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<a href="_z_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_ZSH_h__</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#define __math_ZSH_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 <Eigen/Dense></span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span> </div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="preprocessor">#include "<a class="code" href="legendre_8h.html">math/legendre.h</a>"</span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</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="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="preprocessor">#include "<a class="code" href="_s_h_8h.html">math/SH.h</a>"</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_z_s_h.html"> 30</a></span> <span class="keyword">namespace </span>ZSH</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="l00042" name="l00042"></a><span class="lineno"><a class="line" href="group__zonal__spherical__harmonics.html#ga8df7da8e0754a5e4e0cffb711d37c32c"> 42</a></span> <span class="keyword">inline</span> <span class="keywordtype">size_t</span> <a class="code hl_function" href="group__zonal__spherical__harmonics.html#ga8df7da8e0754a5e4e0cffb711d37c32c">NforL</a> (<span class="keywordtype">int</span> lmax)</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> {</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <span class="keywordflow">return</span> (1 + lmax/2);</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> }</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> </div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"><a class="line" href="group__zonal__spherical__harmonics.html#ga5864439cc87e0e54e0c138400389ca77"> 48</a></span> <span class="keyword">inline</span> <span class="keywordtype">size_t</span> <a class="code hl_function" href="group__zonal__spherical__harmonics.html#ga5864439cc87e0e54e0c138400389ca77">index</a> (<span class="keywordtype">int</span> l)</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> <span class="keywordflow">return</span> (l/2);</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> }</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> </div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"><a class="line" href="group__zonal__spherical__harmonics.html#ga91d0c1c4376953a96dc8f66986326025"> 54</a></span> <span class="keyword">inline</span> <span class="keywordtype">size_t</span> <a class="code hl_function" href="group__zonal__spherical__harmonics.html#ga91d0c1c4376953a96dc8f66986326025">LforN</a> (<span class="keywordtype">int</span> N)</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> <span class="keywordflow">return</span> (2 * (N-1));</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> }</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> </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> </div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> </div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="keyword">template</span> <<span class="keyword">typename</span> value_type, <span class="keyword">class</span> VectorType></div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"><a class="line" href="group__zonal__spherical__harmonics.html#gafc48d35e555ae9719610682ab20e40fd"> 66</a></span> Eigen::Matrix<value_type, Eigen::Dynamic, Eigen::Dynamic> <a class="code hl_function" href="group__zonal__spherical__harmonics.html#gafc48d35e555ae9719610682ab20e40fd">init_amp_transform</a> (<span class="keyword">const</span> VectorType& els, <span class="keyword">const</span> <span class="keywordtype">size_t</span> lmax)</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> Eigen::Matrix<value_type, Eigen::Dynamic, Eigen::Dynamic> ZSHT;</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> ZSHT.resize (els.size(), <a class="code hl_function" href="group__zonal__spherical__harmonics.html#ga8df7da8e0754a5e4e0cffb711d37c32c">ZSH::NforL</a> (lmax));</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> Eigen::Matrix<value_type, Eigen::Dynamic, 1, 0, 64> AL (lmax+1);</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i != size_t(els.size()); i++) {</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</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, std::cos (els[i]));</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> l = 0; l <= lmax; l += 2)</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> ZSHT (i,<a class="code hl_function" href="group__zonal__spherical__harmonics.html#ga5864439cc87e0e54e0c138400389ca77">index</a>(l)) = AL[l];</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> <span class="keywordflow">return</span> ZSHT;</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> }</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> </div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> </div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> </div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> </div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="keyword">template</span> <<span class="keyword">typename</span> value_type, <span class="keyword">class</span> VectorType></div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"><a class="line" href="group__zonal__spherical__harmonics.html#gac82e336c373264a210657efd7916f38d"> 87</a></span> Eigen::Matrix<value_type, Eigen::Dynamic, Eigen::Dynamic> <a class="code hl_function" href="group__zonal__spherical__harmonics.html#gac82e336c373264a210657efd7916f38d">init_deriv_transform</a> (<span class="keyword">const</span> VectorType& els, <span class="keyword">const</span> <span class="keywordtype">size_t</span> lmax)</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> {</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> Eigen::Matrix<value_type, Eigen::Dynamic, Eigen::Dynamic> dZSHdelT;</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> dZSHdelT.resize (els.size(), <a class="code hl_function" href="group__zonal__spherical__harmonics.html#ga8df7da8e0754a5e4e0cffb711d37c32c">ZSH::NforL</a> (lmax));</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> Eigen::Matrix<value_type, Eigen::Dynamic, 1, 0, 64> AL (lmax+1);</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i != size_t(els.size()); i++) {</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <a class="code hl_function" href="namespace_m_r_1_1_math_1_1_legendre.html#ae7d37ead0eeef3573191552be77aa9be">Legendre::Plm_sph</a> (AL, lmax, 1, std::cos (els[i]));</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> dZSHdelT (i,<a class="code hl_function" href="group__zonal__spherical__harmonics.html#ga5864439cc87e0e54e0c138400389ca77">index</a>(0)) = 0.0;</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> l = 2; l <= lmax; l += 2)</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> dZSHdelT (i,<a class="code hl_function" href="group__zonal__spherical__harmonics.html#ga5864439cc87e0e54e0c138400389ca77">index</a>(l)) = AL[l] * sqrt (<a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> (l*(l+1)));</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> }</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="keywordflow">return</span> dZSHdelT;</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> }</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> </div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <span class="keyword">template</span> <<span class="keyword">typename</span> ValueType></div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"><a class="line" href="class_m_r_1_1_math_1_1_z_s_h_1_1_transform.html"> 105</a></span> <span class="keyword">class </span><a class="code hl_class" href="class_m_r_1_1_math_1_1_z_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_z_s_h_1_1_transform.html">Transform<ValueType></a>)</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> <span class="keyword">public</span>:</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</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="l00108" name="l00108"></a><span class="lineno"> 108</span> </div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <span class="keyword">template</span> <<span class="keyword">class</span> MatrixType></div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <a class="code hl_class" href="class_m_r_1_1_math_1_1_z_s_h_1_1_transform.html">Transform</a> (<span class="keyword">const</span> MatrixType& dirs, <span class="keyword">const</span> <span class="keywordtype">size_t</span> lmax) :</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <a class="code hl_variable" href="group__zonal__spherical__harmonics.html#ga54f4e536cedd651e736a1b0ec45e293d">ZSHT</a> (<a class="code hl_function" href="group__zonal__spherical__harmonics.html#gafc48d35e555ae9719610682ab20e40fd">init_amp_transform</a> (dirs.col(1), lmax)), <span class="comment">// Elevation angles are second column of aximuth/elevation matrix</span></div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> <a class="code hl_variable" href="group__zonal__spherical__harmonics.html#ga80cc68559e8f44ab9421be587aead31c">iZSHT</a> (<a class="code hl_function" href="group__ls.html#gaaacadd3d43de898a784044dcfa3e1363">pinv</a> (<a class="code hl_variable" href="group__zonal__spherical__harmonics.html#ga54f4e536cedd651e736a1b0ec45e293d">ZSHT</a>)) { }</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> </div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <span class="keyword">template</span> <<span class="keyword">class</span> VectorType1, <span class="keyword">class</span> VectorType2></div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="keywordtype">void</span> A2ZSH (VectorType1& zsh, <span class="keyword">const</span> VectorType2& amplitudes)<span class="keyword"> const </span>{</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> zsh.noalias() = <a class="code hl_variable" href="group__zonal__spherical__harmonics.html#ga80cc68559e8f44ab9421be587aead31c">iZSHT</a> * amplitudes;</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> }</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <span class="keyword">template</span> <<span class="keyword">class</span> VectorType1, <span class="keyword">class</span> VectorType2></div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <span class="keywordtype">void</span> ZSH2A (VectorType1& amplitudes, <span class="keyword">const</span> VectorType2& zsh)<span class="keyword"> const </span>{</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> amplitudes.noalias() = <a class="code hl_variable" href="group__zonal__spherical__harmonics.html#ga54f4e536cedd651e736a1b0ec45e293d">ZSHT</a> * zsh;</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> }</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> </div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <span class="keywordtype">size_t</span> n_ZSH ()<span class="keyword"> const </span>{</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="group__zonal__spherical__harmonics.html#ga54f4e536cedd651e736a1b0ec45e293d">ZSHT</a>.cols();</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> }</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <span class="keywordtype">size_t</span> n_amp ()<span class="keyword"> const </span>{</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="group__zonal__spherical__harmonics.html#ga54f4e536cedd651e736a1b0ec45e293d">ZSHT</a>.rows();</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> }</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> </div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</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_A2ZSH ()<span class="keyword"> const </span>{</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="group__zonal__spherical__harmonics.html#ga80cc68559e8f44ab9421be587aead31c">iZSHT</a>;</div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> }</div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</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_ZSH2A ()<span class="keyword"> const </span>{</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="group__zonal__spherical__harmonics.html#ga54f4e536cedd651e736a1b0ec45e293d">ZSHT</a>;</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> </div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> <span class="keyword">protected</span>:</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"><a class="line" href="group__zonal__spherical__harmonics.html#ga80cc68559e8f44ab9421be587aead31c"> 138</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="group__zonal__spherical__harmonics.html#ga54f4e536cedd651e736a1b0ec45e293d">ZSHT</a>, <a class="code hl_variable" href="group__zonal__spherical__harmonics.html#ga80cc68559e8f44ab9421be587aead31c">iZSHT</a>;</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> </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> <span class="keyword">template</span> <<span class="keyword">class</span> VectorType></div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"><a class="line" href="group__zonal__spherical__harmonics.html#gad07ed92fb96436c2e32c038501363332"> 144</a></span> <span class="keyword">inline</span> <span class="keyword">typename</span> VectorType::Scalar <a class="code hl_function" href="group__zonal__spherical__harmonics.html#gad07ed92fb96436c2e32c038501363332">value</a> (</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> <span class="keyword">const</span> VectorType& coefs,</div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <span class="keyword">typename</span> VectorType::Scalar elevation,</div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> <span class="keyword">const</span> <span class="keywordtype">size_t</span> lmax)</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> <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="l00150" name="l00150"></a><span class="lineno"> 150</span> Eigen::Matrix<value_type, Eigen::Dynamic, 1, 0, 64> AL (lmax+1);</div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</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, std::cos(elevation));</div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</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="l00153" name="l00153"></a><span class="lineno"> 153</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> l = 0; l <= lmax; l += 2)</div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> amplitude += AL[l] * coefs[<a class="code hl_function" href="group__zonal__spherical__harmonics.html#ga5864439cc87e0e54e0c138400389ca77">index</a>(l)];</div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> <span class="keywordflow">return</span> amplitude;</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> <span class="keyword">template</span> <<span class="keyword">class</span> VectorType></div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"><a class="line" href="group__zonal__spherical__harmonics.html#ga504fda03427ae2e965a29e526543df51"> 161</a></span> <span class="keyword">inline</span> <span class="keyword">typename</span> VectorType::Scalar <a class="code hl_function" href="group__zonal__spherical__harmonics.html#ga504fda03427ae2e965a29e526543df51">derivative</a> (</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> <span class="keyword">const</span> VectorType& coefs,</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> <span class="keyword">const</span> <span class="keyword">typename</span> VectorType::Scalar elevation,</div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> <span class="keyword">const</span> <span class="keywordtype">size_t</span> lmax)</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> {</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</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="l00167" name="l00167"></a><span class="lineno"> 167</span> Eigen::Matrix<value_type, Eigen::Dynamic, 1, 0, 64> AL (lmax+1);</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> <a class="code hl_function" href="namespace_m_r_1_1_math_1_1_legendre.html#ae7d37ead0eeef3573191552be77aa9be">Legendre::Plm_sph</a> (AL, lmax, 1, std::cos (elevation));</div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> <a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> dZSH_del = 0.0;</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> l = 2; l <= lmax; l += 2)</div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> dZSH_del += AL[l] * coefs[<a class="code hl_function" href="group__zonal__spherical__harmonics.html#ga5864439cc87e0e54e0c138400389ca77">index</a>(l)] * sqrt (<a class="code hl_typedef" href="namespace_m_r_1_1_math_1_1_stats.html#a5e7ca9d7689e3c74384e428ec1d9d9a9">value_type</a> (l*(l+1)));</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> <span class="keywordflow">return</span> dZSH_del;</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> <span class="keyword">template</span> <<span class="keyword">class</span> VectorType1, <span class="keyword">class</span> VectorType2></div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"><a class="line" href="group__zonal__spherical__harmonics.html#ga08c23193bee5994196f782d5a01631bf"> 178</a></span> <span class="keyword">inline</span> VectorType1& <a class="code hl_function" href="group__zonal__spherical__harmonics.html#ga08c23193bee5994196f782d5a01631bf">ZSH2SH</a> (VectorType1& sh, <span class="keyword">const</span> VectorType2& zsh)</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> {</div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> <span class="keyword">const</span> <span class="keywordtype">size_t</span> lmax = <a class="code hl_function" href="group__zonal__spherical__harmonics.html#ga91d0c1c4376953a96dc8f66986326025">LforN</a> (zsh.size());</div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> sh.resize (<a class="code hl_function" href="group__spherical__harmonics.html#ga96a93012c20066bfbdb6c1a1ec1cfe15">Math::SH::NforL</a> (lmax));</div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i != size_t(sh.size()); ++i)</div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> sh[i] = 0.0;</div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> l = 0; l <= lmax; l+=2)</div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> sh[<a class="code hl_function" href="group__spherical__harmonics.html#ga12049806261f71471fea43484670d8f5">Math::SH::index</a>(l,0)] = zsh[<a class="code hl_function" href="group__zonal__spherical__harmonics.html#ga5864439cc87e0e54e0c138400389ca77">index</a>(l)];</div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> <span class="keywordflow">return</span> sh;</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> </div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> <span class="keyword">template</span> <<span class="keyword">class</span> VectorType></div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"><a class="line" href="group__zonal__spherical__harmonics.html#gad404aa52b4975653abad431b6140dee5"> 190</a></span> <span class="keyword">inline</span> Eigen::Matrix<typename VectorType::Scalar, Eigen::Dynamic, 1> <a class="code hl_function" href="group__zonal__spherical__harmonics.html#ga08c23193bee5994196f782d5a01631bf">ZSH2SH</a> (<span class="keyword">const</span> VectorType& zsh)</div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> {</div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> Eigen::Matrix<typename VectorType::Scalar, Eigen::Dynamic, 1> sh;</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> <a class="code hl_function" href="group__zonal__spherical__harmonics.html#ga08c23193bee5994196f782d5a01631bf">ZSH2SH</a> (sh, zsh);</div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> <span class="keywordflow">return</span> sh;</div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> }</div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> </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> </div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> </div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> <span class="keyword">template</span> <<span class="keyword">class</span> VectorType1, <span class="keyword">class</span> VectorType2></div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"><a class="line" href="group__zonal__spherical__harmonics.html#ga9be2bfabf4a9cf7decca0d9a4855798b"> 201</a></span> <span class="keyword">inline</span> VectorType1& <a class="code hl_function" href="group__zonal__spherical__harmonics.html#ga9be2bfabf4a9cf7decca0d9a4855798b">SH2ZSH</a> (VectorType1& zsh, <span class="keyword">const</span> VectorType2& sh)</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">const</span> <span class="keywordtype">size_t</span> lmax = <a class="code hl_function" href="group__spherical__harmonics.html#ga28d9e09433f42e5036ec45ed6e7806bf">Math::SH::LforN</a> (sh.size());</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> zsh.resize (<a class="code hl_function" href="group__zonal__spherical__harmonics.html#ga8df7da8e0754a5e4e0cffb711d37c32c">NforL</a> (lmax));</div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> l = 0; l <= lmax; l+=2)</div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> zsh[<a class="code hl_function" href="group__zonal__spherical__harmonics.html#ga5864439cc87e0e54e0c138400389ca77">index</a>(l)] = sh[<a class="code hl_function" href="group__spherical__harmonics.html#ga12049806261f71471fea43484670d8f5">Math::SH::index</a>(l,0)];</div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> <span class="keywordflow">return</span> zsh;</div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> }</div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> </div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> <span class="keyword">template</span> <<span class="keyword">class</span> VectorType></div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"><a class="line" href="group__zonal__spherical__harmonics.html#ga0faf14fe4f77bc398e155ff2b82ab008"> 211</a></span> <span class="keyword">inline</span> Eigen::Matrix<typename VectorType::Scalar, Eigen::Dynamic, 1> <a class="code hl_function" href="group__zonal__spherical__harmonics.html#ga9be2bfabf4a9cf7decca0d9a4855798b">SH2ZSH</a> (<span class="keyword">const</span> VectorType& sh)</div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> {</div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> Eigen::Matrix<typename VectorType::Scalar, Eigen::Dynamic, 1> zsh;</div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> <a class="code hl_function" href="group__zonal__spherical__harmonics.html#ga9be2bfabf4a9cf7decca0d9a4855798b">SH2ZSH</a> (zsh, sh);</div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> <span class="keywordflow">return</span> zsh;</div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> }</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> </div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> <span class="keyword">template</span> <<span class="keyword">class</span> VectorType1, <span class="keyword">class</span> VectorType2></div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"><a class="line" href="group__zonal__spherical__harmonics.html#ga035799977415554aaef1ba6eb7950ab3"> 221</a></span> <span class="keyword">inline</span> VectorType1& <a class="code hl_function" href="group__zonal__spherical__harmonics.html#ga035799977415554aaef1ba6eb7950ab3">ZSH2RH</a> (VectorType1& rh, <span class="keyword">const</span> VectorType2& zsh)</div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> {</div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</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="l00224" name="l00224"></a><span class="lineno"> 224</span> rh.resize (zsh.size());</div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> <span class="keyword">const</span> <span class="keywordtype">size_t</span> lmax = <a class="code hl_function" href="group__zonal__spherical__harmonics.html#ga91d0c1c4376953a96dc8f66986326025">LforN</a> (zsh.size());</div>
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> Eigen::Matrix<value_type,Eigen::Dynamic,1,0,64> AL (lmax+1);</div>
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</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="l00228" name="l00228"></a><span class="lineno"> 228</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> l = 0; l <= lmax; l += 2)</div>
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> rh[<a class="code hl_function" href="group__zonal__spherical__harmonics.html#ga5864439cc87e0e54e0c138400389ca77">index</a>(l)] = zsh[<a class="code hl_function" href="group__zonal__spherical__harmonics.html#ga5864439cc87e0e54e0c138400389ca77">index</a>(l)] / AL[l];</div>
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> <span class="keywordflow">return</span> rh;</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> </div>
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> <span class="keyword">template</span> <<span class="keyword">class</span> VectorType></div>
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"><a class="line" href="group__zonal__spherical__harmonics.html#ga089431f50efa1f7ac0ca5e38e8bbaa22"> 234</a></span> <span class="keyword">inline</span> Eigen::Matrix<typename VectorType::Scalar,Eigen::Dynamic,1> <a class="code hl_function" href="group__zonal__spherical__harmonics.html#ga035799977415554aaef1ba6eb7950ab3">ZSH2RH</a> (<span class="keyword">const</span> VectorType& zsh)</div>
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> {</div>
<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> Eigen::Matrix<typename VectorType::Scalar,Eigen::Dynamic,1> rh (zsh.size());</div>
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span> <a class="code hl_function" href="group__zonal__spherical__harmonics.html#ga035799977415554aaef1ba6eb7950ab3">ZSH2RH</a> (rh, zsh);</div>
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span> <span class="keywordflow">return</span> rh;</div>
<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> }</div>
<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span> </div>
<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> </div>
<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span> </div>
<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span> </div>
<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> <span class="keyword">template</span> <<span class="keyword">class</span> VectorType1, <span class="keyword">class</span> VectorType2></div>
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"><a class="line" href="group__zonal__spherical__harmonics.html#gaad663bad9cad5b0aaa3f5ccfcc5403b1"> 247</a></span> <span class="keyword">inline</span> VectorType1& <a class="code hl_function" href="group__zonal__spherical__harmonics.html#gaad663bad9cad5b0aaa3f5ccfcc5403b1">zsconv</a> (VectorType1& zsh, <span class="keyword">const</span> VectorType2& RH)</div>
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> {</div>
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> assert (zsh.size() >= RH.size());</div>
<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i != size_t(RH.size()); ++i)</div>
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> zsh[i] *= RH[i];</div>
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> <span class="keywordflow">return</span> zsh;</div>
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> }</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> </div>
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> </div>
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</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="l00260" name="l00260"></a><span class="lineno"><a class="line" href="group__zonal__spherical__harmonics.html#gaad2b065dfb17856d2d19dbfc02b542e0"> 260</a></span> <span class="keyword">inline</span> VectorType1& <a class="code hl_function" href="group__zonal__spherical__harmonics.html#gaad663bad9cad5b0aaa3f5ccfcc5403b1">zsconv</a> (VectorType1& C, <span class="keyword">const</span> VectorType2& RH, <span class="keyword">const</span> VectorType3& zsh)</div>
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> {</div>
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> assert (zsh.size() >= RH.size());</div>
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> C.resize (RH.size());</div>
<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i != size_t(RH.size()); ++i)</div>
<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span> C[i] = zsh[i] * RH[i];</div>
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span> <span class="keywordflow">return</span> C;</div>
<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span> }</div>
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span> </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> </div>
<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> </div>
<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> <span class="keyword">template</span> <<span class="keyword">class</span> VectorType></div>
<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"><a class="line" href="group__zonal__spherical__harmonics.html#ga78a9ba8a083ac2ba0b17cfabea459889"> 274</a></span> <span class="keyword">inline</span> VectorType& <a class="code hl_function" href="group__zonal__spherical__harmonics.html#ga78a9ba8a083ac2ba0b17cfabea459889">FA2ZSH</a> (VectorType& zsh, <a class="code hl_typedef" href="namespace_m_r.html#a43bad69d4b870a61e1d93cd69b7b1270">default_type</a> FA, <a class="code hl_typedef" href="namespace_m_r.html#a43bad69d4b870a61e1d93cd69b7b1270">default_type</a> ADC, <a class="code hl_typedef" href="namespace_m_r.html#a43bad69d4b870a61e1d93cd69b7b1270">default_type</a> bvalue, <span class="keyword">const</span> <span class="keywordtype">size_t</span> lmax, <span class="keyword">const</span> <span class="keywordtype">size_t</span> precision = 100)</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> <a class="code hl_typedef" href="namespace_m_r.html#a43bad69d4b870a61e1d93cd69b7b1270">default_type</a> a = FA/sqrt (3.0 - 2.0*FA*FA);</div>
<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span> <a class="code hl_typedef" href="namespace_m_r.html#a43bad69d4b870a61e1d93cd69b7b1270">default_type</a> ev1 = ADC* (1.0+2.0*a), ev2 = ADC* (1.0-a);</div>
<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span> </div>
<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"> 279</span> Eigen::VectorXd sigs (precision);</div>
<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"> 280</span> Eigen::MatrixXd ZSHT (precision, lmax/2+1);</div>
<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</span> Eigen::Matrix<default_type,Eigen::Dynamic,1,0,64> AL;</div>
<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span> </div>
<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i < precision; i++) {</div>
<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span> <a class="code hl_typedef" href="namespace_m_r.html#a43bad69d4b870a61e1d93cd69b7b1270">default_type</a> <a class="code hl_variable" href="calibrator_8h.html#aed7ba788c50defe48678c3e5359c6ceb">el</a> = i*<a class="code hl_variable" href="group__mathconstants.html#gafe1ee4d398733ae71a15130062a9c2a4">Math::pi</a> / (2.0*(precision-1));</div>
<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span> sigs[i] = exp (-bvalue * (ev1*std::cos (<a class="code hl_variable" href="calibrator_8h.html#aed7ba788c50defe48678c3e5359c6ceb">el</a>)*std::cos (<a class="code hl_variable" href="calibrator_8h.html#aed7ba788c50defe48678c3e5359c6ceb">el</a>) + ev2*std::sin (<a class="code hl_variable" href="calibrator_8h.html#aed7ba788c50defe48678c3e5359c6ceb">el</a>)*std::sin (<a class="code hl_variable" href="calibrator_8h.html#aed7ba788c50defe48678c3e5359c6ceb">el</a>)));</div>
<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</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, std::cos (<a class="code hl_variable" href="calibrator_8h.html#aed7ba788c50defe48678c3e5359c6ceb">el</a>));</div>
<div class="line"><a id="l00287" name="l00287"></a><span class="lineno"> 287</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> l = 0; l <= lmax; l+=2)</div>
<div class="line"><a id="l00288" name="l00288"></a><span class="lineno"> 288</span> ZSHT (i,<a class="code hl_function" href="group__zonal__spherical__harmonics.html#ga5864439cc87e0e54e0c138400389ca77">index</a>(l)) = AL[l];</div>
<div class="line"><a id="l00289" name="l00289"></a><span class="lineno"> 289</span> }</div>
<div class="line"><a id="l00290" name="l00290"></a><span class="lineno"> 290</span> </div>
<div class="line"><a id="l00291" name="l00291"></a><span class="lineno"> 291</span> <span class="keywordflow">return</span> (zsh = <a class="code hl_function" href="group__ls.html#gaaacadd3d43de898a784044dcfa3e1363">pinv</a>(ZSHT) * sigs);</div>
<div class="line"><a id="l00292" name="l00292"></a><span class="lineno"> 292</span> }</div>
<div class="line"><a id="l00293" name="l00293"></a><span class="lineno"> 293</span> </div>
<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span> </div>
<div class="line"><a id="l00295" name="l00295"></a><span class="lineno"> 295</span> </div>
<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span> }</div>
<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span> }</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> </div>
<div class="line"><a id="l00300" name="l00300"></a><span class="lineno"> 300</span><span class="preprocessor">#endif</span></div>
<div class="ttc" id="a_s_h_8h_html"><div class="ttname"><a href="_s_h_8h.html">SH.h</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_math_1_1_z_s_h_1_1_transform_html"><div class="ttname"><a href="class_m_r_1_1_math_1_1_z_s_h_1_1_transform.html">MR::Math::ZSH::Transform</a></div><div class="ttdef"><b>Definition:</b> <a href="_z_s_h_8h_source.html#l00105">ZSH.h:105</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_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_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_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_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__zonal__spherical__harmonics_html_ga035799977415554aaef1ba6eb7950ab3"><div class="ttname"><a href="group__zonal__spherical__harmonics.html#ga035799977415554aaef1ba6eb7950ab3">MR::Math::ZSH::ZSH2RH</a></div><div class="ttdeci">VectorType1 & ZSH2RH(VectorType1 &rh, const VectorType2 &zsh)</div><div class="ttdef"><b>Definition:</b> <a href="_z_s_h_8h_source.html#l00221">ZSH.h:221</a></div></div>
<div class="ttc" id="agroup__zonal__spherical__harmonics_html_ga08c23193bee5994196f782d5a01631bf"><div class="ttname"><a href="group__zonal__spherical__harmonics.html#ga08c23193bee5994196f782d5a01631bf">MR::Math::ZSH::ZSH2SH</a></div><div class="ttdeci">VectorType1 & ZSH2SH(VectorType1 &sh, const VectorType2 &zsh)</div><div class="ttdef"><b>Definition:</b> <a href="_z_s_h_8h_source.html#l00178">ZSH.h:178</a></div></div>
<div class="ttc" id="agroup__zonal__spherical__harmonics_html_ga504fda03427ae2e965a29e526543df51"><div class="ttname"><a href="group__zonal__spherical__harmonics.html#ga504fda03427ae2e965a29e526543df51">MR::Math::ZSH::derivative</a></div><div class="ttdeci">VectorType::Scalar derivative(const VectorType &coefs, const typename VectorType::Scalar elevation, const size_t lmax)</div><div class="ttdef"><b>Definition:</b> <a href="_z_s_h_8h_source.html#l00161">ZSH.h:161</a></div></div>
<div class="ttc" id="agroup__zonal__spherical__harmonics_html_ga54f4e536cedd651e736a1b0ec45e293d"><div class="ttname"><a href="group__zonal__spherical__harmonics.html#ga54f4e536cedd651e736a1b0ec45e293d">MR::Math::ZSH::Transform::ZSHT</a></div><div class="ttdeci">matrix_type ZSHT</div><div class="ttdef"><b>Definition:</b> <a href="_z_s_h_8h_source.html#l00138">ZSH.h:138</a></div></div>
<div class="ttc" id="agroup__zonal__spherical__harmonics_html_ga5864439cc87e0e54e0c138400389ca77"><div class="ttname"><a href="group__zonal__spherical__harmonics.html#ga5864439cc87e0e54e0c138400389ca77">MR::Math::ZSH::index</a></div><div class="ttdeci">size_t index(int l)</div><div class="ttdoc">compute the index for coefficient l</div><div class="ttdef"><b>Definition:</b> <a href="_z_s_h_8h_source.html#l00048">ZSH.h:48</a></div></div>
<div class="ttc" id="agroup__zonal__spherical__harmonics_html_ga78a9ba8a083ac2ba0b17cfabea459889"><div class="ttname"><a href="group__zonal__spherical__harmonics.html#ga78a9ba8a083ac2ba0b17cfabea459889">MR::Math::ZSH::FA2ZSH</a></div><div class="ttdeci">VectorType & FA2ZSH(VectorType &zsh, default_type FA, default_type ADC, default_type bvalue, const size_t lmax, const size_t precision=100)</div><div class="ttdoc">compute ZSH coefficients corresponding to specified tensor</div><div class="ttdef"><b>Definition:</b> <a href="_z_s_h_8h_source.html#l00274">ZSH.h:274</a></div></div>
<div class="ttc" id="agroup__zonal__spherical__harmonics_html_ga80cc68559e8f44ab9421be587aead31c"><div class="ttname"><a href="group__zonal__spherical__harmonics.html#ga80cc68559e8f44ab9421be587aead31c">MR::Math::ZSH::Transform::iZSHT</a></div><div class="ttdeci">matrix_type iZSHT</div><div class="ttdef"><b>Definition:</b> <a href="_z_s_h_8h_source.html#l00138">ZSH.h:138</a></div></div>
<div class="ttc" id="agroup__zonal__spherical__harmonics_html_ga8df7da8e0754a5e4e0cffb711d37c32c"><div class="ttname"><a href="group__zonal__spherical__harmonics.html#ga8df7da8e0754a5e4e0cffb711d37c32c">MR::Math::ZSH::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="_z_s_h_8h_source.html#l00042">ZSH.h:42</a></div></div>
<div class="ttc" id="agroup__zonal__spherical__harmonics_html_ga91d0c1c4376953a96dc8f66986326025"><div class="ttname"><a href="group__zonal__spherical__harmonics.html#ga91d0c1c4376953a96dc8f66986326025">MR::Math::ZSH::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="_z_s_h_8h_source.html#l00054">ZSH.h:54</a></div></div>
<div class="ttc" id="agroup__zonal__spherical__harmonics_html_ga9be2bfabf4a9cf7decca0d9a4855798b"><div class="ttname"><a href="group__zonal__spherical__harmonics.html#ga9be2bfabf4a9cf7decca0d9a4855798b">MR::Math::ZSH::SH2ZSH</a></div><div class="ttdeci">VectorType1 & SH2ZSH(VectorType1 &zsh, const VectorType2 &sh)</div><div class="ttdef"><b>Definition:</b> <a href="_z_s_h_8h_source.html#l00201">ZSH.h:201</a></div></div>
<div class="ttc" id="agroup__zonal__spherical__harmonics_html_gaad663bad9cad5b0aaa3f5ccfcc5403b1"><div class="ttname"><a href="group__zonal__spherical__harmonics.html#gaad663bad9cad5b0aaa3f5ccfcc5403b1">MR::Math::ZSH::zsconv</a></div><div class="ttdeci">VectorType1 & zsconv(VectorType1 &zsh, const VectorType2 &RH)</div><div class="ttdoc">perform zonal spherical convolution, in place</div><div class="ttdef"><b>Definition:</b> <a href="_z_s_h_8h_source.html#l00247">ZSH.h:247</a></div></div>
<div class="ttc" id="agroup__zonal__spherical__harmonics_html_gac82e336c373264a210657efd7916f38d"><div class="ttname"><a href="group__zonal__spherical__harmonics.html#gac82e336c373264a210657efd7916f38d">MR::Math::ZSH::init_deriv_transform</a></div><div class="ttdeci">Eigen::Matrix< value_type, Eigen::Dynamic, Eigen::Dynamic > init_deriv_transform(const VectorType &els, const size_t lmax)</div><div class="ttdoc">form the ZSH->derivatives matrix for a set of elevation angles</div><div class="ttdef"><b>Definition:</b> <a href="_z_s_h_8h_source.html#l00087">ZSH.h:87</a></div></div>
<div class="ttc" id="agroup__zonal__spherical__harmonics_html_gad07ed92fb96436c2e32c038501363332"><div class="ttname"><a href="group__zonal__spherical__harmonics.html#gad07ed92fb96436c2e32c038501363332">MR::Math::ZSH::value</a></div><div class="ttdeci">VectorType::Scalar value(const VectorType &coefs, typename VectorType::Scalar elevation, const size_t lmax)</div><div class="ttdef"><b>Definition:</b> <a href="_z_s_h_8h_source.html#l00144">ZSH.h:144</a></div></div>
<div class="ttc" id="agroup__zonal__spherical__harmonics_html_gafc48d35e555ae9719610682ab20e40fd"><div class="ttname"><a href="group__zonal__spherical__harmonics.html#gafc48d35e555ae9719610682ab20e40fd">MR::Math::ZSH::init_amp_transform</a></div><div class="ttdeci">Eigen::Matrix< value_type, Eigen::Dynamic, Eigen::Dynamic > init_amp_transform(const VectorType &els, const size_t lmax)</div><div class="ttdoc">form the ZSH->amplitudes matrix for a set of elevation angles</div><div class="ttdef"><b>Definition:</b> <a href="_z_s_h_8h_source.html#l00066">ZSH.h:66</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>
<div class="ttc" id="alegendre_8h_html"><div class="ttname"><a href="legendre_8h.html">legendre.h</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_a43bad69d4b870a61e1d93cd69b7b1270"><div class="ttname"><a href="namespace_m_r.html#a43bad69d4b870a61e1d93cd69b7b1270">MR::default_type</a></div><div class="ttdeci">double default_type</div><div class="ttdoc">the default type used throughout MRtrix</div><div class="ttdef"><b>Definition:</b> <a href="src_2surface_2types_8h_source.html#l00228">types.h:228</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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