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<a href="_data_assimilator_8cc.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">/* SPDX-FileCopyrightText: Copyright (c) 2021 - 2024, the adamantine authors.</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment"> * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span>  </div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="preprocessor">#include <<a class="code" href="_data_assimilator_8hh.html">DataAssimilator.hh</a>></span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="preprocessor">#include <<a class="code" href="utils_8hh.html">utils.hh</a>></span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span>  </div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="preprocessor">#include <deal.II/arborx/distributed_tree.h></span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="preprocessor">#include <deal.II/base/index_set.h></span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="preprocessor">#include <deal.II/base/mpi.h></span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="preprocessor">#include <deal.II/dofs/dof_tools.h></span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor">#include <deal.II/fe/mapping_q1.h></span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="preprocessor">#include <deal.II/lac/block_vector.h></span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="preprocessor">#include <deal.II/lac/la_parallel_block_vector.h></span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="preprocessor">#include <deal.II/lac/linear_operator_tools.h></span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="preprocessor">#include <deal.II/lac/read_write_vector.h></span></div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="preprocessor">#include <deal.II/lac/trilinos_sparse_matrix.h></span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="preprocessor">#include <deal.II/lac/vector_operation.h></span></div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span>  </div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="preprocessor">#include <boost/algorithm/string/predicate.hpp></span></div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>  </div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="preprocessor">#include <ArborX.hpp></span></div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>  </div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="preprocessor">#ifdef ADAMANTINE_WITH_CALIPER</span></div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="preprocessor">#include <caliper/cali.h></span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  </div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="keyword">namespace </span><a class="code" href="namespaceadamantine.html">adamantine</a></div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> {</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  </div>
<div class="line"><a name="l00031"></a><span class="lineno"><a class="line" href="classadamantine_1_1_data_assimilator.html#a9aca6e1413a227d29e89faa45a8006f0"> 31</a></span> <a class="code" href="classadamantine_1_1_data_assimilator.html#a9aca6e1413a227d29e89faa45a8006f0">DataAssimilator::DataAssimilator</a>(MPI_Comm <span class="keyword">const</span> &global_communicator,</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  MPI_Comm <span class="keyword">const</span> &local_communicator, <span class="keywordtype">int</span> color,</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  boost::property_tree::ptree <span class="keyword">const</span> &database)</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  : _global_communicator(global_communicator),</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  _local_communicator(local_communicator), _color(color)</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> {</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <a class="code" href="classadamantine_1_1_data_assimilator.html#a5420f95c388dec9f638a4f1d4eec1914">_global_rank</a> = dealii::Utilities::MPI::this_mpi_process(<a class="code" href="classadamantine_1_1_data_assimilator.html#aa83bf29573aab1b23211aaeaece2817c">_global_communicator</a>);</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  <a class="code" href="classadamantine_1_1_data_assimilator.html#a1baf2c4af092efb0d076e9071a192d51">_global_comm_size</a> =</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  dealii::Utilities::MPI::n_mpi_processes(<a class="code" href="classadamantine_1_1_data_assimilator.html#aa83bf29573aab1b23211aaeaece2817c">_global_communicator</a>);</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  </div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="comment">// We need all the processors to know the cutoff distance for ArborX</span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  <span class="comment">// DistributedTree to work correctly.</span></div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  <span class="comment">// PropertyTreeInput data_assimilation.localization_cutoff_distance</span></div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <a class="code" href="classadamantine_1_1_data_assimilator.html#a8a976eb6e98d340fe91837cdd541cd36">_localization_cutoff_distance</a> = database.get(</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <span class="stringliteral">"localization_cutoff_distance"</span>, std::numeric_limits<double>::max());</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  </div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  <span class="keywordflow">if</span> (<a class="code" href="classadamantine_1_1_data_assimilator.html#a5420f95c388dec9f638a4f1d4eec1914">_global_rank</a> == 0)</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  {</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  <span class="comment">// Set the solver parameters from the input database</span></div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <span class="comment">// PropertyTreeInput data_assimilation.solver.max_number_of_temp_vectors</span></div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <span class="keywordflow">if</span> (boost::optional<unsigned int> max_num_temp_vectors =</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  database.get_optional<<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>>(</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="stringliteral">"solver.max_number_of_temp_vectors"</span>))</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <a class="code" href="classadamantine_1_1_data_assimilator.html#aef8723a176e59a627727bffa0397d399">_additional_data</a>.max_basis_size = *max_num_temp_vectors;</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  </div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="comment">// PropertyTreeInput data_assimilation.solver.max_iterations</span></div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <span class="keywordflow">if</span> (boost::optional<unsigned int> max_iterations =</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  database.get_optional<<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>>(<span class="stringliteral">"solver.max_iterations"</span>))</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <a class="code" href="classadamantine_1_1_data_assimilator.html#aa3a8ea4992368e7fa15b538ef05ab243">_solver_control</a>.set_max_steps(*max_iterations);</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  </div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <span class="comment">// PropertyTreeInput data_assimilation.solver.convergence_tolerance</span></div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="keywordflow">if</span> (boost::optional<double> tolerance =</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  database.get_optional<<span class="keywordtype">double</span>>(<span class="stringliteral">"solver.convergence_tolerance"</span>))</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <a class="code" href="classadamantine_1_1_data_assimilator.html#aa3a8ea4992368e7fa15b538ef05ab243">_solver_control</a>.set_tolerance(*tolerance);</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  </div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="comment">// PropertyTreeInput data_assimilation.localization_cutoff_function</span></div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  std::string localization_cutoff_function_str =</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  database.get(<span class="stringliteral">"localization_cutoff_function"</span>, <span class="stringliteral">"none"</span>);</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  </div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="keywordflow">if</span> (boost::iequals(localization_cutoff_function_str, <span class="stringliteral">"gaspari_cohn"</span>))</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  {</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <a class="code" href="classadamantine_1_1_data_assimilator.html#a75a7a61d7cf93db94867a0841846c983">_localization_cutoff_function</a> = <a class="code" href="namespaceadamantine.html#ae6f0841ed43262ef1175e2b6075cd66faba6e20e7e1559edeec0c30dab66781a5">LocalizationCutoff::gaspari_cohn</a>;</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  }</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (boost::iequals(localization_cutoff_function_str, <span class="stringliteral">"step_function"</span>))</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  {</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <a class="code" href="classadamantine_1_1_data_assimilator.html#a75a7a61d7cf93db94867a0841846c983">_localization_cutoff_function</a> = <a class="code" href="namespaceadamantine.html#ae6f0841ed43262ef1175e2b6075cd66faa5ca29e51a327d3424eaca38fe8ebc8d">LocalizationCutoff::step_function</a>;</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  }</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (boost::iequals(localization_cutoff_function_str, <span class="stringliteral">"none"</span>))</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  {</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <a class="code" href="classadamantine_1_1_data_assimilator.html#a75a7a61d7cf93db94867a0841846c983">_localization_cutoff_function</a> = <a class="code" href="namespaceadamantine.html#ae6f0841ed43262ef1175e2b6075cd66fa334c4a4c42fdb79d7ebc3e73b517e6f8">LocalizationCutoff::none</a>;</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  }</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  {</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <a class="code" href="namespaceadamantine.html#ac498eafab2c29c90d8f7a40c50bf98b0">ASSERT_THROW</a>(<span class="keyword">false</span>,</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="stringliteral">"Error: Unknown localization cutoff function. Valid options "</span></div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="stringliteral">"are 'gaspari_cohn', 'step_function', and 'none'."</span>);</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  }</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  }</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span> }</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  </div>
<div class="line"><a name="l00091"></a><span class="lineno"><a class="line" href="classadamantine_1_1_data_assimilator.html#ab90c04d7eb24c9202e84409109146143"> 91</a></span> <span class="keywordtype">void</span> <a class="code" href="classadamantine_1_1_data_assimilator.html#ab90c04d7eb24c9202e84409109146143">DataAssimilator::update_ensemble</a>(</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  std::vector<dealii::LA::distributed::BlockVector<double>></div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  &augmented_state_ensemble,</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  std::vector<double> <span class="keyword">const</span> &expt_data, dealii::SparseMatrix<double> <span class="keyword">const</span> &R)</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span> {</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  </div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  std::vector<dealii::LA::distributed::BlockVector<double>></div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  global_augmented_state_ensemble;</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  std::vector<unsigned int> local_n_ensemble_members(<a class="code" href="classadamantine_1_1_data_assimilator.html#a1baf2c4af092efb0d076e9071a192d51">_global_comm_size</a>);</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  std::vector<block_size_type> block_sizes(2, 0);</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  </div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  <a class="code" href="classadamantine_1_1_data_assimilator.html#a85dc10ab67036ce6c85429dd1cf2fce9">gather_ensemble_members</a>(augmented_state_ensemble,</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  global_augmented_state_ensemble,</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  local_n_ensemble_members, block_sizes);</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  </div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="keywordflow">if</span> (<a class="code" href="classadamantine_1_1_data_assimilator.html#a5420f95c388dec9f638a4f1d4eec1914">_global_rank</a> == 0)</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  {</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="comment">// Set some constants</span></div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <a class="code" href="classadamantine_1_1_data_assimilator.html#a09166a5bc460fa193e308ddd2c4238dd">_num_ensemble_members</a> = global_augmented_state_ensemble.size();</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <a class="code" href="classadamantine_1_1_data_assimilator.html#aac440d873ccf340f607f7758de8e7f36">_sim_size</a> = block_sizes[0];</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <a class="code" href="classadamantine_1_1_data_assimilator.html#a41a2e76bc1bcf25d0daad9429ab62a30">_parameter_size</a> = block_sizes[1];</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  </div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <a class="code" href="namespaceadamantine.html#ac498eafab2c29c90d8f7a40c50bf98b0">adamantine::ASSERT_THROW</a>(<a class="code" href="classadamantine_1_1_data_assimilator.html#a9e71ae5b0604f35293dbf7e21a8bbf19">_expt_size</a> == expt_data.size(),</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <span class="stringliteral">"Error: Unexpected experiment vector size."</span>);</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  </div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <span class="comment">// Check if R is diagonal, needed for filling the noise vector</span></div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="keyword">auto</span> bandwidth = R.get_sparsity_pattern().bandwidth();</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <span class="keywordtype">bool</span> <span class="keyword">const</span> R_is_diagonal = bandwidth == 0 ? true : <span class="keyword">false</span>;</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  </div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="comment">// Get the perturbed innovation, ( y+u - Hx )</span></div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <span class="comment">// This is determined using the unaugmented state because the parameters</span></div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  <span class="comment">// are not observable</span></div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  std::cout << <span class="stringliteral">"Getting the perturbed innovation..."</span> << std::endl;</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  </div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span> <span class="preprocessor">#ifdef ADAMANTINE_WITH_CALIPER</span></div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  CALI_MARK_BEGIN(<span class="stringliteral">"da_get_pert_inno"</span>);</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  </div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <span class="keywordtype">int</span> constexpr base_state = 0;</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  std::vector<dealii::Vector<double>> perturbed_innovation(</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <a class="code" href="classadamantine_1_1_data_assimilator.html#a09166a5bc460fa193e308ddd2c4238dd">_num_ensemble_members</a>);</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> member = 0; member < <a class="code" href="classadamantine_1_1_data_assimilator.html#a09166a5bc460fa193e308ddd2c4238dd">_num_ensemble_members</a>; ++member)</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  {</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  perturbed_innovation[member].reinit(<a class="code" href="classadamantine_1_1_data_assimilator.html#a9e71ae5b0604f35293dbf7e21a8bbf19">_expt_size</a>);</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <a class="code" href="classadamantine_1_1_data_assimilator.html#a78e37ebef7fdc3f7a6f3ec4c2b1b9d13">fill_noise_vector</a>(perturbed_innovation[member], R, R_is_diagonal);</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  dealii::Vector<double> temporary =</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <a class="code" href="classadamantine_1_1_data_assimilator.html#a4e5460783efc1dd7b312927576f1fc86">calc_Hx</a>(global_augmented_state_ensemble[member].block(base_state));</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  </div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i = 0; i < <a class="code" href="classadamantine_1_1_data_assimilator.html#a9e71ae5b0604f35293dbf7e21a8bbf19">_expt_size</a>; ++i)</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  {</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  perturbed_innovation[member][i] += expt_data[i] - temporary[i];</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  }</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  }</div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  </div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span> <span class="preprocessor">#ifdef ADAMANTINE_WITH_CALIPER</span></div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  CALI_MARK_END(<span class="stringliteral">"da_get_pert_inno"</span>);</div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  </div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  <span class="comment">// Apply the Kalman gain to update the augmented state ensemble</span></div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  std::cout << <span class="stringliteral">"Applying the Kalman gain..."</span> << std::endl;</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  </div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span> <span class="preprocessor">#ifdef ADAMANTINE_WITH_CALIPER</span></div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  CALI_MARK_BEGIN(<span class="stringliteral">"da_apply_K"</span>);</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  </div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  <span class="comment">// Apply the Kalman filter to the perturbed innovation, K ( y+u - Hx )</span></div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  std::vector<dealii::LA::distributed::BlockVector<double>> forecast_shift =</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  <a class="code" href="classadamantine_1_1_data_assimilator.html#a405e8d43091eca88e94898eb885313c3">apply_kalman_gain</a>(global_augmented_state_ensemble, R,</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  perturbed_innovation);</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  </div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span> <span class="preprocessor">#ifdef ADAMANTINE_WITH_CALIPER</span></div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  CALI_MARK_END(<span class="stringliteral">"da_apply_K"</span>);</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  </div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  <span class="comment">// Update the ensemble, x = x + K ( y+u - Hx )</span></div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  std::cout << <span class="stringliteral">"Updating the ensemble members..."</span> << std::endl;</div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  </div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span> <span class="preprocessor">#ifdef ADAMANTINE_WITH_CALIPER</span></div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  CALI_MARK_BEGIN(<span class="stringliteral">"da_update_members"</span>);</div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  </div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> member = 0; member < <a class="code" href="classadamantine_1_1_data_assimilator.html#a09166a5bc460fa193e308ddd2c4238dd">_num_ensemble_members</a>; ++member)</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  {</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  global_augmented_state_ensemble[member] += forecast_shift[member];</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  }</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  </div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span> <span class="preprocessor">#ifdef ADAMANTINE_WITH_CALIPER</span></div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  CALI_MARK_END(<span class="stringliteral">"da_update_members"</span>);</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  }</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  </div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  <a class="code" href="classadamantine_1_1_data_assimilator.html#ac27d0c63d7e8b2a70bd29d29e6ae8a10">scatter_ensemble_members</a>(augmented_state_ensemble,</div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  global_augmented_state_ensemble,</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  local_n_ensemble_members, block_sizes);</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span> }</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  </div>
<div class="line"><a name="l00187"></a><span class="lineno"><a class="line" href="classadamantine_1_1_data_assimilator.html#a85dc10ab67036ce6c85429dd1cf2fce9"> 187</a></span> <span class="keywordtype">void</span> <a class="code" href="classadamantine_1_1_data_assimilator.html#a85dc10ab67036ce6c85429dd1cf2fce9">DataAssimilator::gather_ensemble_members</a>(</div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  std::vector<dealii::LA::distributed::BlockVector<double>></div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  &augmented_state_ensemble,</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  std::vector<dealii::LA::distributed::BlockVector<double>></div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  &global_augmented_state_ensemble,</div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  std::vector<unsigned int> &local_n_ensemble_members,</div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  std::vector<block_size_type> &block_sizes)</div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span> {</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  <span class="comment">// We need to gather the augmented_state_ensemble from the other processors.</span></div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  <span class="comment">// BlockVector is a complex structure with its own communicator and so we</span></div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  <span class="comment">// cannot simple use dealii's gather to perform the communication. Instead, we</span></div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <span class="comment">// extract the locally owned data and gather it to processor zero. We do this</span></div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <span class="comment">// in a two step process. First, we move the data to local rank zero. Second,</span></div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  <span class="comment">// we move the data to global rank zero. The first step allows to simply move</span></div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <span class="comment">// complete vectors to global rank zero. Otherwise, we have the vector data</span></div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  <span class="comment">// divided in multiple chunks when gathered on global rank zero and we have to</span></div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  <span class="comment">// reconstruct the vector. Finally we can build new BlockVector using the</span></div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  <span class="comment">// local communicator.</span></div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  </div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  <span class="comment">// Extract relevant data</span></div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> <span class="keyword">const</span> n_local_ensemble_members = augmented_state_ensemble.size();</div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  std::vector<std::vector<std::vector<double>>> block_data(</div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  n_local_ensemble_members, std::vector<std::vector<double>>(2));</div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i = 0; i < n_local_ensemble_members; ++i)</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  {</div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> j = 0; j < 2; ++j)</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  {</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  <span class="keyword">auto</span> data_ptr = augmented_state_ensemble[i].block(j).get_values();</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  block_data[i][j].insert(</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  block_data[i][j].end(), data_ptr,</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  data_ptr + augmented_state_ensemble[i].block(j).locally_owned_size());</div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  }</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  }</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  </div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  <span class="comment">// Perform the communications on the local communicator</span></div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  <span class="keyword">auto</span> local_block_data =</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  dealii::Utilities::MPI::gather(<a class="code" href="classadamantine_1_1_data_assimilator.html#a65cf1d6c324239bf4fac98c1f7abcdc9">_local_communicator</a>, block_data);</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  <span class="keyword">auto</span> local_indexsets_block_0 = dealii::Utilities::MPI::gather(</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  <a class="code" href="classadamantine_1_1_data_assimilator.html#a65cf1d6c324239bf4fac98c1f7abcdc9">_local_communicator</a>,</div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  augmented_state_ensemble[0].block(0).locally_owned_elements());</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  <span class="keyword">auto</span> local_indexsets_block_1 = dealii::Utilities::MPI::gather(</div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  <a class="code" href="classadamantine_1_1_data_assimilator.html#a65cf1d6c324239bf4fac98c1f7abcdc9">_local_communicator</a>,</div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  augmented_state_ensemble[0].block(1).locally_owned_elements());</div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  <span class="comment">// The local processor zero has all the data. Reorder the data before</span></div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  <span class="comment">// sending it to the global processor zero</span></div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  std::vector<std::vector<std::vector<double>>> reordered_local_block_data;</div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  <span class="keywordflow">if</span> (dealii::Utilities::MPI::this_mpi_process(<a class="code" href="classadamantine_1_1_data_assimilator.html#a65cf1d6c324239bf4fac98c1f7abcdc9">_local_communicator</a>) == 0)</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  {</div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  reordered_local_block_data.resize(n_local_ensemble_members,</div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  std::vector<std::vector<double>>(2));</div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  </div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i = 0; i < local_indexsets_block_0.size(); ++i)</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  {</div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  block_sizes[0] += local_indexsets_block_0[i].n_elements();</div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  }</div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  <span class="comment">// The augmented parameters are not distributed.</span></div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  block_sizes[1] = local_indexsets_block_1[0].n_elements();</div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  </div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  <span class="comment">// Loop over the ensemble members</span></div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i = 0; i < n_local_ensemble_members; ++i)</div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  {</div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  <span class="comment">// Loop over the processors</span></div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> j = 0; j < local_block_data.size(); ++j)</div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  {</div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  <span class="comment">// Loop over the blocks</span></div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> k = 0; k < 2; ++k)</div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  {</div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  reordered_local_block_data[i][k].resize(block_sizes[k]);</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  <span class="comment">// Loop over the dofs</span></div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  <span class="keywordflow">for</span> (std::size_t m = 0; m < local_block_data[j][i][k].size(); ++m)</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  {</div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  <span class="keyword">auto</span> pos = k == 0 ? local_indexsets_block_0[j].nth_index_in_set(m)</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  : local_indexsets_block_1[j].nth_index_in_set(m);</div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  reordered_local_block_data[i][k][pos] =</div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  local_block_data[j][i][k][m];</div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  }</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  }</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  }</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  }</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  }</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  </div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  <span class="comment">// Perform the global communication.</span></div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  <span class="keyword">auto</span> all_local_block_data = dealii::Utilities::MPI::gather(</div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  <a class="code" href="classadamantine_1_1_data_assimilator.html#aa83bf29573aab1b23211aaeaece2817c">_global_communicator</a>, reordered_local_block_data);</div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  </div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  <span class="keywordflow">if</span> (<a class="code" href="classadamantine_1_1_data_assimilator.html#a5420f95c388dec9f638a4f1d4eec1914">_global_rank</a> == 0)</div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  {</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  <span class="comment">// Build the new BlockVector</span></div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i = 0; i < all_local_block_data.size(); ++i)</div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  {</div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  <span class="keyword">auto</span> <span class="keyword">const</span> &data = all_local_block_data[i];</div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  local_n_ensemble_members[i] = data.size();</div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  <span class="keywordflow">if</span> (data.size())</div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  {</div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  <span class="comment">// Loop over the ensemble members</span></div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> j = 0; j < data.size(); ++j)</div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  {</div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  dealii::LA::distributed::BlockVector<double> ensemble_member(</div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  block_sizes);</div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  <span class="comment">// Copy the values in data to ensemble_member</span></div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> k = 0; k < data[j].size(); ++k)</div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  {</div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> m = 0; m < data[j][k].size(); ++m)</div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  {</div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  ensemble_member.block(k)[m] = data[j][k][m];</div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  }</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  }</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  global_augmented_state_ensemble.push_back(ensemble_member);</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  }</div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  }</div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  }</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  }</div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span> }</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  </div>
<div class="line"><a name="l00301"></a><span class="lineno"><a class="line" href="classadamantine_1_1_data_assimilator.html#ac27d0c63d7e8b2a70bd29d29e6ae8a10"> 301</a></span> <span class="keywordtype">void</span> <a class="code" href="classadamantine_1_1_data_assimilator.html#ac27d0c63d7e8b2a70bd29d29e6ae8a10">DataAssimilator::scatter_ensemble_members</a>(</div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  std::vector<dealii::LA::distributed::BlockVector<double>></div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  &augmented_state_ensemble,</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  std::vector<dealii::LA::distributed::BlockVector<double>> <span class="keyword">const</span></div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  &global_augmented_state_ensemble,</div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  std::vector<unsigned int> <span class="keyword">const</span> &local_n_ensemble_members,</div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  std::vector<block_size_type> <span class="keyword">const</span> &block_sizes)</div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span> {</div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  <span class="comment">// Scatter global_augmented_state_ensemble to augmented_state_ensemble.</span></div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  <span class="comment">// First we split the data to the root of the local communicators and then,</span></div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  <span class="comment">// the data is moved inside each local communicator.</span></div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  <span class="comment">// deal.II has isend and irecv functions but we cannot them. Using these</span></div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  <span class="comment">// functions will result in a deadlock because the future returned by isend</span></div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  <span class="comment">// is blocking until we call the get function of the future returned by</span></div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  <span class="comment">// irecv.</span></div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  </div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  std::vector<char> packed_recv_buffer;</div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  <span class="keywordflow">if</span> (<a class="code" href="classadamantine_1_1_data_assimilator.html#a5420f95c388dec9f638a4f1d4eec1914">_global_rank</a> == 0)</div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  {</div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  std::vector<std::vector<char>> packed_send_buffers(<a class="code" href="classadamantine_1_1_data_assimilator.html#a1baf2c4af092efb0d076e9071a192d51">_global_comm_size</a>);</div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  std::vector<MPI_Request> mpi_requests(<a class="code" href="classadamantine_1_1_data_assimilator.html#a1baf2c4af092efb0d076e9071a192d51">_global_comm_size</a>);</div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> global_member_id = 0;</div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < <a class="code" href="classadamantine_1_1_data_assimilator.html#a1baf2c4af092efb0d076e9071a192d51">_global_comm_size</a>; ++i)</div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  {</div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> <span class="keyword">const</span> local_size = local_n_ensemble_members[i];</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  std::vector<std::vector<double>> send_buffer(local_size);</div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> j = 0; j < local_size; ++j)</div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  {</div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  <span class="keyword">auto</span> <span class="keyword">const</span> &global_state =</div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  global_augmented_state_ensemble[global_member_id];</div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  send_buffer[j].reserve(global_state.size());</div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  <span class="keywordflow">for</span> (<span class="keyword">auto</span> block_vector_it = global_state.begin();</div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  block_vector_it != global_state.end(); ++block_vector_it)</div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  {</div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  send_buffer[j].push_back(*block_vector_it);</div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  }</div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  ++global_member_id;</div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  }</div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  <span class="comment">// Pack and send the data to the local root rank</span></div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  packed_send_buffers[i] = dealii::Utilities::pack(send_buffer);</div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  MPI_Isend(packed_send_buffers[i].data(), packed_send_buffers[i].size(),</div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  MPI_CHAR, i, 0, <a class="code" href="classadamantine_1_1_data_assimilator.html#aa83bf29573aab1b23211aaeaece2817c">_global_communicator</a>, &mpi_requests[i]);</div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  }</div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  </div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  <span class="comment">// Receive the data. First, call MPI_Probe to get the size of the message.</span></div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  MPI_Status status;</div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  MPI_Probe(0, 0, <a class="code" href="classadamantine_1_1_data_assimilator.html#aa83bf29573aab1b23211aaeaece2817c">_global_communicator</a>, &status);</div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  <span class="keywordtype">int</span> packed_recv_buffer_size = -1;</div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  MPI_Get_count(&status, MPI_CHAR, &packed_recv_buffer_size);</div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  packed_recv_buffer.resize(packed_recv_buffer_size);</div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  MPI_Recv(packed_recv_buffer.data(), packed_recv_buffer_size, MPI_CHAR, 0, 0,</div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  <a class="code" href="classadamantine_1_1_data_assimilator.html#aa83bf29573aab1b23211aaeaece2817c">_global_communicator</a>, MPI_STATUS_IGNORE);</div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  </div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  <span class="comment">// Wait for all the sends to be over before freeing the buffers</span></div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  <span class="keywordflow">for</span> (<span class="keyword">auto</span> &request : mpi_requests)</div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  {</div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  MPI_Wait(&request, MPI_STATUS_IGNORE);</div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  }</div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  }</div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  {</div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  MPI_Status status;</div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  MPI_Probe(0, 0, <a class="code" href="classadamantine_1_1_data_assimilator.html#aa83bf29573aab1b23211aaeaece2817c">_global_communicator</a>, &status);</div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  <span class="keywordtype">int</span> packed_recv_buffer_size = -1;</div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  MPI_Get_count(&status, MPI_CHAR, &packed_recv_buffer_size);</div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  packed_recv_buffer.resize(packed_recv_buffer_size);</div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  MPI_Recv(packed_recv_buffer.data(), packed_recv_buffer_size, MPI_CHAR, 0, 0,</div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  <a class="code" href="classadamantine_1_1_data_assimilator.html#aa83bf29573aab1b23211aaeaece2817c">_global_communicator</a>, MPI_STATUS_IGNORE);</div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  }</div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  </div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  <span class="comment">// Unpack the data</span></div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  <span class="keyword">auto</span> recv_buffer =</div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  dealii::Utilities::unpack<std::vector<std::vector<double>>>(</div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  packed_recv_buffer);</div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  </div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  <span class="comment">// The local root ranks have all the data, now we need to update</span></div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  <span class="comment">// augmented_state_ensemble. This communication is easier to do than the</span></div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  <span class="comment">// other communications because we can use deal.II's built-in functions.</span></div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> m = 0; m < augmented_state_ensemble.size(); ++m)</div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  {</div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> b = 0; b < 2; ++b)</div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  {</div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  dealii::LA::ReadWriteVector<double> rw_vector(block_sizes[b]);</div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> offset = b == 0 ? 0 : block_sizes[0];</div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  <span class="keywordflow">for</span> (std::size_t i = 0; i < block_sizes[b]; ++i)</div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  {</div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  rw_vector[i] = recv_buffer[m][offset + i];</div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  }</div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  <span class="comment">// We cannot insert the elements because deal.II checks that the local</span></div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  <span class="comment">// elements and the remote ones match. Instead, we set everything to zero</span></div>
<div class="line"><a name="l00391"></a><span class="lineno"> 391</span>  <span class="comment">// and then, we add the imported elements.</span></div>
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span>  augmented_state_ensemble[m].block(b) = 0.;</div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  augmented_state_ensemble[m].block(b).import_elements(</div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  rw_vector, dealii::VectorOperation::add);</div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  }</div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  }</div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span> }</div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span>  </div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span> std::vector<dealii::LA::distributed::BlockVector<double>></div>
<div class="line"><a name="l00400"></a><span class="lineno"><a class="line" href="classadamantine_1_1_data_assimilator.html#a405e8d43091eca88e94898eb885313c3"> 400</a></span> <a class="code" href="classadamantine_1_1_data_assimilator.html#a405e8d43091eca88e94898eb885313c3">DataAssimilator::apply_kalman_gain</a>(</div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  std::vector<dealii::LA::distributed::BlockVector<double>></div>
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span>  &augmented_state_ensemble,</div>
<div class="line"><a name="l00403"></a><span class="lineno"> 403</span>  dealii::SparseMatrix<double> <span class="keyword">const</span> &R,</div>
<div class="line"><a name="l00404"></a><span class="lineno"> 404</span>  std::vector<dealii::Vector<double>> <span class="keyword">const</span> &perturbed_innovation)</div>
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span> {</div>
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> augmented_state_size = <a class="code" href="classadamantine_1_1_data_assimilator.html#aac440d873ccf340f607f7758de8e7f36">_sim_size</a> + <a class="code" href="classadamantine_1_1_data_assimilator.html#a41a2e76bc1bcf25d0daad9429ab62a30">_parameter_size</a>;</div>
<div class="line"><a name="l00407"></a><span class="lineno"> 407</span>  </div>
<div class="line"><a name="l00408"></a><span class="lineno"> 408</span>  <span class="comment">/*</span></div>
<div class="line"><a name="l00409"></a><span class="lineno"> 409</span> <span class="comment"> * Currently this function uses GMRES to apply the inverse of HPH^T+R in the</span></div>
<div class="line"><a name="l00410"></a><span class="lineno"> 410</span> <span class="comment"> * Kalman gain calculation for each ensemble member individually. Depending</span></div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span> <span class="comment"> * on the size of the datasets, the number of ensembles, and other factors</span></div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span> <span class="comment"> * doing a direct solve of (HPH^T+R)^-1 once and then applying to the</span></div>
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span> <span class="comment"> * perturbed innovation from each ensemble member might be more efficient.</span></div>
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  dealii::SparsityPattern pattern_H(<a class="code" href="classadamantine_1_1_data_assimilator.html#a9e71ae5b0604f35293dbf7e21a8bbf19">_expt_size</a>, augmented_state_size,</div>
<div class="line"><a name="l00416"></a><span class="lineno"> 416</span>  <a class="code" href="classadamantine_1_1_data_assimilator.html#a9e71ae5b0604f35293dbf7e21a8bbf19">_expt_size</a>);</div>
<div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  <span class="keyword">auto</span> H = <a class="code" href="classadamantine_1_1_data_assimilator.html#aeb0f621afcc24939d270c2850d9f628e">calc_H</a>(pattern_H);</div>
<div class="line"><a name="l00418"></a><span class="lineno"> 418</span>  <span class="keyword">auto</span> P = <a class="code" href="classadamantine_1_1_data_assimilator.html#af5bde3f9550c77d9a06d88da422e213e">calc_sample_covariance_sparse</a>(augmented_state_ensemble);</div>
<div class="line"><a name="l00419"></a><span class="lineno"> 419</span>  </div>
<div class="line"><a name="l00420"></a><span class="lineno"> 420</span>  <a class="code" href="utils_8hh.html#aa06eedd6f738a415870e97a375337d51">ASSERT</a>(H.n() == P.m(), <span class="stringliteral">"Matrices dimensions not compatible"</span>);</div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  <a class="code" href="utils_8hh.html#aa06eedd6f738a415870e97a375337d51">ASSERT</a>(H.m() == R.m(), <span class="stringliteral">"Matrices dimensions not compatible"</span>);</div>
<div class="line"><a name="l00422"></a><span class="lineno"> 422</span>  </div>
<div class="line"><a name="l00423"></a><span class="lineno"> 423</span>  <span class="keyword">const</span> <span class="keyword">auto</span> op_H = dealii::linear_operator(H);</div>
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span>  <span class="keyword">const</span> <span class="keyword">auto</span> op_P = dealii::linear_operator(P);</div>
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span>  <span class="keyword">const</span> <span class="keyword">auto</span> op_R = dealii::linear_operator(R);</div>
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span>  </div>
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span>  <span class="keyword">const</span> <span class="keyword">auto</span> op_HPH_plus_R =</div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span>  op_H * op_P * dealii::transpose_operator(op_H) + op_R;</div>
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span>  </div>
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  <span class="keyword">const</span> std::vector<dealii::types::global_dof_index> block_sizes = {</div>
<div class="line"><a name="l00431"></a><span class="lineno"> 431</span>  <a class="code" href="classadamantine_1_1_data_assimilator.html#aac440d873ccf340f607f7758de8e7f36">_sim_size</a>, <a class="code" href="classadamantine_1_1_data_assimilator.html#a41a2e76bc1bcf25d0daad9429ab62a30">_parameter_size</a>};</div>
<div class="line"><a name="l00432"></a><span class="lineno"> 432</span>  std::vector<dealii::LA::distributed::BlockVector<double>> <a class="code" href="namespaceadamantine.html#a7caf29199baef249d0ee5ff6fd81006ba1691b6ec67855c130469a858d0ad41a8">output</a>(</div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span>  <a class="code" href="classadamantine_1_1_data_assimilator.html#a09166a5bc460fa193e308ddd2c4238dd">_num_ensemble_members</a>,</div>
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  dealii::LA::distributed::BlockVector<double>(block_sizes));</div>
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span>  </div>
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span>  <span class="comment">// Create non-member versions of these for use in the lambda function</span></div>
<div class="line"><a name="l00437"></a><span class="lineno"> 437</span>  <span class="keyword">auto</span> solver_control = <a class="code" href="classadamantine_1_1_data_assimilator.html#aa3a8ea4992368e7fa15b538ef05ab243">_solver_control</a>;</div>
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span>  <span class="keyword">auto</span> additional_data = <a class="code" href="classadamantine_1_1_data_assimilator.html#aef8723a176e59a627727bffa0397d399">_additional_data</a>;</div>
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  </div>
<div class="line"><a name="l00440"></a><span class="lineno"> 440</span>  <span class="comment">// Apply the Kalman gain to the perturbed innovation for the ensemble</span></div>
<div class="line"><a name="l00441"></a><span class="lineno"> 441</span>  <span class="comment">// members in parallel</span></div>
<div class="line"><a name="l00442"></a><span class="lineno"> 442</span>  std::transform(</div>
<div class="line"><a name="l00443"></a><span class="lineno"> 443</span>  perturbed_innovation.begin(), perturbed_innovation.end(), <a class="code" href="namespaceadamantine.html#a7caf29199baef249d0ee5ff6fd81006ba1691b6ec67855c130469a858d0ad41a8">output</a>.begin(),</div>
<div class="line"><a name="l00444"></a><span class="lineno"> 444</span>  [&](dealii::Vector<double> <span class="keyword">const</span> &entry)</div>
<div class="line"><a name="l00445"></a><span class="lineno"> 445</span>  {</div>
<div class="line"><a name="l00446"></a><span class="lineno"> 446</span>  dealii::SolverGMRES<dealii::Vector<double>> HPH_plus_R_inv_solver(</div>
<div class="line"><a name="l00447"></a><span class="lineno"> 447</span>  solver_control, additional_data);</div>
<div class="line"><a name="l00448"></a><span class="lineno"> 448</span>  </div>
<div class="line"><a name="l00449"></a><span class="lineno"> 449</span>  auto op_HPH_plus_R_inv =</div>
<div class="line"><a name="l00450"></a><span class="lineno"> 450</span>  dealii::inverse_operator(op_HPH_plus_R, HPH_plus_R_inv_solver);</div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span>  </div>
<div class="line"><a name="l00452"></a><span class="lineno"> 452</span>  const auto op_K =</div>
<div class="line"><a name="l00453"></a><span class="lineno"> 453</span>  op_P * dealii::transpose_operator(op_H) * op_HPH_plus_R_inv;</div>
<div class="line"><a name="l00454"></a><span class="lineno"> 454</span>  </div>
<div class="line"><a name="l00455"></a><span class="lineno"> 455</span>  <span class="comment">// Apply the Kalman gain to each innovation vector</span></div>
<div class="line"><a name="l00456"></a><span class="lineno"> 456</span>  dealii::Vector<double> temporary = op_K * entry;</div>
<div class="line"><a name="l00457"></a><span class="lineno"> 457</span>  </div>
<div class="line"><a name="l00458"></a><span class="lineno"> 458</span>  <span class="comment">// Copy into a distributed block vector, this is the only place where</span></div>
<div class="line"><a name="l00459"></a><span class="lineno"> 459</span>  <span class="comment">// the mismatch matters, using dealii::Vector for the experimental</span></div>
<div class="line"><a name="l00460"></a><span class="lineno"> 460</span>  <span class="comment">// data and dealii::LA::distributed::BlockVector for the simulation</span></div>
<div class="line"><a name="l00461"></a><span class="lineno"> 461</span>  <span class="comment">// data.</span></div>
<div class="line"><a name="l00462"></a><span class="lineno"> 462</span>  dealii::LA::distributed::BlockVector<double> output_member(block_sizes);</div>
<div class="line"><a name="l00463"></a><span class="lineno"> 463</span>  for (unsigned int i = 0; i < augmented_state_size; ++i)</div>
<div class="line"><a name="l00464"></a><span class="lineno"> 464</span>  {</div>
<div class="line"><a name="l00465"></a><span class="lineno"> 465</span>  output_member(i) = temporary(i);</div>
<div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  }</div>
<div class="line"><a name="l00467"></a><span class="lineno"> 467</span>  </div>
<div class="line"><a name="l00468"></a><span class="lineno"> 468</span>  <span class="keywordflow">return</span> output_member;</div>
<div class="line"><a name="l00469"></a><span class="lineno"> 469</span>  });</div>
<div class="line"><a name="l00470"></a><span class="lineno"> 470</span>  </div>
<div class="line"><a name="l00471"></a><span class="lineno"> 471</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceadamantine.html#a7caf29199baef249d0ee5ff6fd81006ba1691b6ec67855c130469a858d0ad41a8">output</a>;</div>
<div class="line"><a name="l00472"></a><span class="lineno"> 472</span> }</div>
<div class="line"><a name="l00473"></a><span class="lineno"> 473</span>  </div>
<div class="line"><a name="l00474"></a><span class="lineno"> 474</span> dealii::SparseMatrix<double></div>
<div class="line"><a name="l00475"></a><span class="lineno"><a class="line" href="classadamantine_1_1_data_assimilator.html#aeb0f621afcc24939d270c2850d9f628e"> 475</a></span> DataAssimilator::calc_H(dealii::SparsityPattern &pattern)<span class="keyword"> const</span></div>
<div class="line"><a name="l00476"></a><span class="lineno"> 476</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00477"></a><span class="lineno"> 477</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> num_expt_dof_map_entries = _expt_to_dof_mapping.first.size();</div>
<div class="line"><a name="l00478"></a><span class="lineno"> 478</span>  </div>
<div class="line"><a name="l00479"></a><span class="lineno"> 479</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i = 0; i < num_expt_dof_map_entries; ++i)</div>
<div class="line"><a name="l00480"></a><span class="lineno"> 480</span>  {</div>
<div class="line"><a name="l00481"></a><span class="lineno"> 481</span>  <span class="keyword">auto</span> sim_index = _expt_to_dof_mapping.second[i];</div>
<div class="line"><a name="l00482"></a><span class="lineno"> 482</span>  <span class="keyword">auto</span> expt_index = _expt_to_dof_mapping.first[i];</div>
<div class="line"><a name="l00483"></a><span class="lineno"> 483</span>  pattern.add(expt_index, sim_index);</div>
<div class="line"><a name="l00484"></a><span class="lineno"> 484</span>  }</div>
<div class="line"><a name="l00485"></a><span class="lineno"> 485</span>  </div>
<div class="line"><a name="l00486"></a><span class="lineno"> 486</span>  pattern.compress();</div>
<div class="line"><a name="l00487"></a><span class="lineno"> 487</span>  </div>
<div class="line"><a name="l00488"></a><span class="lineno"> 488</span>  dealii::SparseMatrix<double> H(pattern);</div>
<div class="line"><a name="l00489"></a><span class="lineno"> 489</span>  </div>
<div class="line"><a name="l00490"></a><span class="lineno"> 490</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i = 0; i < num_expt_dof_map_entries; ++i)</div>
<div class="line"><a name="l00491"></a><span class="lineno"> 491</span>  {</div>
<div class="line"><a name="l00492"></a><span class="lineno"> 492</span>  <span class="keyword">auto</span> sim_index = _expt_to_dof_mapping.second[i];</div>
<div class="line"><a name="l00493"></a><span class="lineno"> 493</span>  <span class="keyword">auto</span> expt_index = _expt_to_dof_mapping.first[i];</div>
<div class="line"><a name="l00494"></a><span class="lineno"> 494</span>  H.add(expt_index, sim_index, 1.0);</div>
<div class="line"><a name="l00495"></a><span class="lineno"> 495</span>  }</div>
<div class="line"><a name="l00496"></a><span class="lineno"> 496</span>  </div>
<div class="line"><a name="l00497"></a><span class="lineno"> 497</span>  <span class="keywordflow">return</span> H;</div>
<div class="line"><a name="l00498"></a><span class="lineno"> 498</span> }</div>
<div class="line"><a name="l00499"></a><span class="lineno"> 499</span>  </div>
<div class="line"><a name="l00500"></a><span class="lineno"> 500</span> <span class="keyword">template</span> <<span class="keywordtype">int</span> dim></div>
<div class="line"><a name="l00501"></a><span class="lineno"><a class="line" href="classadamantine_1_1_data_assimilator.html#a6c09078d680adc5d2a791a570bb5a7ac"> 501</a></span> <span class="keywordtype">void</span> DataAssimilator::update_dof_mapping(</div>
<div class="line"><a name="l00502"></a><span class="lineno"> 502</span>  std::pair<std::vector<int>, std::vector<int>> <span class="keyword">const</span> &expt_to_dof_mapping)</div>
<div class="line"><a name="l00503"></a><span class="lineno"> 503</span> {</div>
<div class="line"><a name="l00504"></a><span class="lineno"> 504</span>  _expt_size = expt_to_dof_mapping.first.size();</div>
<div class="line"><a name="l00505"></a><span class="lineno"> 505</span>  _expt_to_dof_mapping = expt_to_dof_mapping;</div>
<div class="line"><a name="l00506"></a><span class="lineno"> 506</span> }</div>
<div class="line"><a name="l00507"></a><span class="lineno"> 507</span>  </div>
<div class="line"><a name="l00508"></a><span class="lineno"> 508</span> <span class="keyword">template</span> <<span class="keywordtype">int</span> dim></div>
<div class="line"><a name="l00509"></a><span class="lineno"><a class="line" href="classadamantine_1_1_data_assimilator.html#aa589f4a2068eddc12fbb1408ffec04b7"> 509</a></span> <span class="keywordtype">void</span> DataAssimilator::update_covariance_sparsity_pattern(</div>
<div class="line"><a name="l00510"></a><span class="lineno"> 510</span>  dealii::DoFHandler<dim> <span class="keyword">const</span> &dof_handler,</div>
<div class="line"><a name="l00511"></a><span class="lineno"> 511</span>  <span class="keyword">const</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> parameter_size)</div>
<div class="line"><a name="l00512"></a><span class="lineno"> 512</span> {</div>
<div class="line"><a name="l00513"></a><span class="lineno"> 513</span>  <span class="keywordflow">if</span> (_color == 0)</div>
<div class="line"><a name="l00514"></a><span class="lineno"> 514</span>  {</div>
<div class="line"><a name="l00515"></a><span class="lineno"> 515</span>  _sim_size = dof_handler.n_dofs();</div>
<div class="line"><a name="l00516"></a><span class="lineno"> 516</span>  _parameter_size = parameter_size;</div>
<div class="line"><a name="l00517"></a><span class="lineno"> 517</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> augmented_state_size = _sim_size + _parameter_size;</div>
<div class="line"><a name="l00518"></a><span class="lineno"> 518</span>  </div>
<div class="line"><a name="l00519"></a><span class="lineno"> 519</span>  <span class="keyword">auto</span> [dof_indices, support_points] =</div>
<div class="line"><a name="l00520"></a><span class="lineno"> 520</span>  <a class="code" href="namespaceadamantine.html#a12d6157f2693e3b6b9d87f8f515c09b0">get_dof_to_support_mapping</a>(dof_handler);</div>
<div class="line"><a name="l00521"></a><span class="lineno"> 521</span>  </div>
<div class="line"><a name="l00522"></a><span class="lineno"> 522</span>  <span class="comment">// Perform the spatial search using ArborX</span></div>
<div class="line"><a name="l00523"></a><span class="lineno"> 523</span>  dealii::ArborXWrappers::DistributedTree distributed_tree(</div>
<div class="line"><a name="l00524"></a><span class="lineno"> 524</span>  _local_communicator, support_points);</div>
<div class="line"><a name="l00525"></a><span class="lineno"> 525</span>  </div>
<div class="line"><a name="l00526"></a><span class="lineno"> 526</span>  std::vector<std::pair<dealii::Point<dim, double>, <span class="keywordtype">double</span>>> spheres;</div>
<div class="line"><a name="l00527"></a><span class="lineno"> 527</span>  <span class="keywordflow">if</span> (dim == 2)</div>
<div class="line"><a name="l00528"></a><span class="lineno"> 528</span>  <span class="keywordflow">for</span> (<span class="keyword">auto</span> <span class="keyword">const</span> pt : support_points)</div>
<div class="line"><a name="l00529"></a><span class="lineno"> 529</span>  spheres.push_back({{pt[0], pt[1]}, _localization_cutoff_distance});</div>
<div class="line"><a name="l00530"></a><span class="lineno"> 530</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00531"></a><span class="lineno"> 531</span>  <span class="keywordflow">for</span> (<span class="keyword">auto</span> <span class="keyword">const</span> pt : support_points)</div>
<div class="line"><a name="l00532"></a><span class="lineno"> 532</span>  spheres.push_back(</div>
<div class="line"><a name="l00533"></a><span class="lineno"> 533</span>  {{pt[0], pt[1], pt[2]}, _localization_cutoff_distance});</div>
<div class="line"><a name="l00534"></a><span class="lineno"> 534</span>  dealii::ArborXWrappers::SphereIntersectPredicate sph_intersect(spheres);</div>
<div class="line"><a name="l00535"></a><span class="lineno"> 535</span>  <span class="keyword">auto</span> [indices_ranks, offsets] = distributed_tree.query(sph_intersect);</div>
<div class="line"><a name="l00536"></a><span class="lineno"> 536</span>  <a class="code" href="utils_8hh.html#aa06eedd6f738a415870e97a375337d51">ASSERT</a>(offsets.size() == spheres.size() + 1,</div>
<div class="line"><a name="l00537"></a><span class="lineno"> 537</span>  <span class="stringliteral">"There was a problem in ArborX."</span>);</div>
<div class="line"><a name="l00538"></a><span class="lineno"> 538</span>  </div>
<div class="line"><a name="l00539"></a><span class="lineno"> 539</span>  <span class="keyword">auto</span> locally_owned_dofs_per_rank = dealii::Utilities::MPI::gather(</div>
<div class="line"><a name="l00540"></a><span class="lineno"> 540</span>  _local_communicator, dof_handler.locally_owned_dofs());</div>
<div class="line"><a name="l00541"></a><span class="lineno"> 541</span>  <span class="keyword">auto</span> support_points_per_rank =</div>
<div class="line"><a name="l00542"></a><span class="lineno"> 542</span>  dealii::Utilities::MPI::gather(_local_communicator, support_points);</div>
<div class="line"><a name="l00543"></a><span class="lineno"> 543</span>  <span class="keyword">auto</span> indices_ranks_per_rank =</div>
<div class="line"><a name="l00544"></a><span class="lineno"> 544</span>  dealii::Utilities::MPI::gather(_local_communicator, indices_ranks);</div>
<div class="line"><a name="l00545"></a><span class="lineno"> 545</span>  <span class="keyword">auto</span> offsets_per_rank =</div>
<div class="line"><a name="l00546"></a><span class="lineno"> 546</span>  dealii::Utilities::MPI::gather(_local_communicator, offsets);</div>
<div class="line"><a name="l00547"></a><span class="lineno"> 547</span>  </div>
<div class="line"><a name="l00548"></a><span class="lineno"> 548</span>  <span class="keywordflow">if</span> (_global_rank == 0)</div>
<div class="line"><a name="l00549"></a><span class="lineno"> 549</span>  {</div>
<div class="line"><a name="l00550"></a><span class="lineno"> 550</span>  <span class="comment">// We need IndexSet to build the sparsity pattern. Since the data</span></div>
<div class="line"><a name="l00551"></a><span class="lineno"> 551</span>  <span class="comment">// assimilation is done is serial, the IndexSet just contains</span></div>
<div class="line"><a name="l00552"></a><span class="lineno"> 552</span>  <span class="comment">// everything.</span></div>
<div class="line"><a name="l00553"></a><span class="lineno"> 553</span>  dealii::IndexSet parallel_partitioning =</div>
<div class="line"><a name="l00554"></a><span class="lineno"> 554</span>  dealii::complete_index_set(augmented_state_size);</div>
<div class="line"><a name="l00555"></a><span class="lineno"> 555</span>  parallel_partitioning.compress();</div>
<div class="line"><a name="l00556"></a><span class="lineno"> 556</span>  _covariance_sparsity_pattern.reinit(parallel_partitioning, MPI_COMM_SELF);</div>
<div class="line"><a name="l00557"></a><span class="lineno"> 557</span>  </div>
<div class="line"><a name="l00558"></a><span class="lineno"> 558</span>  <span class="comment">// Fill in the SparsityPattern</span></div>
<div class="line"><a name="l00559"></a><span class="lineno"> 559</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> <span class="keyword">const</span> local_comm_size =</div>
<div class="line"><a name="l00560"></a><span class="lineno"> 560</span>  dealii::Utilities::MPI::n_mpi_processes(_local_communicator);</div>
<div class="line"><a name="l00561"></a><span class="lineno"> 561</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> rank = 0; rank < local_comm_size; ++rank)</div>
<div class="line"><a name="l00562"></a><span class="lineno"> 562</span>  {</div>
<div class="line"><a name="l00563"></a><span class="lineno"> 563</span>  <span class="keywordflow">if</span> (offsets_per_rank[rank].size() != 0)</div>
<div class="line"><a name="l00564"></a><span class="lineno"> 564</span>  {</div>
<div class="line"><a name="l00565"></a><span class="lineno"> 565</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i = 0; i < offsets_per_rank[rank].size() - 1; ++i)</div>
<div class="line"><a name="l00566"></a><span class="lineno"> 566</span>  {</div>
<div class="line"><a name="l00567"></a><span class="lineno"> 567</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = offsets_per_rank[rank][i];</div>
<div class="line"><a name="l00568"></a><span class="lineno"> 568</span>  j < offsets_per_rank[rank][i + 1]; ++j)</div>
<div class="line"><a name="l00569"></a><span class="lineno"> 569</span>  {</div>
<div class="line"><a name="l00570"></a><span class="lineno"> 570</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> row =</div>
<div class="line"><a name="l00571"></a><span class="lineno"> 571</span>  locally_owned_dofs_per_rank[rank].nth_index_in_set(i);</div>
<div class="line"><a name="l00572"></a><span class="lineno"> 572</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> other_rank = indices_ranks_per_rank[rank][j].second;</div>
<div class="line"><a name="l00573"></a><span class="lineno"> 573</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> other_i = indices_ranks_per_rank[rank][j].first;</div>
<div class="line"><a name="l00574"></a><span class="lineno"> 574</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> column =</div>
<div class="line"><a name="l00575"></a><span class="lineno"> 575</span>  locally_owned_dofs_per_rank[other_rank].nth_index_in_set(</div>
<div class="line"><a name="l00576"></a><span class="lineno"> 576</span>  other_i);</div>
<div class="line"><a name="l00577"></a><span class="lineno"> 577</span>  _covariance_distance_map[std::make_pair(row, column)] =</div>
<div class="line"><a name="l00578"></a><span class="lineno"> 578</span>  support_points_per_rank[rank][i].distance(</div>
<div class="line"><a name="l00579"></a><span class="lineno"> 579</span>  support_points_per_rank[other_rank][other_i]);</div>
<div class="line"><a name="l00580"></a><span class="lineno"> 580</span>  _covariance_sparsity_pattern.add(row, column);</div>
<div class="line"><a name="l00581"></a><span class="lineno"> 581</span>  }</div>
<div class="line"><a name="l00582"></a><span class="lineno"> 582</span>  }</div>
<div class="line"><a name="l00583"></a><span class="lineno"> 583</span>  }</div>
<div class="line"><a name="l00584"></a><span class="lineno"> 584</span>  }</div>
<div class="line"><a name="l00585"></a><span class="lineno"> 585</span>  </div>
<div class="line"><a name="l00586"></a><span class="lineno"> 586</span>  <span class="comment">// Add entries for the parameter augmentation</span></div>
<div class="line"><a name="l00587"></a><span class="lineno"> 587</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i1 = _sim_size; i1 < augmented_state_size; ++i1)</div>
<div class="line"><a name="l00588"></a><span class="lineno"> 588</span>  {</div>
<div class="line"><a name="l00589"></a><span class="lineno"> 589</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> j1 = 0; j1 < augmented_state_size; ++j1)</div>
<div class="line"><a name="l00590"></a><span class="lineno"> 590</span>  {</div>
<div class="line"><a name="l00591"></a><span class="lineno"> 591</span>  _covariance_sparsity_pattern.add(i1, j1);</div>
<div class="line"><a name="l00592"></a><span class="lineno"> 592</span>  }</div>
<div class="line"><a name="l00593"></a><span class="lineno"> 593</span>  }</div>
<div class="line"><a name="l00594"></a><span class="lineno"> 594</span>  </div>
<div class="line"><a name="l00595"></a><span class="lineno"> 595</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i1 = 0; i1 < _sim_size; ++i1)</div>
<div class="line"><a name="l00596"></a><span class="lineno"> 596</span>  {</div>
<div class="line"><a name="l00597"></a><span class="lineno"> 597</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> j1 = _sim_size; j1 < augmented_state_size; ++j1)</div>
<div class="line"><a name="l00598"></a><span class="lineno"> 598</span>  {</div>
<div class="line"><a name="l00599"></a><span class="lineno"> 599</span>  _covariance_sparsity_pattern.add(i1, j1);</div>
<div class="line"><a name="l00600"></a><span class="lineno"> 600</span>  }</div>
<div class="line"><a name="l00601"></a><span class="lineno"> 601</span>  }</div>
<div class="line"><a name="l00602"></a><span class="lineno"> 602</span>  </div>
<div class="line"><a name="l00603"></a><span class="lineno"> 603</span>  _covariance_sparsity_pattern.compress();</div>
<div class="line"><a name="l00604"></a><span class="lineno"> 604</span>  }</div>
<div class="line"><a name="l00605"></a><span class="lineno"> 605</span>  }</div>
<div class="line"><a name="l00606"></a><span class="lineno"> 606</span> }</div>
<div class="line"><a name="l00607"></a><span class="lineno"> 607</span>  </div>
<div class="line"><a name="l00608"></a><span class="lineno"><a class="line" href="classadamantine_1_1_data_assimilator.html#a4e5460783efc1dd7b312927576f1fc86"> 608</a></span> dealii::Vector<double> DataAssimilator::calc_Hx(</div>
<div class="line"><a name="l00609"></a><span class="lineno"> 609</span>  dealii::LA::distributed::Vector<double> <span class="keyword">const</span> &sim_ensemble_member)<span class="keyword"> const</span></div>
<div class="line"><a name="l00610"></a><span class="lineno"> 610</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00611"></a><span class="lineno"> 611</span>  dealii::Vector<double> out_vec(_expt_size);</div>
<div class="line"><a name="l00612"></a><span class="lineno"> 612</span>  </div>
<div class="line"><a name="l00613"></a><span class="lineno"> 613</span>  <span class="comment">// Loop through the observation map to get the observation indices</span></div>
<div class="line"><a name="l00614"></a><span class="lineno"> 614</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i = 0; i < _expt_size; ++i)</div>
<div class="line"><a name="l00615"></a><span class="lineno"> 615</span>  {</div>
<div class="line"><a name="l00616"></a><span class="lineno"> 616</span>  <span class="keyword">auto</span> sim_index = _expt_to_dof_mapping.second[i];</div>
<div class="line"><a name="l00617"></a><span class="lineno"> 617</span>  <span class="keyword">auto</span> expt_index = _expt_to_dof_mapping.first[i];</div>
<div class="line"><a name="l00618"></a><span class="lineno"> 618</span>  out_vec(expt_index) = sim_ensemble_member(sim_index);</div>
<div class="line"><a name="l00619"></a><span class="lineno"> 619</span>  }</div>
<div class="line"><a name="l00620"></a><span class="lineno"> 620</span>  </div>
<div class="line"><a name="l00621"></a><span class="lineno"> 621</span>  <span class="keywordflow">return</span> out_vec;</div>
<div class="line"><a name="l00622"></a><span class="lineno"> 622</span> }</div>
<div class="line"><a name="l00623"></a><span class="lineno"> 623</span>  </div>
<div class="line"><a name="l00624"></a><span class="lineno"><a class="line" href="classadamantine_1_1_data_assimilator.html#a78e37ebef7fdc3f7a6f3ec4c2b1b9d13"> 624</a></span> <span class="keywordtype">void</span> DataAssimilator::fill_noise_vector(dealii::Vector<double> &vec,</div>
<div class="line"><a name="l00625"></a><span class="lineno"> 625</span>  dealii::SparseMatrix<double> <span class="keyword">const</span> &R,</div>
<div class="line"><a name="l00626"></a><span class="lineno"> 626</span>  <span class="keywordtype">bool</span> <span class="keyword">const</span> R_is_diagonal)</div>
<div class="line"><a name="l00627"></a><span class="lineno"> 627</span> {</div>
<div class="line"><a name="l00628"></a><span class="lineno"> 628</span>  <span class="keyword">auto</span> vector_size = vec.size();</div>
<div class="line"><a name="l00629"></a><span class="lineno"> 629</span>  </div>
<div class="line"><a name="l00630"></a><span class="lineno"> 630</span>  <span class="comment">// If R is diagonal, then the entries in the noise vector are independent</span></div>
<div class="line"><a name="l00631"></a><span class="lineno"> 631</span>  <span class="comment">// and each are simply a scaled output of the pseudo-random number</span></div>
<div class="line"><a name="l00632"></a><span class="lineno"> 632</span>  <span class="comment">// generator. For a more general R, one needs to multiply by the Cholesky</span></div>
<div class="line"><a name="l00633"></a><span class="lineno"> 633</span>  <span class="comment">// decomposition of R to achieve the appropriate correlation between the</span></div>
<div class="line"><a name="l00634"></a><span class="lineno"> 634</span>  <span class="comment">// entries. Deal.II only has a specific Cholesky function for full matrices,</span></div>
<div class="line"><a name="l00635"></a><span class="lineno"> 635</span>  <span class="comment">// which is used in the implementation below. The Cholesky decomposition is</span></div>
<div class="line"><a name="l00636"></a><span class="lineno"> 636</span>  <span class="comment">// a special case of LU decomposition, so we can use a sparse LU solver to</span></div>
<div class="line"><a name="l00637"></a><span class="lineno"> 637</span>  <span class="comment">// obtain the "L" below if needed in the future.</span></div>
<div class="line"><a name="l00638"></a><span class="lineno"> 638</span>  </div>
<div class="line"><a name="l00639"></a><span class="lineno"> 639</span>  <span class="keywordflow">if</span> (R_is_diagonal)</div>
<div class="line"><a name="l00640"></a><span class="lineno"> 640</span>  {</div>
<div class="line"><a name="l00641"></a><span class="lineno"> 641</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i = 0; i < vector_size; ++i)</div>
<div class="line"><a name="l00642"></a><span class="lineno"> 642</span>  {</div>
<div class="line"><a name="l00643"></a><span class="lineno"> 643</span>  vec(i) = _normal_dist_generator(_prng) * std::sqrt(R(i, i));</div>
<div class="line"><a name="l00644"></a><span class="lineno"> 644</span>  }</div>
<div class="line"><a name="l00645"></a><span class="lineno"> 645</span>  }</div>
<div class="line"><a name="l00646"></a><span class="lineno"> 646</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00647"></a><span class="lineno"> 647</span>  {</div>
<div class="line"><a name="l00648"></a><span class="lineno"> 648</span>  <span class="comment">// Do Cholesky decomposition</span></div>
<div class="line"><a name="l00649"></a><span class="lineno"> 649</span>  dealii::FullMatrix<double> L(vector_size);</div>
<div class="line"><a name="l00650"></a><span class="lineno"> 650</span>  dealii::FullMatrix<double> R_full(vector_size);</div>
<div class="line"><a name="l00651"></a><span class="lineno"> 651</span>  R_full.copy_from(R);</div>
<div class="line"><a name="l00652"></a><span class="lineno"> 652</span>  L.cholesky(R_full);</div>
<div class="line"><a name="l00653"></a><span class="lineno"> 653</span>  </div>
<div class="line"><a name="l00654"></a><span class="lineno"> 654</span>  <span class="comment">// Get a vector of normally distributed values</span></div>
<div class="line"><a name="l00655"></a><span class="lineno"> 655</span>  dealii::Vector<double> uncorrelated_noise_vector(vector_size);</div>
<div class="line"><a name="l00656"></a><span class="lineno"> 656</span>  </div>
<div class="line"><a name="l00657"></a><span class="lineno"> 657</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i = 0; i < vector_size; ++i)</div>
<div class="line"><a name="l00658"></a><span class="lineno"> 658</span>  {</div>
<div class="line"><a name="l00659"></a><span class="lineno"> 659</span>  uncorrelated_noise_vector(i) = _normal_dist_generator(_prng);</div>
<div class="line"><a name="l00660"></a><span class="lineno"> 660</span>  }</div>
<div class="line"><a name="l00661"></a><span class="lineno"> 661</span>  </div>
<div class="line"><a name="l00662"></a><span class="lineno"> 662</span>  L.vmult(vec, uncorrelated_noise_vector);</div>
<div class="line"><a name="l00663"></a><span class="lineno"> 663</span>  }</div>
<div class="line"><a name="l00664"></a><span class="lineno"> 664</span> }</div>
<div class="line"><a name="l00665"></a><span class="lineno"> 665</span>  </div>
<div class="line"><a name="l00666"></a><span class="lineno"><a class="line" href="classadamantine_1_1_data_assimilator.html#a1f07102e07d3a696e70288048c803977"> 666</a></span> <span class="keywordtype">double</span> DataAssimilator::gaspari_cohn_function(<span class="keywordtype">double</span> <span class="keyword">const</span> r)<span class="keyword"> const</span></div>
<div class="line"><a name="l00667"></a><span class="lineno"> 667</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00668"></a><span class="lineno"> 668</span>  <span class="keywordflow">if</span> (r < 1.0)</div>
<div class="line"><a name="l00669"></a><span class="lineno"> 669</span>  {</div>
<div class="line"><a name="l00670"></a><span class="lineno"> 670</span>  <span class="keywordflow">return</span> 1. - 5. / 3. * std::pow(r, 2) + 5. / 8. * std::pow(r, 3) +</div>
<div class="line"><a name="l00671"></a><span class="lineno"> 671</span>  0.5 * std::pow(r, 4) - 0.25 * std::pow(r, 5);</div>
<div class="line"><a name="l00672"></a><span class="lineno"> 672</span>  }</div>
<div class="line"><a name="l00673"></a><span class="lineno"> 673</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (r < 2)</div>
<div class="line"><a name="l00674"></a><span class="lineno"> 674</span>  {</div>
<div class="line"><a name="l00675"></a><span class="lineno"> 675</span>  <span class="keywordflow">return</span> 4. - 5. * r + 5. / 3. * std::pow(r, 2) + 5. / 8. * std::pow(r, 3) -</div>
<div class="line"><a name="l00676"></a><span class="lineno"> 676</span>  0.5 * std::pow(r, 4) + 1. / 12. * std::pow(r, 5) - 2. / (3. * r);</div>
<div class="line"><a name="l00677"></a><span class="lineno"> 677</span>  }</div>
<div class="line"><a name="l00678"></a><span class="lineno"> 678</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00679"></a><span class="lineno"> 679</span>  {</div>
<div class="line"><a name="l00680"></a><span class="lineno"> 680</span>  <span class="keywordflow">return</span> 0.;</div>
<div class="line"><a name="l00681"></a><span class="lineno"> 681</span>  }</div>
<div class="line"><a name="l00682"></a><span class="lineno"> 682</span> }</div>
<div class="line"><a name="l00683"></a><span class="lineno"> 683</span>  </div>
<div class="line"><a name="l00684"></a><span class="lineno"> 684</span> dealii::TrilinosWrappers::SparseMatrix</div>
<div class="line"><a name="l00685"></a><span class="lineno"><a class="line" href="classadamantine_1_1_data_assimilator.html#af5bde3f9550c77d9a06d88da422e213e"> 685</a></span> DataAssimilator::calc_sample_covariance_sparse(</div>
<div class="line"><a name="l00686"></a><span class="lineno"> 686</span>  std::vector<dealii::LA::distributed::BlockVector<double>> <span class="keyword">const</span></div>
<div class="line"><a name="l00687"></a><span class="lineno"> 687</span>  &vec_ensemble)<span class="keyword"> const</span></div>
<div class="line"><a name="l00688"></a><span class="lineno"> 688</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00689"></a><span class="lineno"> 689</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> <span class="keyword">const</span> local_size = vec_ensemble[0].locally_owned_size();</div>
<div class="line"><a name="l00690"></a><span class="lineno"> 690</span>  </div>
<div class="line"><a name="l00691"></a><span class="lineno"> 691</span>  <span class="comment">// Calculate the mean</span></div>
<div class="line"><a name="l00692"></a><span class="lineno"> 692</span>  dealii::Vector<double> mean(local_size);</div>
<div class="line"><a name="l00693"></a><span class="lineno"> 693</span>  <span class="keyword">auto</span> sum = vec_ensemble[0];</div>
<div class="line"><a name="l00694"></a><span class="lineno"> 694</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> sample = 1; sample < _num_ensemble_members; ++sample)</div>
<div class="line"><a name="l00695"></a><span class="lineno"> 695</span>  {</div>
<div class="line"><a name="l00696"></a><span class="lineno"> 696</span>  sum += vec_ensemble[sample];</div>
<div class="line"><a name="l00697"></a><span class="lineno"> 697</span>  }</div>
<div class="line"><a name="l00698"></a><span class="lineno"> 698</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> ii = 0;</div>
<div class="line"><a name="l00699"></a><span class="lineno"> 699</span>  <span class="keywordflow">for</span> (<span class="keyword">auto</span> index : sum.locally_owned_elements())</div>
<div class="line"><a name="l00700"></a><span class="lineno"> 700</span>  {</div>
<div class="line"><a name="l00701"></a><span class="lineno"> 701</span>  mean[ii] = sum[index] / _num_ensemble_members;</div>
<div class="line"><a name="l00702"></a><span class="lineno"> 702</span>  ++ii;</div>
<div class="line"><a name="l00703"></a><span class="lineno"> 703</span>  }</div>
<div class="line"><a name="l00704"></a><span class="lineno"> 704</span>  </div>
<div class="line"><a name="l00705"></a><span class="lineno"> 705</span>  dealii::TrilinosWrappers::SparseMatrix cov(_covariance_sparsity_pattern);</div>
<div class="line"><a name="l00706"></a><span class="lineno"> 706</span>  </div>
<div class="line"><a name="l00707"></a><span class="lineno"> 707</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> pos = 0;</div>
<div class="line"><a name="l00708"></a><span class="lineno"> 708</span>  <span class="keywordflow">for</span> (<span class="keyword">auto</span> conv_iter = cov.begin(); conv_iter != cov.end(); ++conv_iter, ++pos)</div>
<div class="line"><a name="l00709"></a><span class="lineno"> 709</span>  {</div>
<div class="line"><a name="l00710"></a><span class="lineno"> 710</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i = conv_iter->row();</div>
<div class="line"><a name="l00711"></a><span class="lineno"> 711</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> j = conv_iter->column();</div>
<div class="line"><a name="l00712"></a><span class="lineno"> 712</span>  </div>
<div class="line"><a name="l00713"></a><span class="lineno"> 713</span>  <span class="comment">// Do the element-wise matrix multiply by hand</span></div>
<div class="line"><a name="l00714"></a><span class="lineno"> 714</span>  <span class="keywordtype">double</span> element_value = 0;</div>
<div class="line"><a name="l00715"></a><span class="lineno"> 715</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> k = 0; k < _num_ensemble_members; ++k)</div>
<div class="line"><a name="l00716"></a><span class="lineno"> 716</span>  {</div>
<div class="line"><a name="l00717"></a><span class="lineno"> 717</span>  element_value +=</div>
<div class="line"><a name="l00718"></a><span class="lineno"> 718</span>  (vec_ensemble[k][i] - mean[i]) * (vec_ensemble[k][j] - mean[j]);</div>
<div class="line"><a name="l00719"></a><span class="lineno"> 719</span>  }</div>
<div class="line"><a name="l00720"></a><span class="lineno"> 720</span>  </div>
<div class="line"><a name="l00721"></a><span class="lineno"> 721</span>  element_value /= (_num_ensemble_members - 1.0);</div>
<div class="line"><a name="l00722"></a><span class="lineno"> 722</span>  </div>
<div class="line"><a name="l00723"></a><span class="lineno"> 723</span>  <span class="comment">// Apply localization</span></div>
<div class="line"><a name="l00724"></a><span class="lineno"> 724</span>  <span class="keywordtype">double</span> localization_scaling = 1.0;</div>
<div class="line"><a name="l00725"></a><span class="lineno"> 725</span>  <span class="keywordflow">if</span> (i < _sim_size && j < _sim_size)</div>
<div class="line"><a name="l00726"></a><span class="lineno"> 726</span>  {</div>
<div class="line"><a name="l00727"></a><span class="lineno"> 727</span>  <span class="keywordtype">double</span> dist = _covariance_distance_map.find(std::make_pair(i, j))->second;</div>
<div class="line"><a name="l00728"></a><span class="lineno"> 728</span>  <span class="keywordflow">if</span> (_localization_cutoff_function == LocalizationCutoff::gaspari_cohn)</div>
<div class="line"><a name="l00729"></a><span class="lineno"> 729</span>  {</div>
<div class="line"><a name="l00730"></a><span class="lineno"> 730</span>  localization_scaling =</div>
<div class="line"><a name="l00731"></a><span class="lineno"> 731</span>  gaspari_cohn_function(2.0 * dist / _localization_cutoff_distance);</div>
<div class="line"><a name="l00732"></a><span class="lineno"> 732</span>  }</div>
<div class="line"><a name="l00733"></a><span class="lineno"> 733</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> ((_localization_cutoff_function ==</div>
<div class="line"><a name="l00734"></a><span class="lineno"> 734</span>  LocalizationCutoff::step_function) &&</div>
<div class="line"><a name="l00735"></a><span class="lineno"> 735</span>  (dist > _localization_cutoff_distance))</div>
<div class="line"><a name="l00736"></a><span class="lineno"> 736</span>  {</div>
<div class="line"><a name="l00737"></a><span class="lineno"> 737</span>  localization_scaling = 0.0;</div>
<div class="line"><a name="l00738"></a><span class="lineno"> 738</span>  }</div>
<div class="line"><a name="l00739"></a><span class="lineno"> 739</span>  }</div>
<div class="line"><a name="l00740"></a><span class="lineno"> 740</span>  </div>
<div class="line"><a name="l00741"></a><span class="lineno"> 741</span>  conv_iter->value() = element_value * localization_scaling;</div>
<div class="line"><a name="l00742"></a><span class="lineno"> 742</span>  }</div>
<div class="line"><a name="l00743"></a><span class="lineno"> 743</span>  </div>
<div class="line"><a name="l00744"></a><span class="lineno"> 744</span>  <span class="keywordflow">return</span> cov;</div>
<div class="line"><a name="l00745"></a><span class="lineno"> 745</span> }</div>
<div class="line"><a name="l00746"></a><span class="lineno"> 746</span>  </div>
<div class="line"><a name="l00747"></a><span class="lineno"> 747</span> <span class="comment">// Explicit instantiation</span></div>
<div class="line"><a name="l00748"></a><span class="lineno"> 748</span> <span class="keyword">template</span> <span class="keywordtype">void</span> DataAssimilator::update_dof_mapping<2>(</div>
<div class="line"><a name="l00749"></a><span class="lineno"> 749</span>  std::pair<std::vector<int>, std::vector<int>> <span class="keyword">const</span> &expt_to_dof_mapping);</div>
<div class="line"><a name="l00750"></a><span class="lineno"> 750</span> <span class="keyword">template</span> <span class="keywordtype">void</span> DataAssimilator::update_dof_mapping<3>(</div>
<div class="line"><a name="l00751"></a><span class="lineno"> 751</span>  std::pair<std::vector<int>, std::vector<int>> <span class="keyword">const</span> &expt_to_dof_mapping);</div>
<div class="line"><a name="l00752"></a><span class="lineno"> 752</span> <span class="keyword">template</span> <span class="keywordtype">void</span> DataAssimilator::update_covariance_sparsity_pattern<2>(</div>
<div class="line"><a name="l00753"></a><span class="lineno"> 753</span>  dealii::DoFHandler<2> <span class="keyword">const</span> &dof_handler,</div>
<div class="line"><a name="l00754"></a><span class="lineno"> 754</span>  <span class="keyword">const</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> parameter_size);</div>
<div class="line"><a name="l00755"></a><span class="lineno"> 755</span> <span class="keyword">template</span> <span class="keywordtype">void</span> DataAssimilator::update_covariance_sparsity_pattern<3>(</div>
<div class="line"><a name="l00756"></a><span class="lineno"> 756</span>  dealii::DoFHandler<3> <span class="keyword">const</span> &dof_handler,</div>
<div class="line"><a name="l00757"></a><span class="lineno"> 757</span>  <span class="keyword">const</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> parameter_size);</div>
<div class="line"><a name="l00758"></a><span class="lineno"> 758</span>  </div>
<div class="line"><a name="l00759"></a><span class="lineno"> 759</span> } <span class="comment">// namespace adamantine</span></div>
<div class="ttc" id="a_data_assimilator_8hh_html"><div class="ttname"><a href="_data_assimilator_8hh.html">DataAssimilator.hh</a></div></div>
<div class="ttc" id="aclassadamantine_1_1_data_assimilator_html_a09166a5bc460fa193e308ddd2c4238dd"><div class="ttname"><a href="classadamantine_1_1_data_assimilator.html#a09166a5bc460fa193e308ddd2c4238dd">adamantine::DataAssimilator::_num_ensemble_members</a></div><div class="ttdeci">unsigned int _num_ensemble_members</div><div class="ttdef"><b>Definition:</b> <a href="_data_assimilator_8hh_source.html#l00214">DataAssimilator.hh:214</a></div></div>
<div class="ttc" id="aclassadamantine_1_1_data_assimilator_html_a1baf2c4af092efb0d076e9071a192d51"><div class="ttname"><a href="classadamantine_1_1_data_assimilator.html#a1baf2c4af092efb0d076e9071a192d51">adamantine::DataAssimilator::_global_comm_size</a></div><div class="ttdeci">int _global_comm_size</div><div class="ttdef"><b>Definition:</b> <a href="_data_assimilator_8hh_source.html#l00204">DataAssimilator.hh:204</a></div></div>
<div class="ttc" id="aclassadamantine_1_1_data_assimilator_html_a405e8d43091eca88e94898eb885313c3"><div class="ttname"><a href="classadamantine_1_1_data_assimilator.html#a405e8d43091eca88e94898eb885313c3">adamantine::DataAssimilator::apply_kalman_gain</a></div><div class="ttdeci">std::vector< dealii::LA::distributed::BlockVector< double > > apply_kalman_gain(std::vector< dealii::LA::distributed::BlockVector< double >> &augmented_state_ensemble, dealii::SparseMatrix< double > const &R, std::vector< dealii::Vector< double >> const &perturbed_innovation)</div><div class="ttdef"><b>Definition:</b> <a href="_data_assimilator_8cc_source.html#l00400">DataAssimilator.cc:400</a></div></div>
<div class="ttc" id="aclassadamantine_1_1_data_assimilator_html_a41a2e76bc1bcf25d0daad9429ab62a30"><div class="ttname"><a href="classadamantine_1_1_data_assimilator.html#a41a2e76bc1bcf25d0daad9429ab62a30">adamantine::DataAssimilator::_parameter_size</a></div><div class="ttdeci">unsigned int _parameter_size</div><div class="ttdef"><b>Definition:</b> <a href="_data_assimilator_8hh_source.html#l00224">DataAssimilator.hh:224</a></div></div>
<div class="ttc" id="aclassadamantine_1_1_data_assimilator_html_a4e5460783efc1dd7b312927576f1fc86"><div class="ttname"><a href="classadamantine_1_1_data_assimilator.html#a4e5460783efc1dd7b312927576f1fc86">adamantine::DataAssimilator::calc_Hx</a></div><div class="ttdeci">dealii::Vector< double > calc_Hx(dealii::LA::distributed::Vector< double > const &sim_ensemble_member) const</div><div class="ttdef"><b>Definition:</b> <a href="_data_assimilator_8cc_source.html#l00608">DataAssimilator.cc:608</a></div></div>
<div class="ttc" id="aclassadamantine_1_1_data_assimilator_html_a5420f95c388dec9f638a4f1d4eec1914"><div class="ttname"><a href="classadamantine_1_1_data_assimilator.html#a5420f95c388dec9f638a4f1d4eec1914">adamantine::DataAssimilator::_global_rank</a></div><div class="ttdeci">int _global_rank</div><div class="ttdef"><b>Definition:</b> <a href="_data_assimilator_8hh_source.html#l00199">DataAssimilator.hh:199</a></div></div>
<div class="ttc" id="aclassadamantine_1_1_data_assimilator_html_a65cf1d6c324239bf4fac98c1f7abcdc9"><div class="ttname"><a href="classadamantine_1_1_data_assimilator.html#a65cf1d6c324239bf4fac98c1f7abcdc9">adamantine::DataAssimilator::_local_communicator</a></div><div class="ttdeci">MPI_Comm _local_communicator</div><div class="ttdef"><b>Definition:</b> <a href="_data_assimilator_8hh_source.html#l00194">DataAssimilator.hh:194</a></div></div>
<div class="ttc" id="aclassadamantine_1_1_data_assimilator_html_a75a7a61d7cf93db94867a0841846c983"><div class="ttname"><a href="classadamantine_1_1_data_assimilator.html#a75a7a61d7cf93db94867a0841846c983">adamantine::DataAssimilator::_localization_cutoff_function</a></div><div class="ttdeci">LocalizationCutoff _localization_cutoff_function</div><div class="ttdef"><b>Definition:</b> <a href="_data_assimilator_8hh_source.html#l00253">DataAssimilator.hh:253</a></div></div>
<div class="ttc" id="aclassadamantine_1_1_data_assimilator_html_a78e37ebef7fdc3f7a6f3ec4c2b1b9d13"><div class="ttname"><a href="classadamantine_1_1_data_assimilator.html#a78e37ebef7fdc3f7a6f3ec4c2b1b9d13">adamantine::DataAssimilator::fill_noise_vector</a></div><div class="ttdeci">void fill_noise_vector(dealii::Vector< double > &vec, dealii::SparseMatrix< double > const &R, bool const R_is_diagonal)</div><div class="ttdef"><b>Definition:</b> <a href="_data_assimilator_8cc_source.html#l00624">DataAssimilator.cc:624</a></div></div>
<div class="ttc" id="aclassadamantine_1_1_data_assimilator_html_a85dc10ab67036ce6c85429dd1cf2fce9"><div class="ttname"><a href="classadamantine_1_1_data_assimilator.html#a85dc10ab67036ce6c85429dd1cf2fce9">adamantine::DataAssimilator::gather_ensemble_members</a></div><div class="ttdeci">void gather_ensemble_members(std::vector< dealii::LA::distributed::BlockVector< double >> &augmented_state_ensemble, std::vector< dealii::LA::distributed::BlockVector< double >> &global_augmented_state_ensemble, std::vector< unsigned int > &local_n_ensemble_members, std::vector< block_size_type > &block_sizes)</div><div class="ttdef"><b>Definition:</b> <a href="_data_assimilator_8cc_source.html#l00187">DataAssimilator.cc:187</a></div></div>
<div class="ttc" id="aclassadamantine_1_1_data_assimilator_html_a8a976eb6e98d340fe91837cdd541cd36"><div class="ttname"><a href="classadamantine_1_1_data_assimilator.html#a8a976eb6e98d340fe91837cdd541cd36">adamantine::DataAssimilator::_localization_cutoff_distance</a></div><div class="ttdeci">double _localization_cutoff_distance</div><div class="ttdef"><b>Definition:</b> <a href="_data_assimilator_8hh_source.html#l00247">DataAssimilator.hh:247</a></div></div>
<div class="ttc" id="aclassadamantine_1_1_data_assimilator_html_a9aca6e1413a227d29e89faa45a8006f0"><div class="ttname"><a href="classadamantine_1_1_data_assimilator.html#a9aca6e1413a227d29e89faa45a8006f0">adamantine::DataAssimilator::DataAssimilator</a></div><div class="ttdeci">DataAssimilator(MPI_Comm const &global_communicator, MPI_Comm const &local_communicator, int my_color, boost::property_tree::ptree const &database)</div><div class="ttdef"><b>Definition:</b> <a href="_data_assimilator_8cc_source.html#l00031">DataAssimilator.cc:31</a></div></div>
<div class="ttc" id="aclassadamantine_1_1_data_assimilator_html_a9e71ae5b0604f35293dbf7e21a8bbf19"><div class="ttname"><a href="classadamantine_1_1_data_assimilator.html#a9e71ae5b0604f35293dbf7e21a8bbf19">adamantine::DataAssimilator::_expt_size</a></div><div class="ttdeci">unsigned int _expt_size</div><div class="ttdef"><b>Definition:</b> <a href="_data_assimilator_8hh_source.html#l00229">DataAssimilator.hh:229</a></div></div>
<div class="ttc" id="aclassadamantine_1_1_data_assimilator_html_aa3a8ea4992368e7fa15b538ef05ab243"><div class="ttname"><a href="classadamantine_1_1_data_assimilator.html#aa3a8ea4992368e7fa15b538ef05ab243">adamantine::DataAssimilator::_solver_control</a></div><div class="ttdeci">dealii::SolverControl _solver_control</div><div class="ttdef"><b>Definition:</b> <a href="_data_assimilator_8hh_source.html#l00280">DataAssimilator.hh:280</a></div></div>
<div class="ttc" id="aclassadamantine_1_1_data_assimilator_html_aa83bf29573aab1b23211aaeaece2817c"><div class="ttname"><a href="classadamantine_1_1_data_assimilator.html#aa83bf29573aab1b23211aaeaece2817c">adamantine::DataAssimilator::_global_communicator</a></div><div class="ttdeci">MPI_Comm _global_communicator</div><div class="ttdef"><b>Definition:</b> <a href="_data_assimilator_8hh_source.html#l00189">DataAssimilator.hh:189</a></div></div>
<div class="ttc" id="aclassadamantine_1_1_data_assimilator_html_aac440d873ccf340f607f7758de8e7f36"><div class="ttname"><a href="classadamantine_1_1_data_assimilator.html#aac440d873ccf340f607f7758de8e7f36">adamantine::DataAssimilator::_sim_size</a></div><div class="ttdeci">unsigned int _sim_size</div><div class="ttdef"><b>Definition:</b> <a href="_data_assimilator_8hh_source.html#l00219">DataAssimilator.hh:219</a></div></div>
<div class="ttc" id="aclassadamantine_1_1_data_assimilator_html_ab90c04d7eb24c9202e84409109146143"><div class="ttname"><a href="classadamantine_1_1_data_assimilator.html#ab90c04d7eb24c9202e84409109146143">adamantine::DataAssimilator::update_ensemble</a></div><div class="ttdeci">void update_ensemble(std::vector< dealii::LA::distributed::BlockVector< double >> &augmented_state_ensemble, std::vector< double > const &expt_data, dealii::SparseMatrix< double > const &R)</div><div class="ttdef"><b>Definition:</b> <a href="_data_assimilator_8cc_source.html#l00091">DataAssimilator.cc:91</a></div></div>
<div class="ttc" id="aclassadamantine_1_1_data_assimilator_html_ac27d0c63d7e8b2a70bd29d29e6ae8a10"><div class="ttname"><a href="classadamantine_1_1_data_assimilator.html#ac27d0c63d7e8b2a70bd29d29e6ae8a10">adamantine::DataAssimilator::scatter_ensemble_members</a></div><div class="ttdeci">void scatter_ensemble_members(std::vector< dealii::LA::distributed::BlockVector< double >> &augmented_state_ensemble, std::vector< dealii::LA::distributed::BlockVector< double >> const &global_augmented_state_ensemble, std::vector< unsigned int > const &local_n_ensemble_members, std::vector< block_size_type > const &block_sizes)</div><div class="ttdef"><b>Definition:</b> <a href="_data_assimilator_8cc_source.html#l00301">DataAssimilator.cc:301</a></div></div>
<div class="ttc" id="aclassadamantine_1_1_data_assimilator_html_aeb0f621afcc24939d270c2850d9f628e"><div class="ttname"><a href="classadamantine_1_1_data_assimilator.html#aeb0f621afcc24939d270c2850d9f628e">adamantine::DataAssimilator::calc_H</a></div><div class="ttdeci">dealii::SparseMatrix< double > calc_H(dealii::SparsityPattern &pattern) const</div><div class="ttdef"><b>Definition:</b> <a href="_data_assimilator_8cc_source.html#l00475">DataAssimilator.cc:475</a></div></div>
<div class="ttc" id="aclassadamantine_1_1_data_assimilator_html_aef8723a176e59a627727bffa0397d399"><div class="ttname"><a href="classadamantine_1_1_data_assimilator.html#aef8723a176e59a627727bffa0397d399">adamantine::DataAssimilator::_additional_data</a></div><div class="ttdeci">dealii::SolverGMRES< dealii::Vector< double > >::AdditionalData _additional_data</div><div class="ttdef"><b>Definition:</b> <a href="_data_assimilator_8hh_source.html#l00286">DataAssimilator.hh:286</a></div></div>
<div class="ttc" id="aclassadamantine_1_1_data_assimilator_html_af5bde3f9550c77d9a06d88da422e213e"><div class="ttname"><a href="classadamantine_1_1_data_assimilator.html#af5bde3f9550c77d9a06d88da422e213e">adamantine::DataAssimilator::calc_sample_covariance_sparse</a></div><div class="ttdeci">dealii::TrilinosWrappers::SparseMatrix calc_sample_covariance_sparse(std::vector< dealii::LA::distributed::BlockVector< double >> const &vec_ensemble) const</div><div class="ttdef"><b>Definition:</b> <a href="_data_assimilator_8cc_source.html#l00685">DataAssimilator.cc:685</a></div></div>
<div class="ttc" id="anamespaceadamantine_html"><div class="ttname"><a href="namespaceadamantine.html">adamantine</a></div><div class="ttdef"><b>Definition:</b> <a href="_beam_heat_source_properties_8hh_source.html#l00014">BeamHeatSourceProperties.hh:15</a></div></div>
<div class="ttc" id="anamespaceadamantine_html_a12d6157f2693e3b6b9d87f8f515c09b0"><div class="ttname"><a href="namespaceadamantine.html#a12d6157f2693e3b6b9d87f8f515c09b0">adamantine::get_dof_to_support_mapping</a></div><div class="ttdeci">std::pair< std::vector< dealii::types::global_dof_index >, std::vector< dealii::Point< dim > > > get_dof_to_support_mapping(dealii::DoFHandler< dim > const &dof_handler)</div><div class="ttdef"><b>Definition:</b> <a href="experimental__data__utils_8cc_source.html#l00024">experimental_data_utils.cc:24</a></div></div>
<div class="ttc" id="anamespaceadamantine_html_a7caf29199baef249d0ee5ff6fd81006ba1691b6ec67855c130469a858d0ad41a8"><div class="ttname"><a href="namespaceadamantine.html#a7caf29199baef249d0ee5ff6fd81006ba1691b6ec67855c130469a858d0ad41a8">adamantine::output</a></div><div class="ttdeci">@ output</div><div class="ttdef"><b>Definition:</b> <a href="types_8hh_source.html#l00147">types.hh:147</a></div></div>
<div class="ttc" id="anamespaceadamantine_html_ac498eafab2c29c90d8f7a40c50bf98b0"><div class="ttname"><a href="namespaceadamantine.html#ac498eafab2c29c90d8f7a40c50bf98b0">adamantine::ASSERT_THROW</a></div><div class="ttdeci">void ASSERT_THROW(bool cond, std::string const &message)</div><div class="ttdef"><b>Definition:</b> <a href="utils_8hh_source.html#l00070">utils.hh:70</a></div></div>
<div class="ttc" id="anamespaceadamantine_html_ae6f0841ed43262ef1175e2b6075cd66fa334c4a4c42fdb79d7ebc3e73b517e6f8"><div class="ttname"><a href="namespaceadamantine.html#ae6f0841ed43262ef1175e2b6075cd66fa334c4a4c42fdb79d7ebc3e73b517e6f8">adamantine::LocalizationCutoff::none</a></div><div class="ttdeci">@ none</div></div>
<div class="ttc" id="anamespaceadamantine_html_ae6f0841ed43262ef1175e2b6075cd66faa5ca29e51a327d3424eaca38fe8ebc8d"><div class="ttname"><a href="namespaceadamantine.html#ae6f0841ed43262ef1175e2b6075cd66faa5ca29e51a327d3424eaca38fe8ebc8d">adamantine::LocalizationCutoff::step_function</a></div><div class="ttdeci">@ step_function</div></div>
<div class="ttc" id="anamespaceadamantine_html_ae6f0841ed43262ef1175e2b6075cd66faba6e20e7e1559edeec0c30dab66781a5"><div class="ttname"><a href="namespaceadamantine.html#ae6f0841ed43262ef1175e2b6075cd66faba6e20e7e1559edeec0c30dab66781a5">adamantine::LocalizationCutoff::gaspari_cohn</a></div><div class="ttdeci">@ gaspari_cohn</div></div>
<div class="ttc" id="autils_8hh_html"><div class="ttname"><a href="utils_8hh.html">utils.hh</a></div></div>
<div class="ttc" id="autils_8hh_html_aa06eedd6f738a415870e97a375337d51"><div class="ttname"><a href="utils_8hh.html#aa06eedd6f738a415870e97a375337d51">ASSERT</a></div><div class="ttdeci">#define ASSERT(condition, message)</div><div class="ttdef"><b>Definition:</b> <a href="utils_8hh_source.html#l00068">utils.hh:68</a></div></div>
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