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<a href="lu__factorization_8cc.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">// Copyright 2010-2021 Google LLC</span></div>
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<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
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<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment">// you may not use this file except in compliance with the License.</span></div>
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<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment">// You may obtain a copy of the License at</span></div>
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<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">//</span></div>
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<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
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<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">//</span></div>
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<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
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<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
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<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
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<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment">// See the License for the specific language governing permissions and</span></div>
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<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment">// limitations under the License.</span></div>
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<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
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<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#include "<a class="code" href="lu__factorization_8h.html">ortools/glop/lu_factorization.h</a>"</span></div>
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<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span> </div>
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<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="preprocessor">#include <cstddef></span></div>
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<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span> </div>
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<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#include "<a class="code" href="lp__types_8h.html">ortools/lp_data/lp_types.h</a>"</span></div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="preprocessor">#include "<a class="code" href="lp__data_2lp__utils_8h.html">ortools/lp_data/lp_utils.h</a>"</span></div>
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<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span> </div>
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<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceoperations__research.html">operations_research</a> {</div>
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<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="keyword">namespace </span>glop {</div>
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<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> </div>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#af0b37b89dc1909384e822287c1091aa0"> 24</a></span><a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#af0b37b89dc1909384e822287c1091aa0">LuFactorization::LuFactorization</a>()</div>
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<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> : is_identity_factorization_(true),</div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> col_perm_(),</div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> inverse_col_perm_(),</div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> row_perm_(),</div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> inverse_row_perm_() {}</div>
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<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> </div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#aa71d36872f416feaa853788a7a7a7ef8"> 31</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#aa71d36872f416feaa853788a7a7a7ef8">LuFactorization::Clear</a>() {</div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> <a class="code hl_define" href="stats_8h.html#a9995704aaaf45fc21e08c847551a8d04">SCOPED_TIME_STAT</a>(&stats_);</div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#aeebcdc829c541f3ca21a15784f02fe9c">Reset</a>(RowIndex(0), ColIndex(0));</div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#aeebcdc829c541f3ca21a15784f02fe9c">Reset</a>(RowIndex(0), ColIndex(0));</div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> transpose_upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#aeebcdc829c541f3ca21a15784f02fe9c">Reset</a>(RowIndex(0), ColIndex(0));</div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> transpose_lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#aeebcdc829c541f3ca21a15784f02fe9c">Reset</a>(RowIndex(0), ColIndex(0));</div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> is_identity_factorization_ = <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> col_perm_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_permutation.html#ac8bb3912a3ce86b15842e79d0b421204">clear</a>();</div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> row_perm_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_permutation.html#ac8bb3912a3ce86b15842e79d0b421204">clear</a>();</div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> inverse_row_perm_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_permutation.html#ac8bb3912a3ce86b15842e79d0b421204">clear</a>();</div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> inverse_col_perm_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_permutation.html#ac8bb3912a3ce86b15842e79d0b421204">clear</a>();</div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span>}</div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> </div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#ace58a4f9d6a147c3455ff8dc029537c4"> 44</a></span><a class="code hl_class" href="classoperations__research_1_1glop_1_1_status.html">Status</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#ace58a4f9d6a147c3455ff8dc029537c4">LuFactorization::ComputeFactorization</a>(</div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html">CompactSparseMatrixView</a>& matrix) {</div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <a class="code hl_define" href="stats_8h.html#a9995704aaaf45fc21e08c847551a8d04">SCOPED_TIME_STAT</a>(&stats_);</div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#aa71d36872f416feaa853788a7a7a7ef8">Clear</a>();</div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <span class="keywordflow">if</span> (matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>().value() != matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a41741829541d089f1c4d34f190884813">num_cols</a>().value()) {</div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <a class="code hl_define" href="status_8h.html#a8c76f1eb9790accd2cd0c5fa5c03c322">GLOP_RETURN_AND_LOG_ERROR</a>(<a class="code hl_enumvalue" href="classoperations__research_1_1glop_1_1_status.html#a59e56af19e754a6aa26a612ebf91d05fafa2ff9c081445bfbfbda10bc41b76a87">Status::ERROR_LU</a>, <span class="stringliteral">"Not a square matrix!!"</span>);</div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> }</div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> </div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <a class="code hl_define" href="status_8h.html#a3efb1c6250c02a5b881f8b82f75f9822">GLOP_RETURN_IF_ERROR</a>(</div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> markowitz_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_markowitz.html#a7ac2557be8cf0394f9953fbdac2f18f4">ComputeLU</a>(matrix, &row_perm_, &col_perm_, &lower_, &upper_));</div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> inverse_col_perm_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_permutation.html#af70191062b734badb4405f2fde63792a">PopulateFromInverse</a>(col_perm_);</div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> inverse_row_perm_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_permutation.html#af70191062b734badb4405f2fde63792a">PopulateFromInverse</a>(row_perm_);</div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> ComputeTransposeUpper();</div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> ComputeTransposeLower();</div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> </div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> is_identity_factorization_ = <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <a class="code hl_define" href="stats_8h.html#a3c3e6b102f0d91c523099325c98e1887">IF_STATS_ENABLED</a>({</div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> stats_.lu_fill_in.Add(<a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a4523b56a271bfeb588757e64e4bf1425">GetFillInPercentage</a>(matrix));</div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> stats_.basis_num_entries.Add(matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#af69d9b7065a8f31604a8134be4307749">num_entries</a>().value());</div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> });</div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(CheckFactorization(matrix, <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a>(1e-6)));</div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="keywordflow">return</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_status.html#a071b1d04197c0ac6e7a4d0ec0b91ff43">Status::OK</a>();</div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span>}</div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> </div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a3c3fa8faef594bd4a249b4aaa5e32d8e"> 68</a></span><a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">RowToColMapping</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a3c3fa8faef594bd4a249b4aaa5e32d8e">LuFactorization::ComputeInitialBasis</a>(</div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html">CompactSparseMatrix</a>& matrix,</div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="keyword">const</span> std::vector<ColIndex>& candidates) {</div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html">CompactSparseMatrixView</a> view(&matrix, &candidates);</div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> (void)markowitz_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_markowitz.html#afd3f022e573b8f4f0901624a813ade07">ComputeRowAndColumnPermutation</a>(view, &row_perm_, &col_perm_);</div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> </div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="comment">// Starts by the missing slacks.</span></div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">RowToColMapping</a> basis;</div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="keywordflow">for</span> (RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> < matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>(); ++<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) {</div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="keywordflow">if</span> (row_perm_[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] == <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a31ee82f6ef05c3da492c0376f910d015">kInvalidRow</a>) {</div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="comment">// Add the slack for this row.</span></div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> basis.<a class="code hl_function" href="classabsl_1_1_strong_vector.html#a9263000d449fdccb6cb70b303063e60b">push_back</a>(matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>() +</div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a8fbc9efd86a3cc862a9079d86ab8b524">RowToColIndex</a>(<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> - matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>()));</div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> }</div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> }</div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> </div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <span class="comment">// Then add the used candidate columns.</span></div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <a class="code hl_define" href="base_2logging_8h.html#a7c0ce053b28d53aa4eaf3eb7fb71663b">CHECK_EQ</a>(col_perm_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_permutation.html#a1df2b3a4485e328397fda9b5f9b3ea2b">size</a>(), candidates.size());</div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < col_perm_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_permutation.html#a1df2b3a4485e328397fda9b5f9b3ea2b">size</a>(); ++i) {</div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="keywordflow">if</span> (col_perm_[ColIndex(i)] != <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>) {</div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> basis.<a class="code hl_function" href="classabsl_1_1_strong_vector.html#a9263000d449fdccb6cb70b303063e60b">push_back</a>(candidates[i]);</div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> }</div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> }</div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> </div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="keywordflow">return</span> basis;</div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span>}</div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> </div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a627511bf305a6af5d7e114817c1792c2"> 95</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a627511bf305a6af5d7e114817c1792c2">LuFactorization::DeterministicTimeOfLastFactorization</a>()<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="keywordflow">return</span> markowitz_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_markowitz.html#a627511bf305a6af5d7e114817c1792c2">DeterministicTimeOfLastFactorization</a>();</div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span>}</div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> </div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a6ec53ed3afa3d8affb6941568dcfec76"> 99</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a6ec53ed3afa3d8affb6941568dcfec76">LuFactorization::RightSolve</a>(<a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* x)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <a class="code hl_define" href="stats_8h.html#a9995704aaaf45fc21e08c847551a8d04">SCOPED_TIME_STAT</a>(&stats_);</div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="keywordflow">if</span> (is_identity_factorization_) <span class="keywordflow">return</span>;</div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> </div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#ad23afb4770e9de727133317f32f68a2f">ApplyPermutation</a>(row_perm_, *x, &dense_column_scratchpad_);</div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a53c98a21d13c8da595c0b4e63b699649">LowerSolve</a>(&dense_column_scratchpad_);</div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a3089393e5f2314b28878f49fd97398b1">UpperSolve</a>(&dense_column_scratchpad_);</div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#ad23afb4770e9de727133317f32f68a2f">ApplyPermutation</a>(inverse_col_perm_, dense_column_scratchpad_, x);</div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span>}</div>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> </div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a6b5f31c4068711b8e6823f4888f410ce"> 109</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a6b5f31c4068711b8e6823f4888f410ce">LuFactorization::LeftSolve</a>(<a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseRow</a>* y)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <a class="code hl_define" href="stats_8h.html#a9995704aaaf45fc21e08c847551a8d04">SCOPED_TIME_STAT</a>(&stats_);</div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <span class="keywordflow">if</span> (is_identity_factorization_) <span class="keywordflow">return</span>;</div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> </div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> <span class="comment">// We need to interpret y as a column for the permutation functions.</span></div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* <span class="keyword">const</span> x = <span class="keyword">reinterpret_cast<</span><a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>*<span class="keyword">></span>(y);</div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a302ba2f0cfbe5918e56eeaaf00231843">ApplyInversePermutation</a>(inverse_col_perm_, *x, &dense_column_scratchpad_);</div>
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<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#ad29d43a5efb42cbdbaa131d8a9dc91f9">TransposeUpperSolve</a>(&dense_column_scratchpad_);</div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#abd6fe5a90f2132529b10c7cb577f04a5">TransposeLowerSolve</a>(&dense_column_scratchpad_);</div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a302ba2f0cfbe5918e56eeaaf00231843">ApplyInversePermutation</a>(row_perm_, dense_column_scratchpad_, x);</div>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span>}</div>
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<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> </div>
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span><span class="keyword">namespace </span>{</div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span><span class="comment">// If non_zeros is empty, uses a dense algorithm to compute the squared L2</span></div>
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span><span class="comment">// norm of the given column, otherwise do the same with a sparse version. In</span></div>
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span><span class="comment">// both cases column is cleared.</span></div>
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<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span><a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> ComputeSquaredNormAndResetToZero(</div>
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <span class="keyword">const</span> std::vector<RowIndex>& non_zeros, <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* column) {</div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> sum = 0.0;</div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> <span class="keywordflow">if</span> (non_zeros.empty()) {</div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> sum = <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a2d53948bf5e999d006e781105aa8bc77">SquaredNorm</a>(*column);</div>
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> column-><a class="code hl_function" href="classabsl_1_1_strong_vector.html#ac8bb3912a3ce86b15842e79d0b421204">clear</a>();</div>
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<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> : non_zeros) {</div>
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<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> sum += <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a1dcd08b0f6c19cd4a302bb5a3a6ea06e">Square</a>((*column)[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>]);</div>
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<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> (*column)[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] = 0.0;</div>
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<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> }</div>
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<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> }</div>
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> <span class="keywordflow">return</span> sum;</div>
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<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span>}</div>
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<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span>} <span class="comment">// namespace</span></div>
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<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> </div>
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<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a4bf241af6b1844669171d6e170ef991d"> 141</a></span><a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a4bf241af6b1844669171d6e170ef991d">LuFactorization::RightSolveSquaredNorm</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_column_view.html">ColumnView</a>& <a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> <a class="code hl_define" href="stats_8h.html#a9995704aaaf45fc21e08c847551a8d04">SCOPED_TIME_STAT</a>(&stats_);</div>
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<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> <span class="keywordflow">if</span> (is_identity_factorization_) <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a2d53948bf5e999d006e781105aa8bc77">SquaredNorm</a>(<a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>);</div>
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<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> </div>
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<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> non_zero_rows_.clear();</div>
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<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> dense_zero_scratchpad_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a64b6b04f3a519d2c61d49daaa88bf06e">resize</a>(lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>(), 0.0);</div>
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<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(<a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a386d851d7c8b409205dd82d87e44f2fe">IsAllZero</a>(dense_zero_scratchpad_));</div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> </div>
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code hl_typedef" href="classoperations__research_1_1glop_1_1_sparse_vector.html#ab38326ea6cb6187267665dd8b2748f3d">SparseColumn::Entry</a> e : <a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>) {</div>
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<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> <span class="keyword">const</span> RowIndex permuted_row = row_perm_[e.row()];</div>
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<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> dense_zero_scratchpad_[permuted_row] = e.coefficient();</div>
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<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> non_zero_rows_.push_back(permuted_row);</div>
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<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> }</div>
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<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> </div>
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<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a985078d2d3022f616d3c355373c7d20e">ComputeRowsToConsiderInSortedOrder</a>(&non_zero_rows_);</div>
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<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> <span class="keywordflow">if</span> (non_zero_rows_.empty()) {</div>
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<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a53c98a21d13c8da595c0b4e63b699649">LowerSolve</a>(&dense_zero_scratchpad_);</div>
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<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a31d19092aa0a8b6a87e8917c956a0610">HyperSparseSolve</a>(&dense_zero_scratchpad_, &non_zero_rows_);</div>
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<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a985078d2d3022f616d3c355373c7d20e">ComputeRowsToConsiderInSortedOrder</a>(&non_zero_rows_);</div>
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<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> }</div>
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<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> <span class="keywordflow">if</span> (non_zero_rows_.empty()) {</div>
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<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a3089393e5f2314b28878f49fd97398b1">UpperSolve</a>(&dense_zero_scratchpad_);</div>
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<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#af3dcc960bfe6b9064cdc9ce6ab04fa1d">HyperSparseSolveWithReversedNonZeros</a>(&dense_zero_scratchpad_,</div>
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<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> &non_zero_rows_);</div>
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<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> }</div>
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<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> <span class="keywordflow">return</span> ComputeSquaredNormAndResetToZero(non_zero_rows_,</div>
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<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> &dense_zero_scratchpad_);</div>
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<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span>}</div>
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<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> </div>
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<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a9b738f6b485a4d4ef866b8d82ac07876"> 172</a></span><a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a9b738f6b485a4d4ef866b8d82ac07876">LuFactorization::DualEdgeSquaredNorm</a>(RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> <span class="keywordflow">if</span> (is_identity_factorization_) <span class="keywordflow">return</span> 1.0;</div>
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<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> <a class="code hl_define" href="stats_8h.html#a9995704aaaf45fc21e08c847551a8d04">SCOPED_TIME_STAT</a>(&stats_);</div>
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<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> <span class="keyword">const</span> RowIndex permuted_row =</div>
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<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> col_perm_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_permutation.html#a644718bb2fb240de962dc3c9a1fdf0dc">empty</a>() ? <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> : <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#ab65a327cfc2a74c15fa26b91f19acc64">ColToRowIndex</a>(col_perm_[<a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a8fbc9efd86a3cc862a9079d86ab8b524">RowToColIndex</a>(<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>)]);</div>
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<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> </div>
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<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> non_zero_rows_.clear();</div>
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<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> dense_zero_scratchpad_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a64b6b04f3a519d2c61d49daaa88bf06e">resize</a>(lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>(), 0.0);</div>
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<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(<a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a386d851d7c8b409205dd82d87e44f2fe">IsAllZero</a>(dense_zero_scratchpad_));</div>
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<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> dense_zero_scratchpad_[permuted_row] = 1.0;</div>
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<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> non_zero_rows_.push_back(permuted_row);</div>
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<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> </div>
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<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> transpose_upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a985078d2d3022f616d3c355373c7d20e">ComputeRowsToConsiderInSortedOrder</a>(&non_zero_rows_);</div>
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<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> <span class="keywordflow">if</span> (non_zero_rows_.empty()) {</div>
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<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> transpose_upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a71d81a062179f9fa4a2c133b72aaf0d8">LowerSolveStartingAt</a>(<a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a8fbc9efd86a3cc862a9079d86ab8b524">RowToColIndex</a>(permuted_row),</div>
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<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> &dense_zero_scratchpad_);</div>
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<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> transpose_upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a31d19092aa0a8b6a87e8917c956a0610">HyperSparseSolve</a>(&dense_zero_scratchpad_, &non_zero_rows_);</div>
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<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> transpose_lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a985078d2d3022f616d3c355373c7d20e">ComputeRowsToConsiderInSortedOrder</a>(&non_zero_rows_);</div>
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<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> }</div>
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<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> <span class="keywordflow">if</span> (non_zero_rows_.empty()) {</div>
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<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> transpose_lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a3089393e5f2314b28878f49fd97398b1">UpperSolve</a>(&dense_zero_scratchpad_);</div>
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<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> transpose_lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#af3dcc960bfe6b9064cdc9ce6ab04fa1d">HyperSparseSolveWithReversedNonZeros</a>(</div>
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<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> &dense_zero_scratchpad_, &non_zero_rows_);</div>
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<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> }</div>
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<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> <span class="keywordflow">return</span> ComputeSquaredNormAndResetToZero(non_zero_rows_,</div>
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<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> &dense_zero_scratchpad_);</div>
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<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span>}</div>
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<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> </div>
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<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span><span class="keyword">namespace </span>{</div>
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<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span><span class="comment">// Returns whether 'b' is equal to 'a' permuted by the given row permutation</span></div>
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<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span><span class="comment">// 'perm'.</span></div>
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<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span><span class="keywordtype">bool</span> AreEqualWithPermutation(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>& <a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>, <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>& <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>,</div>
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<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_permutation.html">RowPermutation</a>& perm) {</div>
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<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> <span class="keyword">const</span> RowIndex num_rows = perm.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_permutation.html#a1df2b3a4485e328397fda9b5f9b3ea2b">size</a>();</div>
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<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> <span class="keywordflow">for</span> (RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> < num_rows; ++<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) {</div>
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<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] != <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>[perm[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>]]) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> }</div>
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<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span>}</div>
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<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span>} <span class="comment">// namespace</span></div>
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<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> </div>
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<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a43e095088501053427e317e905d5fc83"> 215</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a43e095088501053427e317e905d5fc83">LuFactorization::RightSolveLWithPermutedInput</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>& <a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>,</div>
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<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> <a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_column.html">ScatteredColumn</a>* x)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> <a class="code hl_define" href="stats_8h.html#a9995704aaaf45fc21e08c847551a8d04">SCOPED_TIME_STAT</a>(&stats_);</div>
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<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> <span class="keywordflow">if</span> (!is_identity_factorization_) {</div>
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<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(AreEqualWithPermutation(<a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>, x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ae0473e18a367af671dc3f08063c80da4">values</a>, row_perm_));</div>
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<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a985078d2d3022f616d3c355373c7d20e">ComputeRowsToConsiderInSortedOrder</a>(&x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">non_zeros</a>);</div>
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<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> <span class="keywordflow">if</span> (x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">non_zeros</a>.empty()) {</div>
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<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a53c98a21d13c8da595c0b4e63b699649">LowerSolve</a>(&x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ae0473e18a367af671dc3f08063c80da4">values</a>);</div>
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<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a31d19092aa0a8b6a87e8917c956a0610">HyperSparseSolve</a>(&x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ae0473e18a367af671dc3f08063c80da4">values</a>, &x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">non_zeros</a>);</div>
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<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> }</div>
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<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> }</div>
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<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span>}</div>
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<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span> </div>
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<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span><span class="keyword">template</span> <<span class="keyword">typename</span> Column></div>
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<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span><span class="keywordtype">void</span> LuFactorization::RightSolveLInternal(<span class="keyword">const</span> Column& <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>,</div>
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<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> <a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_column.html">ScatteredColumn</a>* x)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> <span class="comment">// This code is equivalent to</span></div>
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<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> <span class="comment">// b.PermutedCopyToDenseVector(row_perm_, num_rows, x);</span></div>
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<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span> <span class="comment">// but it also computes the first column index which does not correspond to an</span></div>
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<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> <span class="comment">// identity column of lower_ thus exploiting a bit the hyper-sparsity</span></div>
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<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> <span class="comment">// of b.</span></div>
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<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span> ColIndex first_column_to_consider(<a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a8fbc9efd86a3cc862a9079d86ab8b524">RowToColIndex</a>(x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ae0473e18a367af671dc3f08063c80da4">values</a>.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a967a5c081ad4195a30c78dc2c0bcabf5">size</a>()));</div>
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<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span> <span class="keyword">const</span> ColIndex limit = lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a3d3abc3e6b522dc60fd8c1168522e09d">GetFirstNonIdentityColumn</a>();</div>
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<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> e : <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>) {</div>
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<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span> <span class="keyword">const</span> RowIndex permuted_row = row_perm_[e.row()];</div>
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<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> (*x)[permuted_row] = e.coefficient();</div>
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<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span> x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">non_zeros</a>.push_back(permuted_row);</div>
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<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span> </div>
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<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span> <span class="comment">// The second condition only works because the elements on the diagonal of</span></div>
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<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> <span class="comment">// lower_ are all equal to 1.0.</span></div>
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<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> <span class="keyword">const</span> ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> = <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a8fbc9efd86a3cc862a9079d86ab8b524">RowToColIndex</a>(permuted_row);</div>
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<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < limit || lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#af0dafb025bcf4174501a93fb91ca4bb6">ColumnIsDiagonalOnly</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)) {</div>
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<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> <a class="code hl_define" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(1.0, lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a4a34504e7ba1673cf24f745d162fda84">GetDiagonalCoefficient</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>));</div>
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|
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> <span class="keywordflow">continue</span>;</div>
|
|
<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> }</div>
|
|
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> first_column_to_consider = <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(first_column_to_consider, <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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|
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> }</div>
|
|
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> </div>
|
|
<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a985078d2d3022f616d3c355373c7d20e">ComputeRowsToConsiderInSortedOrder</a>(&x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">non_zeros</a>);</div>
|
|
<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#a56e67c2fc5b21fd62d8776fa4b149ce6">non_zeros_are_sorted</a> = <span class="keyword">true</span>;</div>
|
|
<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> <span class="keywordflow">if</span> (x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">non_zeros</a>.empty()) {</div>
|
|
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a71d81a062179f9fa4a2c133b72aaf0d8">LowerSolveStartingAt</a>(first_column_to_consider, &x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ae0473e18a367af671dc3f08063c80da4">values</a>);</div>
|
|
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> } <span class="keywordflow">else</span> {</div>
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|
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a31d19092aa0a8b6a87e8917c956a0610">HyperSparseSolve</a>(&x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ae0473e18a367af671dc3f08063c80da4">values</a>, &x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">non_zeros</a>);</div>
|
|
<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span> }</div>
|
|
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span>}</div>
|
|
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> </div>
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|
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a40757145002c85d47ad8df1b53707661"> 263</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a40757145002c85d47ad8df1b53707661">LuFactorization::RightSolveLForColumnView</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_column_view.html">ColumnView</a>& <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>,</div>
|
|
<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span> <a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_column.html">ScatteredColumn</a>* x)<span class="keyword"> const </span>{</div>
|
|
<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span> <a class="code hl_define" href="stats_8h.html#a9995704aaaf45fc21e08c847551a8d04">SCOPED_TIME_STAT</a>(&stats_);</div>
|
|
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(<a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a386d851d7c8b409205dd82d87e44f2fe">IsAllZero</a>(x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ae0473e18a367af671dc3f08063c80da4">values</a>));</div>
|
|
<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span> x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">non_zeros</a>.clear();</div>
|
|
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span> <span class="keywordflow">if</span> (is_identity_factorization_) {</div>
|
|
<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_column_entry.html">ColumnView::Entry</a> e : <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>) {</div>
|
|
<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span> (*x)[e.row()] = e.coefficient();</div>
|
|
<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">non_zeros</a>.push_back(e.row());</div>
|
|
<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span> }</div>
|
|
<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> <span class="keywordflow">return</span>;</div>
|
|
<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> }</div>
|
|
<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span> </div>
|
|
<div class="line"><a id="l00276" name="l00276"></a><span class="lineno"> 276</span> RightSolveLInternal(<a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>, x);</div>
|
|
<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span>}</div>
|
|
<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span> </div>
|
|
<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#aa35c31899babb961a8100bc605136424"> 279</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#aa35c31899babb961a8100bc605136424">LuFactorization::RightSolveLWithNonZeros</a>(<a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_column.html">ScatteredColumn</a>* x)<span class="keyword"> const </span>{</div>
|
|
<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"> 280</span> <span class="keywordflow">if</span> (is_identity_factorization_) <span class="keywordflow">return</span>;</div>
|
|
<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</span> <span class="keywordflow">if</span> (x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">non_zeros</a>.empty()) {</div>
|
|
<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span> <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a08d7a83791c6677d1008336cacf3d591">PermuteWithScratchpad</a>(row_perm_, &dense_zero_scratchpad_, &x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ae0473e18a367af671dc3f08063c80da4">values</a>);</div>
|
|
<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span> lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a53c98a21d13c8da595c0b4e63b699649">LowerSolve</a>(&x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ae0473e18a367af671dc3f08063c80da4">values</a>);</div>
|
|
<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span> <span class="keywordflow">return</span>;</div>
|
|
<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span> }</div>
|
|
<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</span> </div>
|
|
<div class="line"><a id="l00287" name="l00287"></a><span class="lineno"> 287</span> <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a6a2019fc6c15a0413896d3f35057a070">PermuteWithKnownNonZeros</a>(row_perm_, &dense_zero_scratchpad_, &x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ae0473e18a367af671dc3f08063c80da4">values</a>,</div>
|
|
<div class="line"><a id="l00288" name="l00288"></a><span class="lineno"> 288</span> &x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">non_zeros</a>);</div>
|
|
<div class="line"><a id="l00289" name="l00289"></a><span class="lineno"> 289</span> lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a985078d2d3022f616d3c355373c7d20e">ComputeRowsToConsiderInSortedOrder</a>(&x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">non_zeros</a>);</div>
|
|
<div class="line"><a id="l00290" name="l00290"></a><span class="lineno"> 290</span> x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#a56e67c2fc5b21fd62d8776fa4b149ce6">non_zeros_are_sorted</a> = <span class="keyword">true</span>;</div>
|
|
<div class="line"><a id="l00291" name="l00291"></a><span class="lineno"> 291</span> <span class="keywordflow">if</span> (x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">non_zeros</a>.empty()) {</div>
|
|
<div class="line"><a id="l00292" name="l00292"></a><span class="lineno"> 292</span> lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a53c98a21d13c8da595c0b4e63b699649">LowerSolve</a>(&x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ae0473e18a367af671dc3f08063c80da4">values</a>);</div>
|
|
<div class="line"><a id="l00293" name="l00293"></a><span class="lineno"> 293</span> } <span class="keywordflow">else</span> {</div>
|
|
<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span> lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a31d19092aa0a8b6a87e8917c956a0610">HyperSparseSolve</a>(&x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ae0473e18a367af671dc3f08063c80da4">values</a>, &x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">non_zeros</a>);</div>
|
|
<div class="line"><a id="l00295" name="l00295"></a><span class="lineno"> 295</span> }</div>
|
|
<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span>}</div>
|
|
<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span> </div>
|
|
<div class="line"><a id="l00298" name="l00298"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#aa1222207079d0d679ef52f8b465cd00a"> 298</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#aa1222207079d0d679ef52f8b465cd00a">LuFactorization::RightSolveLForScatteredColumn</a>(<span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_column.html">ScatteredColumn</a>& <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>,</div>
|
|
<div class="line"><a id="l00299" name="l00299"></a><span class="lineno"> 299</span> <a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_column.html">ScatteredColumn</a>* x)<span class="keyword"> const </span>{</div>
|
|
<div class="line"><a id="l00300" name="l00300"></a><span class="lineno"> 300</span> <a class="code hl_define" href="stats_8h.html#a9995704aaaf45fc21e08c847551a8d04">SCOPED_TIME_STAT</a>(&stats_);</div>
|
|
<div class="line"><a id="l00301" name="l00301"></a><span class="lineno"> 301</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(<a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a386d851d7c8b409205dd82d87e44f2fe">IsAllZero</a>(x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ae0473e18a367af671dc3f08063c80da4">values</a>));</div>
|
|
<div class="line"><a id="l00302" name="l00302"></a><span class="lineno"> 302</span> x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">non_zeros</a>.clear();</div>
|
|
<div class="line"><a id="l00303" name="l00303"></a><span class="lineno"> 303</span> </div>
|
|
<div class="line"><a id="l00304" name="l00304"></a><span class="lineno"> 304</span> <span class="keywordflow">if</span> (is_identity_factorization_) {</div>
|
|
<div class="line"><a id="l00305" name="l00305"></a><span class="lineno"> 305</span> *x = <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>;</div>
|
|
<div class="line"><a id="l00306" name="l00306"></a><span class="lineno"> 306</span> <span class="keywordflow">return</span>;</div>
|
|
<div class="line"><a id="l00307" name="l00307"></a><span class="lineno"> 307</span> }</div>
|
|
<div class="line"><a id="l00308" name="l00308"></a><span class="lineno"> 308</span> </div>
|
|
<div class="line"><a id="l00309" name="l00309"></a><span class="lineno"> 309</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>.non_zeros.empty()) {</div>
|
|
<div class="line"><a id="l00310" name="l00310"></a><span class="lineno"> 310</span> *x = <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>;</div>
|
|
<div class="line"><a id="l00311" name="l00311"></a><span class="lineno"> 311</span> <span class="keywordflow">return</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#aa35c31899babb961a8100bc605136424">RightSolveLWithNonZeros</a>(x);</div>
|
|
<div class="line"><a id="l00312" name="l00312"></a><span class="lineno"> 312</span> }</div>
|
|
<div class="line"><a id="l00313" name="l00313"></a><span class="lineno"> 313</span> </div>
|
|
<div class="line"><a id="l00314" name="l00314"></a><span class="lineno"> 314</span> RightSolveLInternal(<a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>, x);</div>
|
|
<div class="line"><a id="l00315" name="l00315"></a><span class="lineno"> 315</span>}</div>
|
|
<div class="line"><a id="l00316" name="l00316"></a><span class="lineno"> 316</span> </div>
|
|
<div class="line"><a id="l00317" name="l00317"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a1ea8d0a49dad57416810ab7b1a2e2108"> 317</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a1ea8d0a49dad57416810ab7b1a2e2108">LuFactorization::LeftSolveUWithNonZeros</a>(<a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_row.html">ScatteredRow</a>* y)<span class="keyword"> const </span>{</div>
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|
<div class="line"><a id="l00318" name="l00318"></a><span class="lineno"> 318</span> <a class="code hl_define" href="stats_8h.html#a9995704aaaf45fc21e08c847551a8d04">SCOPED_TIME_STAT</a>(&stats_);</div>
|
|
<div class="line"><a id="l00319" name="l00319"></a><span class="lineno"> 319</span> <a class="code hl_define" href="base_2logging_8h.html#a3e1cfef60e774a81f30eaddf26a3a274">CHECK</a>(col_perm_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_permutation.html#a644718bb2fb240de962dc3c9a1fdf0dc">empty</a>());</div>
|
|
<div class="line"><a id="l00320" name="l00320"></a><span class="lineno"> 320</span> <span class="keywordflow">if</span> (is_identity_factorization_) <span class="keywordflow">return</span>;</div>
|
|
<div class="line"><a id="l00321" name="l00321"></a><span class="lineno"> 321</span> </div>
|
|
<div class="line"><a id="l00322" name="l00322"></a><span class="lineno"> 322</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* <span class="keyword">const</span> x = <span class="keyword">reinterpret_cast<</span><a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>*<span class="keyword">></span>(&y-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ae0473e18a367af671dc3f08063c80da4">values</a>);</div>
|
|
<div class="line"><a id="l00323" name="l00323"></a><span class="lineno"> 323</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#ac014de658aabf122011e8fb07b6f4612">RowIndexVector</a>* <span class="keyword">const</span> nz = <span class="keyword">reinterpret_cast<</span><a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#ac014de658aabf122011e8fb07b6f4612">RowIndexVector</a>*<span class="keyword">></span>(&y-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">non_zeros</a>);</div>
|
|
<div class="line"><a id="l00324" name="l00324"></a><span class="lineno"> 324</span> transpose_upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a985078d2d3022f616d3c355373c7d20e">ComputeRowsToConsiderInSortedOrder</a>(nz);</div>
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<div class="line"><a id="l00325" name="l00325"></a><span class="lineno"> 325</span> y-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#a56e67c2fc5b21fd62d8776fa4b149ce6">non_zeros_are_sorted</a> = <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00326" name="l00326"></a><span class="lineno"> 326</span> <span class="keywordflow">if</span> (nz->empty()) {</div>
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<div class="line"><a id="l00327" name="l00327"></a><span class="lineno"> 327</span> upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#ad29d43a5efb42cbdbaa131d8a9dc91f9">TransposeUpperSolve</a>(x);</div>
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<div class="line"><a id="l00328" name="l00328"></a><span class="lineno"> 328</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00329" name="l00329"></a><span class="lineno"> 329</span> upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a11284f21acc7de7ea63f5ebfebb5c9e7">TransposeHyperSparseSolve</a>(x, nz);</div>
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<div class="line"><a id="l00330" name="l00330"></a><span class="lineno"> 330</span> }</div>
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<div class="line"><a id="l00331" name="l00331"></a><span class="lineno"> 331</span>}</div>
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<div class="line"><a id="l00332" name="l00332"></a><span class="lineno"> 332</span> </div>
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<div class="line"><a id="l00333" name="l00333"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a577c37faff9567f86849dd74c3fcf4ac"> 333</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a577c37faff9567f86849dd74c3fcf4ac">LuFactorization::RightSolveUWithNonZeros</a>(<a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_column.html">ScatteredColumn</a>* x)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00334" name="l00334"></a><span class="lineno"> 334</span> <a class="code hl_define" href="stats_8h.html#a9995704aaaf45fc21e08c847551a8d04">SCOPED_TIME_STAT</a>(&stats_);</div>
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<div class="line"><a id="l00335" name="l00335"></a><span class="lineno"> 335</span> <a class="code hl_define" href="base_2logging_8h.html#a3e1cfef60e774a81f30eaddf26a3a274">CHECK</a>(col_perm_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_permutation.html#a644718bb2fb240de962dc3c9a1fdf0dc">empty</a>());</div>
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<div class="line"><a id="l00336" name="l00336"></a><span class="lineno"> 336</span> <span class="keywordflow">if</span> (is_identity_factorization_) <span class="keywordflow">return</span>;</div>
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<div class="line"><a id="l00337" name="l00337"></a><span class="lineno"> 337</span> </div>
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<div class="line"><a id="l00338" name="l00338"></a><span class="lineno"> 338</span> <span class="comment">// If non-zeros is non-empty, we use an hypersparse solve. Note that if</span></div>
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<div class="line"><a id="l00339" name="l00339"></a><span class="lineno"> 339</span> <span class="comment">// non_zeros starts to be too big, we clear it and thus switch back to a</span></div>
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<div class="line"><a id="l00340" name="l00340"></a><span class="lineno"> 340</span> <span class="comment">// normal sparse solve.</span></div>
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<div class="line"><a id="l00341" name="l00341"></a><span class="lineno"> 341</span> upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a985078d2d3022f616d3c355373c7d20e">ComputeRowsToConsiderInSortedOrder</a>(&x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">non_zeros</a>, 0.1, 0.2);</div>
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<div class="line"><a id="l00342" name="l00342"></a><span class="lineno"> 342</span> x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#a56e67c2fc5b21fd62d8776fa4b149ce6">non_zeros_are_sorted</a> = <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00343" name="l00343"></a><span class="lineno"> 343</span> <span class="keywordflow">if</span> (x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">non_zeros</a>.empty()) {</div>
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<div class="line"><a id="l00344" name="l00344"></a><span class="lineno"> 344</span> transpose_upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#abd6fe5a90f2132529b10c7cb577f04a5">TransposeLowerSolve</a>(&x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ae0473e18a367af671dc3f08063c80da4">values</a>);</div>
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<div class="line"><a id="l00345" name="l00345"></a><span class="lineno"> 345</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00346" name="l00346"></a><span class="lineno"> 346</span> transpose_upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a5e67a7d14b4aed3b0f54e453ed5fc7fe">TransposeHyperSparseSolveWithReversedNonZeros</a>(</div>
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<div class="line"><a id="l00347" name="l00347"></a><span class="lineno"> 347</span> &x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ae0473e18a367af671dc3f08063c80da4">values</a>, &x-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">non_zeros</a>);</div>
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<div class="line"><a id="l00348" name="l00348"></a><span class="lineno"> 348</span> }</div>
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<div class="line"><a id="l00349" name="l00349"></a><span class="lineno"> 349</span>}</div>
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<div class="line"><a id="l00350" name="l00350"></a><span class="lineno"> 350</span> </div>
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<div class="line"><a id="l00351" name="l00351"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a6c5735e4c25655dd4533504d22b1d66c"> 351</a></span><span class="keywordtype">bool</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a6c5735e4c25655dd4533504d22b1d66c">LuFactorization::LeftSolveLWithNonZeros</a>(</div>
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<div class="line"><a id="l00352" name="l00352"></a><span class="lineno"> 352</span> <a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_row.html">ScatteredRow</a>* y, <a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_column.html">ScatteredColumn</a>* result_before_permutation)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00353" name="l00353"></a><span class="lineno"> 353</span> <a class="code hl_define" href="stats_8h.html#a9995704aaaf45fc21e08c847551a8d04">SCOPED_TIME_STAT</a>(&stats_);</div>
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<div class="line"><a id="l00354" name="l00354"></a><span class="lineno"> 354</span> <span class="keywordflow">if</span> (is_identity_factorization_) {</div>
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<div class="line"><a id="l00355" name="l00355"></a><span class="lineno"> 355</span> <span class="comment">// It is not advantageous to fill result_before_permutation in this case.</span></div>
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<div class="line"><a id="l00356" name="l00356"></a><span class="lineno"> 356</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00357" name="l00357"></a><span class="lineno"> 357</span> }</div>
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<div class="line"><a id="l00358" name="l00358"></a><span class="lineno"> 358</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* <span class="keyword">const</span> x = <span class="keyword">reinterpret_cast<</span><a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>*<span class="keyword">></span>(&y-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ae0473e18a367af671dc3f08063c80da4">values</a>);</div>
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<div class="line"><a id="l00359" name="l00359"></a><span class="lineno"> 359</span> std::vector<RowIndex>* nz = <span class="keyword">reinterpret_cast<</span><a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#ac014de658aabf122011e8fb07b6f4612">RowIndexVector</a>*<span class="keyword">></span>(&y-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">non_zeros</a>);</div>
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<div class="line"><a id="l00360" name="l00360"></a><span class="lineno"> 360</span> </div>
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<div class="line"><a id="l00361" name="l00361"></a><span class="lineno"> 361</span> <span class="comment">// Hypersparse?</span></div>
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<div class="line"><a id="l00362" name="l00362"></a><span class="lineno"> 362</span> transpose_lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a985078d2d3022f616d3c355373c7d20e">ComputeRowsToConsiderInSortedOrder</a>(nz);</div>
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<div class="line"><a id="l00363" name="l00363"></a><span class="lineno"> 363</span> y-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#a56e67c2fc5b21fd62d8776fa4b149ce6">non_zeros_are_sorted</a> = <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00364" name="l00364"></a><span class="lineno"> 364</span> <span class="keywordflow">if</span> (nz->empty()) {</div>
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<div class="line"><a id="l00365" name="l00365"></a><span class="lineno"> 365</span> lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#abd6fe5a90f2132529b10c7cb577f04a5">TransposeLowerSolve</a>(x);</div>
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<div class="line"><a id="l00366" name="l00366"></a><span class="lineno"> 366</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00367" name="l00367"></a><span class="lineno"> 367</span> lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a5e67a7d14b4aed3b0f54e453ed5fc7fe">TransposeHyperSparseSolveWithReversedNonZeros</a>(x, nz);</div>
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<div class="line"><a id="l00368" name="l00368"></a><span class="lineno"> 368</span> }</div>
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<div class="line"><a id="l00369" name="l00369"></a><span class="lineno"> 369</span> </div>
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<div class="line"><a id="l00370" name="l00370"></a><span class="lineno"> 370</span> <span class="keywordflow">if</span> (result_before_permutation == <span class="keyword">nullptr</span>) {</div>
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<div class="line"><a id="l00371" name="l00371"></a><span class="lineno"> 371</span> <span class="comment">// Note(user): For the behavior of the two functions to be exactly the same,</span></div>
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<div class="line"><a id="l00372" name="l00372"></a><span class="lineno"> 372</span> <span class="comment">// we need the positions listed in nz to be the "exact" non-zeros of x. This</span></div>
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<div class="line"><a id="l00373" name="l00373"></a><span class="lineno"> 373</span> <span class="comment">// should be the case because the hyper-sparse functions makes sure of that.</span></div>
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<div class="line"><a id="l00374" name="l00374"></a><span class="lineno"> 374</span> <span class="comment">// We also DCHECK() this below.</span></div>
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<div class="line"><a id="l00375" name="l00375"></a><span class="lineno"> 375</span> <span class="keywordflow">if</span> (nz->empty()) {</div>
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<div class="line"><a id="l00376" name="l00376"></a><span class="lineno"> 376</span> <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a08d7a83791c6677d1008336cacf3d591">PermuteWithScratchpad</a>(inverse_row_perm_, &dense_zero_scratchpad_, x);</div>
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<div class="line"><a id="l00377" name="l00377"></a><span class="lineno"> 377</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00378" name="l00378"></a><span class="lineno"> 378</span> <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a6a2019fc6c15a0413896d3f35057a070">PermuteWithKnownNonZeros</a>(inverse_row_perm_, &dense_zero_scratchpad_, x,</div>
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<div class="line"><a id="l00379" name="l00379"></a><span class="lineno"> 379</span> nz);</div>
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<div class="line"><a id="l00380" name="l00380"></a><span class="lineno"> 380</span> }</div>
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<div class="line"><a id="l00381" name="l00381"></a><span class="lineno"> 381</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="macros_8h.html#a7f536a3b33f9bed8f75734e035d30725">DEBUG_MODE</a>) {</div>
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<div class="line"><a id="l00382" name="l00382"></a><span class="lineno"> 382</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> : *nz) {</div>
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<div class="line"><a id="l00383" name="l00383"></a><span class="lineno"> 383</span> <a class="code hl_define" href="base_2logging_8h.html#a46e69120fbd3b36e6960e096d23b66f0">DCHECK_NE</a>((*x)[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>], 0.0);</div>
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<div class="line"><a id="l00384" name="l00384"></a><span class="lineno"> 384</span> }</div>
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<div class="line"><a id="l00385" name="l00385"></a><span class="lineno"> 385</span> }</div>
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<div class="line"><a id="l00386" name="l00386"></a><span class="lineno"> 386</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00387" name="l00387"></a><span class="lineno"> 387</span> }</div>
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<div class="line"><a id="l00388" name="l00388"></a><span class="lineno"> 388</span> </div>
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<div class="line"><a id="l00389" name="l00389"></a><span class="lineno"> 389</span> <span class="comment">// This computes the same thing as in the other branch but also keeps the</span></div>
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<div class="line"><a id="l00390" name="l00390"></a><span class="lineno"> 390</span> <span class="comment">// original x in result_before_permutation. Because of this, it is faster to</span></div>
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<div class="line"><a id="l00391" name="l00391"></a><span class="lineno"> 391</span> <span class="comment">// use a different algorithm.</span></div>
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<div class="line"><a id="l00392" name="l00392"></a><span class="lineno"> 392</span> <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#aa6c552b94fa80def1d4d1ea64697afb1">ClearAndResizeVectorWithNonZeros</a>(x-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a967a5c081ad4195a30c78dc2c0bcabf5">size</a>(), result_before_permutation);</div>
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<div class="line"><a id="l00393" name="l00393"></a><span class="lineno"> 393</span> x-><a class="code hl_function" href="classabsl_1_1_strong_vector.html#aa5d16d85614c5d518ae10f882e6fb981">swap</a>(result_before_permutation-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ae0473e18a367af671dc3f08063c80da4">values</a>);</div>
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<div class="line"><a id="l00394" name="l00394"></a><span class="lineno"> 394</span> <span class="keywordflow">if</span> (nz->empty()) {</div>
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<div class="line"><a id="l00395" name="l00395"></a><span class="lineno"> 395</span> <span class="keywordflow">for</span> (RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> < inverse_row_perm_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_permutation.html#a1df2b3a4485e328397fda9b5f9b3ea2b">size</a>(); ++<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) {</div>
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<div class="line"><a id="l00396" name="l00396"></a><span class="lineno"> 396</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_variable" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a> = (*result_before_permutation)[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>];</div>
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<div class="line"><a id="l00397" name="l00397"></a><span class="lineno"> 397</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a> != 0.0) {</div>
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<div class="line"><a id="l00398" name="l00398"></a><span class="lineno"> 398</span> <span class="keyword">const</span> RowIndex permuted_row = inverse_row_perm_[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>];</div>
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<div class="line"><a id="l00399" name="l00399"></a><span class="lineno"> 399</span> (*x)[permuted_row] = <a class="code hl_variable" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>;</div>
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<div class="line"><a id="l00400" name="l00400"></a><span class="lineno"> 400</span> }</div>
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<div class="line"><a id="l00401" name="l00401"></a><span class="lineno"> 401</span> }</div>
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<div class="line"><a id="l00402" name="l00402"></a><span class="lineno"> 402</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00403" name="l00403"></a><span class="lineno"> 403</span> nz->swap(result_before_permutation-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">non_zeros</a>);</div>
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<div class="line"><a id="l00404" name="l00404"></a><span class="lineno"> 404</span> nz->reserve(result_before_permutation-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">non_zeros</a>.size());</div>
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<div class="line"><a id="l00405" name="l00405"></a><span class="lineno"> 405</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> : result_before_permutation-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">non_zeros</a>) {</div>
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<div class="line"><a id="l00406" name="l00406"></a><span class="lineno"> 406</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_variable" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a> = (*result_before_permutation)[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>];</div>
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<div class="line"><a id="l00407" name="l00407"></a><span class="lineno"> 407</span> <span class="keyword">const</span> RowIndex permuted_row = inverse_row_perm_[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>];</div>
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<div class="line"><a id="l00408" name="l00408"></a><span class="lineno"> 408</span> (*x)[permuted_row] = <a class="code hl_variable" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>;</div>
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<div class="line"><a id="l00409" name="l00409"></a><span class="lineno"> 409</span> nz->push_back(permuted_row);</div>
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<div class="line"><a id="l00410" name="l00410"></a><span class="lineno"> 410</span> }</div>
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<div class="line"><a id="l00411" name="l00411"></a><span class="lineno"> 411</span> y-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#a56e67c2fc5b21fd62d8776fa4b149ce6">non_zeros_are_sorted</a> = <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00412" name="l00412"></a><span class="lineno"> 412</span> }</div>
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<div class="line"><a id="l00413" name="l00413"></a><span class="lineno"> 413</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00414" name="l00414"></a><span class="lineno"> 414</span>}</div>
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<div class="line"><a id="l00415" name="l00415"></a><span class="lineno"> 415</span> </div>
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<div class="line"><a id="l00416" name="l00416"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a8d3b56a6aa858cdd6dab9fdc1ffa5c84"> 416</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a6c5735e4c25655dd4533504d22b1d66c">LuFactorization::LeftSolveLWithNonZeros</a>(<a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_row.html">ScatteredRow</a>* y)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00417" name="l00417"></a><span class="lineno"> 417</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a6c5735e4c25655dd4533504d22b1d66c">LeftSolveLWithNonZeros</a>(y, <span class="keyword">nullptr</span>);</div>
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<div class="line"><a id="l00418" name="l00418"></a><span class="lineno"> 418</span>}</div>
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<div class="line"><a id="l00419" name="l00419"></a><span class="lineno"> 419</span> </div>
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<div class="line"><a id="l00420" name="l00420"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a9438a3ceb0327c1bd75ff3b4fa58d3b0"> 420</a></span>ColIndex <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a9438a3ceb0327c1bd75ff3b4fa58d3b0">LuFactorization::LeftSolveUForUnitRow</a>(ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>,</div>
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<div class="line"><a id="l00421" name="l00421"></a><span class="lineno"> 421</span> <a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_row.html">ScatteredRow</a>* y)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00422" name="l00422"></a><span class="lineno"> 422</span> <a class="code hl_define" href="stats_8h.html#a9995704aaaf45fc21e08c847551a8d04">SCOPED_TIME_STAT</a>(&stats_);</div>
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<div class="line"><a id="l00423" name="l00423"></a><span class="lineno"> 423</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(<a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a386d851d7c8b409205dd82d87e44f2fe">IsAllZero</a>(y-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ae0473e18a367af671dc3f08063c80da4">values</a>));</div>
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<div class="line"><a id="l00424" name="l00424"></a><span class="lineno"> 424</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(y-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">non_zeros</a>.empty());</div>
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<div class="line"><a id="l00425" name="l00425"></a><span class="lineno"> 425</span> <span class="keywordflow">if</span> (is_identity_factorization_) {</div>
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<div class="line"><a id="l00426" name="l00426"></a><span class="lineno"> 426</span> (*y)[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = 1.0;</div>
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<div class="line"><a id="l00427" name="l00427"></a><span class="lineno"> 427</span> y-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">non_zeros</a>.push_back(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00428" name="l00428"></a><span class="lineno"> 428</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>;</div>
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<div class="line"><a id="l00429" name="l00429"></a><span class="lineno"> 429</span> }</div>
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<div class="line"><a id="l00430" name="l00430"></a><span class="lineno"> 430</span> <span class="keyword">const</span> ColIndex permuted_col = col_perm_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_permutation.html#a644718bb2fb240de962dc3c9a1fdf0dc">empty</a>() ? <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> : col_perm_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>];</div>
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<div class="line"><a id="l00431" name="l00431"></a><span class="lineno"> 431</span> (*y)[permuted_col] = 1.0;</div>
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<div class="line"><a id="l00432" name="l00432"></a><span class="lineno"> 432</span> y-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">non_zeros</a>.push_back(permuted_col);</div>
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<div class="line"><a id="l00433" name="l00433"></a><span class="lineno"> 433</span> </div>
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<div class="line"><a id="l00434" name="l00434"></a><span class="lineno"> 434</span> <span class="comment">// Using the transposed matrix here is faster (even accounting the time to</span></div>
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<div class="line"><a id="l00435" name="l00435"></a><span class="lineno"> 435</span> <span class="comment">// construct it). Note the small optimization in case the inversion is</span></div>
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<div class="line"><a id="l00436" name="l00436"></a><span class="lineno"> 436</span> <span class="comment">// trivial.</span></div>
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<div class="line"><a id="l00437" name="l00437"></a><span class="lineno"> 437</span> <span class="keywordflow">if</span> (transpose_upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#af0dafb025bcf4174501a93fb91ca4bb6">ColumnIsDiagonalOnly</a>(permuted_col)) {</div>
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<div class="line"><a id="l00438" name="l00438"></a><span class="lineno"> 438</span> (*y)[permuted_col] /= transpose_upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a4a34504e7ba1673cf24f745d162fda84">GetDiagonalCoefficient</a>(permuted_col);</div>
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<div class="line"><a id="l00439" name="l00439"></a><span class="lineno"> 439</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00440" name="l00440"></a><span class="lineno"> 440</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#ac014de658aabf122011e8fb07b6f4612">RowIndexVector</a>* <span class="keyword">const</span> nz = <span class="keyword">reinterpret_cast<</span><a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#ac014de658aabf122011e8fb07b6f4612">RowIndexVector</a>*<span class="keyword">></span>(&y-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">non_zeros</a>);</div>
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<div class="line"><a id="l00441" name="l00441"></a><span class="lineno"> 441</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* <span class="keyword">const</span> x = <span class="keyword">reinterpret_cast<</span><a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>*<span class="keyword">></span>(&y-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ae0473e18a367af671dc3f08063c80da4">values</a>);</div>
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<div class="line"><a id="l00442" name="l00442"></a><span class="lineno"> 442</span> transpose_upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a985078d2d3022f616d3c355373c7d20e">ComputeRowsToConsiderInSortedOrder</a>(nz);</div>
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<div class="line"><a id="l00443" name="l00443"></a><span class="lineno"> 443</span> y-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#a56e67c2fc5b21fd62d8776fa4b149ce6">non_zeros_are_sorted</a> = <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00444" name="l00444"></a><span class="lineno"> 444</span> <span class="keywordflow">if</span> (y-><a class="code hl_variable" href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">non_zeros</a>.empty()) {</div>
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<div class="line"><a id="l00445" name="l00445"></a><span class="lineno"> 445</span> transpose_upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a71d81a062179f9fa4a2c133b72aaf0d8">LowerSolveStartingAt</a>(permuted_col, x);</div>
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<div class="line"><a id="l00446" name="l00446"></a><span class="lineno"> 446</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00447" name="l00447"></a><span class="lineno"> 447</span> transpose_upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a31d19092aa0a8b6a87e8917c956a0610">HyperSparseSolve</a>(x, nz);</div>
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|
<div class="line"><a id="l00448" name="l00448"></a><span class="lineno"> 448</span> }</div>
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<div class="line"><a id="l00449" name="l00449"></a><span class="lineno"> 449</span> }</div>
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<div class="line"><a id="l00450" name="l00450"></a><span class="lineno"> 450</span> <span class="keywordflow">return</span> permuted_col;</div>
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<div class="line"><a id="l00451" name="l00451"></a><span class="lineno"> 451</span>}</div>
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<div class="line"><a id="l00452" name="l00452"></a><span class="lineno"> 452</span> </div>
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<div class="line"><a id="l00453" name="l00453"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a3042b0778d3d901556345438e482d88a"> 453</a></span><span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>& <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a3042b0778d3d901556345438e482d88a">LuFactorization::GetColumnOfU</a>(ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00454" name="l00454"></a><span class="lineno"> 454</span> <span class="keywordflow">if</span> (is_identity_factorization_) {</div>
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<div class="line"><a id="l00455" name="l00455"></a><span class="lineno"> 455</span> column_of_upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_vector.html#aa71d36872f416feaa853788a7a7a7ef8">Clear</a>();</div>
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<div class="line"><a id="l00456" name="l00456"></a><span class="lineno"> 456</span> column_of_upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_sparse_vector.html#aeff6ae7073f423651fc0352d50cadfa6">SetCoefficient</a>(<a class="code hl_function" href="namespaceoperations__research_1_1glop.html#ab65a327cfc2a74c15fa26b91f19acc64">ColToRowIndex</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>), 1.0);</div>
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<div class="line"><a id="l00457" name="l00457"></a><span class="lineno"> 457</span> <span class="keywordflow">return</span> column_of_upper_;</div>
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<div class="line"><a id="l00458" name="l00458"></a><span class="lineno"> 458</span> }</div>
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<div class="line"><a id="l00459" name="l00459"></a><span class="lineno"> 459</span> upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a8c7ec7f3a8ab57639b0d1ea69b9e0e65">CopyColumnToSparseColumn</a>(col_perm_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_permutation.html#a644718bb2fb240de962dc3c9a1fdf0dc">empty</a>() ? <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> : col_perm_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>],</div>
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<div class="line"><a id="l00460" name="l00460"></a><span class="lineno"> 460</span> &column_of_upper_);</div>
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<div class="line"><a id="l00461" name="l00461"></a><span class="lineno"> 461</span> <span class="keywordflow">return</span> column_of_upper_;</div>
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<div class="line"><a id="l00462" name="l00462"></a><span class="lineno"> 462</span>}</div>
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<div class="line"><a id="l00463" name="l00463"></a><span class="lineno"> 463</span> </div>
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<div class="line"><a id="l00464" name="l00464"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a4523b56a271bfeb588757e64e4bf1425"> 464</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a4523b56a271bfeb588757e64e4bf1425">LuFactorization::GetFillInPercentage</a>(</div>
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<div class="line"><a id="l00465" name="l00465"></a><span class="lineno"> 465</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html">CompactSparseMatrixView</a>& matrix)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00466" name="l00466"></a><span class="lineno"> 466</span> <span class="keyword">const</span> <span class="keywordtype">int</span> initial_num_entries = matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#af69d9b7065a8f31604a8134be4307749">num_entries</a>().value();</div>
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<div class="line"><a id="l00467" name="l00467"></a><span class="lineno"> 467</span> <span class="keyword">const</span> <span class="keywordtype">int</span> lu_num_entries =</div>
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<div class="line"><a id="l00468" name="l00468"></a><span class="lineno"> 468</span> (lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#af69d9b7065a8f31604a8134be4307749">num_entries</a>() + upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#af69d9b7065a8f31604a8134be4307749">num_entries</a>()).<a class="code hl_variable" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>();</div>
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<div class="line"><a id="l00469" name="l00469"></a><span class="lineno"> 469</span> <span class="keywordflow">if</span> (is_identity_factorization_ || initial_num_entries == 0) <span class="keywordflow">return</span> 1.0;</div>
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<div class="line"><a id="l00470" name="l00470"></a><span class="lineno"> 470</span> <span class="keywordflow">return</span> <span class="keyword">static_cast<</span><span class="keywordtype">double</span><span class="keyword">></span>(lu_num_entries) /</div>
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<div class="line"><a id="l00471" name="l00471"></a><span class="lineno"> 471</span> <span class="keyword">static_cast<</span><span class="keywordtype">double</span><span class="keyword">></span>(initial_num_entries);</div>
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<div class="line"><a id="l00472" name="l00472"></a><span class="lineno"> 472</span>}</div>
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<div class="line"><a id="l00473" name="l00473"></a><span class="lineno"> 473</span> </div>
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<div class="line"><a id="l00474" name="l00474"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#ad9e11229fed5416bf22fb3b4fa65f4c1"> 474</a></span>EntryIndex <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#ad9e11229fed5416bf22fb3b4fa65f4c1">LuFactorization::NumberOfEntries</a>()<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00475" name="l00475"></a><span class="lineno"> 475</span> <span class="keywordflow">return</span> is_identity_factorization_</div>
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<div class="line"><a id="l00476" name="l00476"></a><span class="lineno"> 476</span> ? EntryIndex(0)</div>
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<div class="line"><a id="l00477" name="l00477"></a><span class="lineno"> 477</span> : lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#af69d9b7065a8f31604a8134be4307749">num_entries</a>() + upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#af69d9b7065a8f31604a8134be4307749">num_entries</a>();</div>
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<div class="line"><a id="l00478" name="l00478"></a><span class="lineno"> 478</span>}</div>
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<div class="line"><a id="l00479" name="l00479"></a><span class="lineno"> 479</span> </div>
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<div class="line"><a id="l00480" name="l00480"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#aa40655f0310c3616632354ffeb7d466e"> 480</a></span><a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#aa40655f0310c3616632354ffeb7d466e">LuFactorization::ComputeDeterminant</a>()<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00481" name="l00481"></a><span class="lineno"> 481</span> <span class="keywordflow">if</span> (is_identity_factorization_) <span class="keywordflow">return</span> 1.0;</div>
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<div class="line"><a id="l00482" name="l00482"></a><span class="lineno"> 482</span> <a class="code hl_define" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>().value(), upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>().value());</div>
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<div class="line"><a id="l00483" name="l00483"></a><span class="lineno"> 483</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> product(1.0);</div>
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<div class="line"><a id="l00484" name="l00484"></a><span class="lineno"> 484</span> <span class="keywordflow">for</span> (ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>(); ++<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a id="l00485" name="l00485"></a><span class="lineno"> 485</span> product *= upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a4a34504e7ba1673cf24f745d162fda84">GetDiagonalCoefficient</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00486" name="l00486"></a><span class="lineno"> 486</span> }</div>
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<div class="line"><a id="l00487" name="l00487"></a><span class="lineno"> 487</span> <span class="keywordflow">return</span> product * row_perm_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_permutation.html#a76e3e0c8f9806aee8b9e23679974071a">ComputeSignature</a>() *</div>
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<div class="line"><a id="l00488" name="l00488"></a><span class="lineno"> 488</span> inverse_col_perm_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_permutation.html#a76e3e0c8f9806aee8b9e23679974071a">ComputeSignature</a>();</div>
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<div class="line"><a id="l00489" name="l00489"></a><span class="lineno"> 489</span>}</div>
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<div class="line"><a id="l00490" name="l00490"></a><span class="lineno"> 490</span> </div>
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<div class="line"><a id="l00491" name="l00491"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a05d6979828b99ac719553f75335a1937"> 491</a></span><a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a05d6979828b99ac719553f75335a1937">LuFactorization::ComputeInverseOneNorm</a>()<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00492" name="l00492"></a><span class="lineno"> 492</span> <span class="keywordflow">if</span> (is_identity_factorization_) <span class="keywordflow">return</span> 1.0;</div>
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<div class="line"><a id="l00493" name="l00493"></a><span class="lineno"> 493</span> <span class="keyword">const</span> RowIndex num_rows = lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>();</div>
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<div class="line"><a id="l00494" name="l00494"></a><span class="lineno"> 494</span> <span class="keyword">const</span> ColIndex num_cols = lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>();</div>
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<div class="line"><a id="l00495" name="l00495"></a><span class="lineno"> 495</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> norm = 0.0;</div>
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<div class="line"><a id="l00496" name="l00496"></a><span class="lineno"> 496</span> <span class="keywordflow">for</span> (ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < num_cols; ++<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a id="l00497" name="l00497"></a><span class="lineno"> 497</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a> right_hand_side(num_rows, 0.0);</div>
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<div class="line"><a id="l00498" name="l00498"></a><span class="lineno"> 498</span> right_hand_side[<a class="code hl_function" href="namespaceoperations__research_1_1glop.html#ab65a327cfc2a74c15fa26b91f19acc64">ColToRowIndex</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)] = 1.0;</div>
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<div class="line"><a id="l00499" name="l00499"></a><span class="lineno"> 499</span> <span class="comment">// Get a column of the matrix inverse.</span></div>
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<div class="line"><a id="l00500" name="l00500"></a><span class="lineno"> 500</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a6ec53ed3afa3d8affb6941568dcfec76">RightSolve</a>(&right_hand_side);</div>
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<div class="line"><a id="l00501" name="l00501"></a><span class="lineno"> 501</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> column_norm = 0.0;</div>
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<div class="line"><a id="l00502" name="l00502"></a><span class="lineno"> 502</span> <span class="comment">// Compute sum_i |basis_matrix_ij|.</span></div>
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<div class="line"><a id="l00503" name="l00503"></a><span class="lineno"> 503</span> <span class="keywordflow">for</span> (RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> < num_rows; ++<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) {</div>
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<div class="line"><a id="l00504" name="l00504"></a><span class="lineno"> 504</span> column_norm += std::abs(right_hand_side[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>]);</div>
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<div class="line"><a id="l00505" name="l00505"></a><span class="lineno"> 505</span> }</div>
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<div class="line"><a id="l00506" name="l00506"></a><span class="lineno"> 506</span> <span class="comment">// Compute max_j sum_i |basis_matrix_ij|</span></div>
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<div class="line"><a id="l00507" name="l00507"></a><span class="lineno"> 507</span> norm = <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(norm, column_norm);</div>
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<div class="line"><a id="l00508" name="l00508"></a><span class="lineno"> 508</span> }</div>
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<div class="line"><a id="l00509" name="l00509"></a><span class="lineno"> 509</span> <span class="keywordflow">return</span> norm;</div>
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<div class="line"><a id="l00510" name="l00510"></a><span class="lineno"> 510</span>}</div>
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<div class="line"><a id="l00511" name="l00511"></a><span class="lineno"> 511</span> </div>
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<div class="line"><a id="l00512" name="l00512"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a3a6bb95b9009b1c578a27e6139d52696"> 512</a></span><a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a3a6bb95b9009b1c578a27e6139d52696">LuFactorization::ComputeInverseInfinityNorm</a>()<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00513" name="l00513"></a><span class="lineno"> 513</span> <span class="keywordflow">if</span> (is_identity_factorization_) <span class="keywordflow">return</span> 1.0;</div>
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<div class="line"><a id="l00514" name="l00514"></a><span class="lineno"> 514</span> <span class="keyword">const</span> RowIndex num_rows = lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a960110e64357a3e69162ebf1f71959dd">num_rows</a>();</div>
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<div class="line"><a id="l00515" name="l00515"></a><span class="lineno"> 515</span> <span class="keyword">const</span> ColIndex num_cols = lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a41741829541d089f1c4d34f190884813">num_cols</a>();</div>
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<div class="line"><a id="l00516" name="l00516"></a><span class="lineno"> 516</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a> row_sum(num_rows, 0.0);</div>
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<div class="line"><a id="l00517" name="l00517"></a><span class="lineno"> 517</span> <span class="keywordflow">for</span> (ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < num_cols; ++<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a id="l00518" name="l00518"></a><span class="lineno"> 518</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a> right_hand_side(num_rows, 0.0);</div>
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<div class="line"><a id="l00519" name="l00519"></a><span class="lineno"> 519</span> right_hand_side[<a class="code hl_function" href="namespaceoperations__research_1_1glop.html#ab65a327cfc2a74c15fa26b91f19acc64">ColToRowIndex</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)] = 1.0;</div>
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<div class="line"><a id="l00520" name="l00520"></a><span class="lineno"> 520</span> <span class="comment">// Get a column of the matrix inverse.</span></div>
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<div class="line"><a id="l00521" name="l00521"></a><span class="lineno"> 521</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a6ec53ed3afa3d8affb6941568dcfec76">RightSolve</a>(&right_hand_side);</div>
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<div class="line"><a id="l00522" name="l00522"></a><span class="lineno"> 522</span> <span class="comment">// Compute sum_j |basis_matrix_ij|.</span></div>
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<div class="line"><a id="l00523" name="l00523"></a><span class="lineno"> 523</span> <span class="keywordflow">for</span> (RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> < num_rows; ++<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) {</div>
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<div class="line"><a id="l00524" name="l00524"></a><span class="lineno"> 524</span> row_sum[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] += std::abs(right_hand_side[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>]);</div>
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<div class="line"><a id="l00525" name="l00525"></a><span class="lineno"> 525</span> }</div>
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<div class="line"><a id="l00526" name="l00526"></a><span class="lineno"> 526</span> }</div>
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<div class="line"><a id="l00527" name="l00527"></a><span class="lineno"> 527</span> <span class="comment">// Compute max_i sum_j |basis_matrix_ij|</span></div>
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<div class="line"><a id="l00528" name="l00528"></a><span class="lineno"> 528</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> norm = 0.0;</div>
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<div class="line"><a id="l00529" name="l00529"></a><span class="lineno"> 529</span> <span class="keywordflow">for</span> (RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> < num_rows; ++<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) {</div>
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<div class="line"><a id="l00530" name="l00530"></a><span class="lineno"> 530</span> norm = <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(norm, row_sum[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>]);</div>
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<div class="line"><a id="l00531" name="l00531"></a><span class="lineno"> 531</span> }</div>
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<div class="line"><a id="l00532" name="l00532"></a><span class="lineno"> 532</span> <span class="keywordflow">return</span> norm;</div>
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<div class="line"><a id="l00533" name="l00533"></a><span class="lineno"> 533</span>}</div>
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<div class="line"><a id="l00534" name="l00534"></a><span class="lineno"> 534</span> </div>
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<div class="line"><a id="l00535" name="l00535"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#af03b66d5eb557d6d95ad01d446c2cba8"> 535</a></span><a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#af03b66d5eb557d6d95ad01d446c2cba8">LuFactorization::ComputeOneNormConditionNumber</a>(</div>
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<div class="line"><a id="l00536" name="l00536"></a><span class="lineno"> 536</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html">CompactSparseMatrixView</a>& matrix)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00537" name="l00537"></a><span class="lineno"> 537</span> <span class="keywordflow">if</span> (is_identity_factorization_) <span class="keywordflow">return</span> 1.0;</div>
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<div class="line"><a id="l00538" name="l00538"></a><span class="lineno"> 538</span> <span class="keywordflow">return</span> matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a64fea3282d498f3eb2d4af70692bb117">ComputeOneNorm</a>() * <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a05d6979828b99ac719553f75335a1937">ComputeInverseOneNorm</a>();</div>
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<div class="line"><a id="l00539" name="l00539"></a><span class="lineno"> 539</span>}</div>
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<div class="line"><a id="l00540" name="l00540"></a><span class="lineno"> 540</span> </div>
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<div class="line"><a id="l00541" name="l00541"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#ac22943ff00ae631c58ad2c42932d4657"> 541</a></span><a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#ac22943ff00ae631c58ad2c42932d4657">LuFactorization::ComputeInfinityNormConditionNumber</a>(</div>
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<div class="line"><a id="l00542" name="l00542"></a><span class="lineno"> 542</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html">CompactSparseMatrixView</a>& matrix)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00543" name="l00543"></a><span class="lineno"> 543</span> <span class="keywordflow">if</span> (is_identity_factorization_) <span class="keywordflow">return</span> 1.0;</div>
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<div class="line"><a id="l00544" name="l00544"></a><span class="lineno"> 544</span> <span class="keywordflow">return</span> matrix.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a3f219a081f88c22ae282ada4f0bdddd3">ComputeInfinityNorm</a>() * <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a3a6bb95b9009b1c578a27e6139d52696">ComputeInverseInfinityNorm</a>();</div>
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<div class="line"><a id="l00545" name="l00545"></a><span class="lineno"> 545</span>}</div>
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<div class="line"><a id="l00546" name="l00546"></a><span class="lineno"> 546</span> </div>
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<div class="line"><a id="l00547" name="l00547"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_lu_factorization.html#ada69c9026d5d933471bf27c9ad2d1b38"> 547</a></span><a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#ada69c9026d5d933471bf27c9ad2d1b38">LuFactorization::ComputeInverseInfinityNormUpperBound</a>()<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00548" name="l00548"></a><span class="lineno"> 548</span> <span class="keywordflow">return</span> lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#ada69c9026d5d933471bf27c9ad2d1b38">ComputeInverseInfinityNormUpperBound</a>() *</div>
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<div class="line"><a id="l00549" name="l00549"></a><span class="lineno"> 549</span> upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#ada69c9026d5d933471bf27c9ad2d1b38">ComputeInverseInfinityNormUpperBound</a>();</div>
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<div class="line"><a id="l00550" name="l00550"></a><span class="lineno"> 550</span>}</div>
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<div class="line"><a id="l00551" name="l00551"></a><span class="lineno"> 551</span> </div>
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<div class="line"><a id="l00552" name="l00552"></a><span class="lineno"> 552</span><span class="keyword">namespace </span>{</div>
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<div class="line"><a id="l00553" name="l00553"></a><span class="lineno"> 553</span><span class="comment">// Returns the density of the sparse column 'b' w.r.t. the given permutation.</span></div>
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<div class="line"><a id="l00554" name="l00554"></a><span class="lineno"> 554</span><span class="keywordtype">double</span> ComputeDensity(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a>& <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>, <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_permutation.html">RowPermutation</a>& row_perm) {</div>
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<div class="line"><a id="l00555" name="l00555"></a><span class="lineno"> 555</span> <span class="keywordtype">double</span> density = 0.0;</div>
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<div class="line"><a id="l00556" name="l00556"></a><span class="lineno"> 556</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code hl_typedef" href="classoperations__research_1_1glop_1_1_sparse_vector.html#ab38326ea6cb6187267665dd8b2748f3d">SparseColumn::Entry</a> e : <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>) {</div>
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<div class="line"><a id="l00557" name="l00557"></a><span class="lineno"> 557</span> <span class="keywordflow">if</span> (row_perm[e.row()] != <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#abbaca14cc7f5a0f3aaeb027fef37e0ca">kNonPivotal</a> && e.coefficient() != 0.0) {</div>
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<div class="line"><a id="l00558" name="l00558"></a><span class="lineno"> 558</span> ++density;</div>
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<div class="line"><a id="l00559" name="l00559"></a><span class="lineno"> 559</span> }</div>
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<div class="line"><a id="l00560" name="l00560"></a><span class="lineno"> 560</span> }</div>
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<div class="line"><a id="l00561" name="l00561"></a><span class="lineno"> 561</span> <span class="keyword">const</span> RowIndex num_rows = row_perm.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_permutation.html#a1df2b3a4485e328397fda9b5f9b3ea2b">size</a>();</div>
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<div class="line"><a id="l00562" name="l00562"></a><span class="lineno"> 562</span> <span class="keywordflow">return</span> density / num_rows.value();</div>
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<div class="line"><a id="l00563" name="l00563"></a><span class="lineno"> 563</span>}</div>
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<div class="line"><a id="l00564" name="l00564"></a><span class="lineno"> 564</span>} <span class="comment">// anonymous namespace</span></div>
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<div class="line"><a id="l00565" name="l00565"></a><span class="lineno"> 565</span> </div>
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<div class="line"><a id="l00566" name="l00566"></a><span class="lineno"> 566</span><span class="keywordtype">void</span> LuFactorization::ComputeTransposeUpper() {</div>
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<div class="line"><a id="l00567" name="l00567"></a><span class="lineno"> 567</span> <a class="code hl_define" href="stats_8h.html#a9995704aaaf45fc21e08c847551a8d04">SCOPED_TIME_STAT</a>(&stats_);</div>
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<div class="line"><a id="l00568" name="l00568"></a><span class="lineno"> 568</span> transpose_upper_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a7323fee992a8f4516433b6928fedead6">PopulateFromTranspose</a>(upper_);</div>
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<div class="line"><a id="l00569" name="l00569"></a><span class="lineno"> 569</span>}</div>
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<div class="line"><a id="l00570" name="l00570"></a><span class="lineno"> 570</span> </div>
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<div class="line"><a id="l00571" name="l00571"></a><span class="lineno"> 571</span><span class="keywordtype">void</span> LuFactorization::ComputeTransposeLower()<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00572" name="l00572"></a><span class="lineno"> 572</span> <a class="code hl_define" href="stats_8h.html#a9995704aaaf45fc21e08c847551a8d04">SCOPED_TIME_STAT</a>(&stats_);</div>
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<div class="line"><a id="l00573" name="l00573"></a><span class="lineno"> 573</span> transpose_lower_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a7323fee992a8f4516433b6928fedead6">PopulateFromTranspose</a>(lower_);</div>
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<div class="line"><a id="l00574" name="l00574"></a><span class="lineno"> 574</span>}</div>
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<div class="line"><a id="l00575" name="l00575"></a><span class="lineno"> 575</span> </div>
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<div class="line"><a id="l00576" name="l00576"></a><span class="lineno"> 576</span><span class="keywordtype">bool</span> LuFactorization::CheckFactorization(<span class="keyword">const</span> CompactSparseMatrixView& matrix,</div>
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<div class="line"><a id="l00577" name="l00577"></a><span class="lineno"> 577</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> tolerance)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00578" name="l00578"></a><span class="lineno"> 578</span> <span class="keywordflow">if</span> (is_identity_factorization_) <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00579" name="l00579"></a><span class="lineno"> 579</span> SparseMatrix lu;</div>
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<div class="line"><a id="l00580" name="l00580"></a><span class="lineno"> 580</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#acd3d874c6fe9195587688508b6cd0305">ComputeLowerTimesUpper</a>(&lu);</div>
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<div class="line"><a id="l00581" name="l00581"></a><span class="lineno"> 581</span> SparseMatrix paq;</div>
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<div class="line"><a id="l00582" name="l00582"></a><span class="lineno"> 582</span> paq.PopulateFromPermutedMatrix(matrix, row_perm_, inverse_col_perm_);</div>
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<div class="line"><a id="l00583" name="l00583"></a><span class="lineno"> 583</span> <span class="keywordflow">if</span> (!row_perm_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_permutation.html#a49b06b04b3aa7a76149ce864098a0f15">Check</a>()) {</div>
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<div class="line"><a id="l00584" name="l00584"></a><span class="lineno"> 584</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00585" name="l00585"></a><span class="lineno"> 585</span> }</div>
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<div class="line"><a id="l00586" name="l00586"></a><span class="lineno"> 586</span> <span class="keywordflow">if</span> (!inverse_col_perm_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_permutation.html#a49b06b04b3aa7a76149ce864098a0f15">Check</a>()) {</div>
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<div class="line"><a id="l00587" name="l00587"></a><span class="lineno"> 587</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00588" name="l00588"></a><span class="lineno"> 588</span> }</div>
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<div class="line"><a id="l00589" name="l00589"></a><span class="lineno"> 589</span> </div>
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<div class="line"><a id="l00590" name="l00590"></a><span class="lineno"> 590</span> SparseMatrix should_be_zero;</div>
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<div class="line"><a id="l00591" name="l00591"></a><span class="lineno"> 591</span> should_be_zero.PopulateFromLinearCombination(<a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a>(1.0), paq,</div>
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<div class="line"><a id="l00592" name="l00592"></a><span class="lineno"> 592</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a>(-1.0), lu);</div>
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<div class="line"><a id="l00593" name="l00593"></a><span class="lineno"> 593</span> </div>
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<div class="line"><a id="l00594" name="l00594"></a><span class="lineno"> 594</span> <span class="keywordflow">for</span> (ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> < should_be_zero.num_cols(); ++<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a id="l00595" name="l00595"></a><span class="lineno"> 595</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code hl_typedef" href="classoperations__research_1_1glop_1_1_sparse_vector.html#ab38326ea6cb6187267665dd8b2748f3d">SparseColumn::Entry</a> e : should_be_zero.column(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)) {</div>
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<div class="line"><a id="l00596" name="l00596"></a><span class="lineno"> 596</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> magnitude = std::abs(e.coefficient());</div>
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<div class="line"><a id="l00597" name="l00597"></a><span class="lineno"> 597</span> <span class="keywordflow">if</span> (magnitude > tolerance) {</div>
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<div class="line"><a id="l00598" name="l00598"></a><span class="lineno"> 598</span> <a class="code hl_define" href="base_2logging_8h.html#afcaa7cadd41741bb855c2ada1d2ef927">VLOG</a>(2) << magnitude << <span class="stringliteral">" != 0, at column "</span> << <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>;</div>
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<div class="line"><a id="l00599" name="l00599"></a><span class="lineno"> 599</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00600" name="l00600"></a><span class="lineno"> 600</span> }</div>
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<div class="line"><a id="l00601" name="l00601"></a><span class="lineno"> 601</span> }</div>
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<div class="line"><a id="l00602" name="l00602"></a><span class="lineno"> 602</span> }</div>
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<div class="line"><a id="l00603" name="l00603"></a><span class="lineno"> 603</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00604" name="l00604"></a><span class="lineno"> 604</span>}</div>
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<div class="line"><a id="l00605" name="l00605"></a><span class="lineno"> 605</span> </div>
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<div class="line"><a id="l00606" name="l00606"></a><span class="lineno"> 606</span>} <span class="comment">// namespace glop</span></div>
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<div class="line"><a id="l00607" name="l00607"></a><span class="lineno"> 607</span>} <span class="comment">// namespace operations_research</span></div>
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<div class="ttc" id="aalldiff__cst_8cc_html_a26e6db9bcc64b584051ecc28171ed11f"><div class="ttname"><a href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a></div><div class="ttdeci">int64_t max</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00140">alldiff_cst.cc:140</a></div></div>
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<div class="ttc" id="aalldiff__cst_8cc_html_ad10edae0a852d72fb76afb1c77735045"><div class="ttname"><a href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">min</a></div><div class="ttdeci">int64_t min</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00139">alldiff_cst.cc:139</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_a3e1cfef60e774a81f30eaddf26a3a274"><div class="ttname"><a href="base_2logging_8h.html#a3e1cfef60e774a81f30eaddf26a3a274">CHECK</a></div><div class="ttdeci">#define CHECK(condition)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00495">base/logging.h:495</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_a46e69120fbd3b36e6960e096d23b66f0"><div class="ttname"><a href="base_2logging_8h.html#a46e69120fbd3b36e6960e096d23b66f0">DCHECK_NE</a></div><div class="ttdeci">#define DCHECK_NE(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00891">base/logging.h:891</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_a7c0ce053b28d53aa4eaf3eb7fb71663b"><div class="ttname"><a href="base_2logging_8h.html#a7c0ce053b28d53aa4eaf3eb7fb71663b">CHECK_EQ</a></div><div class="ttdeci">#define CHECK_EQ(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00702">base/logging.h:702</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_ae17f8119c108cf3070bad3449c7e0006"><div class="ttname"><a href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a></div><div class="ttdeci">#define DCHECK(condition)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00889">base/logging.h:889</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_ae89df3243bbb8341130c7b3f44145ea0"><div class="ttname"><a href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a></div><div class="ttdeci">#define DCHECK_EQ(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00890">base/logging.h:890</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_afcaa7cadd41741bb855c2ada1d2ef927"><div class="ttname"><a href="base_2logging_8h.html#afcaa7cadd41741bb855c2ada1d2ef927">VLOG</a></div><div class="ttdeci">#define VLOG(verboselevel)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00983">base/logging.h:983</a></div></div>
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<div class="ttc" id="aclassabsl_1_1_strong_vector_html_a9263000d449fdccb6cb70b303063e60b"><div class="ttname"><a href="classabsl_1_1_strong_vector.html#a9263000d449fdccb6cb70b303063e60b">absl::StrongVector::push_back</a></div><div class="ttdeci">void push_back(const value_type &x)</div><div class="ttdef"><b>Definition:</b> <a href="strong__vector_8h_source.html#l00158">strong_vector.h:158</a></div></div>
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<div class="ttc" id="aclassabsl_1_1_strong_vector_html_aa5d16d85614c5d518ae10f882e6fb981"><div class="ttname"><a href="classabsl_1_1_strong_vector.html#aa5d16d85614c5d518ae10f882e6fb981">absl::StrongVector::swap</a></div><div class="ttdeci">void swap(StrongVector &x)</div><div class="ttdef"><b>Definition:</b> <a href="strong__vector_8h_source.html#l00169">strong_vector.h:169</a></div></div>
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<div class="ttc" id="aclassabsl_1_1_strong_vector_html_ac8bb3912a3ce86b15842e79d0b421204"><div class="ttname"><a href="classabsl_1_1_strong_vector.html#ac8bb3912a3ce86b15842e79d0b421204">absl::StrongVector::clear</a></div><div class="ttdeci">void clear()</div><div class="ttdef"><b>Definition:</b> <a href="strong__vector_8h_source.html#l00170">strong_vector.h:170</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_column_view_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_column_view.html">operations_research::glop::ColumnView</a></div><div class="ttdef"><b>Definition:</b> <a href="sparse__column_8h_source.html#l00065">sparse_column.h:65</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html">operations_research::glop::CompactSparseMatrix</a></div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00289">sparse.h:289</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html_a41741829541d089f1c4d34f190884813"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a41741829541d089f1c4d34f190884813">operations_research::glop::CompactSparseMatrix::num_cols</a></div><div class="ttdeci">ColIndex num_cols() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00350">sparse.h:350</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html_a960110e64357a3e69162ebf1f71959dd"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#a960110e64357a3e69162ebf1f71959dd">operations_research::glop::CompactSparseMatrix::num_rows</a></div><div class="ttdeci">RowIndex num_rows() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00349">sparse.h:349</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_view_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html">operations_research::glop::CompactSparseMatrixView</a></div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00476">sparse.h:476</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_view_html_a3f219a081f88c22ae282ada4f0bdddd3"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a3f219a081f88c22ae282ada4f0bdddd3">operations_research::glop::CompactSparseMatrixView::ComputeInfinityNorm</a></div><div class="ttdeci">Fractional ComputeInfinityNorm() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00634">sparse.cc:634</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_view_html_a41741829541d089f1c4d34f190884813"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a41741829541d089f1c4d34f190884813">operations_research::glop::CompactSparseMatrixView::num_cols</a></div><div class="ttdeci">ColIndex num_cols() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00489">sparse.h:489</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_view_html_a64fea3282d498f3eb2d4af70692bb117"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a64fea3282d498f3eb2d4af70692bb117">operations_research::glop::CompactSparseMatrixView::ComputeOneNorm</a></div><div class="ttdeci">Fractional ComputeOneNorm() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00631">sparse.cc:631</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_view_html_a960110e64357a3e69162ebf1f71959dd"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#a960110e64357a3e69162ebf1f71959dd">operations_research::glop::CompactSparseMatrixView::num_rows</a></div><div class="ttdeci">RowIndex num_rows() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00488">sparse.h:488</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_view_html_af69d9b7065a8f31604a8134be4307749"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix_view.html#af69d9b7065a8f31604a8134be4307749">operations_research::glop::CompactSparseMatrixView::num_entries</a></div><div class="ttdeci">EntryIndex num_entries() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00628">sparse.cc:628</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a05d6979828b99ac719553f75335a1937"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a05d6979828b99ac719553f75335a1937">operations_research::glop::LuFactorization::ComputeInverseOneNorm</a></div><div class="ttdeci">Fractional ComputeInverseOneNorm() const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00491">lu_factorization.cc:491</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a1ea8d0a49dad57416810ab7b1a2e2108"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a1ea8d0a49dad57416810ab7b1a2e2108">operations_research::glop::LuFactorization::LeftSolveUWithNonZeros</a></div><div class="ttdeci">void LeftSolveUWithNonZeros(ScatteredRow *y) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00317">lu_factorization.cc:317</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a3042b0778d3d901556345438e482d88a"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a3042b0778d3d901556345438e482d88a">operations_research::glop::LuFactorization::GetColumnOfU</a></div><div class="ttdeci">const SparseColumn & GetColumnOfU(ColIndex col) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00453">lu_factorization.cc:453</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a3a6bb95b9009b1c578a27e6139d52696"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a3a6bb95b9009b1c578a27e6139d52696">operations_research::glop::LuFactorization::ComputeInverseInfinityNorm</a></div><div class="ttdeci">Fractional ComputeInverseInfinityNorm() const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00512">lu_factorization.cc:512</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a3c3fa8faef594bd4a249b4aaa5e32d8e"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a3c3fa8faef594bd4a249b4aaa5e32d8e">operations_research::glop::LuFactorization::ComputeInitialBasis</a></div><div class="ttdeci">RowToColMapping ComputeInitialBasis(const CompactSparseMatrix &matrix, const std::vector< ColIndex > &candidates)</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00068">lu_factorization.cc:68</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a40757145002c85d47ad8df1b53707661"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a40757145002c85d47ad8df1b53707661">operations_research::glop::LuFactorization::RightSolveLForColumnView</a></div><div class="ttdeci">void RightSolveLForColumnView(const ColumnView &b, ScatteredColumn *x) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00263">lu_factorization.cc:263</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a43e095088501053427e317e905d5fc83"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a43e095088501053427e317e905d5fc83">operations_research::glop::LuFactorization::RightSolveLWithPermutedInput</a></div><div class="ttdeci">void RightSolveLWithPermutedInput(const DenseColumn &a, ScatteredColumn *x) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00215">lu_factorization.cc:215</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a4523b56a271bfeb588757e64e4bf1425"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a4523b56a271bfeb588757e64e4bf1425">operations_research::glop::LuFactorization::GetFillInPercentage</a></div><div class="ttdeci">double GetFillInPercentage(const CompactSparseMatrixView &matrix) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00464">lu_factorization.cc:464</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a4bf241af6b1844669171d6e170ef991d"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a4bf241af6b1844669171d6e170ef991d">operations_research::glop::LuFactorization::RightSolveSquaredNorm</a></div><div class="ttdeci">Fractional RightSolveSquaredNorm(const ColumnView &a) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00141">lu_factorization.cc:141</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a577c37faff9567f86849dd74c3fcf4ac"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a577c37faff9567f86849dd74c3fcf4ac">operations_research::glop::LuFactorization::RightSolveUWithNonZeros</a></div><div class="ttdeci">void RightSolveUWithNonZeros(ScatteredColumn *x) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00333">lu_factorization.cc:333</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a627511bf305a6af5d7e114817c1792c2"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a627511bf305a6af5d7e114817c1792c2">operations_research::glop::LuFactorization::DeterministicTimeOfLastFactorization</a></div><div class="ttdeci">double DeterministicTimeOfLastFactorization() const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00095">lu_factorization.cc:95</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a6b5f31c4068711b8e6823f4888f410ce"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a6b5f31c4068711b8e6823f4888f410ce">operations_research::glop::LuFactorization::LeftSolve</a></div><div class="ttdeci">void LeftSolve(DenseRow *y) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00109">lu_factorization.cc:109</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a6c5735e4c25655dd4533504d22b1d66c"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a6c5735e4c25655dd4533504d22b1d66c">operations_research::glop::LuFactorization::LeftSolveLWithNonZeros</a></div><div class="ttdeci">bool LeftSolveLWithNonZeros(ScatteredRow *y, ScatteredColumn *result_before_permutation) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00351">lu_factorization.cc:351</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a6ec53ed3afa3d8affb6941568dcfec76"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a6ec53ed3afa3d8affb6941568dcfec76">operations_research::glop::LuFactorization::RightSolve</a></div><div class="ttdeci">void RightSolve(DenseColumn *x) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00099">lu_factorization.cc:99</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a9438a3ceb0327c1bd75ff3b4fa58d3b0"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a9438a3ceb0327c1bd75ff3b4fa58d3b0">operations_research::glop::LuFactorization::LeftSolveUForUnitRow</a></div><div class="ttdeci">ColIndex LeftSolveUForUnitRow(ColIndex col, ScatteredRow *y) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00420">lu_factorization.cc:420</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a9b738f6b485a4d4ef866b8d82ac07876"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a9b738f6b485a4d4ef866b8d82ac07876">operations_research::glop::LuFactorization::DualEdgeSquaredNorm</a></div><div class="ttdeci">Fractional DualEdgeSquaredNorm(RowIndex row) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00172">lu_factorization.cc:172</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_aa1222207079d0d679ef52f8b465cd00a"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#aa1222207079d0d679ef52f8b465cd00a">operations_research::glop::LuFactorization::RightSolveLForScatteredColumn</a></div><div class="ttdeci">void RightSolveLForScatteredColumn(const ScatteredColumn &b, ScatteredColumn *x) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00298">lu_factorization.cc:298</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_aa35c31899babb961a8100bc605136424"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#aa35c31899babb961a8100bc605136424">operations_research::glop::LuFactorization::RightSolveLWithNonZeros</a></div><div class="ttdeci">void RightSolveLWithNonZeros(ScatteredColumn *x) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00279">lu_factorization.cc:279</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_aa40655f0310c3616632354ffeb7d466e"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#aa40655f0310c3616632354ffeb7d466e">operations_research::glop::LuFactorization::ComputeDeterminant</a></div><div class="ttdeci">Fractional ComputeDeterminant() const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00480">lu_factorization.cc:480</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_aa71d36872f416feaa853788a7a7a7ef8"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#aa71d36872f416feaa853788a7a7a7ef8">operations_research::glop::LuFactorization::Clear</a></div><div class="ttdeci">void Clear()</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00031">lu_factorization.cc:31</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_ac22943ff00ae631c58ad2c42932d4657"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#ac22943ff00ae631c58ad2c42932d4657">operations_research::glop::LuFactorization::ComputeInfinityNormConditionNumber</a></div><div class="ttdeci">Fractional ComputeInfinityNormConditionNumber(const CompactSparseMatrixView &matrix) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00541">lu_factorization.cc:541</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_acd3d874c6fe9195587688508b6cd0305"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#acd3d874c6fe9195587688508b6cd0305">operations_research::glop::LuFactorization::ComputeLowerTimesUpper</a></div><div class="ttdeci">void ComputeLowerTimesUpper(SparseMatrix *product) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8h_source.html#l00209">lu_factorization.h:209</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_ace58a4f9d6a147c3455ff8dc029537c4"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#ace58a4f9d6a147c3455ff8dc029537c4">operations_research::glop::LuFactorization::ComputeFactorization</a></div><div class="ttdeci">ABSL_MUST_USE_RESULT Status ComputeFactorization(const CompactSparseMatrixView &compact_matrix)</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00044">lu_factorization.cc:44</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_ad9e11229fed5416bf22fb3b4fa65f4c1"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#ad9e11229fed5416bf22fb3b4fa65f4c1">operations_research::glop::LuFactorization::NumberOfEntries</a></div><div class="ttdeci">EntryIndex NumberOfEntries() const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00474">lu_factorization.cc:474</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_ada69c9026d5d933471bf27c9ad2d1b38"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#ada69c9026d5d933471bf27c9ad2d1b38">operations_research::glop::LuFactorization::ComputeInverseInfinityNormUpperBound</a></div><div class="ttdeci">Fractional ComputeInverseInfinityNormUpperBound() const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00547">lu_factorization.cc:547</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_af03b66d5eb557d6d95ad01d446c2cba8"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#af03b66d5eb557d6d95ad01d446c2cba8">operations_research::glop::LuFactorization::ComputeOneNormConditionNumber</a></div><div class="ttdeci">Fractional ComputeOneNormConditionNumber(const CompactSparseMatrixView &matrix) const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00535">lu_factorization.cc:535</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_af0b37b89dc1909384e822287c1091aa0"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#af0b37b89dc1909384e822287c1091aa0">operations_research::glop::LuFactorization::LuFactorization</a></div><div class="ttdeci">LuFactorization()</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8cc_source.html#l00024">lu_factorization.cc:24</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_markowitz_html_a627511bf305a6af5d7e114817c1792c2"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_markowitz.html#a627511bf305a6af5d7e114817c1792c2">operations_research::glop::Markowitz::DeterministicTimeOfLastFactorization</a></div><div class="ttdeci">double DeterministicTimeOfLastFactorization() const</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00553">markowitz.cc:553</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_markowitz_html_a7ac2557be8cf0394f9953fbdac2f18f4"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_markowitz.html#a7ac2557be8cf0394f9953fbdac2f18f4">operations_research::glop::Markowitz::ComputeLU</a></div><div class="ttdeci">ABSL_MUST_USE_RESULT Status ComputeLU(const CompactSparseMatrixView &basis_matrix, RowPermutation *row_perm, ColumnPermutation *col_perm, TriangularMatrix *lower, TriangularMatrix *upper)</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00149">markowitz.cc:149</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_markowitz_html_afd3f022e573b8f4f0901624a813ade07"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_markowitz.html#afd3f022e573b8f4f0901624a813ade07">operations_research::glop::Markowitz::ComputeRowAndColumnPermutation</a></div><div class="ttdeci">ABSL_MUST_USE_RESULT Status ComputeRowAndColumnPermutation(const CompactSparseMatrixView &basis_matrix, RowPermutation *row_perm, ColumnPermutation *col_perm)</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00027">markowitz.cc:27</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_permutation_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_permutation.html">operations_research::glop::Permutation< RowIndex ></a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_permutation_html_a1df2b3a4485e328397fda9b5f9b3ea2b"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_permutation.html#a1df2b3a4485e328397fda9b5f9b3ea2b">operations_research::glop::Permutation::size</a></div><div class="ttdeci">IndexType size() const</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2permutation_8h_source.html#l00050">lp_data/permutation.h:50</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_permutation_html_a49b06b04b3aa7a76149ce864098a0f15"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_permutation.html#a49b06b04b3aa7a76149ce864098a0f15">operations_research::glop::Permutation::Check</a></div><div class="ttdeci">bool Check() const</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2permutation_8h_source.html#l00151">lp_data/permutation.h:151</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_permutation_html_a644718bb2fb240de962dc3c9a1fdf0dc"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_permutation.html#a644718bb2fb240de962dc3c9a1fdf0dc">operations_research::glop::Permutation::empty</a></div><div class="ttdeci">bool empty() const</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2permutation_8h_source.html#l00051">lp_data/permutation.h:51</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_permutation_html_a76e3e0c8f9806aee8b9e23679974071a"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_permutation.html#a76e3e0c8f9806aee8b9e23679974071a">operations_research::glop::Permutation::ComputeSignature</a></div><div class="ttdeci">int ComputeSignature() const</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2permutation_8h_source.html#l00169">lp_data/permutation.h:169</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_permutation_html_ac8bb3912a3ce86b15842e79d0b421204"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_permutation.html#ac8bb3912a3ce86b15842e79d0b421204">operations_research::glop::Permutation::clear</a></div><div class="ttdeci">void clear()</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2permutation_8h_source.html#l00053">lp_data/permutation.h:53</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_permutation_html_af70191062b734badb4405f2fde63792a"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_permutation.html#af70191062b734badb4405f2fde63792a">operations_research::glop::Permutation::PopulateFromInverse</a></div><div class="ttdeci">void PopulateFromInverse(const Permutation &inverse)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2permutation_8h_source.html#l00127">lp_data/permutation.h:127</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_column_entry_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_column_entry.html">operations_research::glop::SparseColumnEntry</a></div><div class="ttdef"><b>Definition:</b> <a href="sparse__column_8h_source.html#l00028">sparse_column.h:28</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_column_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_column.html">operations_research::glop::SparseColumn</a></div><div class="ttdef"><b>Definition:</b> <a href="sparse__column_8h_source.html#l00044">sparse_column.h:44</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_vector_html_aa71d36872f416feaa853788a7a7a7ef8"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_vector.html#aa71d36872f416feaa853788a7a7a7ef8">operations_research::glop::SparseVector::Clear</a></div><div class="ttdeci">void Clear()</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2sparse__vector_8h_source.html#l00479">lp_data/sparse_vector.h:479</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_vector_html_ab38326ea6cb6187267665dd8b2748f3d"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_vector.html#ab38326ea6cb6187267665dd8b2748f3d">operations_research::glop::SparseVector< RowIndex, SparseColumnIterator >::Entry</a></div><div class="ttdeci">typename Iterator::Entry Entry</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2sparse__vector_8h_source.html#l00091">lp_data/sparse_vector.h:91</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_vector_html_aeff6ae7073f423651fc0352d50cadfa6"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_vector.html#aeff6ae7073f423651fc0352d50cadfa6">operations_research::glop::SparseVector::SetCoefficient</a></div><div class="ttdeci">void SetCoefficient(Index index, Fractional value)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2sparse__vector_8h_source.html#l00685">lp_data/sparse_vector.h:685</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_status_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_status.html">operations_research::glop::Status</a></div><div class="ttdef"><b>Definition:</b> <a href="status_8h_source.html#l00026">status.h:26</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_status_html_a071b1d04197c0ac6e7a4d0ec0b91ff43"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_status.html#a071b1d04197c0ac6e7a4d0ec0b91ff43">operations_research::glop::Status::OK</a></div><div class="ttdeci">static const Status OK()</div><div class="ttdef"><b>Definition:</b> <a href="status_8h_source.html#l00056">status.h:56</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_status_html_a59e56af19e754a6aa26a612ebf91d05fafa2ff9c081445bfbfbda10bc41b76a87"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_status.html#a59e56af19e754a6aa26a612ebf91d05fafa2ff9c081445bfbfbda10bc41b76a87">operations_research::glop::Status::ERROR_LU</a></div><div class="ttdeci">@ ERROR_LU</div><div class="ttdef"><b>Definition:</b> <a href="status_8h_source.html#l00034">status.h:34</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_strict_i_t_i_vector_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">operations_research::glop::StrictITIVector< RowIndex, ColIndex ></a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_strict_i_t_i_vector_html_a64b6b04f3a519d2c61d49daaa88bf06e"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a64b6b04f3a519d2c61d49daaa88bf06e">operations_research::glop::StrictITIVector::resize</a></div><div class="ttdeci">void resize(IntType size)</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00273">lp_types.h:273</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_strict_i_t_i_vector_html_a967a5c081ad4195a30c78dc2c0bcabf5"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a967a5c081ad4195a30c78dc2c0bcabf5">operations_research::glop::StrictITIVector::size</a></div><div class="ttdeci">IntType size() const</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00280">lp_types.h:280</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_a11284f21acc7de7ea63f5ebfebb5c9e7"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a11284f21acc7de7ea63f5ebfebb5c9e7">operations_research::glop::TriangularMatrix::TransposeHyperSparseSolve</a></div><div class="ttdeci">void TransposeHyperSparseSolve(DenseColumn *rhs, RowIndexVector *non_zero_rows) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00957">sparse.cc:957</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_a3089393e5f2314b28878f49fd97398b1"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a3089393e5f2314b28878f49fd97398b1">operations_research::glop::TriangularMatrix::UpperSolve</a></div><div class="ttdeci">void UpperSolve(DenseColumn *rhs) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00797">sparse.cc:797</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_a31d19092aa0a8b6a87e8917c956a0610"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a31d19092aa0a8b6a87e8917c956a0610">operations_research::glop::TriangularMatrix::HyperSparseSolve</a></div><div class="ttdeci">void HyperSparseSolve(DenseColumn *rhs, RowIndexVector *non_zero_rows) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00896">sparse.cc:896</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_a3d3abc3e6b522dc60fd8c1168522e09d"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a3d3abc3e6b522dc60fd8c1168522e09d">operations_research::glop::TriangularMatrix::GetFirstNonIdentityColumn</a></div><div class="ttdeci">ColIndex GetFirstNonIdentityColumn() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00576">sparse.h:576</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_a41741829541d089f1c4d34f190884813"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a41741829541d089f1c4d34f190884813">operations_research::glop::TriangularMatrix::num_cols</a></div><div class="ttdeci">ColIndex num_cols() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00522">sparse.h:522</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_a4a34504e7ba1673cf24f745d162fda84"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a4a34504e7ba1673cf24f745d162fda84">operations_research::glop::TriangularMatrix::GetDiagonalCoefficient</a></div><div class="ttdeci">Fractional GetDiagonalCoefficient(ColIndex col) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00581">sparse.h:581</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_a53c98a21d13c8da595c0b4e63b699649"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a53c98a21d13c8da595c0b4e63b699649">operations_research::glop::TriangularMatrix::LowerSolve</a></div><div class="ttdeci">void LowerSolve(DenseColumn *rhs) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00764">sparse.cc:764</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_a5e67a7d14b4aed3b0f54e453ed5fc7fe"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a5e67a7d14b4aed3b0f54e453ed5fc7fe">operations_research::glop::TriangularMatrix::TransposeHyperSparseSolveWithReversedNonZeros</a></div><div class="ttdeci">void TransposeHyperSparseSolveWithReversedNonZeros(DenseColumn *rhs, RowIndexVector *non_zero_rows) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00987">sparse.cc:987</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_a71d81a062179f9fa4a2c133b72aaf0d8"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a71d81a062179f9fa4a2c133b72aaf0d8">operations_research::glop::TriangularMatrix::LowerSolveStartingAt</a></div><div class="ttdeci">void LowerSolveStartingAt(ColIndex start, DenseColumn *rhs) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00768">sparse.cc:768</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_a7323fee992a8f4516433b6928fedead6"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a7323fee992a8f4516433b6928fedead6">operations_research::glop::TriangularMatrix::PopulateFromTranspose</a></div><div class="ttdeci">void PopulateFromTranspose(const TriangularMatrix &input)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00518">sparse.cc:518</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_a8c7ec7f3a8ab57639b0d1ea69b9e0e65"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a8c7ec7f3a8ab57639b0d1ea69b9e0e65">operations_research::glop::TriangularMatrix::CopyColumnToSparseColumn</a></div><div class="ttdeci">void CopyColumnToSparseColumn(ColIndex col, SparseColumn *output) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00747">sparse.cc:747</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_a960110e64357a3e69162ebf1f71959dd"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a960110e64357a3e69162ebf1f71959dd">operations_research::glop::TriangularMatrix::num_rows</a></div><div class="ttdeci">RowIndex num_rows() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00521">sparse.h:521</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_a985078d2d3022f616d3c355373c7d20e"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#a985078d2d3022f616d3c355373c7d20e">operations_research::glop::TriangularMatrix::ComputeRowsToConsiderInSortedOrder</a></div><div class="ttdeci">void ComputeRowsToConsiderInSortedOrder(RowIndexVector *non_zero_rows, Fractional sparsity_ratio, Fractional num_ops_ratio) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l01343">sparse.cc:1343</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_abd6fe5a90f2132529b10c7cb577f04a5"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#abd6fe5a90f2132529b10c7cb577f04a5">operations_research::glop::TriangularMatrix::TransposeLowerSolve</a></div><div class="ttdeci">void TransposeLowerSolve(DenseColumn *rhs) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00858">sparse.cc:858</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_ad29d43a5efb42cbdbaa131d8a9dc91f9"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#ad29d43a5efb42cbdbaa131d8a9dc91f9">operations_research::glop::TriangularMatrix::TransposeUpperSolve</a></div><div class="ttdeci">void TransposeUpperSolve(DenseColumn *rhs) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00828">sparse.cc:828</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_ada69c9026d5d933471bf27c9ad2d1b38"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#ada69c9026d5d933471bf27c9ad2d1b38">operations_research::glop::TriangularMatrix::ComputeInverseInfinityNormUpperBound</a></div><div class="ttdeci">Fractional ComputeInverseInfinityNormUpperBound() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l01386">sparse.cc:1386</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_aeebcdc829c541f3ca21a15784f02fe9c"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#aeebcdc829c541f3ca21a15784f02fe9c">operations_research::glop::TriangularMatrix::Reset</a></div><div class="ttdeci">void Reset(RowIndex num_rows, ColIndex col_capacity)</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00551">sparse.cc:551</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_af0dafb025bcf4174501a93fb91ca4bb6"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#af0dafb025bcf4174501a93fb91ca4bb6">operations_research::glop::TriangularMatrix::ColumnIsDiagonalOnly</a></div><div class="ttdeci">bool ColumnIsDiagonalOnly(ColIndex col) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00586">sparse.h:586</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_af3dcc960bfe6b9064cdc9ce6ab04fa1d"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#af3dcc960bfe6b9064cdc9ce6ab04fa1d">operations_research::glop::TriangularMatrix::HyperSparseSolveWithReversedNonZeros</a></div><div class="ttdeci">void HyperSparseSolveWithReversedNonZeros(DenseColumn *rhs, RowIndexVector *non_zero_rows) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8cc_source.html#l00926">sparse.cc:926</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_triangular_matrix_html_af69d9b7065a8f31604a8134be4307749"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_triangular_matrix.html#af69d9b7065a8f31604a8134be4307749">operations_research::glop::TriangularMatrix::num_entries</a></div><div class="ttdeci">EntryIndex num_entries() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00523">sparse.h:523</a></div></div>
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<div class="ttc" id="aconstraint__solver_2table_8cc_html_a9293e4d29cac928301645070dd307683"><div class="ttname"><a href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a></div><div class="ttdeci">int64_t b</div><div class="ttdef"><b>Definition:</b> <a href="constraint__solver_2table_8cc_source.html#l00047">constraint_solver/table.cc:47</a></div></div>
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<div class="ttc" id="aconstraint__solver_2table_8cc_html_acb18315d548212835cd8ed4287e6c0b6"><div class="ttname"><a href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a></div><div class="ttdeci">int64_t a</div><div class="ttdef"><b>Definition:</b> <a href="constraint__solver_2table_8cc_source.html#l00046">constraint_solver/table.cc:46</a></div></div>
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<div class="ttc" id="ademon__profiler_8cc_html_ac072af30c4ffbc834bb4c681f6ecb514"><div class="ttname"><a href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a></div><div class="ttdeci">int64_t value</div><div class="ttdef"><b>Definition:</b> <a href="demon__profiler_8cc_source.html#l00044">demon_profiler.cc:44</a></div></div>
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<div class="ttc" id="alp__data_2lp__utils_8h_html"><div class="ttname"><a href="lp__data_2lp__utils_8h.html">lp_utils.h</a></div></div>
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<div class="ttc" id="alp__types_8h_html"><div class="ttname"><a href="lp__types_8h.html">lp_types.h</a></div></div>
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<div class="ttc" id="alu__factorization_8h_html"><div class="ttname"><a href="lu__factorization_8h.html">lu_factorization.h</a></div></div>
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<div class="ttc" id="amacros_8h_html_a7f536a3b33f9bed8f75734e035d30725"><div class="ttname"><a href="macros_8h.html#a7f536a3b33f9bed8f75734e035d30725">DEBUG_MODE</a></div><div class="ttdeci">const bool DEBUG_MODE</div><div class="ttdef"><b>Definition:</b> <a href="macros_8h_source.html#l00024">macros.h:24</a></div></div>
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<div class="ttc" id="amarkowitz_8cc_html_aa9d6c98fdf8d89b0e2321fda02adc82c"><div class="ttname"><a href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a></div><div class="ttdeci">ColIndex col</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00183">markowitz.cc:183</a></div></div>
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<div class="ttc" id="amarkowitz_8cc_html_aea35f36ba98d5bbd8d033382f50c9e52"><div class="ttname"><a href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a></div><div class="ttdeci">RowIndex row</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00182">markowitz.cc:182</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a08d7a83791c6677d1008336cacf3d591"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a08d7a83791c6677d1008336cacf3d591">operations_research::glop::PermuteWithScratchpad</a></div><div class="ttdeci">void PermuteWithScratchpad(const Permutation< PermutationIndexType > &permutation, StrictITIVector< IndexType, Fractional > *zero_scratchpad, StrictITIVector< IndexType, Fractional > *input_output)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2lp__utils_8h_source.html#l00237">lp_data/lp_utils.h:237</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a1dcd08b0f6c19cd4a302bb5a3a6ea06e"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a1dcd08b0f6c19cd4a302bb5a3a6ea06e">operations_research::glop::Square</a></div><div class="ttdeci">Fractional Square(Fractional f)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2lp__utils_8h_source.html#l00036">lp_data/lp_utils.h:36</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a2d53948bf5e999d006e781105aa8bc77"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a2d53948bf5e999d006e781105aa8bc77">operations_research::glop::SquaredNorm</a></div><div class="ttdeci">Fractional SquaredNorm(const SparseColumn &v)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2lp__utils_8cc_source.html#l00030">lp_data/lp_utils.cc:30</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a302ba2f0cfbe5918e56eeaaf00231843"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a302ba2f0cfbe5918e56eeaaf00231843">operations_research::glop::ApplyInversePermutation</a></div><div class="ttdeci">void ApplyInversePermutation(const Permutation< IndexType > &perm, const ITIVectorType &b, ITIVectorType *result)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2permutation_8h_source.html#l00207">lp_data/permutation.h:207</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a31ee82f6ef05c3da492c0376f910d015"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a31ee82f6ef05c3da492c0376f910d015">operations_research::glop::kInvalidRow</a></div><div class="ttdeci">const RowIndex kInvalidRow(-1)</div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a386d851d7c8b409205dd82d87e44f2fe"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a386d851d7c8b409205dd82d87e44f2fe">operations_research::glop::IsAllZero</a></div><div class="ttdeci">bool IsAllZero(const Container &input)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2lp__utils_8h_source.html#l00222">lp_data/lp_utils.h:222</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a6a2019fc6c15a0413896d3f35057a070"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a6a2019fc6c15a0413896d3f35057a070">operations_research::glop::PermuteWithKnownNonZeros</a></div><div class="ttdeci">void PermuteWithKnownNonZeros(const Permutation< IndexType > &permutation, StrictITIVector< IndexType, Fractional > *zero_scratchpad, StrictITIVector< IndexType, Fractional > *output, std::vector< IndexType > *non_zeros)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2lp__utils_8h_source.html#l00259">lp_data/lp_utils.h:259</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a733947145e3e1631165b618b05c9ccb7"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">operations_research::glop::Fractional</a></div><div class="ttdeci">double Fractional</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00078">lp_types.h:78</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a8fbc9efd86a3cc862a9079d86ab8b524"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a8fbc9efd86a3cc862a9079d86ab8b524">operations_research::glop::RowToColIndex</a></div><div class="ttdeci">ColIndex RowToColIndex(RowIndex row)</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00049">lp_types.h:49</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_aa6c552b94fa80def1d4d1ea64697afb1"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#aa6c552b94fa80def1d4d1ea64697afb1">operations_research::glop::ClearAndResizeVectorWithNonZeros</a></div><div class="ttdeci">void ClearAndResizeVectorWithNonZeros(IndexType size, ScatteredRowOrCol *v)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2lp__utils_8h_source.html#l00278">lp_data/lp_utils.h:278</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_ab65a327cfc2a74c15fa26b91f19acc64"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#ab65a327cfc2a74c15fa26b91f19acc64">operations_research::glop::ColToRowIndex</a></div><div class="ttdeci">RowIndex ColToRowIndex(ColIndex col)</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00052">lp_types.h:52</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_abbaca14cc7f5a0f3aaeb027fef37e0ca"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#abbaca14cc7f5a0f3aaeb027fef37e0ca">operations_research::glop::kNonPivotal</a></div><div class="ttdeci">const RowIndex kNonPivotal(-1)</div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_ac014de658aabf122011e8fb07b6f4612"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#ac014de658aabf122011e8fb07b6f4612">operations_research::glop::RowIndexVector</a></div><div class="ttdeci">std::vector< RowIndex > RowIndexVector</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00313">lp_types.h:313</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_ad23afb4770e9de727133317f32f68a2f"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#ad23afb4770e9de727133317f32f68a2f">operations_research::glop::ApplyPermutation</a></div><div class="ttdeci">void ApplyPermutation(const Permutation< IndexType > &perm, const ITIVectorType &b, ITIVectorType *result)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2permutation_8h_source.html#l00192">lp_data/permutation.h:192</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_afb755b7934d8679476e2f05a89739bcd"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">operations_research::glop::kInvalidCol</a></div><div class="ttdeci">const ColIndex kInvalidCol(-1)</div></div>
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<div class="ttc" id="anamespaceoperations__research_html"><div class="ttname"><a href="namespaceoperations__research.html">operations_research</a></div><div class="ttdoc">Collection of objects used to extend the Constraint Solver library.</div><div class="ttdef"><b>Definition:</b> <a href="dense__doubly__linked__list_8h_source.html#l00021">dense_doubly_linked_list.h:21</a></div></div>
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<div class="ttc" id="astats_8h_html_a3c3e6b102f0d91c523099325c98e1887"><div class="ttname"><a href="stats_8h.html#a3c3e6b102f0d91c523099325c98e1887">IF_STATS_ENABLED</a></div><div class="ttdeci">#define IF_STATS_ENABLED(instructions)</div><div class="ttdef"><b>Definition:</b> <a href="stats_8h_source.html#l00437">stats.h:437</a></div></div>
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<div class="ttc" id="astats_8h_html_a9995704aaaf45fc21e08c847551a8d04"><div class="ttname"><a href="stats_8h.html#a9995704aaaf45fc21e08c847551a8d04">SCOPED_TIME_STAT</a></div><div class="ttdeci">#define SCOPED_TIME_STAT(stats)</div><div class="ttdef"><b>Definition:</b> <a href="stats_8h_source.html#l00438">stats.h:438</a></div></div>
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<div class="ttc" id="astatus_8h_html_a3efb1c6250c02a5b881f8b82f75f9822"><div class="ttname"><a href="status_8h.html#a3efb1c6250c02a5b881f8b82f75f9822">GLOP_RETURN_IF_ERROR</a></div><div class="ttdeci">#define GLOP_RETURN_IF_ERROR(function_call)</div><div class="ttdef"><b>Definition:</b> <a href="status_8h_source.html#l00072">status.h:72</a></div></div>
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<div class="ttc" id="astatus_8h_html_a8c76f1eb9790accd2cd0c5fa5c03c322"><div class="ttname"><a href="status_8h.html#a8c76f1eb9790accd2cd0c5fa5c03c322">GLOP_RETURN_AND_LOG_ERROR</a></div><div class="ttdeci">#define GLOP_RETURN_AND_LOG_ERROR(error_code, message)</div><div class="ttdef"><b>Definition:</b> <a href="status_8h_source.html#l00079">status.h:79</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1glop_1_1_scattered_column_html"><div class="ttname"><a href="structoperations__research_1_1glop_1_1_scattered_column.html">operations_research::glop::ScatteredColumn</a></div><div class="ttdef"><b>Definition:</b> <a href="scattered__vector_8h_source.html#l00196">scattered_vector.h:197</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1glop_1_1_scattered_row_html"><div class="ttname"><a href="structoperations__research_1_1glop_1_1_scattered_row.html">operations_research::glop::ScatteredRow</a></div><div class="ttdef"><b>Definition:</b> <a href="scattered__vector_8h_source.html#l00198">scattered_vector.h:198</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1glop_1_1_scattered_vector_html_a56e67c2fc5b21fd62d8776fa4b149ce6"><div class="ttname"><a href="structoperations__research_1_1glop_1_1_scattered_vector.html#a56e67c2fc5b21fd62d8776fa4b149ce6">operations_research::glop::ScatteredVector::non_zeros_are_sorted</a></div><div class="ttdeci">bool non_zeros_are_sorted</div><div class="ttdef"><b>Definition:</b> <a href="scattered__vector_8h_source.html#l00061">scattered_vector.h:61</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1glop_1_1_scattered_vector_html_ac146d47daa294f7e6546c7569c9c881b"><div class="ttname"><a href="structoperations__research_1_1glop_1_1_scattered_vector.html#ac146d47daa294f7e6546c7569c9c881b">operations_research::glop::ScatteredVector::non_zeros</a></div><div class="ttdeci">std::vector< Index > non_zeros</div><div class="ttdef"><b>Definition:</b> <a href="scattered__vector_8h_source.html#l00062">scattered_vector.h:62</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1glop_1_1_scattered_vector_html_ae0473e18a367af671dc3f08063c80da4"><div class="ttname"><a href="structoperations__research_1_1glop_1_1_scattered_vector.html#ae0473e18a367af671dc3f08063c80da4">operations_research::glop::ScatteredVector::values</a></div><div class="ttdeci">StrictITIVector< Index, Fractional > values</div><div class="ttdef"><b>Definition:</b> <a href="scattered__vector_8h_source.html#l00057">scattered_vector.h:57</a></div></div>
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