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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">/*</span></div><div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<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>&#160;<span class="comment"> *</span></div><div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<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>&#160;<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>&#160;<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>&#160;<span class="comment"> * version.</span></div><div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment"> *</span></div><div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<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>&#160;<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>&#160;<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>&#160;<span class="comment"> * details.</span></div><div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="comment"> *</span></div><div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<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>&#160;<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>&#160;<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>&#160;<span class="comment"> */</span></div><div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;</div><div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="preprocessor">#include &lt;math.h&gt;</span></div><div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="preprocessor">#include &lt;stdio.h&gt;</span></div><div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="preprocessor">#include &quot;infft.h&quot;</span></div><div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="wigner_8h.html">wigner.h</a>&quot;</span></div><div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;<span class="preprocessor">#include &quot;infft.h&quot;</span></div><div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;</div><div class="line"><a name="l00025"></a><span class="lineno"><a class="line" href="wigner_8h.html#ab67e240f23c39daa7283fee9025a8f03">   25</a></span>&#160;<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>&#160;{</div><div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;  <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>&#160;</div><div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;  <span class="keywordflow">if</span> (j &lt; 0)</div><div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;    <span class="keywordflow">return</span> K(0.0);</div><div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;  <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>&#160;  {</div><div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;    <span class="keywordflow">if</span> (m1 == 0 &amp;&amp; m2 == 0)</div><div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;      <span class="keywordflow">return</span> K(1.0);</div><div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;    <span class="keywordflow">if</span> (m1 == m2)</div><div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;      <span class="keywordflow">return</span> K(0.5);</div><div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;    <span class="keywordflow">else</span></div><div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;      <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>&#160;  }</div><div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (j &lt; M - mini)</div><div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;    <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>&#160;  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (j &lt; M)</div><div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;    <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>&#160;  <span class="keywordflow">else</span></div><div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;    <span class="keywordflow">return</span></div><div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;      SQRT(((R)(j+1))/((R)(j+1-m1)))</div><div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;      * SQRT(((R)(2*j+1))/((R)(j+1+m1)))</div><div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;      * SQRT(((R)(j+1))/((R)(j+1-m2)))</div><div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;      * SQRT(((R)(2*j+1))/((R)(j+1+m2)));</div><div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;}</div><div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;</div><div class="line"><a name="l00052"></a><span class="lineno"><a class="line" href="wigner_8h.html#a6722aa3212be1361b531751a850056f6">   52</a></span>&#160;<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>&#160;{</div><div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;  <span class="keywordflow">if</span> (j &lt; 0)</div><div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;    <span class="keywordflow">return</span> K(0.0);</div><div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (j &lt; MAX(ABS(m1),ABS(m2)))</div><div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;    <span class="keywordflow">return</span> K(0.5);</div><div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;  <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>&#160;    <span class="keywordflow">return</span> K(0.0);</div><div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;  <span class="keywordflow">else</span></div><div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;  {</div><div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;    <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>&#160;    <span class="keywordflow">return</span> -COPYSIGN(</div><div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;      ((SQRT(m1a)*SQRT(m2a))/((R)j))</div><div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;      * SQRT(m1a/((R)(j+1-m1)))</div><div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;      * SQRT(((R)(2*j+1))/((R)(j+1+m1)))</div><div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;      * SQRT(m2a/((R)(j+1-m2)))</div><div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;      * SQRT(((R)(2*j+1))/((R)(j+1+m2))),</div><div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;      SIGNF((R)m1)*SIGNF((R)m2));</div><div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;  }</div><div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;}</div><div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;</div><div class="line"><a name="l00073"></a><span class="lineno"><a class="line" href="wigner_8h.html#a6b13b24d727910800b9f1c0da29f5f73">   73</a></span>&#160;<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>&#160;{</div><div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;  <span class="keywordflow">if</span> (MAX(ABS(m1),ABS(m2)) &lt; j)</div><div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;    <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>&#160;        *(((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>&#160;        *(((R)(j+m2))/((R)(j+1+m2))));</div><div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;  <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>&#160;    <span class="keywordflow">return</span> IF(m1 &gt; m2 || !((m1 + m2) % 2), K(1.0), K(-1.0))</div><div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;      * nfft_lambda2((R)ABS(m2 - m1),(R)ABS(m2 + m1));</div><div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;  <span class="keywordflow">else</span></div><div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;    <span class="keywordflow">return</span> K(0.0);</div><div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;}</div><div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;</div><div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;<span class="comment">/*compute the coefficients for all degrees*/</span></div><div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;</div><div class="line"><a name="l00088"></a><span class="lineno"><a class="line" href="wigner_8h.html#ae9c3c9a11f1da35bb0cfbed1fb828ad2">   88</a></span>&#160;<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>&#160;{</div><div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;  <span class="keywordtype">int</span> j;</div><div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;  <span class="keywordtype">double</span> *alpha_act = alpha;</div><div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;  <span class="keywordflow">for</span> (j = -1; j &lt;= N; j++)</div><div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;    *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>&#160;}</div><div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;</div><div class="line"><a name="l00096"></a><span class="lineno"><a class="line" href="wigner_8h.html#a1b82e072be0c3e0d45426ed56e4e6a9d">   96</a></span>&#160;<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>&#160;{</div><div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;  <span class="keywordtype">int</span> j;</div><div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;  <span class="keywordtype">double</span> *beta_act = beta;</div><div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;  <span class="keywordflow">for</span> (j = -1; j &lt;= N; j++)</div><div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;    *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>&#160;}</div><div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;</div><div class="line"><a name="l00104"></a><span class="lineno"><a class="line" href="wigner_8h.html#a46516d6ec71efab3c80eecd459ad20ee">  104</a></span>&#160;<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>&#160;{</div><div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;  <span class="keywordtype">int</span> j;</div><div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;  <span class="keywordtype">double</span> *gamma_act = gamma;</div><div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;  <span class="keywordflow">for</span> (j = -1; j &lt;= N; j++)</div><div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;    *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>&#160;}</div><div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;</div><div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;<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>&#160;</div><div class="line"><a name="l00114"></a><span class="lineno"><a class="line" href="wigner_8h.html#a9ab913c454dd078bed0db8b4aa9365e1">  114</a></span>&#160;<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>&#160;{</div><div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;  <span class="keywordtype">int</span> i, j;</div><div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;  <span class="keywordtype">double</span> *alpha_act = alpha;</div><div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;  <span class="keywordflow">for</span> (i = -N; i &lt;= N; i++)</div><div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;  {</div><div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;    <span class="keywordflow">for</span> (j = -1; j &lt;= N; j++)</div><div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;    {</div><div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;      *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>&#160;      alpha_act++;</div><div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;    }</div><div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;  }</div><div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;}</div><div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;</div><div class="line"><a name="l00128"></a><span class="lineno"><a class="line" href="wigner_8h.html#a742f6babb80797e003835bc66cfe9080">  128</a></span>&#160;<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>&#160;{</div><div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;  <span class="keywordtype">int</span> i, j;</div><div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;  <span class="keywordtype">double</span> *alpha_act = alpha;</div><div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;  <span class="keywordflow">for</span> (i = -N; i &lt;= N; i++)</div><div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;  {</div><div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;    <span class="keywordflow">for</span> (j = -1; j &lt;= N; j++)</div><div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;    {</div><div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;      *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>&#160;      alpha_act++;</div><div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;    }</div><div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;  }</div><div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;}</div><div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;</div><div class="line"><a name="l00142"></a><span class="lineno"><a class="line" href="wigner_8h.html#aa9850cfec93784e536a728f13db4c5cb">  142</a></span>&#160;<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>&#160;{</div><div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;  <span class="keywordtype">int</span> i, j;</div><div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;  <span class="keywordtype">double</span> *alpha_act = alpha;</div><div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;  <span class="keywordflow">for</span> (i = -N; i &lt;= N; i++)</div><div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;  {</div><div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;    <span class="keywordflow">for</span> (j = -1; j &lt;= N; j++)</div><div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;    {</div><div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;      *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>&#160;      alpha_act++;</div><div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;    }</div><div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;  }</div><div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;}</div><div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;</div><div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;<span class="comment">/*compute all 3termrecurrence coeffs*/</span></div><div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;</div><div class="line"><a name="l00158"></a><span class="lineno"><a class="line" href="wigner_8h.html#aef802fd511b566392a8b2cbb9fcd6678">  158</a></span>&#160;<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>&#160;{</div><div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;  <span class="keywordtype">int</span> q;</div><div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;  <span class="keywordtype">int</span> i, j, m;</div><div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;  <span class="keywordtype">double</span> *alpha_act = alpha;</div><div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;  q = 0;</div><div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;  <span class="keywordflow">for</span> (m = -N; m &lt;= N; m++)</div><div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;  {</div><div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;    <span class="keywordflow">for</span> (i = -N; i &lt;= N; i++)</div><div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;    {</div><div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;      <span class="keywordflow">for</span> (j = -1; j &lt;= N; j++)</div><div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;      {</div><div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;        *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>&#160;        fprintf(stdout, <span class="stringliteral">&quot;alpha_all_%d^[%d,%d]=%f\n&quot;</span>, j, i, m,</div><div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;            <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>&#160;        alpha_act++;</div><div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;        q = q + 1;</div><div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;</div><div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;      }</div><div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;    }</div><div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;  }</div><div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;}</div><div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;</div><div class="line"><a name="l00181"></a><span class="lineno"><a class="line" href="wigner_8h.html#aa981c92edca3fac2f04a7d3524b8425a">  181</a></span>&#160;<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>&#160;{</div><div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;  <span class="keywordtype">int</span> i, j, m;</div><div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;  <span class="keywordtype">double</span> *alpha_act = alpha;</div><div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;  <span class="keywordflow">for</span> (m = -N; m &lt;= N; m++)</div><div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;  {</div><div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;    <span class="keywordflow">for</span> (i = -N; i &lt;= N; i++)</div><div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;    {</div><div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;      <span class="keywordflow">for</span> (j = -1; j &lt;= N; j++)</div><div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;      {</div><div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;        *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>&#160;        alpha_act++;</div><div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;      }</div><div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;    }</div><div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;  }</div><div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;}</div><div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;</div><div class="line"><a name="l00198"></a><span class="lineno"><a class="line" href="wigner_8h.html#a4ff3aa0c3afb226613100df410cbef7f">  198</a></span>&#160;<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>&#160;{</div><div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;  <span class="keywordtype">int</span> i, j, m;</div><div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;  <span class="keywordtype">double</span> *alpha_act = alpha;</div><div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;  <span class="keywordflow">for</span> (m = -N; m &lt;= N; m++)</div><div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;  {</div><div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;    <span class="keywordflow">for</span> (i = -N; i &lt;= N; i++)</div><div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;    {</div><div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;      <span class="keywordflow">for</span> (j = -1; j &lt;= N; j++)</div><div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;      {</div><div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;        *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>&#160;        alpha_act++;</div><div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;      }</div><div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;    }</div><div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;  }</div><div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;}</div><div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;</div><div class="line"><a name="l00215"></a><span class="lineno"><a class="line" href="wigner_8h.html#a86975b8841ed9b6bb3e1484130658f19">  215</a></span>&#160;<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>&#160;    <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>&#160;{</div><div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;  <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>&#160;<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>&#160;<span class="comment">   */</span></div><div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;  <span class="keywordtype">int</span> i, j;</div><div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;  <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>&#160; 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       gamma_act--;</div><div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;      }</div><div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;      *y_act = (a * ((*alpha_act) * x_val_act + (*beta_act)) + b);</div><div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;    }</div><div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;    x_act++;</div><div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;    y_act++;</div><div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;  }</div><div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;}</div><div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;</div><div class="line"><a name="l00260"></a><span class="lineno"><a class="line" href="wigner_8h.html#ae5933af03f4536a70ddfc744f16c9c55">  260</a></span>&#160;<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>&#160;    <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>&#160;{</div><div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;</div><div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;  <span class="keywordtype">int</span> i, j;</div><div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;  <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>&#160;  <span class="keywordtype">double</span> *x_act, *y_act;</div><div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;  <span class="keywordtype">double</span> *alpha_act, *beta_act, *gamma_act;</div><div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;</div><div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;  <span class="comment">/* Traverse all nodes. */</span></div><div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;  x_act = x;</div><div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;  y_act = y;</div><div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;  <span class="keywordflow">for</span> (i = 0; i &lt; size; i++)</div><div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;  {</div><div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;    a = 1.0;</div><div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;    b = 0.0;</div><div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;    x_val_act = *x_act;</div><div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;</div><div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;    <span class="keywordflow">if</span> (k == 0)</div><div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;    {</div><div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;      *y_act = 1.0;</div><div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;    }</div><div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;    <span class="keywordflow">else</span></div><div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;    {</div><div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;      alpha_act = &amp;(alpha[k]);</div><div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;      beta_act = &amp;(beta[k]);</div><div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;      gamma_act = &amp;(gamma[k]);</div><div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;      <span class="keywordflow">for</span> (j = k; j &gt; 1; j--)</div><div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;      {</div><div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;        a_old = a;</div><div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;        a = b + a_old * ((*alpha_act) * x_val_act + (*beta_act));</div><div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;        b = a_old * (*gamma_act);</div><div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;        alpha_act--;</div><div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;        beta_act--;</div><div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;        gamma_act--;</div><div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;      }</div><div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;      *y_act = (a * ((*alpha_act) * x_val_act + (*beta_act)) + b);</div><div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;      <span class="keywordflow">if</span> (fabs(*y_act) &gt; threshold)</div><div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;      {</div><div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;        <span class="keywordflow">return</span> 1;</div><div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;      }</div><div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;    }</div><div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;    x_act++;</div><div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;    y_act++;</div><div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;  }</div><div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;  <span class="keywordflow">return</span> 0;</div><div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;}</div><div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;</div><div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;<span class="comment">/************************************************************************/</span></div><div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;<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>&#160;<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>&#160;<span class="comment"> three-term recurrence at orders (m1,m2)</span></div><div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;<span class="comment"></span></div><div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;<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>&#160;<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>&#160;<span class="comment"> */</span></div><div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;</div><div class="line"><a name="l00317"></a><span class="lineno"><a class="line" href="wigner_8h.html#a6c43c1f82cf3efa9cb1343ec9dcd07ed">  317</a></span>&#160;<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>&#160;{</div><div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;</div><div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;  <span class="keywordtype">int</span> i, l, delta;</div><div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;  <span class="keywordtype">int</span> cosPower, sinPower;</div><div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;  <span class="keywordtype">int</span> absM1, absM2;</div><div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;  <span class="keywordtype">double</span> dl, dm1, dm2, normFactor, sinSign;</div><div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;  <span class="keywordtype">double</span> dCP, dSP;</div><div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;  <span class="keywordtype">double</span> max;</div><div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;  <span class="keywordtype">double</span> min;</div><div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;</div><div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;  max = (double) (ABS(m1) &gt; ABS(m2) ? ABS(m1) : ABS(m2));</div><div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;  min = (double) (ABS(m1) &lt; ABS(m2) ? ABS(m1) : ABS(m2));</div><div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;</div><div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;  l = max;</div><div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;  delta = l - min;</div><div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;</div><div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;  absM1 = ABS(m1);</div><div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;  absM2 = ABS(m2);</div><div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;  dl = (double) l;</div><div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;  dm1 = (double) m1;</div><div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;  dm2 = (double) m2;</div><div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;  sinSign = 1.;</div><div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;  normFactor = 1.;</div><div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;</div><div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;  <span class="keywordflow">for</span> (i = 0; i &lt; delta; i++)</div><div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;    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>&#160;</div><div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;  <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>&#160;</div><div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;  normFactor *= SQRT((2. * dl + 1.) / 2.);</div><div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;</div><div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;  <span class="keywordflow">if</span> (l == absM1)</div><div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;    <span class="keywordflow">if</span> (m1 &gt;= 0)</div><div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;    {</div><div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;      cosPower = l + m2;</div><div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;      sinPower = l - m2;</div><div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;      <span class="keywordflow">if</span> ((l - m2) % 2)</div><div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;        sinSign = -1.;</div><div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;    }</div><div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;    <span class="keywordflow">else</span></div><div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;    {</div><div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;      cosPower = l - m2;</div><div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;      sinPower = l + m2;</div><div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;    }</div><div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (m2 &gt;= 0)</div><div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;  {</div><div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;    cosPower = l + m1;</div><div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;    sinPower = l - m1;</div><div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;  }</div><div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;  <span class="keywordflow">else</span></div><div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;  {</div><div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;    cosPower = l - m1;</div><div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;    sinPower = l + m1;</div><div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;    <span class="keywordflow">if</span> ((l + m1) % 2)</div><div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;      sinSign = -1.;</div><div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;  }</div><div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;</div><div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;  dCP = (double) cosPower;</div><div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;  dSP = (double) sinPower;</div><div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;</div><div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;  <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>&#160;      dCP);</div><div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;}</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 &quot;old&quot; 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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