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<div class="header">
<div class="headertitle"><div class="title">SH.h</div></div>
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<div class="contents">
<a href="_s_h_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">/* Copyright (c) 2008-2022 the MRtrix3 contributors.</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment"> *</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment"> * This Source Code Form is subject to the terms of the Mozilla Public</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment"> * License, v. 2.0. If a copy of the MPL was not distributed with this</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment"> * file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment"> *</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment"> * Covered Software is provided under this License on an "as is"</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment"> * basis, without warranty of any kind, either expressed, implied, or</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment"> * statutory, including, without limitation, warranties that the</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment"> * Covered Software is free of defects, merchantable, fit for a</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment"> * particular purpose or non-infringing.</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment"> * See the Mozilla Public License v. 2.0 for more details.</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="comment"> *</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="comment"> * For more details, see http://www.mrtrix.org/.</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="comment"> */</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span> </div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#ifndef __math_SH_h__</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#define __math_SH_h__</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> </div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#include "<a class="code" href="legendre_8h.html">math/legendre.h</a>"</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#include "<a class="code" href="least__squares_8h.html">math/least_squares.h</a>"</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span> </div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"><a class="line" href="_s_h_8h.html#a4ee2d519e14dc95a5ed11efa93fe465f"> 23</a></span><span class="preprocessor">#define MAX_DIR_CHANGE 0.2</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"><a class="line" href="_s_h_8h.html#a5835d2253221816d4f18e65f9796d3c6"> 24</a></span><span class="preprocessor">#define ANGLE_TOLERANCE 1e-4</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> </div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespace_m_r.html">MR</a></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span>{</div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> <span class="keyword">namespace </span>Math</div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> {</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"><a class="line" href="namespace_m_r_1_1_math_1_1_s_h.html"> 30</a></span> <span class="keyword">namespace </span>SH</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> {</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> </div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> </div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <span class="keyword">extern</span> <span class="keyword">const</span> <span class="keywordtype">char</span>* <a class="code hl_variable" href="group__spherical__harmonics.html#gaafe2e54ee9df648cfb1372aa7ae2fa6a">encoding_description</a>;</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> </div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"><a class="line" href="group__spherical__harmonics.html#ga96a93012c20066bfbdb6c1a1ec1cfe15"> 46</a></span> <span class="keyword">inline</span> <span class="keywordtype">size_t</span> <a class="code hl_function" href="group__spherical__harmonics.html#ga96a93012c20066bfbdb6c1a1ec1cfe15">NforL</a> (<span class="keywordtype">int</span> lmax)</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> {</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <span class="keywordflow">return</span> (lmax+1) * (lmax+2) /2;</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> }</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> </div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"><a class="line" href="group__spherical__harmonics.html#ga12049806261f71471fea43484670d8f5"> 52</a></span> <span class="keyword">inline</span> <span class="keywordtype">size_t</span> <a class="code hl_function" href="group__spherical__harmonics.html#ga12049806261f71471fea43484670d8f5">index</a> (<span class="keywordtype">int</span> l, <span class="keywordtype">int</span> m)</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> {</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="keywordflow">return</span> l * (l+1) /2 + m;</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> }</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> </div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"><a class="line" href="group__spherical__harmonics.html#ga8bc0c976c67b9eb91e2dfd71bede4fe1"> 58</a></span> <span class="keyword">inline</span> <span class="keywordtype">size_t</span> <a class="code hl_function" href="group__spherical__harmonics.html#ga8bc0c976c67b9eb91e2dfd71bede4fe1">NforL_mpos</a> (<span class="keywordtype">int</span> lmax)</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> {</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keywordflow">return</span> (lmax/2+1) * (lmax/2+1);</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> }</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> </div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"><a class="line" href="group__spherical__harmonics.html#ga5296aa18ca79b9a88a46cee00c47667a"> 64</a></span> <span class="keyword">inline</span> <span class="keywordtype">size_t</span> <a class="code hl_function" href="group__spherical__harmonics.html#ga5296aa18ca79b9a88a46cee00c47667a">index_mpos</a> (<span class="keywordtype">int</span> l, <span class="keywordtype">int</span> m)</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> {</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="keywordflow">return</span> l*l/4 + m;</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> }</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> </div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"><a class="line" href="group__spherical__harmonics.html#ga28d9e09433f42e5036ec45ed6e7806bf"> 70</a></span> <span class="keyword">inline</span> <span class="keywordtype">size_t</span> <a class="code hl_function" href="group__spherical__harmonics.html#ga28d9e09433f42e5036ec45ed6e7806bf">LforN</a> (<span class="keywordtype">int</span> N)</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> {</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="keywordflow">return</span> N ? 2 * std::floor<size_t> ( (std::sqrt (<span class="keywordtype">float</span> (1+8*N))-3.0) /4.0) : 0;</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> }</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> </div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> </div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> </div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> </div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="keyword">template</span> <<span class="keyword">class</span> MatrixType></div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"><a class="line" href="group__spherical__harmonics.html#gac81b86466a7e80070f5161be93cebd6a"> 82</a></span> Eigen::Matrix<typename MatrixType::Scalar,Eigen::Dynamic, Eigen::Dynamic> <a class="code hl_function" href="group__spherical__harmonics.html#gac81b86466a7e80070f5161be93cebd6a">init_transform</a> (<span class="keyword">const</span> MatrixType& dirs, <span class="keyword">const</span> <span class="keywordtype">int</span> lmax)</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> {</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <span class="keyword">using namespace </span>Eigen;</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <span class="keyword">using</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> = <span class="keyword">typename</span> MatrixType::Scalar;</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="keywordflow">if</span> (dirs.cols() != 2)</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="keywordflow">throw</span> <a class="code hl_class" href="class_m_r_1_1_exception.html">Exception</a> (<span class="stringliteral">"direction matrix should have 2 columns: [ azimuth elevation ]"</span>);</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> Matrix<value_type,Dynamic,Dynamic> SHT (dirs.rows(), <a class="code hl_function" href="group__spherical__harmonics.html#ga96a93012c20066bfbdb6c1a1ec1cfe15">NforL</a> (lmax));</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> Matrix<value_type,Dynamic,1,0,64> AL (lmax+1);</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="keywordflow">for</span> (ssize_t i = 0; i < dirs.rows(); i++) {</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> z = std::cos (dirs (i,1));</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <a class="code hl_function" href="namespace_m_r_1_1_math_1_1_legendre.html#ae7d37ead0eeef3573191552be77aa9be">Legendre::Plm_sph</a> (AL, lmax, 0, z);</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> l = 0; l <= lmax; l+=2)</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> SHT (i,<a class="code hl_function" href="group__spherical__harmonics.html#ga12049806261f71471fea43484670d8f5">index</a> (l,0)) = AL[l];</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> m = 1; m <= lmax; m++) {</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <a class="code hl_function" href="namespace_m_r_1_1_math_1_1_legendre.html#ae7d37ead0eeef3573191552be77aa9be">Legendre::Plm_sph</a> (AL, lmax, m, z);</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> l = ( (m&1) ? m+1 : m); l <= lmax; l+=2) {</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> SHT(i, <a class="code hl_function" href="group__spherical__harmonics.html#ga12049806261f71471fea43484670d8f5">index</a>(l, m)) = <a class="code hl_variable" href="group__mathconstants.html#ga21f6e669f12fc0caf970538de21793de">Math::sqrt2</a> * AL[l]*std::cos (m*dirs (i,0));</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> SHT(i, <a class="code hl_function" href="group__spherical__harmonics.html#ga12049806261f71471fea43484670d8f5">index</a>(l,-m)) = <a class="code hl_variable" href="group__mathconstants.html#ga21f6e669f12fc0caf970538de21793de">Math::sqrt2</a> * AL[l]*std::sin (m*dirs (i,0));</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> }</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> }</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> }</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="keywordflow">return</span> SHT;</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> }</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> </div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> </div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <span class="keyword">template</span> <<span class="keyword">class</span> MatrixType></div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"><a class="line" href="group__spherical__harmonics.html#ga38a57752a9e47b22f391d7952a24e91e"> 111</a></span> Eigen::Matrix<typename MatrixType::Scalar,Eigen::Dynamic, Eigen::Dynamic> <a class="code hl_function" href="group__spherical__harmonics.html#ga38a57752a9e47b22f391d7952a24e91e">init_transform_cart</a> (<span class="keyword">const</span> MatrixType& dirs, <span class="keyword">const</span> <span class="keywordtype">int</span> lmax)</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> {</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> <span class="keyword">using namespace </span>Eigen;</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <span class="keyword">using</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> = <span class="keyword">typename</span> MatrixType::Scalar;</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="keywordflow">if</span> (dirs.cols() != 3)</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <span class="keywordflow">throw</span> <a class="code hl_class" href="class_m_r_1_1_exception.html">Exception</a> (<span class="stringliteral">"direction matrix should have 3 columns: [ x y z ]"</span>);</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> Matrix<value_type,Dynamic,Dynamic> SHT (dirs.rows(), <a class="code hl_function" href="group__spherical__harmonics.html#ga96a93012c20066bfbdb6c1a1ec1cfe15">NforL</a> (lmax));</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> Matrix<value_type,Dynamic,1,0,64> AL (lmax+1);</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <span class="keywordflow">for</span> (ssize_t i = 0; i < dirs.rows(); i++) {</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> z = dirs (i,2);</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> rxy = std::hypot(dirs(i,0), dirs(i,1));</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> cp = (rxy) ? dirs(i,0)/rxy : 1.0;</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> sp = (rxy) ? dirs(i,1)/rxy : 0.0;</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> <a class="code hl_function" href="namespace_m_r_1_1_math_1_1_legendre.html#ae7d37ead0eeef3573191552be77aa9be">Legendre::Plm_sph</a> (AL, lmax, 0, z);</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> l = 0; l <= lmax; l+=2)</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> SHT (i,<a class="code hl_function" href="group__spherical__harmonics.html#ga12049806261f71471fea43484670d8f5">index</a> (l,0)) = AL[l];</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> c0 (1.0), s0 (0.0);</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> m = 1; m <= lmax; m++) {</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> <a class="code hl_function" href="namespace_m_r_1_1_math_1_1_legendre.html#ae7d37ead0eeef3573191552be77aa9be">Legendre::Plm_sph</a> (AL, lmax, m, z);</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> c = c0 * cp - s0 * sp;</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> s = s0 * cp + c0 * sp;</div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> l = ( (m&1) ? m+1 : m); l <= lmax; l+=2) {</div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> SHT(i, <a class="code hl_function" href="group__spherical__harmonics.html#ga12049806261f71471fea43484670d8f5">index</a>(l, m)) = <a class="code hl_variable" href="group__mathconstants.html#ga21f6e669f12fc0caf970538de21793de">Math::sqrt2</a> * AL[l] * c;</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> SHT(i, <a class="code hl_function" href="group__spherical__harmonics.html#ga12049806261f71471fea43484670d8f5">index</a>(l,-m)) = <a class="code hl_variable" href="group__mathconstants.html#ga21f6e669f12fc0caf970538de21793de">Math::sqrt2</a> * AL[l] * s;</div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> }</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> c0 = c;</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> s0 = s;</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> }</div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> }</div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> <span class="keywordflow">return</span> SHT;</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> }</div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> </div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> </div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> </div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <span class="keyword">template</span> <<span class="keyword">class</span> MatrixType, <span class="keyword">class</span> VectorType></div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"><a class="line" href="group__spherical__harmonics.html#ga301ff6a6409f78ce405d2ed51f2bdbde"> 147</a></span> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code hl_function" href="group__spherical__harmonics.html#ga301ff6a6409f78ce405d2ed51f2bdbde">scale_degrees_forward</a> (MatrixType& SH2amp_mapping, <span class="keyword">const</span> VectorType& coefs)</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> {</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> ssize_t l = 0, nl = 1;</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> <span class="keywordflow">for</span> (ssize_t col = 0; col < SH2amp_mapping.cols(); ++col) {</div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> <span class="keywordflow">if</span> (col >= nl) {</div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> l++;</div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> nl = <a class="code hl_function" href="group__spherical__harmonics.html#ga96a93012c20066bfbdb6c1a1ec1cfe15">NforL</a> (2*l);</div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> }</div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> SH2amp_mapping.col(col) *= coefs[l];</div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> }</div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> }</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> </div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> </div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> </div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, <span class="keyword">class</span> VectorType></div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"><a class="line" href="group__spherical__harmonics.html#ga24a1163b39e02424abbe3ed456bb0a1c"> 163</a></span> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code hl_function" href="group__spherical__harmonics.html#ga24a1163b39e02424abbe3ed456bb0a1c">scale_degrees_inverse</a> (MatrixType& amp2SH_mapping, <span class="keyword">const</span> VectorType& coefs)</div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> {</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> ssize_t l = 0, nl = 1;</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> <span class="keywordflow">for</span> (ssize_t row = 0; row < amp2SH_mapping.rows(); ++row) {</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> <span class="keywordflow">if</span> (row >= nl) {</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> l++;</div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> nl = <a class="code hl_function" href="group__spherical__harmonics.html#ga96a93012c20066bfbdb6c1a1ec1cfe15">NforL</a> (2*l);</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> }</div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> amp2SH_mapping.row(row) *= coefs[l];</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> }</div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> }</div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> </div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> </div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> </div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> </div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> <span class="keyword">template</span> <<span class="keyword">typename</span> VectorType></div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"><a class="line" href="group__spherical__harmonics.html#gaf710913e46f5cbefa76894d6135aef4c"> 180</a></span> <span class="keyword">inline</span> Eigen::Matrix<typename VectorType::Scalar,Eigen::Dynamic,1> <a class="code hl_function" href="group__spherical__harmonics.html#gaf710913e46f5cbefa76894d6135aef4c">invert</a> (<span class="keyword">const</span> VectorType& coefs)</div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> {</div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> Eigen::Matrix<typename VectorType::Scalar,Eigen::Dynamic,1> ret (coefs.size());</div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> n = 0; n < coefs.size(); ++n)</div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> ret[n] = ( coefs[n] ? 1.0 / coefs[n] : 0.0 );</div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> <span class="keywordflow">return</span> ret;</div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> }</div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> </div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> <span class="keyword">template</span> <<span class="keyword">typename</span> ValueType></div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"><a class="line" href="class_m_r_1_1_math_1_1_s_h_1_1_transform.html"> 189</a></span> <span class="keyword">class </span><a class="code hl_class" href="class_m_r_1_1_math_1_1_s_h_1_1_transform.html">Transform</a> { <a class="code hl_define" href="src_2surface_2types_8h.html#a11d7eae3ab5178ebcf0e62cae9c26cd4">MEMALIGN</a>(<a class="code hl_class" href="class_m_r_1_1_math_1_1_s_h_1_1_transform.html">Transform<ValueType></a>)</div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> <span class="keyword">public</span>:</div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> <span class="keyword">using</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#ab2ff7634bcab80ba308522254376964e">matrix_type</a> = Eigen::Matrix<ValueType,Eigen::Dynamic,Eigen::Dynamic>;</div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> </div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> <span class="keyword">template</span> <<span class="keyword">class</span> MatrixType></div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> <a class="code hl_class" href="class_m_r_1_1_math_1_1_s_h_1_1_transform.html">Transform</a> (<span class="keyword">const</span> MatrixType& dirs, <span class="keywordtype">int</span> lmax) :</div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_transform.html#a3f3e81061b4248a70e8ccca3c13fa903">SHT</a> (<a class="code hl_function" href="group__spherical__harmonics.html#gac81b86466a7e80070f5161be93cebd6a">init_transform</a> (dirs, lmax)),</div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_transform.html#a090fc82b5df426e29a31cfe1d85cba72">iSHT</a> (<a class="code hl_function" href="group__ls.html#gaaacadd3d43de898a784044dcfa3e1363">pinv</a> (<a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_transform.html#a3f3e81061b4248a70e8ccca3c13fa903">SHT</a>)) { }</div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> </div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> <span class="keyword">template</span> <<span class="keyword">class</span> VectorType></div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> <span class="keywordtype">void</span> set_filter (<span class="keyword">const</span> VectorType& filter) {</div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> <a class="code hl_function" href="group__spherical__harmonics.html#ga301ff6a6409f78ce405d2ed51f2bdbde">scale_degrees_forward</a> (<a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_transform.html#a3f3e81061b4248a70e8ccca3c13fa903">SHT</a>, <a class="code hl_function" href="group__spherical__harmonics.html#gaf710913e46f5cbefa76894d6135aef4c">invert</a> (filter));</div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> <a class="code hl_function" href="group__spherical__harmonics.html#ga24a1163b39e02424abbe3ed456bb0a1c">scale_degrees_inverse</a> (<a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_transform.html#a090fc82b5df426e29a31cfe1d85cba72">iSHT</a>, filter);</div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> }</div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> <span class="keyword">template</span> <<span class="keyword">class</span> VectorType1, <span class="keyword">class</span> VectorType2></div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> <span class="keywordtype">void</span> A2SH (VectorType1& sh, <span class="keyword">const</span> VectorType2& amplitudes)<span class="keyword"> const </span>{</div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> sh.noalias() = <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_transform.html#a090fc82b5df426e29a31cfe1d85cba72">iSHT</a> * amplitudes;</div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> }</div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> <span class="keyword">template</span> <<span class="keyword">class</span> VectorType1, <span class="keyword">class</span> VectorType2></div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> <span class="keywordtype">void</span> SH2A (VectorType1& amplitudes, <span class="keyword">const</span> VectorType2& sh)<span class="keyword"> const </span>{</div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> amplitudes.noalias() = <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_transform.html#a3f3e81061b4248a70e8ccca3c13fa903">SHT</a> * sh;</div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> }</div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> </div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> <span class="keywordtype">size_t</span> n_SH ()<span class="keyword"> const </span>{</div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_transform.html#a3f3e81061b4248a70e8ccca3c13fa903">SHT</a>.cols();</div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> }</div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> <span class="keywordtype">size_t</span> n_amp ()<span class="keyword"> const </span>{</div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_transform.html#a3f3e81061b4248a70e8ccca3c13fa903">SHT</a>.rows();</div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> }</div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> </div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#ab2ff7634bcab80ba308522254376964e">matrix_type</a>& mat_A2SH ()<span class="keyword"> const </span>{</div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_transform.html#a090fc82b5df426e29a31cfe1d85cba72">iSHT</a>;</div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> }</div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#ab2ff7634bcab80ba308522254376964e">matrix_type</a>& mat_SH2A ()<span class="keyword"> const </span>{</div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_transform.html#a3f3e81061b4248a70e8ccca3c13fa903">SHT</a>;</div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> }</div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> </div>
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> <span class="keyword">protected</span>:</div>
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"><a class="line" href="class_m_r_1_1_math_1_1_s_h_1_1_transform.html#a090fc82b5df426e29a31cfe1d85cba72"> 227</a></span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#ab2ff7634bcab80ba308522254376964e">matrix_type</a> <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_transform.html#a3f3e81061b4248a70e8ccca3c13fa903">SHT</a>, <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_transform.html#a090fc82b5df426e29a31cfe1d85cba72">iSHT</a>;</div>
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span> };</div>
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> </div>
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> </div>
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> </div>
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> <span class="keyword">template</span> <<span class="keyword">class</span> VectorType></div>
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"><a class="line" href="group__spherical__harmonics.html#gac405578b4137cf1c22a0cf646d260b05"> 233</a></span> <span class="keyword">inline</span> <span class="keyword">typename</span> VectorType::Scalar <a class="code hl_function" href="group__spherical__harmonics.html#gac405578b4137cf1c22a0cf646d260b05">value</a> (<span class="keyword">const</span> VectorType& coefs,</div>
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span> <span class="keyword">typename</span> VectorType::Scalar cos_elevation,</div>
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> <span class="keyword">typename</span> VectorType::Scalar cos_azimuth,</div>
<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> <span class="keyword">typename</span> VectorType::Scalar sin_azimuth,</div>
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span> <span class="keywordtype">int</span> lmax)</div>
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span> {</div>
<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> <span class="keyword">using</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> = <span class="keyword">typename</span> VectorType::Scalar;</div>
<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> amplitude = 0.0;</div>
<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> Eigen::Matrix<value_type,Eigen::Dynamic,1,0,64> AL (lmax+1);</div>
<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span> <a class="code hl_function" href="namespace_m_r_1_1_math_1_1_legendre.html#ae7d37ead0eeef3573191552be77aa9be">Legendre::Plm_sph</a> (AL, lmax, 0, cos_elevation);</div>
<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> l = 0; l <= lmax; l+=2)</div>
<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span> amplitude += AL[l] * coefs[<a class="code hl_function" href="group__spherical__harmonics.html#ga12049806261f71471fea43484670d8f5">index</a> (l,0)];</div>
<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> c0 (1.0), s0 (0.0);</div>
<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> m = 1; m <= lmax; m++) {</div>
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> <a class="code hl_function" href="namespace_m_r_1_1_math_1_1_legendre.html#ae7d37ead0eeef3573191552be77aa9be">Legendre::Plm_sph</a> (AL, lmax, m, cos_elevation);</div>
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> c = c0 * cos_azimuth - s0 * sin_azimuth; <span class="comment">// std::cos(m*azimuth)</span></div>
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> s = s0 * cos_azimuth + c0 * sin_azimuth; <span class="comment">// std::sin(m*azimuth)</span></div>
<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> l = ( (m&1) ? m+1 : m); l <= lmax; l+=2)</div>
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> amplitude += AL[l] * <a class="code hl_variable" href="group__mathconstants.html#ga21f6e669f12fc0caf970538de21793de">Math::sqrt2</a> * (c * coefs[<a class="code hl_function" href="group__spherical__harmonics.html#ga12049806261f71471fea43484670d8f5">index</a> (l,m)] + s * coefs[<a class="code hl_function" href="group__spherical__harmonics.html#ga12049806261f71471fea43484670d8f5">index</a> (l,-m)]);</div>
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> c0 = c;</div>
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> s0 = s;</div>
<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> }</div>
<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> <span class="keywordflow">return</span> amplitude;</div>
<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> }</div>
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> </div>
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> <span class="keyword">template</span> <<span class="keyword">class</span> VectorType></div>
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"><a class="line" href="group__spherical__harmonics.html#ga7516a6376d493b95726c8c41ee8ecd84"> 259</a></span> <span class="keyword">inline</span> <span class="keyword">typename</span> VectorType::Scalar <a class="code hl_function" href="group__spherical__harmonics.html#gac405578b4137cf1c22a0cf646d260b05">value</a> (<span class="keyword">const</span> VectorType& coefs,</div>
<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span> <span class="keyword">typename</span> VectorType::Scalar cos_elevation,</div>
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> <span class="keyword">typename</span> VectorType::Scalar azimuth,</div>
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> <span class="keywordtype">int</span> lmax)</div>
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> {</div>
<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span> <span class="keywordflow">return</span> <a class="code hl_function" href="group__spherical__harmonics.html#gac405578b4137cf1c22a0cf646d260b05">value</a> (coefs, cos_elevation, std::cos(azimuth), std::sin(azimuth), lmax);</div>
<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span> }</div>
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span> </div>
<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span> <span class="keyword">template</span> <<span class="keyword">class</span> VectorType1, <span class="keyword">class</span> VectorType2></div>
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"><a class="line" href="group__spherical__harmonics.html#ga9a848ad288e26cd2bdf74da968ea14cd"> 268</a></span> <span class="keyword">inline</span> <span class="keyword">typename</span> VectorType1::Scalar <a class="code hl_function" href="group__spherical__harmonics.html#gac405578b4137cf1c22a0cf646d260b05">value</a> (<span class="keyword">const</span> VectorType1& coefs, <span class="keyword">const</span> VectorType2& unit_dir, <span class="keywordtype">int</span> lmax)</div>
<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span> {</div>
<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span> <span class="keyword">using</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> = <span class="keyword">typename</span> VectorType1::Scalar;</div>
<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> rxy = std::sqrt ( <a class="code hl_function" href="group__elfun.html#ga8bf8967471ef09d762367a1844985db8">pow2</a>(unit_dir[1]) + <a class="code hl_function" href="group__elfun.html#ga8bf8967471ef09d762367a1844985db8">pow2</a>(unit_dir[0]) );</div>
<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> cp = (rxy) ? unit_dir[0]/rxy : 1.0;</div>
<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> sp = (rxy) ? unit_dir[1]/rxy : 0.0;</div>
<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> <span class="keywordflow">return</span> <a class="code hl_function" href="group__spherical__harmonics.html#gac405578b4137cf1c22a0cf646d260b05">value</a> (coefs, unit_dir[2], cp, sp, lmax);</div>
<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span> }</div>
<div class="line"><a id="l00276" name="l00276"></a><span class="lineno"> 276</span> </div>
<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span> </div>
<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span> <span class="keyword">template</span> <<span class="keyword">class</span> VectorType1, <span class="keyword">class</span> VectorType2></div>
<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"><a class="line" href="group__spherical__harmonics.html#ga52bc9df51a5f151972235a9a0df09c51"> 279</a></span> <span class="keyword">inline</span> VectorType1& <a class="code hl_function" href="group__spherical__harmonics.html#ga52bc9df51a5f151972235a9a0df09c51">delta</a> (VectorType1& delta_vec, <span class="keyword">const</span> VectorType2& unit_dir, <span class="keywordtype">int</span> lmax)</div>
<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"> 280</span> {</div>
<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</span> <span class="keyword">using</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> = <span class="keyword">typename</span> VectorType1::Scalar;</div>
<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span> delta_vec.resize (<a class="code hl_function" href="group__spherical__harmonics.html#ga96a93012c20066bfbdb6c1a1ec1cfe15">NforL</a> (lmax));</div>
<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> rxy = std::sqrt ( <a class="code hl_function" href="group__elfun.html#ga8bf8967471ef09d762367a1844985db8">pow2</a>(unit_dir[1]) + <a class="code hl_function" href="group__elfun.html#ga8bf8967471ef09d762367a1844985db8">pow2</a>(unit_dir[0]) );</div>
<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> cp = (rxy) ? unit_dir[0]/rxy : 1.0;</div>
<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> sp = (rxy) ? unit_dir[1]/rxy : 0.0;</div>
<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</span> Eigen::Matrix<value_type,Eigen::Dynamic,1,0,64> AL (lmax+1);</div>
<div class="line"><a id="l00287" name="l00287"></a><span class="lineno"> 287</span> <a class="code hl_function" href="namespace_m_r_1_1_math_1_1_legendre.html#ae7d37ead0eeef3573191552be77aa9be">Legendre::Plm_sph</a> (AL, lmax, 0, unit_dir[2]);</div>
<div class="line"><a id="l00288" name="l00288"></a><span class="lineno"> 288</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> l = 0; l <= lmax; l+=2)</div>
<div class="line"><a id="l00289" name="l00289"></a><span class="lineno"> 289</span> delta_vec[<a class="code hl_function" href="group__spherical__harmonics.html#ga12049806261f71471fea43484670d8f5">index</a> (l,0)] = AL[l];</div>
<div class="line"><a id="l00290" name="l00290"></a><span class="lineno"> 290</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> c0 (1.0), s0 (0.0);</div>
<div class="line"><a id="l00291" name="l00291"></a><span class="lineno"> 291</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> m = 1; m <= lmax; m++) {</div>
<div class="line"><a id="l00292" name="l00292"></a><span class="lineno"> 292</span> <a class="code hl_function" href="namespace_m_r_1_1_math_1_1_legendre.html#ae7d37ead0eeef3573191552be77aa9be">Legendre::Plm_sph</a> (AL, lmax, m, unit_dir[2]);</div>
<div class="line"><a id="l00293" name="l00293"></a><span class="lineno"> 293</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> c = c0 * cp - s0 * sp;</div>
<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> s = s0 * cp + c0 * sp;</div>
<div class="line"><a id="l00295" name="l00295"></a><span class="lineno"> 295</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> l = ( (m&1) ? m+1 : m); l <= lmax; l+=2) {</div>
<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span> delta_vec[<a class="code hl_function" href="group__spherical__harmonics.html#ga12049806261f71471fea43484670d8f5">index</a> (l,m)] = AL[l] * <a class="code hl_variable" href="group__mathconstants.html#ga21f6e669f12fc0caf970538de21793de">Math::sqrt2</a> * c;</div>
<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span> delta_vec[<a class="code hl_function" href="group__spherical__harmonics.html#ga12049806261f71471fea43484670d8f5">index</a> (l,-m)] = AL[l] * <a class="code hl_variable" href="group__mathconstants.html#ga21f6e669f12fc0caf970538de21793de">Math::sqrt2</a> * s;</div>
<div class="line"><a id="l00298" name="l00298"></a><span class="lineno"> 298</span> }</div>
<div class="line"><a id="l00299" name="l00299"></a><span class="lineno"> 299</span> c0 = c;</div>
<div class="line"><a id="l00300" name="l00300"></a><span class="lineno"> 300</span> s0 = s;</div>
<div class="line"><a id="l00301" name="l00301"></a><span class="lineno"> 301</span> }</div>
<div class="line"><a id="l00302" name="l00302"></a><span class="lineno"> 302</span> <span class="keywordflow">return</span> delta_vec;</div>
<div class="line"><a id="l00303" name="l00303"></a><span class="lineno"> 303</span> }</div>
<div class="line"><a id="l00304" name="l00304"></a><span class="lineno"> 304</span> </div>
<div class="line"><a id="l00305" name="l00305"></a><span class="lineno"> 305</span> </div>
<div class="line"><a id="l00306" name="l00306"></a><span class="lineno"> 306</span> </div>
<div class="line"><a id="l00307" name="l00307"></a><span class="lineno"> 307</span> <span class="keyword">template</span> <<span class="keyword">class</span> VectorType1, <span class="keyword">class</span> VectorType2></div>
<div class="line"><a id="l00308" name="l00308"></a><span class="lineno"><a class="line" href="group__spherical__harmonics.html#gae4d9b83d1a1e715d2faebceaf79c559a"> 308</a></span> <span class="keyword">inline</span> VectorType1& <a class="code hl_function" href="group__spherical__harmonics.html#gae4d9b83d1a1e715d2faebceaf79c559a">SH2RH</a> (VectorType1& RH, <span class="keyword">const</span> VectorType2& sh)</div>
<div class="line"><a id="l00309" name="l00309"></a><span class="lineno"> 309</span> {</div>
<div class="line"><a id="l00310" name="l00310"></a><span class="lineno"> 310</span> <span class="keyword">using</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> = <span class="keyword">typename</span> VectorType2::Scalar;</div>
<div class="line"><a id="l00311" name="l00311"></a><span class="lineno"> 311</span> RH.resize (sh.size());</div>
<div class="line"><a id="l00312" name="l00312"></a><span class="lineno"> 312</span> <span class="keywordtype">int</span> lmax = 2*sh.size() +1;</div>
<div class="line"><a id="l00313" name="l00313"></a><span class="lineno"> 313</span> Eigen::Matrix<value_type,Eigen::Dynamic,1,0,64> AL (lmax+1);</div>
<div class="line"><a id="l00314" name="l00314"></a><span class="lineno"> 314</span> <a class="code hl_function" href="namespace_m_r_1_1_math_1_1_legendre.html#ae7d37ead0eeef3573191552be77aa9be">Legendre::Plm_sph</a> (AL, lmax, 0, 1.0);</div>
<div class="line"><a id="l00315" name="l00315"></a><span class="lineno"> 315</span> <span class="keywordflow">for</span> (ssize_t l = 0; l < sh.size(); l++)</div>
<div class="line"><a id="l00316" name="l00316"></a><span class="lineno"> 316</span> RH[l] = sh[l]/ AL[2*l];</div>
<div class="line"><a id="l00317" name="l00317"></a><span class="lineno"> 317</span> <span class="keywordflow">return</span> RH;</div>
<div class="line"><a id="l00318" name="l00318"></a><span class="lineno"> 318</span> }</div>
<div class="line"><a id="l00319" name="l00319"></a><span class="lineno"> 319</span> </div>
<div class="line"><a id="l00320" name="l00320"></a><span class="lineno"> 320</span> <span class="keyword">template</span> <<span class="keyword">class</span> VectorType></div>
<div class="line"><a id="l00321" name="l00321"></a><span class="lineno"><a class="line" href="group__spherical__harmonics.html#gaac9cc994993087db75c3ac3af4afcbf9"> 321</a></span> <span class="keyword">inline</span> Eigen::Matrix<typename VectorType::Scalar,Eigen::Dynamic,1> <a class="code hl_function" href="group__spherical__harmonics.html#gae4d9b83d1a1e715d2faebceaf79c559a">SH2RH</a> (<span class="keyword">const</span> VectorType& sh)</div>
<div class="line"><a id="l00322" name="l00322"></a><span class="lineno"> 322</span> {</div>
<div class="line"><a id="l00323" name="l00323"></a><span class="lineno"> 323</span> Eigen::Matrix<typename VectorType::Scalar,Eigen::Dynamic,1> RH (sh.size());</div>
<div class="line"><a id="l00324" name="l00324"></a><span class="lineno"> 324</span> <a class="code hl_function" href="group__spherical__harmonics.html#gae4d9b83d1a1e715d2faebceaf79c559a">SH2RH</a> (RH, sh);</div>
<div class="line"><a id="l00325" name="l00325"></a><span class="lineno"> 325</span> <span class="keywordflow">return</span> RH;</div>
<div class="line"><a id="l00326" name="l00326"></a><span class="lineno"> 326</span> }</div>
<div class="line"><a id="l00327" name="l00327"></a><span class="lineno"> 327</span> </div>
<div class="line"><a id="l00328" name="l00328"></a><span class="lineno"> 328</span> </div>
<div class="line"><a id="l00330" name="l00330"></a><span class="lineno"> 330</span> </div>
<div class="line"><a id="l00332" name="l00332"></a><span class="lineno"> 332</span> <span class="keyword">template</span> <<span class="keyword">class</span> VectorType1, <span class="keyword">class</span> VectorType2></div>
<div class="line"><a id="l00333" name="l00333"></a><span class="lineno"><a class="line" href="group__spherical__harmonics.html#ga3f0ca8fb7a027f28cf4360d4c81cec04"> 333</a></span> <span class="keyword">inline</span> VectorType1& <a class="code hl_function" href="group__spherical__harmonics.html#ga3f0ca8fb7a027f28cf4360d4c81cec04">sconv</a> (VectorType1& sh, <span class="keyword">const</span> VectorType2& RH)</div>
<div class="line"><a id="l00334" name="l00334"></a><span class="lineno"> 334</span> {</div>
<div class="line"><a id="l00335" name="l00335"></a><span class="lineno"> 335</span> assert (sh.size() >= ssize_t (<a class="code hl_function" href="group__spherical__harmonics.html#ga96a93012c20066bfbdb6c1a1ec1cfe15">NforL</a> (2* (RH.size()-1))));</div>
<div class="line"><a id="l00336" name="l00336"></a><span class="lineno"> 336</span> <span class="keywordflow">for</span> (ssize_t i = 0; i < RH.size(); ++i) {</div>
<div class="line"><a id="l00337" name="l00337"></a><span class="lineno"> 337</span> <span class="keywordtype">int</span> l = 2*i;</div>
<div class="line"><a id="l00338" name="l00338"></a><span class="lineno"> 338</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> m = -l; m <= l; ++m)</div>
<div class="line"><a id="l00339" name="l00339"></a><span class="lineno"> 339</span> sh[<a class="code hl_function" href="group__spherical__harmonics.html#ga12049806261f71471fea43484670d8f5">index</a> (l,m)] *= RH[i];</div>
<div class="line"><a id="l00340" name="l00340"></a><span class="lineno"> 340</span> }</div>
<div class="line"><a id="l00341" name="l00341"></a><span class="lineno"> 341</span> <span class="keywordflow">return</span> sh;</div>
<div class="line"><a id="l00342" name="l00342"></a><span class="lineno"> 342</span> }</div>
<div class="line"><a id="l00343" name="l00343"></a><span class="lineno"> 343</span> </div>
<div class="line"><a id="l00344" name="l00344"></a><span class="lineno"> 344</span> </div>
<div class="line"><a id="l00346" name="l00346"></a><span class="lineno"> 346</span> </div>
<div class="line"><a id="l00348" name="l00348"></a><span class="lineno"> 348</span> <span class="keyword">template</span> <<span class="keyword">class</span> VectorType1, <span class="keyword">class</span> VectorType2, <span class="keyword">class</span> VectorType3></div>
<div class="line"><a id="l00349" name="l00349"></a><span class="lineno"><a class="line" href="group__spherical__harmonics.html#ga5ce9a41648fd661144c2abe953f3ff89"> 349</a></span> <span class="keyword">inline</span> VectorType1& <a class="code hl_function" href="group__spherical__harmonics.html#ga3f0ca8fb7a027f28cf4360d4c81cec04">sconv</a> (VectorType1& C, <span class="keyword">const</span> VectorType2& RH, <span class="keyword">const</span> VectorType3& sh)</div>
<div class="line"><a id="l00350" name="l00350"></a><span class="lineno"> 350</span> {</div>
<div class="line"><a id="l00351" name="l00351"></a><span class="lineno"> 351</span> assert (sh.size() >= ssize_t (<a class="code hl_function" href="group__spherical__harmonics.html#ga96a93012c20066bfbdb6c1a1ec1cfe15">NforL</a> (2* (RH.size()-1))));</div>
<div class="line"><a id="l00352" name="l00352"></a><span class="lineno"> 352</span> C.resize (<a class="code hl_function" href="group__spherical__harmonics.html#ga96a93012c20066bfbdb6c1a1ec1cfe15">NforL</a> (2* (RH.size()-1)));</div>
<div class="line"><a id="l00353" name="l00353"></a><span class="lineno"> 353</span> <span class="keywordflow">for</span> (ssize_t i = 0; i < RH.size(); ++i) {</div>
<div class="line"><a id="l00354" name="l00354"></a><span class="lineno"> 354</span> <span class="keywordtype">int</span> l = 2*i;</div>
<div class="line"><a id="l00355" name="l00355"></a><span class="lineno"> 355</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> m = -l; m <= l; ++m)</div>
<div class="line"><a id="l00356" name="l00356"></a><span class="lineno"> 356</span> C[<a class="code hl_function" href="group__spherical__harmonics.html#ga12049806261f71471fea43484670d8f5">index</a> (l,m)] = RH[i] * sh[<a class="code hl_function" href="group__spherical__harmonics.html#ga12049806261f71471fea43484670d8f5">index</a> (l,m)];</div>
<div class="line"><a id="l00357" name="l00357"></a><span class="lineno"> 357</span> }</div>
<div class="line"><a id="l00358" name="l00358"></a><span class="lineno"> 358</span> <span class="keywordflow">return</span> C;</div>
<div class="line"><a id="l00359" name="l00359"></a><span class="lineno"> 359</span> }</div>
<div class="line"><a id="l00360" name="l00360"></a><span class="lineno"> 360</span> </div>
<div class="line"><a id="l00361" name="l00361"></a><span class="lineno"> 361</span> </div>
<div class="line"><a id="l00363" name="l00363"></a><span class="lineno"> 363</span> </div>
<div class="line"><a id="l00366" name="l00366"></a><span class="lineno"> 366</span> <span class="keyword">template</span> <<span class="keyword">class</span> MatrixType1, <span class="keyword">class</span> VectorType2></div>
<div class="line"><a id="l00367" name="l00367"></a><span class="lineno"><a class="line" href="group__spherical__harmonics.html#gaa0311aadd5154d4d23d2cdaa29532bac"> 367</a></span> <span class="keyword">inline</span> MatrixType1& <a class="code hl_function" href="group__spherical__harmonics.html#gaa0311aadd5154d4d23d2cdaa29532bac">sconv_mat</a> (MatrixType1& sh, <span class="keyword">const</span> VectorType2& RH)</div>
<div class="line"><a id="l00368" name="l00368"></a><span class="lineno"> 368</span> {</div>
<div class="line"><a id="l00369" name="l00369"></a><span class="lineno"> 369</span> assert (sh.cols() >= ssize_t (<a class="code hl_function" href="group__spherical__harmonics.html#ga96a93012c20066bfbdb6c1a1ec1cfe15">NforL</a> (2* (RH.size()-1))));</div>
<div class="line"><a id="l00370" name="l00370"></a><span class="lineno"> 370</span> <span class="keywordflow">for</span> (ssize_t i = 0; i < RH.size(); ++i) {</div>
<div class="line"><a id="l00371" name="l00371"></a><span class="lineno"> 371</span> <span class="keywordtype">int</span> l = 2*i;</div>
<div class="line"><a id="l00372" name="l00372"></a><span class="lineno"> 372</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> m = -l; m <= l; ++m)</div>
<div class="line"><a id="l00373" name="l00373"></a><span class="lineno"> 373</span> sh.col(<a class="code hl_function" href="group__spherical__harmonics.html#ga12049806261f71471fea43484670d8f5">index</a> (l,m)) *= RH[i];</div>
<div class="line"><a id="l00374" name="l00374"></a><span class="lineno"> 374</span> }</div>
<div class="line"><a id="l00375" name="l00375"></a><span class="lineno"> 375</span> <span class="keywordflow">return</span> sh;</div>
<div class="line"><a id="l00376" name="l00376"></a><span class="lineno"> 376</span> }</div>
<div class="line"><a id="l00377" name="l00377"></a><span class="lineno"> 377</span> </div>
<div class="line"><a id="l00378" name="l00378"></a><span class="lineno"> 378</span> </div>
<div class="line"><a id="l00379" name="l00379"></a><span class="lineno"> 379</span> <span class="keyword">namespace </span>{</div>
<div class="line"><a id="l00380" name="l00380"></a><span class="lineno"> 380</span> <span class="keyword">template</span> <<span class="keyword">typename</span>> <span class="keyword">struct </span>__dummy { <a class="code hl_define" href="memory_8h.html#a5d1aa93e600a93cee8523d1d34c1ace5">NOMEMALIGN</a> <span class="keyword">using</span> type = int; };</div>
<div class="line"><a id="l00381" name="l00381"></a><span class="lineno"> 381</span> }</div>
<div class="line"><a id="l00382" name="l00382"></a><span class="lineno"> 382</span> </div>
<div class="line"><a id="l00383" name="l00383"></a><span class="lineno"> 383</span> </div>
<div class="line"><a id="l00384" name="l00384"></a><span class="lineno"> 384</span> </div>
<div class="line"><a id="l00385" name="l00385"></a><span class="lineno"> 385</span> </div>
<div class="line"><a id="l00386" name="l00386"></a><span class="lineno"> 386</span> </div>
<div class="line"><a id="l00387" name="l00387"></a><span class="lineno"> 387</span> </div>
<div class="line"><a id="l00389" name="l00389"></a><span class="lineno"><a class="line" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html"> 389</a></span> <span class="keyword">template</span> <<span class="keyword">typename</span> ValueType> <span class="keyword">class </span><a class="code hl_class" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html">PrecomputedFraction</a></div>
<div class="line"><a id="l00390" name="l00390"></a><span class="lineno"> 390</span> { <a class="code hl_define" href="memory_8h.html#a5d1aa93e600a93cee8523d1d34c1ace5">NOMEMALIGN</a></div>
<div class="line"><a id="l00391" name="l00391"></a><span class="lineno"> 391</span> <span class="keyword">public</span>:</div>
<div class="line"><a id="l00392" name="l00392"></a><span class="lineno"><a class="line" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#aae6e40afb9de8d1797b0b363b891e137"> 392</a></span> <a class="code hl_function" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#aae6e40afb9de8d1797b0b363b891e137">PrecomputedFraction</a> () : <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#a37ad42ae2b21d95dd7c78ec4157c13ec">f1</a> (0.0), <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#a1451b1b8c15f79fc827d649b8b08a307">f2</a> (0.0) { }</div>
<div class="line"><a id="l00393" name="l00393"></a><span class="lineno"><a class="line" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#a37ad42ae2b21d95dd7c78ec4157c13ec"> 393</a></span> ValueType <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#a37ad42ae2b21d95dd7c78ec4157c13ec">f1</a>, <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#a1451b1b8c15f79fc827d649b8b08a307">f2</a>;</div>
<div class="line"><a id="l00394" name="l00394"></a><span class="lineno"><a class="line" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#a436160f61b3c92f8857bc39877138aac"> 394</a></span> <span class="keyword">typename</span> <a class="code hl_class" href="class_m_r_1_1vector.html">vector<ValueType>::const_iterator</a> <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#a436160f61b3c92f8857bc39877138aac">p1</a>, <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#a641595bdfbc4a2c80b8a947bda6a4d49">p2</a>;</div>
<div class="line"><a id="l00395" name="l00395"></a><span class="lineno"> 395</span> };</div>
<div class="line"><a id="l00396" name="l00396"></a><span class="lineno"> 396</span> </div>
<div class="line"><a id="l00397" name="l00397"></a><span class="lineno"> 397</span> </div>
<div class="line"><a id="l00399" name="l00399"></a><span class="lineno"><a class="line" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html"> 399</a></span> <span class="keyword">template</span> <<span class="keyword">typename</span> ValueType> <span class="keyword">class </span><a class="code hl_class" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html">PrecomputedAL</a></div>
<div class="line"><a id="l00400" name="l00400"></a><span class="lineno"> 400</span> { <a class="code hl_define" href="memory_8h.html#a5d1aa93e600a93cee8523d1d34c1ace5">NOMEMALIGN</a></div>
<div class="line"><a id="l00401" name="l00401"></a><span class="lineno"> 401</span> <span class="keyword">public</span>:</div>
<div class="line"><a id="l00402" name="l00402"></a><span class="lineno"><a class="line" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a5200182a2011b5d515566206c19e7cf9"> 402</a></span> <span class="keyword">using</span> <a class="code hl_typedef" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a5200182a2011b5d515566206c19e7cf9">value_type</a> = ValueType;</div>
<div class="line"><a id="l00403" name="l00403"></a><span class="lineno"> 403</span> </div>
<div class="line"><a id="l00404" name="l00404"></a><span class="lineno"><a class="line" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a696f88bb74943bca452a577e66881ae2"> 404</a></span> <a class="code hl_function" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a696f88bb74943bca452a577e66881ae2">PrecomputedAL</a> () : <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a43f9092cedbb0dbcb85bad991b8836d1">lmax</a> (0), <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#ae7c66cf90354d50a6ea0f7185baabf75">ndir</a> (0), <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a6a6119d535416f86f36e9727525edcdd">nAL</a> (0), <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a18ec793089fa14f86aa33895b2fe9ae2">inc</a> (0.0) { }</div>
<div class="line"><a id="l00405" name="l00405"></a><span class="lineno"><a class="line" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#aad1616bf86f6cdaf3082883cb4587235"> 405</a></span> <a class="code hl_function" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#aad1616bf86f6cdaf3082883cb4587235">PrecomputedAL</a> (<span class="keywordtype">int</span> up_to_lmax, <span class="keywordtype">int</span> num_dir = 512) {</div>
<div class="line"><a id="l00406" name="l00406"></a><span class="lineno"> 406</span> <a class="code hl_function" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#abf387a092dd79918ee55850af5fc4487">init</a> (up_to_lmax, num_dir);</div>
<div class="line"><a id="l00407" name="l00407"></a><span class="lineno"> 407</span> }</div>
<div class="line"><a id="l00408" name="l00408"></a><span class="lineno"> 408</span> </div>
<div class="line"><a id="l00409" name="l00409"></a><span class="lineno"><a class="line" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a8f99a41e649a21f5b720dfba19adfb6d"> 409</a></span> <span class="keywordtype">bool</span> <a class="code hl_function" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a8f99a41e649a21f5b720dfba19adfb6d">operator! </a>()<span class="keyword"> const </span>{</div>
<div class="line"><a id="l00410" name="l00410"></a><span class="lineno"> 410</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#ad8a14f9e24c12642b7032b368ef153ce">AL</a>.empty();</div>
<div class="line"><a id="l00411" name="l00411"></a><span class="lineno"> 411</span> }</div>
<div class="line"><a id="l00412" name="l00412"></a><span class="lineno"><a class="line" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#aa6fe2e696d712f9f9efbeae9adfe28a1"> 412</a></span> <span class="keyword">operator</span> bool ()<span class="keyword"> const </span>{</div>
<div class="line"><a id="l00413" name="l00413"></a><span class="lineno"> 413</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#ad8a14f9e24c12642b7032b368ef153ce">AL</a>.size();</div>
<div class="line"><a id="l00414" name="l00414"></a><span class="lineno"> 414</span> }</div>
<div class="line"><a id="l00415" name="l00415"></a><span class="lineno"> 415</span> </div>
<div class="line"><a id="l00416" name="l00416"></a><span class="lineno"><a class="line" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#abf387a092dd79918ee55850af5fc4487"> 416</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#abf387a092dd79918ee55850af5fc4487">init</a> (<span class="keywordtype">int</span> up_to_lmax, <span class="keywordtype">int</span> num_dir = 512) {</div>
<div class="line"><a id="l00417" name="l00417"></a><span class="lineno"> 417</span> <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a43f9092cedbb0dbcb85bad991b8836d1">lmax</a> = up_to_lmax;</div>
<div class="line"><a id="l00418" name="l00418"></a><span class="lineno"> 418</span> <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#ae7c66cf90354d50a6ea0f7185baabf75">ndir</a> = num_dir;</div>
<div class="line"><a id="l00419" name="l00419"></a><span class="lineno"> 419</span> <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a6a6119d535416f86f36e9727525edcdd">nAL</a> = <a class="code hl_function" href="group__spherical__harmonics.html#ga8bc0c976c67b9eb91e2dfd71bede4fe1">NforL_mpos</a> (<a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a43f9092cedbb0dbcb85bad991b8836d1">lmax</a>);</div>
<div class="line"><a id="l00420" name="l00420"></a><span class="lineno"> 420</span> <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a18ec793089fa14f86aa33895b2fe9ae2">inc</a> = <a class="code hl_variable" href="group__mathconstants.html#gafe1ee4d398733ae71a15130062a9c2a4">Math::pi</a> / (<a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#ae7c66cf90354d50a6ea0f7185baabf75">ndir</a>-1);</div>
<div class="line"><a id="l00421" name="l00421"></a><span class="lineno"> 421</span> <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#ad8a14f9e24c12642b7032b368ef153ce">AL</a>.resize (<a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#ae7c66cf90354d50a6ea0f7185baabf75">ndir</a>*<a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a6a6119d535416f86f36e9727525edcdd">nAL</a>);</div>
<div class="line"><a id="l00422" name="l00422"></a><span class="lineno"> 422</span> Eigen::Matrix<value_type,Eigen::Dynamic,1,0,64> buf (<a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a43f9092cedbb0dbcb85bad991b8836d1">lmax</a>+1);</div>
<div class="line"><a id="l00423" name="l00423"></a><span class="lineno"> 423</span> </div>
<div class="line"><a id="l00424" name="l00424"></a><span class="lineno"> 424</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> n = 0; n < <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#ae7c66cf90354d50a6ea0f7185baabf75">ndir</a>; n++) {</div>
<div class="line"><a id="l00425" name="l00425"></a><span class="lineno"> 425</span> <span class="keyword">typename</span> <a class="code hl_class" href="class_m_r_1_1vector.html">vector<value_type>::iterator</a> p = <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#ad8a14f9e24c12642b7032b368ef153ce">AL</a>.begin() + n*<a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a6a6119d535416f86f36e9727525edcdd">nAL</a>;</div>
<div class="line"><a id="l00426" name="l00426"></a><span class="lineno"> 426</span> <a class="code hl_typedef" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a5200182a2011b5d515566206c19e7cf9">value_type</a> cos_el = std::cos (n*<a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a18ec793089fa14f86aa33895b2fe9ae2">inc</a>);</div>
<div class="line"><a id="l00427" name="l00427"></a><span class="lineno"> 427</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> m = 0; m <= <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a43f9092cedbb0dbcb85bad991b8836d1">lmax</a>; m++) {</div>
<div class="line"><a id="l00428" name="l00428"></a><span class="lineno"> 428</span> <a class="code hl_function" href="namespace_m_r_1_1_math_1_1_legendre.html#ae7d37ead0eeef3573191552be77aa9be">Legendre::Plm_sph</a> (buf, <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a43f9092cedbb0dbcb85bad991b8836d1">lmax</a>, m, cos_el);</div>
<div class="line"><a id="l00429" name="l00429"></a><span class="lineno"> 429</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> l = ( (m&1) ?m+1:m); l <= <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a43f9092cedbb0dbcb85bad991b8836d1">lmax</a>; l+=2)</div>
<div class="line"><a id="l00430" name="l00430"></a><span class="lineno"> 430</span> p[<a class="code hl_function" href="group__spherical__harmonics.html#ga5296aa18ca79b9a88a46cee00c47667a">index_mpos</a> (l,m)] = buf[l];</div>
<div class="line"><a id="l00431" name="l00431"></a><span class="lineno"> 431</span> }</div>
<div class="line"><a id="l00432" name="l00432"></a><span class="lineno"> 432</span> }</div>
<div class="line"><a id="l00433" name="l00433"></a><span class="lineno"> 433</span> }</div>
<div class="line"><a id="l00434" name="l00434"></a><span class="lineno"> 434</span> </div>
<div class="line"><a id="l00435" name="l00435"></a><span class="lineno"><a class="line" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a257f9f632bd008b2e05f1daf9f63fde5"> 435</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a257f9f632bd008b2e05f1daf9f63fde5">set</a> (<a class="code hl_class" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html">PrecomputedFraction<ValueType></a>& f, <span class="keyword">const</span> ValueType elevation)<span class="keyword"> const </span>{</div>
<div class="line"><a id="l00436" name="l00436"></a><span class="lineno"> 436</span> f.<a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#a1451b1b8c15f79fc827d649b8b08a307">f2</a> = elevation / <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a18ec793089fa14f86aa33895b2fe9ae2">inc</a>;</div>
<div class="line"><a id="l00437" name="l00437"></a><span class="lineno"> 437</span> <span class="keywordtype">int</span> i = int (f.<a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#a1451b1b8c15f79fc827d649b8b08a307">f2</a>);</div>
<div class="line"><a id="l00438" name="l00438"></a><span class="lineno"> 438</span> <span class="keywordflow">if</span> (i < 0) {</div>
<div class="line"><a id="l00439" name="l00439"></a><span class="lineno"> 439</span> i = 0;</div>
<div class="line"><a id="l00440" name="l00440"></a><span class="lineno"> 440</span> f.<a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#a37ad42ae2b21d95dd7c78ec4157c13ec">f1</a> = 1.0;</div>
<div class="line"><a id="l00441" name="l00441"></a><span class="lineno"> 441</span> f.<a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#a1451b1b8c15f79fc827d649b8b08a307">f2</a> = 0.0;</div>
<div class="line"><a id="l00442" name="l00442"></a><span class="lineno"> 442</span> }</div>
<div class="line"><a id="l00443" name="l00443"></a><span class="lineno"> 443</span> <span class="keywordflow">else</span> <span class="keywordflow">if</span> (i >= <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#ae7c66cf90354d50a6ea0f7185baabf75">ndir</a>-1) {</div>
<div class="line"><a id="l00444" name="l00444"></a><span class="lineno"> 444</span> i = <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#ae7c66cf90354d50a6ea0f7185baabf75">ndir</a>-1;</div>
<div class="line"><a id="l00445" name="l00445"></a><span class="lineno"> 445</span> f.<a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#a37ad42ae2b21d95dd7c78ec4157c13ec">f1</a> = 1.0;</div>
<div class="line"><a id="l00446" name="l00446"></a><span class="lineno"> 446</span> f.<a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#a1451b1b8c15f79fc827d649b8b08a307">f2</a> = 0.0;</div>
<div class="line"><a id="l00447" name="l00447"></a><span class="lineno"> 447</span> }</div>
<div class="line"><a id="l00448" name="l00448"></a><span class="lineno"> 448</span> <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00449" name="l00449"></a><span class="lineno"> 449</span> f.<a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#a1451b1b8c15f79fc827d649b8b08a307">f2</a> -= i;</div>
<div class="line"><a id="l00450" name="l00450"></a><span class="lineno"> 450</span> f.<a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#a37ad42ae2b21d95dd7c78ec4157c13ec">f1</a> = 1.0 - f.<a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#a1451b1b8c15f79fc827d649b8b08a307">f2</a>;</div>
<div class="line"><a id="l00451" name="l00451"></a><span class="lineno"> 451</span> }</div>
<div class="line"><a id="l00452" name="l00452"></a><span class="lineno"> 452</span> </div>
<div class="line"><a id="l00453" name="l00453"></a><span class="lineno"> 453</span> f.<a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#a436160f61b3c92f8857bc39877138aac">p1</a> = <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#ad8a14f9e24c12642b7032b368ef153ce">AL</a>.begin() + i*<a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a6a6119d535416f86f36e9727525edcdd">nAL</a>;</div>
<div class="line"><a id="l00454" name="l00454"></a><span class="lineno"> 454</span> f.<a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#a641595bdfbc4a2c80b8a947bda6a4d49">p2</a> = f.<a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#a436160f61b3c92f8857bc39877138aac">p1</a> + <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a6a6119d535416f86f36e9727525edcdd">nAL</a>;</div>
<div class="line"><a id="l00455" name="l00455"></a><span class="lineno"> 455</span> }</div>
<div class="line"><a id="l00456" name="l00456"></a><span class="lineno"> 456</span> </div>
<div class="line"><a id="l00457" name="l00457"></a><span class="lineno"><a class="line" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a952511ac3879736dca7627605b40a4d1"> 457</a></span> ValueType <a class="code hl_function" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a952511ac3879736dca7627605b40a4d1">get</a> (<span class="keyword">const</span> <a class="code hl_class" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html">PrecomputedFraction<ValueType></a>& f, <span class="keywordtype">int</span> i)<span class="keyword"> const </span>{</div>
<div class="line"><a id="l00458" name="l00458"></a><span class="lineno"> 458</span> ValueType v = f.<a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#a37ad42ae2b21d95dd7c78ec4157c13ec">f1</a>*f.<a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#a436160f61b3c92f8857bc39877138aac">p1</a>[i];</div>
<div class="line"><a id="l00459" name="l00459"></a><span class="lineno"> 459</span> <span class="keywordflow">if</span> (f.<a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#a1451b1b8c15f79fc827d649b8b08a307">f2</a>) v += f.<a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#a1451b1b8c15f79fc827d649b8b08a307">f2</a>*f.<a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#a641595bdfbc4a2c80b8a947bda6a4d49">p2</a>[i];</div>
<div class="line"><a id="l00460" name="l00460"></a><span class="lineno"> 460</span> <span class="keywordflow">return</span> v;</div>
<div class="line"><a id="l00461" name="l00461"></a><span class="lineno"> 461</span> }</div>
<div class="line"><a id="l00462" name="l00462"></a><span class="lineno"><a class="line" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a0994485fcb0b088197d079b5e4aefdcb"> 462</a></span> ValueType <a class="code hl_function" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a0994485fcb0b088197d079b5e4aefdcb">get</a> (<span class="keyword">const</span> <a class="code hl_class" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html">PrecomputedFraction<ValueType></a>& f, <span class="keywordtype">int</span> l, <span class="keywordtype">int</span> m)<span class="keyword"> const </span>{</div>
<div class="line"><a id="l00463" name="l00463"></a><span class="lineno"> 463</span> <span class="keywordflow">return</span> <a class="code hl_function" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a952511ac3879736dca7627605b40a4d1">get</a> (f, <a class="code hl_function" href="group__spherical__harmonics.html#ga5296aa18ca79b9a88a46cee00c47667a">index_mpos</a> (l,m));</div>
<div class="line"><a id="l00464" name="l00464"></a><span class="lineno"> 464</span> }</div>
<div class="line"><a id="l00465" name="l00465"></a><span class="lineno"> 465</span> </div>
<div class="line"><a id="l00466" name="l00466"></a><span class="lineno"><a class="line" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a21f948c41eea2390efb0776e3e4967c7"> 466</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a21f948c41eea2390efb0776e3e4967c7">get</a> (ValueType* dest, <span class="keyword">const</span> <a class="code hl_class" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html">PrecomputedFraction<ValueType></a>& f)<span class="keyword"> const </span>{</div>
<div class="line"><a id="l00467" name="l00467"></a><span class="lineno"> 467</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> l = 0; l <= <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a43f9092cedbb0dbcb85bad991b8836d1">lmax</a>; l+=2) {</div>
<div class="line"><a id="l00468" name="l00468"></a><span class="lineno"> 468</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> m = 0; m <= l; m++) {</div>
<div class="line"><a id="l00469" name="l00469"></a><span class="lineno"> 469</span> <span class="keywordtype">int</span> i = <a class="code hl_function" href="group__spherical__harmonics.html#ga5296aa18ca79b9a88a46cee00c47667a">index_mpos</a> (l,m);</div>
<div class="line"><a id="l00470" name="l00470"></a><span class="lineno"> 470</span> dest[i] = <a class="code hl_function" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a952511ac3879736dca7627605b40a4d1">get</a> (f,i);</div>
<div class="line"><a id="l00471" name="l00471"></a><span class="lineno"> 471</span> }</div>
<div class="line"><a id="l00472" name="l00472"></a><span class="lineno"> 472</span> }</div>
<div class="line"><a id="l00473" name="l00473"></a><span class="lineno"> 473</span> }</div>
<div class="line"><a id="l00474" name="l00474"></a><span class="lineno"> 474</span> </div>
<div class="line"><a id="l00475" name="l00475"></a><span class="lineno"> 475</span> <span class="keyword">template</span> <<span class="keyword">class</span> VectorType, <span class="keyword">class</span> UnitVectorType></div>
<div class="line"><a id="l00476" name="l00476"></a><span class="lineno"><a class="line" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#ad067209a63dbe423ca33287d50af65cb"> 476</a></span> ValueType <a class="code hl_function" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#ad067209a63dbe423ca33287d50af65cb">value</a> (<span class="keyword">const</span> VectorType& val, <span class="keyword">const</span> UnitVectorType& unit_dir)<span class="keyword"> const </span>{</div>
<div class="line"><a id="l00477" name="l00477"></a><span class="lineno"> 477</span> <a class="code hl_class" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html">PrecomputedFraction<ValueType></a> f;</div>
<div class="line"><a id="l00478" name="l00478"></a><span class="lineno"> 478</span> <a class="code hl_function" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a257f9f632bd008b2e05f1daf9f63fde5">set</a> (f, std::acos (unit_dir[2]));</div>
<div class="line"><a id="l00479" name="l00479"></a><span class="lineno"> 479</span> ValueType rxy = std::sqrt ( <a class="code hl_function" href="group__elfun.html#ga8bf8967471ef09d762367a1844985db8">pow2</a>(unit_dir[1]) + <a class="code hl_function" href="group__elfun.html#ga8bf8967471ef09d762367a1844985db8">pow2</a>(unit_dir[0]) );</div>
<div class="line"><a id="l00480" name="l00480"></a><span class="lineno"> 480</span> ValueType cp = (rxy) ? unit_dir[0]/rxy : 1.0;</div>
<div class="line"><a id="l00481" name="l00481"></a><span class="lineno"> 481</span> ValueType sp = (rxy) ? unit_dir[1]/rxy : 0.0;</div>
<div class="line"><a id="l00482" name="l00482"></a><span class="lineno"> 482</span> ValueType v = 0.0;</div>
<div class="line"><a id="l00483" name="l00483"></a><span class="lineno"> 483</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> l = 0; l <= <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a43f9092cedbb0dbcb85bad991b8836d1">lmax</a>; l+=2)</div>
<div class="line"><a id="l00484" name="l00484"></a><span class="lineno"> 484</span> v += <a class="code hl_function" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a952511ac3879736dca7627605b40a4d1">get</a> (f,l,0) * val[<a class="code hl_function" href="group__spherical__harmonics.html#ga12049806261f71471fea43484670d8f5">index</a> (l,0)];</div>
<div class="line"><a id="l00485" name="l00485"></a><span class="lineno"> 485</span> ValueType c0 (1.0), s0 (0.0);</div>
<div class="line"><a id="l00486" name="l00486"></a><span class="lineno"> 486</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> m = 1; m <= <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a43f9092cedbb0dbcb85bad991b8836d1">lmax</a>; m++) {</div>
<div class="line"><a id="l00487" name="l00487"></a><span class="lineno"> 487</span> ValueType c = c0 * cp - s0 * sp;</div>
<div class="line"><a id="l00488" name="l00488"></a><span class="lineno"> 488</span> ValueType s = s0 * cp + c0 * sp;</div>
<div class="line"><a id="l00489" name="l00489"></a><span class="lineno"> 489</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> l = ( (m&1) ? m+1 : m); l <= <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a43f9092cedbb0dbcb85bad991b8836d1">lmax</a>; l+=2)</div>
<div class="line"><a id="l00490" name="l00490"></a><span class="lineno"> 490</span> v += <a class="code hl_function" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a952511ac3879736dca7627605b40a4d1">get</a> (f,l,m) * <a class="code hl_variable" href="group__mathconstants.html#ga21f6e669f12fc0caf970538de21793de">Math::sqrt2</a> * (c * val[<a class="code hl_function" href="group__spherical__harmonics.html#ga12049806261f71471fea43484670d8f5">index</a> (l,m)] + s * val[<a class="code hl_function" href="group__spherical__harmonics.html#ga12049806261f71471fea43484670d8f5">index</a> (l,-m)]);</div>
<div class="line"><a id="l00491" name="l00491"></a><span class="lineno"> 491</span> c0 = c;</div>
<div class="line"><a id="l00492" name="l00492"></a><span class="lineno"> 492</span> s0 = s;</div>
<div class="line"><a id="l00493" name="l00493"></a><span class="lineno"> 493</span> }</div>
<div class="line"><a id="l00494" name="l00494"></a><span class="lineno"> 494</span> <span class="keywordflow">return</span> v;</div>
<div class="line"><a id="l00495" name="l00495"></a><span class="lineno"> 495</span> }</div>
<div class="line"><a id="l00496" name="l00496"></a><span class="lineno"> 496</span> </div>
<div class="line"><a id="l00497" name="l00497"></a><span class="lineno"> 497</span> <span class="keyword">protected</span>:</div>
<div class="line"><a id="l00498" name="l00498"></a><span class="lineno"><a class="line" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a43f9092cedbb0dbcb85bad991b8836d1"> 498</a></span> <span class="keywordtype">int</span> <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a43f9092cedbb0dbcb85bad991b8836d1">lmax</a>, <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#ae7c66cf90354d50a6ea0f7185baabf75">ndir</a>, <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a6a6119d535416f86f36e9727525edcdd">nAL</a>;</div>
<div class="line"><a id="l00499" name="l00499"></a><span class="lineno"><a class="line" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a18ec793089fa14f86aa33895b2fe9ae2"> 499</a></span> ValueType <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a18ec793089fa14f86aa33895b2fe9ae2">inc</a>;</div>
<div class="line"><a id="l00500" name="l00500"></a><span class="lineno"><a class="line" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#ad8a14f9e24c12642b7032b368ef153ce"> 500</a></span> <a class="code hl_class" href="class_m_r_1_1vector.html">vector<ValueType></a> <a class="code hl_variable" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#ad8a14f9e24c12642b7032b368ef153ce">AL</a>;</div>
<div class="line"><a id="l00501" name="l00501"></a><span class="lineno"> 501</span> };</div>
<div class="line"><a id="l00502" name="l00502"></a><span class="lineno"> 502</span> </div>
<div class="line"><a id="l00503" name="l00503"></a><span class="lineno"> 503</span> </div>
<div class="line"><a id="l00504" name="l00504"></a><span class="lineno"> 504</span> </div>
<div class="line"><a id="l00505" name="l00505"></a><span class="lineno"> 505</span> </div>
<div class="line"><a id="l00506" name="l00506"></a><span class="lineno"> 506</span> </div>
<div class="line"><a id="l00507" name="l00507"></a><span class="lineno"> 507</span> </div>
<div class="line"><a id="l00509" name="l00509"></a><span class="lineno"> 509</span> </div>
<div class="line"><a id="l00514" name="l00514"></a><span class="lineno"> 514</span> <span class="keyword">template</span> <<span class="keyword">class</span> VectorType, <span class="keyword">class</span> UnitVectorType, <span class="keyword">class</span> ValueType = <span class="keywordtype">float</span>></div>
<div class="line"><a id="l00515" name="l00515"></a><span class="lineno"><a class="line" href="group__spherical__harmonics.html#gab875ad53d217ba8e06a79749d3901f68"> 515</a></span> <span class="keyword">inline</span> <span class="keyword">typename</span> VectorType::Scalar <a class="code hl_function" href="group__spherical__harmonics.html#gab875ad53d217ba8e06a79749d3901f68">get_peak</a> (</div>
<div class="line"><a id="l00516" name="l00516"></a><span class="lineno"> 516</span> <span class="keyword">const</span> VectorType& sh,</div>
<div class="line"><a id="l00517" name="l00517"></a><span class="lineno"> 517</span> <span class="keywordtype">int</span> lmax,</div>
<div class="line"><a id="l00518" name="l00518"></a><span class="lineno"> 518</span> UnitVectorType& unit_init_dir,</div>
<div class="line"><a id="l00519" name="l00519"></a><span class="lineno"> 519</span> <a class="code hl_class" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html">PrecomputedAL<typename VectorType::Scalar></a>* precomputer = <span class="keyword">nullptr</span>)</div>
<div class="line"><a id="l00520" name="l00520"></a><span class="lineno"> 520</span> {</div>
<div class="line"><a id="l00521" name="l00521"></a><span class="lineno"> 521</span> <span class="keyword">using</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> = <span class="keyword">typename</span> VectorType::Scalar;</div>
<div class="line"><a id="l00522" name="l00522"></a><span class="lineno"> 522</span> assert (std::isfinite (unit_init_dir[0]));</div>
<div class="line"><a id="l00523" name="l00523"></a><span class="lineno"> 523</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < 50; i++) {</div>
<div class="line"><a id="l00524" name="l00524"></a><span class="lineno"> 524</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> az = std::atan2 (unit_init_dir[1], unit_init_dir[0]);</div>
<div class="line"><a id="l00525" name="l00525"></a><span class="lineno"> 525</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> <a class="code hl_variable" href="calibrator_8h.html#aed7ba788c50defe48678c3e5359c6ceb">el</a> = std::acos (unit_init_dir[2]);</div>
<div class="line"><a id="l00526" name="l00526"></a><span class="lineno"> 526</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> amplitude, dSH_del, dSH_daz, d2SH_del2, d2SH_deldaz, d2SH_daz2;</div>
<div class="line"><a id="l00527" name="l00527"></a><span class="lineno"> 527</span> <a class="code hl_function" href="group__spherical__harmonics.html#ga3da04937bcc39217f2c49365eb286315">derivatives</a> (sh, lmax, <a class="code hl_variable" href="calibrator_8h.html#aed7ba788c50defe48678c3e5359c6ceb">el</a>, az, amplitude, dSH_del, dSH_daz, d2SH_del2, d2SH_deldaz, d2SH_daz2, precomputer);</div>
<div class="line"><a id="l00528" name="l00528"></a><span class="lineno"> 528</span> </div>
<div class="line"><a id="l00529" name="l00529"></a><span class="lineno"> 529</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> del = sqrt (dSH_del*dSH_del + dSH_daz*dSH_daz);</div>
<div class="line"><a id="l00530" name="l00530"></a><span class="lineno"> 530</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> daz = 0.0;</div>
<div class="line"><a id="l00531" name="l00531"></a><span class="lineno"> 531</span> <span class="keywordflow">if</span> (del != 0.0) {</div>
<div class="line"><a id="l00532" name="l00532"></a><span class="lineno"> 532</span> daz = dSH_daz/del;</div>
<div class="line"><a id="l00533" name="l00533"></a><span class="lineno"> 533</span> del = dSH_del/del;</div>
<div class="line"><a id="l00534" name="l00534"></a><span class="lineno"> 534</span> }</div>
<div class="line"><a id="l00535" name="l00535"></a><span class="lineno"> 535</span> </div>
<div class="line"><a id="l00536" name="l00536"></a><span class="lineno"> 536</span> </div>
<div class="line"><a id="l00537" name="l00537"></a><span class="lineno"> 537</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> dSH_dt = daz*dSH_daz + del*dSH_del;</div>
<div class="line"><a id="l00538" name="l00538"></a><span class="lineno"> 538</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> d2SH_dt2 = daz*daz*d2SH_daz2 + 2.0*daz*del*d2SH_deldaz + del*del*d2SH_del2;</div>
<div class="line"><a id="l00539" name="l00539"></a><span class="lineno"> 539</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> dt = d2SH_dt2 ? (-dSH_dt / d2SH_dt2) : 0.0;</div>
<div class="line"><a id="l00540" name="l00540"></a><span class="lineno"> 540</span> </div>
<div class="line"><a id="l00541" name="l00541"></a><span class="lineno"> 541</span> <span class="keywordflow">if</span> (dt < 0.0) dt = -dt;</div>
<div class="line"><a id="l00542" name="l00542"></a><span class="lineno"> 542</span> <span class="keywordflow">if</span> (dt > <a class="code hl_define" href="_s_h_8h.html#a4ee2d519e14dc95a5ed11efa93fe465f">MAX_DIR_CHANGE</a>) dt = <a class="code hl_define" href="_s_h_8h.html#a4ee2d519e14dc95a5ed11efa93fe465f">MAX_DIR_CHANGE</a>;</div>
<div class="line"><a id="l00543" name="l00543"></a><span class="lineno"> 543</span> </div>
<div class="line"><a id="l00544" name="l00544"></a><span class="lineno"> 544</span> del *= dt;</div>
<div class="line"><a id="l00545" name="l00545"></a><span class="lineno"> 545</span> daz *= dt;</div>
<div class="line"><a id="l00546" name="l00546"></a><span class="lineno"> 546</span> </div>
<div class="line"><a id="l00547" name="l00547"></a><span class="lineno"> 547</span> unit_init_dir[0] += del*std::cos (az) *std::cos (<a class="code hl_variable" href="calibrator_8h.html#aed7ba788c50defe48678c3e5359c6ceb">el</a>) - daz*std::sin (az);</div>
<div class="line"><a id="l00548" name="l00548"></a><span class="lineno"> 548</span> unit_init_dir[1] += del*std::sin (az) *std::cos (<a class="code hl_variable" href="calibrator_8h.html#aed7ba788c50defe48678c3e5359c6ceb">el</a>) + daz*std::cos (az);</div>
<div class="line"><a id="l00549" name="l00549"></a><span class="lineno"> 549</span> unit_init_dir[2] -= del*std::sin (<a class="code hl_variable" href="calibrator_8h.html#aed7ba788c50defe48678c3e5359c6ceb">el</a>);</div>
<div class="line"><a id="l00550" name="l00550"></a><span class="lineno"> 550</span> unit_init_dir.normalize();</div>
<div class="line"><a id="l00551" name="l00551"></a><span class="lineno"> 551</span> </div>
<div class="line"><a id="l00552" name="l00552"></a><span class="lineno"> 552</span> <span class="keywordflow">if</span> (dt < <a class="code hl_define" href="_s_h_8h.html#a5835d2253221816d4f18e65f9796d3c6">ANGLE_TOLERANCE</a>)</div>
<div class="line"><a id="l00553" name="l00553"></a><span class="lineno"> 553</span> <span class="keywordflow">return</span> amplitude;</div>
<div class="line"><a id="l00554" name="l00554"></a><span class="lineno"> 554</span> }</div>
<div class="line"><a id="l00555" name="l00555"></a><span class="lineno"> 555</span> </div>
<div class="line"><a id="l00556" name="l00556"></a><span class="lineno"> 556</span> unit_init_dir = { <a class="code hl_variable" href="namespace_m_r.html#ac8c755bf9a6bd0ee7dfe784c1aff7fcb">NaN</a>, <a class="code hl_variable" href="namespace_m_r.html#ac8c755bf9a6bd0ee7dfe784c1aff7fcb">NaN</a>, <a class="code hl_variable" href="namespace_m_r.html#ac8c755bf9a6bd0ee7dfe784c1aff7fcb">NaN</a> };</div>
<div class="line"><a id="l00557" name="l00557"></a><span class="lineno"> 557</span> <a class="code hl_define" href="exception_8h.html#aecc1f7a8a2493b9e021e5bff76a00a5b">DEBUG</a> (<span class="stringliteral">"failed to find SH peak!"</span>);</div>
<div class="line"><a id="l00558" name="l00558"></a><span class="lineno"> 558</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="namespace_m_r.html#ac8c755bf9a6bd0ee7dfe784c1aff7fcb">NaN</a>;</div>
<div class="line"><a id="l00559" name="l00559"></a><span class="lineno"> 559</span> }</div>
<div class="line"><a id="l00560" name="l00560"></a><span class="lineno"> 560</span> </div>
<div class="line"><a id="l00561" name="l00561"></a><span class="lineno"> 561</span> </div>
<div class="line"><a id="l00562" name="l00562"></a><span class="lineno"> 562</span> </div>
<div class="line"><a id="l00563" name="l00563"></a><span class="lineno"> 563</span> </div>
<div class="line"><a id="l00564" name="l00564"></a><span class="lineno"> 564</span> </div>
<div class="line"><a id="l00565" name="l00565"></a><span class="lineno"> 565</span> </div>
<div class="line"><a id="l00567" name="l00567"></a><span class="lineno"> 567</span> </div>
<div class="line"><a id="l00568" name="l00568"></a><span class="lineno"> 568</span> <span class="keyword">template</span> <<span class="keyword">class</span> VectorType></div>
<div class="line"><a id="l00569" name="l00569"></a><span class="lineno"><a class="line" href="group__spherical__harmonics.html#ga3da04937bcc39217f2c49365eb286315"> 569</a></span> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code hl_function" href="group__spherical__harmonics.html#ga3da04937bcc39217f2c49365eb286315">derivatives</a> (</div>
<div class="line"><a id="l00570" name="l00570"></a><span class="lineno"> 570</span> <span class="keyword">const</span> VectorType& sh,</div>
<div class="line"><a id="l00571" name="l00571"></a><span class="lineno"> 571</span> <span class="keyword">const</span> <span class="keywordtype">int</span> lmax,</div>
<div class="line"><a id="l00572" name="l00572"></a><span class="lineno"> 572</span> <span class="keyword">const</span> <span class="keyword">typename</span> VectorType::Scalar elevation,</div>
<div class="line"><a id="l00573" name="l00573"></a><span class="lineno"> 573</span> <span class="keyword">const</span> <span class="keyword">typename</span> VectorType::Scalar azimuth,</div>
<div class="line"><a id="l00574" name="l00574"></a><span class="lineno"> 574</span> <span class="keyword">typename</span> VectorType::Scalar& amplitude,</div>
<div class="line"><a id="l00575" name="l00575"></a><span class="lineno"> 575</span> <span class="keyword">typename</span> VectorType::Scalar& dSH_del,</div>
<div class="line"><a id="l00576" name="l00576"></a><span class="lineno"> 576</span> <span class="keyword">typename</span> VectorType::Scalar& dSH_daz,</div>
<div class="line"><a id="l00577" name="l00577"></a><span class="lineno"> 577</span> <span class="keyword">typename</span> VectorType::Scalar& d2SH_del2,</div>
<div class="line"><a id="l00578" name="l00578"></a><span class="lineno"> 578</span> <span class="keyword">typename</span> VectorType::Scalar& d2SH_deldaz,</div>
<div class="line"><a id="l00579" name="l00579"></a><span class="lineno"> 579</span> <span class="keyword">typename</span> VectorType::Scalar& d2SH_daz2,</div>
<div class="line"><a id="l00580" name="l00580"></a><span class="lineno"> 580</span> <a class="code hl_class" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html">PrecomputedAL<typename VectorType::Scalar></a>* precomputer)</div>
<div class="line"><a id="l00581" name="l00581"></a><span class="lineno"> 581</span> {</div>
<div class="line"><a id="l00582" name="l00582"></a><span class="lineno"> 582</span> <span class="keyword">using</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> = <span class="keyword">typename</span> VectorType::Scalar;</div>
<div class="line"><a id="l00583" name="l00583"></a><span class="lineno"> 583</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> sel = std::sin (elevation);</div>
<div class="line"><a id="l00584" name="l00584"></a><span class="lineno"> 584</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> cel = std::cos (elevation);</div>
<div class="line"><a id="l00585" name="l00585"></a><span class="lineno"> 585</span> <span class="keywordtype">bool</span> atpole = sel < 1<a class="code hl_variable" href="group__mathconstants.html#ga4bded66901b06bc4f71952e3cd3185ea">e</a>-4;</div>
<div class="line"><a id="l00586" name="l00586"></a><span class="lineno"> 586</span> </div>
<div class="line"><a id="l00587" name="l00587"></a><span class="lineno"> 587</span> dSH_del = dSH_daz = d2SH_del2 = d2SH_deldaz = d2SH_daz2 = 0.0;</div>
<div class="line"><a id="l00588" name="l00588"></a><span class="lineno"> 588</span> <a class="code hl_define" href="group___v_l_a.html#ga5b4337ca14d00af715a3548de3d9bb84">VLA_MAX</a> (AL, <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a>, <a class="code hl_function" href="group__spherical__harmonics.html#ga8bc0c976c67b9eb91e2dfd71bede4fe1">NforL_mpos</a> (lmax), 64);</div>
<div class="line"><a id="l00589" name="l00589"></a><span class="lineno"> 589</span> </div>
<div class="line"><a id="l00590" name="l00590"></a><span class="lineno"> 590</span> <span class="keywordflow">if</span> (precomputer) {</div>
<div class="line"><a id="l00591" name="l00591"></a><span class="lineno"> 591</span> <a class="code hl_class" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html">PrecomputedFraction<value_type></a> f;</div>
<div class="line"><a id="l00592" name="l00592"></a><span class="lineno"> 592</span> precomputer-><a class="code hl_function" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a257f9f632bd008b2e05f1daf9f63fde5">set</a> (f, elevation);</div>
<div class="line"><a id="l00593" name="l00593"></a><span class="lineno"> 593</span> precomputer-><a class="code hl_function" href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a952511ac3879736dca7627605b40a4d1">get</a> (AL, f);</div>
<div class="line"><a id="l00594" name="l00594"></a><span class="lineno"> 594</span> }</div>
<div class="line"><a id="l00595" name="l00595"></a><span class="lineno"> 595</span> <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00596" name="l00596"></a><span class="lineno"> 596</span> Eigen::Matrix<value_type,Eigen::Dynamic,1,0,64> buf (lmax+1);</div>
<div class="line"><a id="l00597" name="l00597"></a><span class="lineno"> 597</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> m = 0; m <= lmax; m++) {</div>
<div class="line"><a id="l00598" name="l00598"></a><span class="lineno"> 598</span> <a class="code hl_function" href="namespace_m_r_1_1_math_1_1_legendre.html#ae7d37ead0eeef3573191552be77aa9be">Legendre::Plm_sph</a> (buf, lmax, m, cel);</div>
<div class="line"><a id="l00599" name="l00599"></a><span class="lineno"> 599</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> l = ( (m&1) ?m+1:m); l <= lmax; l+=2)</div>
<div class="line"><a id="l00600" name="l00600"></a><span class="lineno"> 600</span> AL[<a class="code hl_function" href="group__spherical__harmonics.html#ga5296aa18ca79b9a88a46cee00c47667a">index_mpos</a> (l,m)] = buf[l];</div>
<div class="line"><a id="l00601" name="l00601"></a><span class="lineno"> 601</span> }</div>
<div class="line"><a id="l00602" name="l00602"></a><span class="lineno"> 602</span> }</div>
<div class="line"><a id="l00603" name="l00603"></a><span class="lineno"> 603</span> </div>
<div class="line"><a id="l00604" name="l00604"></a><span class="lineno"> 604</span> amplitude = sh[0] * AL[0];</div>
<div class="line"><a id="l00605" name="l00605"></a><span class="lineno"> 605</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> l = 2; l <= (int) lmax; l+=2) {</div>
<div class="line"><a id="l00606" name="l00606"></a><span class="lineno"> 606</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a>& v (sh[<a class="code hl_function" href="group__spherical__harmonics.html#ga12049806261f71471fea43484670d8f5">index</a> (l,0)]);</div>
<div class="line"><a id="l00607" name="l00607"></a><span class="lineno"> 607</span> amplitude += v * AL[<a class="code hl_function" href="group__spherical__harmonics.html#ga5296aa18ca79b9a88a46cee00c47667a">index_mpos</a> (l,0)];</div>
<div class="line"><a id="l00608" name="l00608"></a><span class="lineno"> 608</span> dSH_del += v * sqrt (<a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> (l* (l+1))) * AL[<a class="code hl_function" href="group__spherical__harmonics.html#ga5296aa18ca79b9a88a46cee00c47667a">index_mpos</a> (l,1)];</div>
<div class="line"><a id="l00609" name="l00609"></a><span class="lineno"> 609</span> d2SH_del2 += v * (sqrt (<a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> (l* (l+1) * (l-1) * (l+2))) * AL[<a class="code hl_function" href="group__spherical__harmonics.html#ga5296aa18ca79b9a88a46cee00c47667a">index_mpos</a> (l,2)] - l* (l+1) * AL[<a class="code hl_function" href="group__spherical__harmonics.html#ga5296aa18ca79b9a88a46cee00c47667a">index_mpos</a> (l,0)]) /2.0;</div>
<div class="line"><a id="l00610" name="l00610"></a><span class="lineno"> 610</span> }</div>
<div class="line"><a id="l00611" name="l00611"></a><span class="lineno"> 611</span> </div>
<div class="line"><a id="l00612" name="l00612"></a><span class="lineno"> 612</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> m = 1; m <= lmax; m++) {</div>
<div class="line"><a id="l00613" name="l00613"></a><span class="lineno"> 613</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> caz = <a class="code hl_variable" href="group__mathconstants.html#ga21f6e669f12fc0caf970538de21793de">Math::sqrt2</a> * std::cos (m*azimuth);</div>
<div class="line"><a id="l00614" name="l00614"></a><span class="lineno"> 614</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> saz = <a class="code hl_variable" href="group__mathconstants.html#ga21f6e669f12fc0caf970538de21793de">Math::sqrt2</a> * std::sin (m*azimuth);</div>
<div class="line"><a id="l00615" name="l00615"></a><span class="lineno"> 615</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> l = ( (m&1) ? m+1 : m); l <= lmax; l+=2) {</div>
<div class="line"><a id="l00616" name="l00616"></a><span class="lineno"> 616</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a>& vp (sh[<a class="code hl_function" href="group__spherical__harmonics.html#ga12049806261f71471fea43484670d8f5">index</a> (l,m)]);</div>
<div class="line"><a id="l00617" name="l00617"></a><span class="lineno"> 617</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a>& vm (sh[<a class="code hl_function" href="group__spherical__harmonics.html#ga12049806261f71471fea43484670d8f5">index</a> (l,-m)]);</div>
<div class="line"><a id="l00618" name="l00618"></a><span class="lineno"> 618</span> amplitude += (vp*caz + vm*saz) * AL[<a class="code hl_function" href="group__spherical__harmonics.html#ga5296aa18ca79b9a88a46cee00c47667a">index_mpos</a> (l,m)];</div>
<div class="line"><a id="l00619" name="l00619"></a><span class="lineno"> 619</span> </div>
<div class="line"><a id="l00620" name="l00620"></a><span class="lineno"> 620</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> tmp = sqrt (<a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> ( (l+m) * (l-m+1))) * AL[<a class="code hl_function" href="group__spherical__harmonics.html#ga5296aa18ca79b9a88a46cee00c47667a">index_mpos</a> (l,m-1)];</div>
<div class="line"><a id="l00621" name="l00621"></a><span class="lineno"> 621</span> <span class="keywordflow">if</span> (l > m) tmp -= sqrt (<a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> ( (l-m) * (l+m+1))) * AL[<a class="code hl_function" href="group__spherical__harmonics.html#ga5296aa18ca79b9a88a46cee00c47667a">index_mpos</a> (l,m+1)];</div>
<div class="line"><a id="l00622" name="l00622"></a><span class="lineno"> 622</span> tmp /= -2.0;</div>
<div class="line"><a id="l00623" name="l00623"></a><span class="lineno"> 623</span> dSH_del += (vp*caz + vm*saz) * tmp;</div>
<div class="line"><a id="l00624" name="l00624"></a><span class="lineno"> 624</span> </div>
<div class="line"><a id="l00625" name="l00625"></a><span class="lineno"> 625</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> tmp2 = - ( (l+m) * (l-m+1) + (l-m) * (l+m+1)) * AL[<a class="code hl_function" href="group__spherical__harmonics.html#ga5296aa18ca79b9a88a46cee00c47667a">index_mpos</a> (l,m)];</div>
<div class="line"><a id="l00626" name="l00626"></a><span class="lineno"> 626</span> <span class="keywordflow">if</span> (m == 1) tmp2 -= sqrt (<a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> ( (l+m) * (l-m+1) * (l+m-1) * (l-m+2))) * AL[<a class="code hl_function" href="group__spherical__harmonics.html#ga5296aa18ca79b9a88a46cee00c47667a">index_mpos</a> (l,1)];</div>
<div class="line"><a id="l00627" name="l00627"></a><span class="lineno"> 627</span> <span class="keywordflow">else</span> tmp2 += sqrt (<a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> ( (l+m) * (l-m+1) * (l+m-1) * (l-m+2))) * AL[<a class="code hl_function" href="group__spherical__harmonics.html#ga5296aa18ca79b9a88a46cee00c47667a">index_mpos</a> (l,m-2)];</div>
<div class="line"><a id="l00628" name="l00628"></a><span class="lineno"> 628</span> <span class="keywordflow">if</span> (l > m+1) tmp2 += sqrt (<a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> ( (l-m) * (l+m+1) * (l-m-1) * (l+m+2))) * AL[<a class="code hl_function" href="group__spherical__harmonics.html#ga5296aa18ca79b9a88a46cee00c47667a">index_mpos</a> (l,m+2)];</div>
<div class="line"><a id="l00629" name="l00629"></a><span class="lineno"> 629</span> tmp2 /= 4.0;</div>
<div class="line"><a id="l00630" name="l00630"></a><span class="lineno"> 630</span> d2SH_del2 += (vp*caz + vm*saz) * tmp2;</div>
<div class="line"><a id="l00631" name="l00631"></a><span class="lineno"> 631</span> </div>
<div class="line"><a id="l00632" name="l00632"></a><span class="lineno"> 632</span> <span class="keywordflow">if</span> (atpole) dSH_daz += (vm*caz - vp*saz) * tmp;</div>
<div class="line"><a id="l00633" name="l00633"></a><span class="lineno"> 633</span> <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00634" name="l00634"></a><span class="lineno"> 634</span> d2SH_deldaz += m * (vm*caz - vp*saz) * tmp;</div>
<div class="line"><a id="l00635" name="l00635"></a><span class="lineno"> 635</span> dSH_daz += m * (vm*caz - vp*saz) * AL[<a class="code hl_function" href="group__spherical__harmonics.html#ga5296aa18ca79b9a88a46cee00c47667a">index_mpos</a> (l,m)];</div>
<div class="line"><a id="l00636" name="l00636"></a><span class="lineno"> 636</span> d2SH_daz2 -= (vp*caz + vm*saz) * m*m * AL[<a class="code hl_function" href="group__spherical__harmonics.html#ga5296aa18ca79b9a88a46cee00c47667a">index_mpos</a> (l,m)];</div>
<div class="line"><a id="l00637" name="l00637"></a><span class="lineno"> 637</span> }</div>
<div class="line"><a id="l00638" name="l00638"></a><span class="lineno"> 638</span> </div>
<div class="line"><a id="l00639" name="l00639"></a><span class="lineno"> 639</span> }</div>
<div class="line"><a id="l00640" name="l00640"></a><span class="lineno"> 640</span> }</div>
<div class="line"><a id="l00641" name="l00641"></a><span class="lineno"> 641</span> </div>
<div class="line"><a id="l00642" name="l00642"></a><span class="lineno"> 642</span> <span class="keywordflow">if</span> (!atpole) {</div>
<div class="line"><a id="l00643" name="l00643"></a><span class="lineno"> 643</span> dSH_daz /= sel;</div>
<div class="line"><a id="l00644" name="l00644"></a><span class="lineno"> 644</span> d2SH_deldaz /= sel;</div>
<div class="line"><a id="l00645" name="l00645"></a><span class="lineno"> 645</span> d2SH_daz2 /= sel*sel;</div>
<div class="line"><a id="l00646" name="l00646"></a><span class="lineno"> 646</span> }</div>
<div class="line"><a id="l00647" name="l00647"></a><span class="lineno"> 647</span> }</div>
<div class="line"><a id="l00648" name="l00648"></a><span class="lineno"> 648</span> </div>
<div class="line"><a id="l00649" name="l00649"></a><span class="lineno"> 649</span> </div>
<div class="line"><a id="l00650" name="l00650"></a><span class="lineno"> 650</span> </div>
<div class="line"><a id="l00652" name="l00652"></a><span class="lineno"><a class="line" href="class_m_r_1_1_math_1_1_s_h_1_1a_p_s_f.html"> 652</a></span> <span class="keyword">template</span> <<span class="keyword">typename</span> ValueType> <span class="keyword">class </span><a class="code hl_class" href="class_m_r_1_1_math_1_1_s_h_1_1a_p_s_f.html">aPSF</a></div>
<div class="line"><a id="l00653" name="l00653"></a><span class="lineno"> 653</span> { MEMALIGN(<a class="code hl_class" href="class_m_r_1_1_math_1_1_s_h_1_1a_p_s_f.html">aPSF<ValueType></a>)</div>
<div class="line"><a id="l00654" name="l00654"></a><span class="lineno"> 654</span> <span class="keyword">public</span>:</div>
<div class="line"><a id="l00655" name="l00655"></a><span class="lineno"> 655</span> <a class="code hl_class" href="class_m_r_1_1_math_1_1_s_h_1_1a_p_s_f.html">aPSF</a> (<span class="keyword">const</span> <span class="keywordtype">size_t</span> lmax) :</div>
<div class="line"><a id="l00656" name="l00656"></a><span class="lineno"> 656</span> lmax (lmax),</div>
<div class="line"><a id="l00657" name="l00657"></a><span class="lineno"> 657</span> RH (lmax/2 + 1)</div>
<div class="line"><a id="l00658" name="l00658"></a><span class="lineno"> 658</span> {</div>
<div class="line"><a id="l00659" name="l00659"></a><span class="lineno"> 659</span> <span class="keywordflow">switch</span> (lmax) {</div>
<div class="line"><a id="l00660" name="l00660"></a><span class="lineno"> 660</span> <span class="keywordflow">case</span> 2:</div>
<div class="line"><a id="l00661" name="l00661"></a><span class="lineno"> 661</span> RH[0] = ValueType(1.00000000);</div>
<div class="line"><a id="l00662" name="l00662"></a><span class="lineno"> 662</span> RH[1] = ValueType(0.41939279);</div>
<div class="line"><a id="l00663" name="l00663"></a><span class="lineno"> 663</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00664" name="l00664"></a><span class="lineno"> 664</span> <span class="keywordflow">case</span> 4:</div>
<div class="line"><a id="l00665" name="l00665"></a><span class="lineno"> 665</span> RH[0] = ValueType(1.00000000);</div>
<div class="line"><a id="l00666" name="l00666"></a><span class="lineno"> 666</span> RH[1] = ValueType(0.63608543);</div>
<div class="line"><a id="l00667" name="l00667"></a><span class="lineno"> 667</span> RH[2] = ValueType(0.18487087);</div>
<div class="line"><a id="l00668" name="l00668"></a><span class="lineno"> 668</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00669" name="l00669"></a><span class="lineno"> 669</span> <span class="keywordflow">case</span> 6:</div>
<div class="line"><a id="l00670" name="l00670"></a><span class="lineno"> 670</span> RH[0] = ValueType(1.00000000);</div>
<div class="line"><a id="l00671" name="l00671"></a><span class="lineno"> 671</span> RH[1] = ValueType(0.75490341);</div>
<div class="line"><a id="l00672" name="l00672"></a><span class="lineno"> 672</span> RH[2] = ValueType(0.37126442);</div>
<div class="line"><a id="l00673" name="l00673"></a><span class="lineno"> 673</span> RH[3] = ValueType(0.09614699);</div>
<div class="line"><a id="l00674" name="l00674"></a><span class="lineno"> 674</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00675" name="l00675"></a><span class="lineno"> 675</span> <span class="keywordflow">case</span> 8:</div>
<div class="line"><a id="l00676" name="l00676"></a><span class="lineno"> 676</span> RH[0] = ValueType(1.00000000);</div>
<div class="line"><a id="l00677" name="l00677"></a><span class="lineno"> 677</span> RH[1] = ValueType(0.82384816);</div>
<div class="line"><a id="l00678" name="l00678"></a><span class="lineno"> 678</span> RH[2] = ValueType(0.51261696);</div>
<div class="line"><a id="l00679" name="l00679"></a><span class="lineno"> 679</span> RH[3] = ValueType(0.22440563);</div>
<div class="line"><a id="l00680" name="l00680"></a><span class="lineno"> 680</span> RH[4] = ValueType(0.05593079);</div>
<div class="line"><a id="l00681" name="l00681"></a><span class="lineno"> 681</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00682" name="l00682"></a><span class="lineno"> 682</span> <span class="keywordflow">case</span> 10:</div>
<div class="line"><a id="l00683" name="l00683"></a><span class="lineno"> 683</span> RH[0] = ValueType(1.00000000);</div>
<div class="line"><a id="l00684" name="l00684"></a><span class="lineno"> 684</span> RH[1] = ValueType(0.86725945);</div>
<div class="line"><a id="l00685" name="l00685"></a><span class="lineno"> 685</span> RH[2] = ValueType(0.61519436);</div>
<div class="line"><a id="l00686" name="l00686"></a><span class="lineno"> 686</span> RH[3] = ValueType(0.34570667);</div>
<div class="line"><a id="l00687" name="l00687"></a><span class="lineno"> 687</span> RH[4] = ValueType(0.14300355);</div>
<div class="line"><a id="l00688" name="l00688"></a><span class="lineno"> 688</span> RH[5] = ValueType(0.03548062);</div>
<div class="line"><a id="l00689" name="l00689"></a><span class="lineno"> 689</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00690" name="l00690"></a><span class="lineno"> 690</span> <span class="keywordflow">case</span> 12:</div>
<div class="line"><a id="l00691" name="l00691"></a><span class="lineno"> 691</span> RH[0] = ValueType(1.00000000);</div>
<div class="line"><a id="l00692" name="l00692"></a><span class="lineno"> 692</span> RH[1] = ValueType(0.89737759);</div>
<div class="line"><a id="l00693" name="l00693"></a><span class="lineno"> 693</span> RH[2] = ValueType(0.69278503);</div>
<div class="line"><a id="l00694" name="l00694"></a><span class="lineno"> 694</span> RH[3] = ValueType(0.45249879);</div>
<div class="line"><a id="l00695" name="l00695"></a><span class="lineno"> 695</span> RH[4] = ValueType(0.24169922);</div>
<div class="line"><a id="l00696" name="l00696"></a><span class="lineno"> 696</span> RH[5] = ValueType(0.09826171);</div>
<div class="line"><a id="l00697" name="l00697"></a><span class="lineno"> 697</span> RH[6] = ValueType(0.02502481);</div>
<div class="line"><a id="l00698" name="l00698"></a><span class="lineno"> 698</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00699" name="l00699"></a><span class="lineno"> 699</span> <span class="keywordflow">case</span> 14:</div>
<div class="line"><a id="l00700" name="l00700"></a><span class="lineno"> 700</span> RH[0] = ValueType(1.00000000);</div>
<div class="line"><a id="l00701" name="l00701"></a><span class="lineno"> 701</span> RH[1] = ValueType(0.91717853);</div>
<div class="line"><a id="l00702" name="l00702"></a><span class="lineno"> 702</span> RH[2] = ValueType(0.74685644);</div>
<div class="line"><a id="l00703" name="l00703"></a><span class="lineno"> 703</span> RH[3] = ValueType(0.53467773);</div>
<div class="line"><a id="l00704" name="l00704"></a><span class="lineno"> 704</span> RH[4] = ValueType(0.33031863);</div>
<div class="line"><a id="l00705" name="l00705"></a><span class="lineno"> 705</span> RH[5] = ValueType(0.17013825);</div>
<div class="line"><a id="l00706" name="l00706"></a><span class="lineno"> 706</span> RH[6] = ValueType(0.06810155);</div>
<div class="line"><a id="l00707" name="l00707"></a><span class="lineno"> 707</span> RH[7] = ValueType(0.01754930);</div>
<div class="line"><a id="l00708" name="l00708"></a><span class="lineno"> 708</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00709" name="l00709"></a><span class="lineno"> 709</span> <span class="keywordflow">case</span> 16:</div>
<div class="line"><a id="l00710" name="l00710"></a><span class="lineno"> 710</span> RH[0] = ValueType(1.00000000);</div>
<div class="line"><a id="l00711" name="l00711"></a><span class="lineno"> 711</span> RH[1] = ValueType(0.93261196);</div>
<div class="line"><a id="l00712" name="l00712"></a><span class="lineno"> 712</span> RH[2] = ValueType(0.79064858);</div>
<div class="line"><a id="l00713" name="l00713"></a><span class="lineno"> 713</span> RH[3] = ValueType(0.60562880);</div>
<div class="line"><a id="l00714" name="l00714"></a><span class="lineno"> 714</span> RH[4] = ValueType(0.41454703);</div>
<div class="line"><a id="l00715" name="l00715"></a><span class="lineno"> 715</span> RH[5] = ValueType(0.24880754);</div>
<div class="line"><a id="l00716" name="l00716"></a><span class="lineno"> 716</span> RH[6] = ValueType(0.12661242);</div>
<div class="line"><a id="l00717" name="l00717"></a><span class="lineno"> 717</span> RH[7] = ValueType(0.05106681);</div>
<div class="line"><a id="l00718" name="l00718"></a><span class="lineno"> 718</span> RH[8] = ValueType(0.01365433);</div>
<div class="line"><a id="l00719" name="l00719"></a><span class="lineno"> 719</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00720" name="l00720"></a><span class="lineno"> 720</span> <span class="keywordflow">default</span>:</div>
<div class="line"><a id="l00721" name="l00721"></a><span class="lineno"> 721</span> <span class="keywordflow">throw</span> <a class="code hl_class" href="class_m_r_1_1_exception.html">Exception</a> (<span class="stringliteral">"No aPSF RH data for lmax "</span> + <a class="code hl_function" href="namespace_m_r.html#a7dcea37fdb5fba1961d121fca36c22c4">str</a>(lmax));</div>
<div class="line"><a id="l00722" name="l00722"></a><span class="lineno"> 722</span> }</div>
<div class="line"><a id="l00723" name="l00723"></a><span class="lineno"> 723</span> }</div>
<div class="line"><a id="l00724" name="l00724"></a><span class="lineno"> 724</span> </div>
<div class="line"><a id="l00725" name="l00725"></a><span class="lineno"> 725</span> </div>
<div class="line"><a id="l00726" name="l00726"></a><span class="lineno"> 726</span> <span class="keyword">template</span> <<span class="keyword">class</span> VectorType, <span class="keyword">class</span> UnitVectorType></div>
<div class="line"><a id="l00727" name="l00727"></a><span class="lineno"> 727</span> VectorType& operator() (VectorType& sh, <span class="keyword">const</span> UnitVectorType& dir)<span class="keyword"> const</span></div>
<div class="line"><a id="l00728" name="l00728"></a><span class="lineno"> 728</span><span class="keyword"> </span>{</div>
<div class="line"><a id="l00729" name="l00729"></a><span class="lineno"> 729</span> sh.resize (RH.size());</div>
<div class="line"><a id="l00730" name="l00730"></a><span class="lineno"> 730</span> <a class="code hl_function" href="group__spherical__harmonics.html#ga52bc9df51a5f151972235a9a0df09c51">delta</a> (sh, dir, lmax);</div>
<div class="line"><a id="l00731" name="l00731"></a><span class="lineno"> 731</span> <span class="keywordflow">return</span> <a class="code hl_function" href="group__spherical__harmonics.html#ga3f0ca8fb7a027f28cf4360d4c81cec04">sconv</a> (sh, RH);</div>
<div class="line"><a id="l00732" name="l00732"></a><span class="lineno"> 732</span> }</div>
<div class="line"><a id="l00733" name="l00733"></a><span class="lineno"> 733</span> </div>
<div class="line"><a id="l00734" name="l00734"></a><span class="lineno"> 734</span> <span class="keyword">inline</span> <span class="keyword">const</span> Eigen::Matrix<ValueType,Eigen::Dynamic,1>& RH_coefs()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> RH; }</div>
<div class="line"><a id="l00735" name="l00735"></a><span class="lineno"> 735</span> </div>
<div class="line"><a id="l00736" name="l00736"></a><span class="lineno"> 736</span> <span class="keyword">private</span>:</div>
<div class="line"><a id="l00737" name="l00737"></a><span class="lineno"> 737</span> <span class="keyword">const</span> <span class="keywordtype">size_t</span> lmax;</div>
<div class="line"><a id="l00738" name="l00738"></a><span class="lineno"> 738</span> Eigen::Matrix<ValueType,Eigen::Dynamic,1> RH;</div>
<div class="line"><a id="l00739" name="l00739"></a><span class="lineno"> 739</span> </div>
<div class="line"><a id="l00740" name="l00740"></a><span class="lineno"> 740</span> };</div>
<div class="line"><a id="l00741" name="l00741"></a><span class="lineno"> 741</span> </div>
<div class="line"><a id="l00742" name="l00742"></a><span class="lineno"> 742</span> </div>
<div class="line"><a id="l00744" name="l00744"></a><span class="lineno"> 744</span> <span class="keyword">template</span> <<span class="keyword">class</span> ImageType></div>
<div class="line"><a id="l00745" name="l00745"></a><span class="lineno"><a class="line" href="group__spherical__harmonics.html#ga02fbff506863d7c1a4b79eea0ac5660c"> 745</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="group__spherical__harmonics.html#ga02fbff506863d7c1a4b79eea0ac5660c">check</a> (<span class="keyword">const</span> ImageType& <a class="code hl_variable" href="noise__estimator_8h.html#aaebed747e975509a9b8470c6d7ba93b3">H</a>) {</div>
<div class="line"><a id="l00746" name="l00746"></a><span class="lineno"> 746</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="noise__estimator_8h.html#aaebed747e975509a9b8470c6d7ba93b3">H</a>.ndim() < 4)</div>
<div class="line"><a id="l00747" name="l00747"></a><span class="lineno"> 747</span> <span class="keywordflow">throw</span> <a class="code hl_class" href="class_m_r_1_1_exception.html">Exception</a> (<span class="stringliteral">"image \""</span> + <a class="code hl_variable" href="noise__estimator_8h.html#aaebed747e975509a9b8470c6d7ba93b3">H</a>.name() + <span class="stringliteral">"\" does not contain SH coefficients - not 4D"</span>);</div>
<div class="line"><a id="l00748" name="l00748"></a><span class="lineno"> 748</span> <span class="keywordtype">size_t</span> l = <a class="code hl_function" href="group__spherical__harmonics.html#ga28d9e09433f42e5036ec45ed6e7806bf">LforN</a> (<a class="code hl_variable" href="noise__estimator_8h.html#aaebed747e975509a9b8470c6d7ba93b3">H</a>.size(3));</div>
<div class="line"><a id="l00749" name="l00749"></a><span class="lineno"> 749</span> <span class="keywordflow">if</span> (l%2 || <a class="code hl_function" href="group__spherical__harmonics.html#ga96a93012c20066bfbdb6c1a1ec1cfe15">NforL</a> (l) != <span class="keywordtype">size_t</span> (<a class="code hl_variable" href="noise__estimator_8h.html#aaebed747e975509a9b8470c6d7ba93b3">H</a>.size(3)))</div>
<div class="line"><a id="l00750" name="l00750"></a><span class="lineno"> 750</span> <span class="keywordflow">throw</span> <a class="code hl_class" href="class_m_r_1_1_exception.html">Exception</a> (<span class="stringliteral">"image \""</span> + <a class="code hl_variable" href="noise__estimator_8h.html#aaebed747e975509a9b8470c6d7ba93b3">H</a>.name() + <span class="stringliteral">"\" does not contain SH coefficients - unexpected number of coefficients"</span>);</div>
<div class="line"><a id="l00751" name="l00751"></a><span class="lineno"> 751</span> }</div>
<div class="line"><a id="l00754" name="l00754"></a><span class="lineno"> 754</span> }</div>
<div class="line"><a id="l00755" name="l00755"></a><span class="lineno"> 755</span> }</div>
<div class="line"><a id="l00756" name="l00756"></a><span class="lineno"> 756</span>}</div>
<div class="line"><a id="l00757" name="l00757"></a><span class="lineno"> 757</span> </div>
<div class="line"><a id="l00758" name="l00758"></a><span class="lineno"> 758</span><span class="preprocessor">#endif</span></div>
<div class="ttc" id="a_s_h_8h_html_a4ee2d519e14dc95a5ed11efa93fe465f"><div class="ttname"><a href="_s_h_8h.html#a4ee2d519e14dc95a5ed11efa93fe465f">MAX_DIR_CHANGE</a></div><div class="ttdeci">#define MAX_DIR_CHANGE</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00023">SH.h:23</a></div></div>
<div class="ttc" id="a_s_h_8h_html_a5835d2253221816d4f18e65f9796d3c6"><div class="ttname"><a href="_s_h_8h.html#a5835d2253221816d4f18e65f9796d3c6">ANGLE_TOLERANCE</a></div><div class="ttdeci">#define ANGLE_TOLERANCE</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00024">SH.h:24</a></div></div>
<div class="ttc" id="acalibrator_8h_html_aed7ba788c50defe48678c3e5359c6ceb"><div class="ttname"><a href="calibrator_8h.html#aed7ba788c50defe48678c3e5359c6ceb">el</a></div><div class="ttdeci">float el</div><div class="ttdef"><b>Definition:</b> <a href="calibrator_8h_source.html#l00061">calibrator.h:61</a></div></div>
<div class="ttc" id="aclass_m_r_1_1_exception_html"><div class="ttname"><a href="class_m_r_1_1_exception.html">MR::Exception</a></div><div class="ttdef"><b>Definition:</b> <a href="exception_8h_source.html#l00080">exception.h:80</a></div></div>
<div class="ttc" id="aclass_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l_html"><div class="ttname"><a href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html">MR::Math::SH::PrecomputedAL</a></div><div class="ttdoc">Precomputed Associated Legrendre Polynomials - used to speed up SH calculation.</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00399">SH.h:400</a></div></div>
<div class="ttc" id="aclass_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l_html_a0994485fcb0b088197d079b5e4aefdcb"><div class="ttname"><a href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a0994485fcb0b088197d079b5e4aefdcb">MR::Math::SH::PrecomputedAL::get</a></div><div class="ttdeci">ValueType get(const PrecomputedFraction< ValueType > &f, int l, int m) const</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00462">SH.h:462</a></div></div>
<div class="ttc" id="aclass_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l_html_a18ec793089fa14f86aa33895b2fe9ae2"><div class="ttname"><a href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a18ec793089fa14f86aa33895b2fe9ae2">MR::Math::SH::PrecomputedAL::inc</a></div><div class="ttdeci">ValueType inc</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00499">SH.h:499</a></div></div>
<div class="ttc" id="aclass_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l_html_a21f948c41eea2390efb0776e3e4967c7"><div class="ttname"><a href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a21f948c41eea2390efb0776e3e4967c7">MR::Math::SH::PrecomputedAL::get</a></div><div class="ttdeci">void get(ValueType *dest, const PrecomputedFraction< ValueType > &f) const</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00466">SH.h:466</a></div></div>
<div class="ttc" id="aclass_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l_html_a257f9f632bd008b2e05f1daf9f63fde5"><div class="ttname"><a href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a257f9f632bd008b2e05f1daf9f63fde5">MR::Math::SH::PrecomputedAL::set</a></div><div class="ttdeci">void set(PrecomputedFraction< ValueType > &f, const ValueType elevation) const</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00435">SH.h:435</a></div></div>
<div class="ttc" id="aclass_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l_html_a43f9092cedbb0dbcb85bad991b8836d1"><div class="ttname"><a href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a43f9092cedbb0dbcb85bad991b8836d1">MR::Math::SH::PrecomputedAL::lmax</a></div><div class="ttdeci">int lmax</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00498">SH.h:498</a></div></div>
<div class="ttc" id="aclass_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l_html_a5200182a2011b5d515566206c19e7cf9"><div class="ttname"><a href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a5200182a2011b5d515566206c19e7cf9">MR::Math::SH::PrecomputedAL::value_type</a></div><div class="ttdeci">ValueType value_type</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00402">SH.h:402</a></div></div>
<div class="ttc" id="aclass_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l_html_a696f88bb74943bca452a577e66881ae2"><div class="ttname"><a href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a696f88bb74943bca452a577e66881ae2">MR::Math::SH::PrecomputedAL::PrecomputedAL</a></div><div class="ttdeci">PrecomputedAL()</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00404">SH.h:404</a></div></div>
<div class="ttc" id="aclass_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l_html_a6a6119d535416f86f36e9727525edcdd"><div class="ttname"><a href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a6a6119d535416f86f36e9727525edcdd">MR::Math::SH::PrecomputedAL::nAL</a></div><div class="ttdeci">int nAL</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00498">SH.h:498</a></div></div>
<div class="ttc" id="aclass_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l_html_a8f99a41e649a21f5b720dfba19adfb6d"><div class="ttname"><a href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a8f99a41e649a21f5b720dfba19adfb6d">MR::Math::SH::PrecomputedAL::operator!</a></div><div class="ttdeci">bool operator!() const</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00409">SH.h:409</a></div></div>
<div class="ttc" id="aclass_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l_html_a952511ac3879736dca7627605b40a4d1"><div class="ttname"><a href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#a952511ac3879736dca7627605b40a4d1">MR::Math::SH::PrecomputedAL::get</a></div><div class="ttdeci">ValueType get(const PrecomputedFraction< ValueType > &f, int i) const</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00457">SH.h:457</a></div></div>
<div class="ttc" id="aclass_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l_html_aad1616bf86f6cdaf3082883cb4587235"><div class="ttname"><a href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#aad1616bf86f6cdaf3082883cb4587235">MR::Math::SH::PrecomputedAL::PrecomputedAL</a></div><div class="ttdeci">PrecomputedAL(int up_to_lmax, int num_dir=512)</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00405">SH.h:405</a></div></div>
<div class="ttc" id="aclass_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l_html_abf387a092dd79918ee55850af5fc4487"><div class="ttname"><a href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#abf387a092dd79918ee55850af5fc4487">MR::Math::SH::PrecomputedAL::init</a></div><div class="ttdeci">void init(int up_to_lmax, int num_dir=512)</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00416">SH.h:416</a></div></div>
<div class="ttc" id="aclass_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l_html_ad067209a63dbe423ca33287d50af65cb"><div class="ttname"><a href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#ad067209a63dbe423ca33287d50af65cb">MR::Math::SH::PrecomputedAL::value</a></div><div class="ttdeci">ValueType value(const VectorType &val, const UnitVectorType &unit_dir) const</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00476">SH.h:476</a></div></div>
<div class="ttc" id="aclass_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l_html_ad8a14f9e24c12642b7032b368ef153ce"><div class="ttname"><a href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#ad8a14f9e24c12642b7032b368ef153ce">MR::Math::SH::PrecomputedAL::AL</a></div><div class="ttdeci">vector< ValueType > AL</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00500">SH.h:500</a></div></div>
<div class="ttc" id="aclass_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l_html_ae7c66cf90354d50a6ea0f7185baabf75"><div class="ttname"><a href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_a_l.html#ae7c66cf90354d50a6ea0f7185baabf75">MR::Math::SH::PrecomputedAL::ndir</a></div><div class="ttdeci">int ndir</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00498">SH.h:498</a></div></div>
<div class="ttc" id="aclass_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction_html"><div class="ttname"><a href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html">MR::Math::SH::PrecomputedFraction</a></div><div class="ttdoc">used to speed up SH calculation</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00389">SH.h:390</a></div></div>
<div class="ttc" id="aclass_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction_html_a1451b1b8c15f79fc827d649b8b08a307"><div class="ttname"><a href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#a1451b1b8c15f79fc827d649b8b08a307">MR::Math::SH::PrecomputedFraction::f2</a></div><div class="ttdeci">ValueType f2</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00393">SH.h:393</a></div></div>
<div class="ttc" id="aclass_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction_html_a37ad42ae2b21d95dd7c78ec4157c13ec"><div class="ttname"><a href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#a37ad42ae2b21d95dd7c78ec4157c13ec">MR::Math::SH::PrecomputedFraction::f1</a></div><div class="ttdeci">ValueType f1</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00393">SH.h:393</a></div></div>
<div class="ttc" id="aclass_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction_html_a436160f61b3c92f8857bc39877138aac"><div class="ttname"><a href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#a436160f61b3c92f8857bc39877138aac">MR::Math::SH::PrecomputedFraction::p1</a></div><div class="ttdeci">vector< ValueType >::const_iterator p1</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00394">SH.h:394</a></div></div>
<div class="ttc" id="aclass_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction_html_a641595bdfbc4a2c80b8a947bda6a4d49"><div class="ttname"><a href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#a641595bdfbc4a2c80b8a947bda6a4d49">MR::Math::SH::PrecomputedFraction::p2</a></div><div class="ttdeci">vector< ValueType >::const_iterator p2</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00394">SH.h:394</a></div></div>
<div class="ttc" id="aclass_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction_html_aae6e40afb9de8d1797b0b363b891e137"><div class="ttname"><a href="class_m_r_1_1_math_1_1_s_h_1_1_precomputed_fraction.html#aae6e40afb9de8d1797b0b363b891e137">MR::Math::SH::PrecomputedFraction::PrecomputedFraction</a></div><div class="ttdeci">PrecomputedFraction()</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00392">SH.h:392</a></div></div>
<div class="ttc" id="aclass_m_r_1_1_math_1_1_s_h_1_1_transform_html"><div class="ttname"><a href="class_m_r_1_1_math_1_1_s_h_1_1_transform.html">MR::Math::SH::Transform</a></div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00189">SH.h:189</a></div></div>
<div class="ttc" id="aclass_m_r_1_1_math_1_1_s_h_1_1_transform_html_a090fc82b5df426e29a31cfe1d85cba72"><div class="ttname"><a href="class_m_r_1_1_math_1_1_s_h_1_1_transform.html#a090fc82b5df426e29a31cfe1d85cba72">MR::Math::SH::Transform::iSHT</a></div><div class="ttdeci">matrix_type iSHT</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00227">SH.h:227</a></div></div>
<div class="ttc" id="aclass_m_r_1_1_math_1_1_s_h_1_1_transform_html_a3f3e81061b4248a70e8ccca3c13fa903"><div class="ttname"><a href="class_m_r_1_1_math_1_1_s_h_1_1_transform.html#a3f3e81061b4248a70e8ccca3c13fa903">MR::Math::SH::Transform::SHT</a></div><div class="ttdeci">matrix_type SHT</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00227">SH.h:227</a></div></div>
<div class="ttc" id="aclass_m_r_1_1_math_1_1_s_h_1_1a_p_s_f_html"><div class="ttname"><a href="class_m_r_1_1_math_1_1_s_h_1_1a_p_s_f.html">MR::Math::SH::aPSF</a></div><div class="ttdoc">a class to hold the coefficients for an apodised point-spread function.</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00652">SH.h:653</a></div></div>
<div class="ttc" id="aclass_m_r_1_1vector_html"><div class="ttname"><a href="class_m_r_1_1vector.html">MR::vector</a></div><div class="ttdef"><b>Definition:</b> <a href="src_2surface_2types_8h_source.html#l00253">types.h:253</a></div></div>
<div class="ttc" id="aexception_8h_html_aecc1f7a8a2493b9e021e5bff76a00a5b"><div class="ttname"><a href="exception_8h.html#aecc1f7a8a2493b9e021e5bff76a00a5b">DEBUG</a></div><div class="ttdeci">#define DEBUG(msg)</div><div class="ttdef"><b>Definition:</b> <a href="exception_8h_source.html#l00075">exception.h:75</a></div></div>
<div class="ttc" id="agroup___v_l_a_html_ga5b4337ca14d00af715a3548de3d9bb84"><div class="ttname"><a href="group___v_l_a.html#ga5b4337ca14d00af715a3548de3d9bb84">VLA_MAX</a></div><div class="ttdeci">#define VLA_MAX(name, type, num, max)</div><div class="ttdef"><b>Definition:</b> <a href="src_2surface_2types_8h_source.html#l00119">types.h:119</a></div></div>
<div class="ttc" id="agroup__elfun_html_ga8bf8967471ef09d762367a1844985db8"><div class="ttname"><a href="group__elfun.html#ga8bf8967471ef09d762367a1844985db8">MR::Math::pow2</a></div><div class="ttdeci">constexpr T pow2(const T &v)</div><div class="ttdef"><b>Definition:</b> <a href="math_8h_source.html#l00053">math.h:53</a></div></div>
<div class="ttc" id="agroup__ls_html_gaaacadd3d43de898a784044dcfa3e1363"><div class="ttname"><a href="group__ls.html#gaaacadd3d43de898a784044dcfa3e1363">MR::Math::pinv</a></div><div class="ttdeci">Eigen::Matrix< typename MatrixType::Scalar, Eigen::Dynamic, Eigen::Dynamic > pinv(const MatrixType &M)</div><div class="ttdoc">return Moore-Penrose pseudo-inverse of M</div><div class="ttdef"><b>Definition:</b> <a href="least__squares_8h_source.html#l00039">least_squares.h:39</a></div></div>
<div class="ttc" id="agroup__mathconstants_html_ga21f6e669f12fc0caf970538de21793de"><div class="ttname"><a href="group__mathconstants.html#ga21f6e669f12fc0caf970538de21793de">MR::Math::sqrt2</a></div><div class="ttdeci">constexpr double sqrt2</div><div class="ttdef"><b>Definition:</b> <a href="math_8h_source.html#l00043">math.h:43</a></div></div>
<div class="ttc" id="agroup__mathconstants_html_ga4bded66901b06bc4f71952e3cd3185ea"><div class="ttname"><a href="group__mathconstants.html#ga4bded66901b06bc4f71952e3cd3185ea">MR::Math::e</a></div><div class="ttdeci">constexpr double e</div><div class="ttdef"><b>Definition:</b> <a href="math_8h_source.html#l00039">math.h:39</a></div></div>
<div class="ttc" id="agroup__mathconstants_html_gafe1ee4d398733ae71a15130062a9c2a4"><div class="ttname"><a href="group__mathconstants.html#gafe1ee4d398733ae71a15130062a9c2a4">MR::Math::pi</a></div><div class="ttdeci">constexpr double pi</div><div class="ttdef"><b>Definition:</b> <a href="math_8h_source.html#l00040">math.h:40</a></div></div>
<div class="ttc" id="agroup__spherical__harmonics_html_ga02fbff506863d7c1a4b79eea0ac5660c"><div class="ttname"><a href="group__spherical__harmonics.html#ga02fbff506863d7c1a4b79eea0ac5660c">MR::Math::SH::check</a></div><div class="ttdeci">void check(const ImageType &H)</div><div class="ttdoc">convenience function to check if an input image can contain SH coefficients</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00745">SH.h:745</a></div></div>
<div class="ttc" id="agroup__spherical__harmonics_html_ga12049806261f71471fea43484670d8f5"><div class="ttname"><a href="group__spherical__harmonics.html#ga12049806261f71471fea43484670d8f5">MR::Math::SH::index</a></div><div class="ttdeci">size_t index(int l, int m)</div><div class="ttdoc">compute the index for coefficient (l,m)</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00052">SH.h:52</a></div></div>
<div class="ttc" id="agroup__spherical__harmonics_html_ga24a1163b39e02424abbe3ed456bb0a1c"><div class="ttname"><a href="group__spherical__harmonics.html#ga24a1163b39e02424abbe3ed456bb0a1c">MR::Math::SH::scale_degrees_inverse</a></div><div class="ttdeci">void scale_degrees_inverse(MatrixType &amp2SH_mapping, const VectorType &coefs)</div><div class="ttdoc">scale the coefficients of each SH degree by the corresponding value in coefs</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00163">SH.h:163</a></div></div>
<div class="ttc" id="agroup__spherical__harmonics_html_ga28d9e09433f42e5036ec45ed6e7806bf"><div class="ttname"><a href="group__spherical__harmonics.html#ga28d9e09433f42e5036ec45ed6e7806bf">MR::Math::SH::LforN</a></div><div class="ttdeci">size_t LforN(int N)</div><div class="ttdoc">returns the largest lmax given N parameters</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00070">SH.h:70</a></div></div>
<div class="ttc" id="agroup__spherical__harmonics_html_ga301ff6a6409f78ce405d2ed51f2bdbde"><div class="ttname"><a href="group__spherical__harmonics.html#ga301ff6a6409f78ce405d2ed51f2bdbde">MR::Math::SH::scale_degrees_forward</a></div><div class="ttdeci">void scale_degrees_forward(MatrixType &SH2amp_mapping, const VectorType &coefs)</div><div class="ttdoc">scale the coefficients of each SH degree by the corresponding value in coefs</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00147">SH.h:147</a></div></div>
<div class="ttc" id="agroup__spherical__harmonics_html_ga38a57752a9e47b22f391d7952a24e91e"><div class="ttname"><a href="group__spherical__harmonics.html#ga38a57752a9e47b22f391d7952a24e91e">MR::Math::SH::init_transform_cart</a></div><div class="ttdeci">Eigen::Matrix< typename MatrixType::Scalar, Eigen::Dynamic, Eigen::Dynamic > init_transform_cart(const MatrixType &dirs, const int lmax)</div><div class="ttdoc">form the SH->amplitudes matrix</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00111">SH.h:111</a></div></div>
<div class="ttc" id="agroup__spherical__harmonics_html_ga3da04937bcc39217f2c49365eb286315"><div class="ttname"><a href="group__spherical__harmonics.html#ga3da04937bcc39217f2c49365eb286315">MR::Math::SH::derivatives</a></div><div class="ttdeci">void derivatives(const VectorType &sh, const int lmax, const typename VectorType::Scalar elevation, const typename VectorType::Scalar azimuth, typename VectorType::Scalar &amplitude, typename VectorType::Scalar &dSH_del, typename VectorType::Scalar &dSH_daz, typename VectorType::Scalar &d2SH_del2, typename VectorType::Scalar &d2SH_deldaz, typename VectorType::Scalar &d2SH_daz2, PrecomputedAL< typename VectorType::Scalar > *precomputer)</div><div class="ttdoc">computes first and second order derivatives of SH series</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00569">SH.h:569</a></div></div>
<div class="ttc" id="agroup__spherical__harmonics_html_ga3f0ca8fb7a027f28cf4360d4c81cec04"><div class="ttname"><a href="group__spherical__harmonics.html#ga3f0ca8fb7a027f28cf4360d4c81cec04">MR::Math::SH::sconv</a></div><div class="ttdeci">VectorType1 & sconv(VectorType1 &sh, const VectorType2 &RH)</div><div class="ttdoc">perform spherical convolution, in place</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00333">SH.h:333</a></div></div>
<div class="ttc" id="agroup__spherical__harmonics_html_ga5296aa18ca79b9a88a46cee00c47667a"><div class="ttname"><a href="group__spherical__harmonics.html#ga5296aa18ca79b9a88a46cee00c47667a">MR::Math::SH::index_mpos</a></div><div class="ttdeci">size_t index_mpos(int l, int m)</div><div class="ttdoc">same as index(), but consider only non-negative orders m</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00064">SH.h:64</a></div></div>
<div class="ttc" id="agroup__spherical__harmonics_html_ga52bc9df51a5f151972235a9a0df09c51"><div class="ttname"><a href="group__spherical__harmonics.html#ga52bc9df51a5f151972235a9a0df09c51">MR::Math::SH::delta</a></div><div class="ttdeci">VectorType1 & delta(VectorType1 &delta_vec, const VectorType2 &unit_dir, int lmax)</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00279">SH.h:279</a></div></div>
<div class="ttc" id="agroup__spherical__harmonics_html_ga8bc0c976c67b9eb91e2dfd71bede4fe1"><div class="ttname"><a href="group__spherical__harmonics.html#ga8bc0c976c67b9eb91e2dfd71bede4fe1">MR::Math::SH::NforL_mpos</a></div><div class="ttdeci">size_t NforL_mpos(int lmax)</div><div class="ttdoc">same as NforL(), but consider only non-negative orders m</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00058">SH.h:58</a></div></div>
<div class="ttc" id="agroup__spherical__harmonics_html_ga96a93012c20066bfbdb6c1a1ec1cfe15"><div class="ttname"><a href="group__spherical__harmonics.html#ga96a93012c20066bfbdb6c1a1ec1cfe15">MR::Math::SH::NforL</a></div><div class="ttdeci">size_t NforL(int lmax)</div><div class="ttdoc">the number of (even-degree) coefficients for the given value of lmax</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00046">SH.h:46</a></div></div>
<div class="ttc" id="agroup__spherical__harmonics_html_gaa0311aadd5154d4d23d2cdaa29532bac"><div class="ttname"><a href="group__spherical__harmonics.html#gaa0311aadd5154d4d23d2cdaa29532bac">MR::Math::SH::sconv_mat</a></div><div class="ttdeci">MatrixType1 & sconv_mat(MatrixType1 &sh, const VectorType2 &RH)</div><div class="ttdoc">perform spherical convolution, in place</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00367">SH.h:367</a></div></div>
<div class="ttc" id="agroup__spherical__harmonics_html_gaafe2e54ee9df648cfb1372aa7ae2fa6a"><div class="ttname"><a href="group__spherical__harmonics.html#gaafe2e54ee9df648cfb1372aa7ae2fa6a">MR::Math::SH::encoding_description</a></div><div class="ttdeci">const char * encoding_description</div><div class="ttdoc">a string containing a description of the SH storage convention</div></div>
<div class="ttc" id="agroup__spherical__harmonics_html_gab875ad53d217ba8e06a79749d3901f68"><div class="ttname"><a href="group__spherical__harmonics.html#gab875ad53d217ba8e06a79749d3901f68">MR::Math::SH::get_peak</a></div><div class="ttdeci">VectorType::Scalar get_peak(const VectorType &sh, int lmax, UnitVectorType &unit_init_dir, PrecomputedAL< typename VectorType::Scalar > *precomputer=nullptr)</div><div class="ttdoc">estimate direction & amplitude of SH peak</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00515">SH.h:515</a></div></div>
<div class="ttc" id="agroup__spherical__harmonics_html_gac405578b4137cf1c22a0cf646d260b05"><div class="ttname"><a href="group__spherical__harmonics.html#gac405578b4137cf1c22a0cf646d260b05">MR::Math::SH::value</a></div><div class="ttdeci">VectorType::Scalar value(const VectorType &coefs, typename VectorType::Scalar cos_elevation, typename VectorType::Scalar cos_azimuth, typename VectorType::Scalar sin_azimuth, int lmax)</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00233">SH.h:233</a></div></div>
<div class="ttc" id="agroup__spherical__harmonics_html_gac81b86466a7e80070f5161be93cebd6a"><div class="ttname"><a href="group__spherical__harmonics.html#gac81b86466a7e80070f5161be93cebd6a">MR::Math::SH::init_transform</a></div><div class="ttdeci">Eigen::Matrix< typename MatrixType::Scalar, Eigen::Dynamic, Eigen::Dynamic > init_transform(const MatrixType &dirs, const int lmax)</div><div class="ttdoc">form the SH->amplitudes matrix</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00082">SH.h:82</a></div></div>
<div class="ttc" id="agroup__spherical__harmonics_html_gae4d9b83d1a1e715d2faebceaf79c559a"><div class="ttname"><a href="group__spherical__harmonics.html#gae4d9b83d1a1e715d2faebceaf79c559a">MR::Math::SH::SH2RH</a></div><div class="ttdeci">VectorType1 & SH2RH(VectorType1 &RH, const VectorType2 &sh)</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00308">SH.h:308</a></div></div>
<div class="ttc" id="agroup__spherical__harmonics_html_gaf710913e46f5cbefa76894d6135aef4c"><div class="ttname"><a href="group__spherical__harmonics.html#gaf710913e46f5cbefa76894d6135aef4c">MR::Math::SH::invert</a></div><div class="ttdeci">Eigen::Matrix< typename VectorType::Scalar, Eigen::Dynamic, 1 > invert(const VectorType &coefs)</div><div class="ttdoc">invert any non-zero coefficients in coefs</div><div class="ttdef"><b>Definition:</b> <a href="_s_h_8h_source.html#l00180">SH.h:180</a></div></div>
<div class="ttc" id="aleast__squares_8h_html"><div class="ttname"><a href="least__squares_8h.html">least_squares.h</a></div></div>
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<div class="ttc" id="amemory_8h_html_a5d1aa93e600a93cee8523d1d34c1ace5"><div class="ttname"><a href="memory_8h.html#a5d1aa93e600a93cee8523d1d34c1ace5">NOMEMALIGN</a></div><div class="ttdeci">#define NOMEMALIGN</div><div class="ttdef"><b>Definition:</b> <a href="memory_8h_source.html#l00022">memory.h:22</a></div></div>
<div class="ttc" id="anamespace_m_r_1_1_math_1_1_legendre_html_ae7d37ead0eeef3573191552be77aa9be"><div class="ttname"><a href="namespace_m_r_1_1_math_1_1_legendre.html#ae7d37ead0eeef3573191552be77aa9be">MR::Math::Legendre::Plm_sph</a></div><div class="ttdeci">ValueType Plm_sph(const int l, const int m, const ValueType x)</div><div class="ttdef"><b>Definition:</b> <a href="legendre_8h_source.html#l00073">legendre.h:73</a></div></div>
<div class="ttc" id="anamespace_m_r_1_1_math_1_1_stats_html_a5e7ca9d7689e3c74384e428ec1d9d9a9"><div class="ttname"><a href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">MR::Math::Stats::value_type</a></div><div class="ttdeci">MR::default_type value_type</div><div class="ttdef"><b>Definition:</b> <a href="typedefs_8h_source.html#l00033">typedefs.h:33</a></div></div>
<div class="ttc" id="anamespace_m_r_1_1_math_1_1_stats_html_ab2ff7634bcab80ba308522254376964e"><div class="ttname"><a href="namespace_m_r_1_1_math_1_1_stats.html#ab2ff7634bcab80ba308522254376964e">MR::Math::Stats::matrix_type</a></div><div class="ttdeci">Eigen::Matrix< value_type, Eigen::Dynamic, Eigen::Dynamic > matrix_type</div><div class="ttdef"><b>Definition:</b> <a href="typedefs_8h_source.html#l00034">typedefs.h:34</a></div></div>
<div class="ttc" id="anamespace_m_r_html"><div class="ttname"><a href="namespace_m_r.html">MR</a></div><div class="ttdef"><b>Definition:</b> <a href="core_2adapter_2base_8h_source.html#l00023">base.h:24</a></div></div>
<div class="ttc" id="anamespace_m_r_html_a7dcea37fdb5fba1961d121fca36c22c4"><div class="ttname"><a href="namespace_m_r.html#a7dcea37fdb5fba1961d121fca36c22c4">MR::str</a></div><div class="ttdeci">std::string str(const T &value, int precision=0)</div><div class="ttdef"><b>Definition:</b> <a href="mrtrix_8h_source.html#l00247">mrtrix.h:247</a></div></div>
<div class="ttc" id="anamespace_m_r_html_ac8c755bf9a6bd0ee7dfe784c1aff7fcb"><div class="ttname"><a href="namespace_m_r.html#ac8c755bf9a6bd0ee7dfe784c1aff7fcb">MR::NaN</a></div><div class="ttdeci">constexpr default_type NaN</div><div class="ttdef"><b>Definition:</b> <a href="src_2surface_2types_8h_source.html#l00230">types.h:230</a></div></div>
<div class="ttc" id="anoise__estimator_8h_html_aaebed747e975509a9b8470c6d7ba93b3"><div class="ttname"><a href="noise__estimator_8h.html#aaebed747e975509a9b8470c6d7ba93b3">H</a></div><div class="ttdeci">Eigen::MatrixXd H</div><div class="ttdef"><b>Definition:</b> <a href="noise__estimator_8h_source.html#l00065">noise_estimator.h:65</a></div></div>
<div class="ttc" id="asrc_2surface_2types_8h_html_a11d7eae3ab5178ebcf0e62cae9c26cd4"><div class="ttname"><a href="src_2surface_2types_8h.html#a11d7eae3ab5178ebcf0e62cae9c26cd4">MEMALIGN</a></div><div class="ttdeci">#define MEMALIGN(...)</div><div class="ttdef"><b>Definition:</b> <a href="src_2surface_2types_8h_source.html#l00185">types.h:185</a></div></div>
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