fee9025a8f03">SO3_alpha</a>(i, m, j);</div><div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  alpha_act++;</div><div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  }</div><div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  }</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="l00128"></a><span class="lineno"><a class="line" href="wigner_8h.html#a742f6babb80797e003835bc66cfe9080"> 128</a></span> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="wigner_8h.html#a742f6babb80797e003835bc66cfe9080">SO3_beta_matrix</a>(<span class="keywordtype">double</span> *alpha, <span class="keywordtype">int</span> N, <span class="keywordtype">int</span> m)</div><div class="line"><a name="l00129"></a><span class="lineno"> 129</span> {</div><div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="keywordtype">int</span> i, j;</div><div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <span class="keywordtype">double</span> *alpha_act = alpha;</div><div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="keywordflow">for</span> (i = -N; i <= N; i++)</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>  <span class="keywordflow">for</span> (j = -1; j <= N; j++)</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>  *alpha_act = <a class="code" href="wigner_8h.html#a6722aa3212be1361b531751a850056f6">SO3_beta</a>(i, m, j);</div><div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  alpha_act++;</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>  }</div><div class="line"><a name="l00140"></a><span class="lineno"> 140</span> }</div><div class="line"><a name="l00141"></a><span class="lineno"> 141</span> </div><div class="line"><a name="l00142"></a><span class="lineno"><a class="line" href="wigner_8h.html#aa9850cfec93784e536a728f13db4c5cb"> 142</a></span> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="wigner_8h.html#aa9850cfec93784e536a728f13db4c5cb">SO3_gamma_matrix</a>(<span class="keywordtype">double</span> *alpha, <span class="keywordtype">int</span> N, <span class="keywordtype">int</span> m)</div><div class="line"><a name="l00143"></a><span class="lineno"> 143</span> {</div><div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  <span class="keywordtype">int</span> i, j;</div><div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  <span class="keywordtype">double</span> *alpha_act = alpha;</div><div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <span class="keywordflow">for</span> (i = -N; i <= N; i++)</div><div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  {</div><div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  <span class="keywordflow">for</span> (j = -1; j <= N; j++)</div><div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  {</div><div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  *alpha_act = <a class="code" href="wigner_8h.html#a6b13b24d727910800b9f1c0da29f5f73">SO3_gamma</a>(i, m, j);</div><div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  alpha_act++;</div><div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  }</div><div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  }</div><div class="line"><a name="l00154"></a><span class="lineno"> 154</span> }</div><div class="line"><a name="l00155"></a><span class="lineno"> 155</span> </div><div class="line"><a name="l00156"></a><span class="lineno"> 156</span> <span class="comment">/*compute all 3termrecurrence coeffs*/</span></div><div class="line"><a name="l00157"></a><span class="lineno"> 157</span> </div><div class="line"><a name="l00158"></a><span class="lineno"><a class="line" href="wigner_8h.html#aef802fd511b566392a8b2cbb9fcd6678"> 158</a></span> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="wigner_8h.html#aef802fd511b566392a8b2cbb9fcd6678">SO3_alpha_all</a>(<span class="keywordtype">double</span> *alpha, <span class="keywordtype">int</span> N)</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>  <span class="keywordtype">int</span> q;</div><div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  <span class="keywordtype">int</span> i, j, m;</div><div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  <span class="keywordtype">double</span> *alpha_act = alpha;</div><div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  q = 0;</div><div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  <span class="keywordflow">for</span> (m = -N; m <= N; m++)</div><div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  {</div><div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  <span class="keywordflow">for</span> (i = -N; i <= N; i++)</div><div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  {</div><div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  <span class="keywordflow">for</span> (j = -1; j <= N; j++)</div><div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  {</div><div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  *alpha_act = <a class="code" href="wigner_8h.html#ab67e240f23c39daa7283fee9025a8f03">SO3_alpha</a>(i, m, j);</div><div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  fprintf(stdout, <span class="stringliteral">"alpha_all_%d^[%d,%d]=%f\n"</span>, j, i, m,</div><div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <a class="code" href="wigner_8h.html#ab67e240f23c39daa7283fee9025a8f03">SO3_alpha</a>(i, m, j));</div><div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  alpha_act++;</div><div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  q = q + 1;</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>  }</div><div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  }</div><div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  }</div><div class="line"><a name="l00179"></a><span class="lineno"> 179</span> }</div><div class="line"><a name="l00180"></a><span class="lineno"> 180</span> </div><div class="line"><a name="l00181"></a><span class="lineno"><a class="line" href="wigner_8h.html#aa981c92edca3fac2f04a7d3524b8425a"> 181</a></span> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="wigner_8h.html#aa981c92edca3fac2f04a7d3524b8425a">SO3_beta_all</a>(<span class="keywordtype">double</span> *alpha, <span class="keywordtype">int</span> N)</div><div class="line"><a name="l00182"></a><span class="lineno"> 182</span> {</div><div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  <span class="keywordtype">int</span> i, j, m;</div><div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  <span class="keywordtype">double</span> *alpha_act = alpha;</div><div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  <span class="keywordflow">for</span> (m = -N; m <= N; m++)</div><div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  {</div><div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  <span class="keywordflow">for</span> (i = -N; i <= N; i++)</div><div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  {</div><div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  <span class="keywordflow">for</span> (j = -1; j <= N; j++)</div><div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  {</div><div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  *alpha_act = <a class="code" href="wigner_8h.html#a6722aa3212be1361b531751a850056f6">SO3_beta</a>(i, m, j);</div><div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  alpha_act++;</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>  }</div><div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  }</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> </div><div class="line"><a name="l00198"></a><span class="lineno"><a class="line" href="wigner_8h.html#a4ff3aa0c3afb226613100df410cbef7f"> 198</a></span> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="wigner_8h.html#a4ff3aa0c3afb226613100df410cbef7f">SO3_gamma_all</a>(<span class="keywordtype">double</span> *alpha, <span class="keywordtype">int</span> N)</div><div class="line"><a name="l00199"></a><span class="lineno"> 199</span> {</div><div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  <span class="keywordtype">int</span> i, j, m;</div><div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <span class="keywordtype">double</span> *alpha_act = alpha;</div><div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  <span class="keywordflow">for</span> (m = -N; m <= N; m++)</div><div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  {</div><div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  <span class="keywordflow">for</span> (i = -N; i <= N; i++)</div><div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  {</div><div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  <span class="keywordflow">for</span> (j = -1; j <= N; j++)</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>  *alpha_act = <a class="code" href="wigner_8h.html#a6b13b24d727910800b9f1c0da29f5f73">SO3_gamma</a>(i, m, j);</div><div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  alpha_act++;</div><div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  }</div><div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  }</div><div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  }</div><div class="line"><a name="l00213"></a><span class="lineno"> 213</span> }</div><div class="line"><a name="l00214"></a><span class="lineno"> 214</span> </div><div class="line"><a name="l00215"></a><span class="lineno"><a class="line" href="wigner_8h.html#a86975b8841ed9b6bb3e1484130658f19"> 215</a></span> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="wigner_8h.html#a86975b8841ed9b6bb3e1484130658f19">eval_wigner</a>(<span class="keywordtype">double</span> *x, <span class="keywordtype">double</span> *y, <span class="keywordtype">int</span> size, <span class="keywordtype">int</span> k, <span class="keywordtype">double</span> *alpha,</div><div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  <span class="keywordtype">double</span> *beta, <span class="keywordtype">double</span> *gamma)</div><div class="line"><a name="l00217"></a><span class="lineno"> 217</span> {</div><div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <span class="comment">/* Evaluate the wigner function d_{k,nleg} (l,x) for the vector</span></div><div class="line"><a name="l00219"></a><span class="lineno"> 219</span> <span class="comment"> * of knots x[0], ..., x[size-1] by the Clenshaw algorithm</span></div><div class="line"><a name="l00220"></a><span class="lineno"> 220</span> <span class="comment"> */</span></div><div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  <span class="keywordtype">int</span> i, j;</div><div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  <span class="keywordtype">double</span> a, b, x_val_act, a_old;</div><div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  <span class="keywordtype">double</span> *x_act, *y_act;</div><div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  <span class="keywordtype">double</span> *alpha_act, *beta_act, *gamma_act;</div><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">/* Traverse all nodes. */</span></div><div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  x_act = x;</div><div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  y_act = y;</div><div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  <span class="keywordflow">for</span> (i = 0; i < size; i++)</div><div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  {</div><div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  a = 1.0;</div><div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  b = 0.0;</div><div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  x_val_act = *x_act;</div><div class="line"><a name="l00234"></a><span class="lineno"> 234</span> </div><div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  <span class="keywordflow">if</span> (k == 0)</div><div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  {</div><div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  *y_act = 1.0;</div><div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  }</div><div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  {</div><div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  alpha_act = &(alpha[k]);</div><div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  beta_act = &(beta[k]);</div><div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  gamma_act = &(gamma[k]);</div><div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  <span class="keywordflow">for</span> (j = k; j > 1; j--)</div><div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  {</div><div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  a_old = a;</div><div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  a = b + a_old * ((*alpha_act) * x_val_act + (*beta_act));</div><div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  b = a_old * (*gamma_act);</div><div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  alpha_act--;</div><div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  beta_act--;</div><div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  gamma_act--;</div><div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  }</div><div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  *y_act = (a * ((*alpha_act) * x_val_act + (*beta_act)) + b);</div><div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  }</div><div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  x_act++;</div><div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  y_act++;</div><div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  }</div><div class="line"><a name="l00258"></a><span class="lineno"> 258</span> }</div><div class="line"><a name="l00259"></a><span class="lineno"> 259</span> </div><div class="line"><a name="l00260"></a><span class="lineno"><a class="line" href="wigner_8h.html#ae5933af03f4536a70ddfc744f16c9c55"> 260</a></span> <span class="keyword">inline</span> <span class="keywordtype">int</span> <a class="code" href="wigner_8h.html#ae5933af03f4536a70ddfc744f16c9c55">eval_wigner_thresh</a>(<span class="keywordtype">double</span> *x, <span class="keywordtype">double</span> *y, <span class="keywordtype">int</span> size, <span class="keywordtype">int</span> k,</div><div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  <span class="keywordtype">double</span> *alpha, <span class="keywordtype">double</span> *beta, <span class="keywordtype">double</span> *gamma, <span class="keywordtype">double</span> threshold)</div><div class="line"><a name="l00262"></a><span class="lineno"> 262</span> {</div><div class="line"><a name="l00263"></a><span class="lineno"> 263</span> </div><div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  <span class="keywordtype">int</span> i, j;</div><div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  <span class="keywordtype">double</span> a, b, x_val_act, a_old;</div><div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  <span class="keywordtype">double</span> *x_act, *y_act;</div><div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  <span class="keywordtype">double</span> *alpha_act, *beta_act, *gamma_act;</div><div class="line"><a name="l00268"></a><span class="lineno"> 268</span> </div><div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  <span class="comment">/* Traverse all nodes. */</span></div><div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  x_act = x;</div><div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  y_act = y;</div><div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  <span class="keywordflow">for</span> (i = 0; i < size; i++)</div><div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  {</div><div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  a = 1.0;</div><div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  b = 0.0;</div><div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  x_val_act = *x_act;</div><div class="line"><a name="l00277"></a><span class="lineno"> 277</span> </div><div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  <span class="keywordflow">if</span> (k == 0)</div><div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  {</div><div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  *y_act = 1.0;</div><div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  }</div><div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  {</div><div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  alpha_act = &(alpha[k]);</div><div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  beta_act = &(beta[k]);</div><div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  gamma_act = &(gamma[k]);</div><div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  <span class="keywordflow">for</span> (j = k; j > 1; j--)</div><div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  {</div><div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  a_old = a;</div><div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  a = b + a_old * ((*alpha_act) * x_val_act + (*beta_act));</div><div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  b = a_old * (*gamma_act);</div><div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  alpha_act--;</div><div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  beta_act--;</div><div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  gamma_act--;</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>  *y_act = (a * ((*alpha_act) * x_val_act + (*beta_act)) + b);</div><div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  <span class="keywordflow">if</span> (fabs(*y_act) > threshold)</div><div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  {</div><div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  <span class="keywordflow">return</span> 1;</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>  x_act++;</div><div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  y_act++;</div><div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  }</div><div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  <span class="keywordflow">return</span> 0;</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> </div><div class="line"><a name="l00308"></a><span class="lineno"> 308</span> <span class="comment">/************************************************************************/</span></div><div class="line"><a name="l00309"></a><span class="lineno"> 309</span> <span class="comment">/* L2 normed wigner little d, WHERE THE DEGREE OF THE FUNCTION IS EQUAL</span></div><div class="line"><a name="l00310"></a><span class="lineno"> 310</span> <span class="comment"> TO ONE OF ITS ORDERS. This is the function to use when starting the</span></div><div class="line"><a name="l00311"></a><span class="lineno"> 311</span> <span class="comment"> three-term recurrence at orders (m1,m2)</span></div><div class="line"><a name="l00312"></a><span class="lineno"> 312</span> <span class="comment"></span></div><div class="line"><a name="l00313"></a><span class="lineno"> 313</span> <span class="comment"> Note that, by definition, since I am starting the recurrence with this</span></div><div class="line"><a name="l00314"></a><span class="lineno"> 314</span> <span class="comment"> function, that the degree j of the function is equal to max(abs(m1), abs(m2) ).</span></div><div class="line"><a name="l00315"></a><span class="lineno"> 315</span> <span class="comment"> */</span></div><div class="line"><a name="l00316"></a><span class="lineno"> 316</span> </div><div class="line"><a name="l00317"></a><span class="lineno"><a class="line" href="wigner_8h.html#a6c43c1f82cf3efa9cb1343ec9dcd07ed"> 317</a></span> <span class="keywordtype">double</span> <a class="code" href="wigner_8h.html#a6c43c1f82cf3efa9cb1343ec9dcd07ed">wigner_start</a>(<span class="keywordtype">int</span> m1, <span class="keywordtype">int</span> m2, <span class="keywordtype">double</span> theta)</div><div class="line"><a name="l00318"></a><span class="lineno"> 318</span> {</div><div class="line"><a name="l00319"></a><span class="lineno"> 319</span> </div><div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  <span class="keywordtype">int</span> i, l, delta;</div><div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  <span class="keywordtype">int</span> cosPower, sinPower;</div><div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  <span class="keywordtype">int</span> absM1, absM2;</div><div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  <span class="keywordtype">double</span> dl, dm1, dm2, normFactor, sinSign;</div><div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  <span class="keywordtype">double</span> dCP, dSP;</div><div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  <span class="keywordtype">double</span> max;</div><div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  <span class="keywordtype">double</span> min;</div><div class="line"><a name="l00327"></a><span class="lineno"> 327</span> </div><div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  max = (double) (ABS(m1) > ABS(m2) ? ABS(m1) : ABS(m2));</div><div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  min = (double) (ABS(m1) < ABS(m2) ? ABS(m1) : ABS(m2));</div><div class="line"><a name="l00330"></a><span class="lineno"> 330</span> </div><div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  l = max;</div><div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  delta = l - min;</div><div class="line"><a name="l00333"></a><span class="lineno"> 333</span> </div><div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  absM1 = ABS(m1);</div><div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  absM2 = ABS(m2);</div><div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  dl = (double) l;</div><div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  dm1 = (double) m1;</div><div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  dm2 = (double) m2;</div><div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  sinSign = 1.;</div><div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  normFactor = 1.;</div><div class="line"><a name="l00341"></a><span class="lineno"> 341</span> </div><div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  <span class="keywordflow">for</span> (i = 0; i < delta; i++)</div><div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  normFactor *= SQRT((2. * dl - ((<span class="keywordtype">double</span>) i)) / (((double) i) + 1.));</div><div class="line"><a name="l00344"></a><span class="lineno"> 344</span> </div><div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  <span class="comment">/* need to adjust to make the L2-norm equal to 1 */</span></div><div class="line"><a name="l00346"></a><span class="lineno"> 346</span> </div><div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  normFactor *= SQRT((2. * dl + 1.) / 2.);</div><div class="line"><a name="l00348"></a><span class="lineno"> 348</span> </div><div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  <span class="keywordflow">if</span> (l == absM1)</div><div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  <span class="keywordflow">if</span> (m1 >= 0)</div><div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  {</div><div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  cosPower = l + m2;</div><div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  sinPower = l - m2;</div><div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  <span class="keywordflow">if</span> ((l - m2) % 2)</div><div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  sinSign = -1.;</div><div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  }</div><div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  {</div><div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  cosPower = l - m2;</div><div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  sinPower = l + m2;</div><div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  }</div><div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (m2 >= 0)</div><div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  {</div><div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  cosPower = l + m1;</div><div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  sinPower = l - m1;</div><div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  }</div><div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  {</div><div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  cosPower = l - m1;</div><div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  sinPower = l + m1;</div><div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  <span class="keywordflow">if</span> ((l + m1) % 2)</div><div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  sinSign = -1.;</div><div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  }</div><div class="line"><a name="l00374"></a><span class="lineno"> 374</span> </div><div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  dCP = (double) cosPower;</div><div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  dSP = (double) sinPower;</div><div class="line"><a name="l00377"></a><span class="lineno"> 377</span> </div><div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  <span class="keywordflow">return</span> normFactor * sinSign * POW(sin(theta / 2), dSP) * POW(cos(theta / 2),</div><div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  dCP);</div><div class="line"><a name="l00380"></a><span class="lineno"> 380</span> }</div><div class="ttc" id="wigner_8h_html_a6c43c1f82cf3efa9cb1343ec9dcd07ed"><div class="ttname"><a href="wigner_8h.html#a6c43c1f82cf3efa9cb1343ec9dcd07ed">wigner_start</a></div><div class="ttdeci">double wigner_start(int n1, int n2, double theta)</div><div class="ttdoc">A method used for debugging, gives the values to start the "old" three-term recurrence generates WHE...</div><div class="ttdef"><b>Definition:</b> <a href="wigner_8c_source.html#l00317">wigner.c:317</a></div></div>
<div class="ttc" id="wigner_8h_html_a46516d6ec71efab3c80eecd459ad20ee"><div class="ttname"><a href="wigner_8h.html#a46516d6ec71efab3c80eecd459ad20ee">SO3_gamma_row</a></div><div class="ttdeci">void SO3_gamma_row(double *gamma, int N, int m, int n)</div><div class="ttdoc">Compute three-term-recurrence coefficients of Wigner-d functions for all degrees ...</div><div class="ttdef"><b>Definition:</b> <a href="wigner_8c_source.html#l00104">wigner.c:104</a></div></div>
<div class="ttc" id="wigner_8h_html_aa9850cfec93784e536a728f13db4c5cb"><div class="ttname"><a href="wigner_8h.html#aa9850cfec93784e536a728f13db4c5cb">SO3_gamma_matrix</a></div><div class="ttdeci">void SO3_gamma_matrix(double *gamma, int N, int n)</div><div class="ttdoc">Compute three-term-recurrence coefficients of Wigner-d functions for all order and degrees ...</div><div class="ttdef"><b>Definition:</b> <a href="wigner_8c_source.html#l00142">wigner.c:142</a></div></div>
<div class="ttc" id="wigner_8h_html_aef802fd511b566392a8b2cbb9fcd6678"><div class="ttname"><a href="wigner_8h.html#aef802fd511b566392a8b2cbb9fcd6678">SO3_alpha_all</a></div><div class="ttdeci">void SO3_alpha_all(double *alpha, int N)</div><div class="ttdoc">Compute three-term-recurrence coefficients of Wigner-d functions for all and . </div><div class="ttdef"><b>Definition:</b> <a href="wigner_8c_source.html#l00158">wigner.c:158</a></div></div>
<div class="ttc" id="wigner_8h_html_a1b82e072be0c3e0d45426ed56e4e6a9d"><div class="ttname"><a href="wigner_8h.html#a1b82e072be0c3e0d45426ed56e4e6a9d">SO3_beta_row</a></div><div class="ttdeci">void SO3_beta_row(double *beta, int N, int m, int n)</div><div class="ttdoc">Compute three-term-recurrence coefficients of Wigner-d functions for all degrees ...</div><div class="ttdef"><b>Definition:</b> <a href="wigner_8c_source.html#l00096">wigner.c:96</a></div></div>
<div class="ttc" id="wigner_8h_html_a9ab913c454dd078bed0db8b4aa9365e1"><div class="ttname"><a href="wigner_8h.html#a9ab913c454dd078bed0db8b4aa9365e1">SO3_alpha_matrix</a></div><div class="ttdeci">void SO3_alpha_matrix(double *alpha, int N, int n)</div><div class="ttdoc">Compute three-term-recurrence coefficients of Wigner-d functions for all order and degrees ...</div><div class="ttdef"><b>Definition:</b> <a href="wigner_8c_source.html#l00114">wigner.c:114</a></div></div>
<div class="ttc" id="wigner_8h_html_a4ff3aa0c3afb226613100df410cbef7f"><div class="ttname"><a href="wigner_8h.html#a4ff3aa0c3afb226613100df410cbef7f">SO3_gamma_all</a></div><div class="ttdeci">void SO3_gamma_all(double *gamma, int N)</div><div class="ttdoc">Compute three-term-recurrence coefficients of Wigner-d functions for all and . </div><div class="ttdef"><b>Definition:</b> <a href="wigner_8c_source.html#l00198">wigner.c:198</a></div></div>
<div class="ttc" id="wigner_8h_html_ab67e240f23c39daa7283fee9025a8f03"><div class="ttname"><a href="wigner_8h.html#ab67e240f23c39daa7283fee9025a8f03">SO3_alpha</a></div><div class="ttdeci">double SO3_alpha(int k, int m, int l)</div><div class="ttdoc">Computes three-term recurrence coefficients of Wigner-d functions. </div><div class="ttdef"><b>Definition:</b> <a href="wigner_8c_source.html#l00025">wigner.c:25</a></div></div>
<div class="ttc" id="wigner_8h_html_a6722aa3212be1361b531751a850056f6"><div class="ttname"><a href="wigner_8h.html#a6722aa3212be1361b531751a850056f6">SO3_beta</a></div><div class="ttdeci">double SO3_beta(int k, int m, int l)</div><div class="ttdoc">Computes three-term recurrence coefficients of Wigner-d functions. </div><div class="ttdef"><b>Definition:</b> <a href="wigner_8c_source.html#l00052">wigner.c:52</a></div></div>
<div class="ttc" id="wigner_8h_html_a6b13b24d727910800b9f1c0da29f5f73"><div class="ttname"><a href="wigner_8h.html#a6b13b24d727910800b9f1c0da29f5f73">SO3_gamma</a></div><div class="ttdeci">double SO3_gamma(int k, int m, int l)</div><div class="ttdoc">Computes three-term recurrence coefficients of Wigner-d functions. </div><div class="ttdef"><b>Definition:</b> <a href="wigner_8c_source.html#l00073">wigner.c:73</a></div></div>
<div class="ttc" id="wigner_8h_html_ae9c3c9a11f1da35bb0cfbed1fb828ad2"><div class="ttname"><a href="wigner_8h.html#ae9c3c9a11f1da35bb0cfbed1fb828ad2">SO3_alpha_row</a></div><div class="ttdeci">void SO3_alpha_row(double *alpha, int N, int m, int n)</div><div class="ttdoc">Compute three-term-recurrence coefficients of Wigner-d functions for all degrees ...</div><div class="ttdef"><b>Definition:</b> <a href="wigner_8c_source.html#l00088">wigner.c:88</a></div></div>
<div class="ttc" id="wigner_8h_html_a742f6babb80797e003835bc66cfe9080"><div class="ttname"><a href="wigner_8h.html#a742f6babb80797e003835bc66cfe9080">SO3_beta_matrix</a></div><div class="ttdeci">void SO3_beta_matrix(double *beta, int N, int n)</div><div class="ttdoc">Compute three-term-recurrence coefficients of Wigner-d functions for all order and degrees ...</div><div class="ttdef"><b>Definition:</b> <a href="wigner_8c_source.html#l00128">wigner.c:128</a></div></div>
<div class="ttc" id="wigner_8h_html_aa981c92edca3fac2f04a7d3524b8425a"><div class="ttname"><a href="wigner_8h.html#aa981c92edca3fac2f04a7d3524b8425a">SO3_beta_all</a></div><div class="ttdeci">void SO3_beta_all(double *beta, int N)</div><div class="ttdoc">Compute three-term-recurrence coefficients of Wigner-d functions for all and . </div><div class="ttdef"><b>Definition:</b> <a href="wigner_8c_source.html#l00181">wigner.c:181</a></div></div>
<div class="ttc" id="wigner_8h_html_ae5933af03f4536a70ddfc744f16c9c55"><div class="ttname"><a href="wigner_8h.html#ae5933af03f4536a70ddfc744f16c9c55">eval_wigner_thresh</a></div><div class="ttdeci">int eval_wigner_thresh(double *x, double *y, int size, int l, double *alpha, double *beta, double *gamma, double threshold)</div><div class="ttdoc">Evaluates Wigner-d functions using the Clenshaw-algorithm if it not exceeds a given threshold...</div><div class="ttdef"><b>Definition:</b> <a href="wigner_8c_source.html#l00260">wigner.c:260</a></div></div>
<div class="ttc" id="wigner_8h_html"><div class="ttname"><a href="wigner_8h.html">wigner.h</a></div><div class="ttdoc">Header file for functions related to Wigner-d/D functions. </div></div>
<div class="ttc" id="wigner_8h_html_a86975b8841ed9b6bb3e1484130658f19"><div class="ttname"><a href="wigner_8h.html#a86975b8841ed9b6bb3e1484130658f19">eval_wigner</a></div><div class="ttdeci">void eval_wigner(double *x, double *y, int size, int l, double *alpha, double *beta, double *gamma)</div><div class="ttdoc">Evaluates Wigner-d functions using the Clenshaw-algorithm. </div><div class="ttdef"><b>Definition:</b> <a href="wigner_8c_source.html#l00215">wigner.c:215</a></div></div>
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