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594 lines
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<a href="initial__basis_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="initial__basis_8h.html">ortools/glop/initial_basis.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 <queue></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="markowitz_8h.html">ortools/glop/markowitz.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_initial_basis.html#a438d4b4af9e16ef2e33252a47d2cbdcc"> 24</a></span><a class="code hl_function" href="classoperations__research_1_1glop_1_1_initial_basis.html#a438d4b4af9e16ef2e33252a47d2cbdcc">InitialBasis::InitialBasis</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html">CompactSparseMatrix</a>& compact_matrix,</div>
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<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseRow</a>& objective,</div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseRow</a>& <a class="code hl_variable" href="gscip__solver_8cc.html#a1e2f9a2352c1d9a6cada9544898fceec">lower_bound</a>,</div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseRow</a>& <a class="code hl_variable" href="gscip__solver_8cc.html#a1ba5ca0f61f2fa13bd23bf0f89004f35">upper_bound</a>,</div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">VariableTypeRow</a>& variable_type)</div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> : max_scaled_abs_cost_(0.0),</div>
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<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> bixby_column_comparator_(*this),</div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> triangular_column_comparator_(*this),</div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> compact_matrix_(compact_matrix),</div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> <a class="code hl_variable" href="search_8cc.html#a9c6d2505b571d11bc113813060f465a3">objective_</a>(objective),</div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> lower_bound_(<a class="code hl_variable" href="gscip__solver_8cc.html#a1e2f9a2352c1d9a6cada9544898fceec">lower_bound</a>),</div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> upper_bound_(<a class="code hl_variable" href="gscip__solver_8cc.html#a1ba5ca0f61f2fa13bd23bf0f89004f35">upper_bound</a>),</div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> variable_type_(variable_type) {}</div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> </div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_initial_basis.html#a5131899a6d009ae005c0ed3bdc610bc2"> 38</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_initial_basis.html#a5131899a6d009ae005c0ed3bdc610bc2">InitialBasis::CompleteBixbyBasis</a>(ColIndex num_cols,</div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</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="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="comment">// Initialize can_be_replaced ('I' in Bixby's paper) and has_zero_coefficient</span></div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// ('r' in Bixby's paper).</span></div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <span class="keyword">const</span> RowIndex num_rows = compact_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="l00043" name="l00043"></a><span class="lineno"> 43</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseBooleanColumn</a> can_be_replaced(num_rows, <span class="keyword">false</span>);</div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseBooleanColumn</a> has_zero_coefficient(num_rows, <span class="keyword">false</span>);</div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <a class="code hl_define" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(num_rows, basis-><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="l00046" name="l00046"></a><span class="lineno"> 46</span> basis-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a64b6b04f3a519d2c61d49daaa88bf06e">resize</a>(num_rows, <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>);</div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</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="l00048" name="l00048"></a><span class="lineno"> 48</span> <span class="keywordflow">if</span> ((*basis)[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] == <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>) {</div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> can_be_replaced[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] = <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> has_zero_coefficient[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] = <span class="keyword">true</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> }</div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> </div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="comment">// This is 'v' in Bixby's paper.</span></div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a> scaled_diagonal_abs(compact_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="namespaceoperations__research_1_1glop.html#af9a790b7e8c5b0c6d55b336177378e78">kInfinity</a>);</div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> </div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="comment">// Compute a list of candidate indices and sort them using the heuristic</span></div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="comment">// described in Bixby's paper.</span></div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> std::vector<ColIndex> candidates;</div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_initial_basis.html#aed74a869cec0e008dc81b453176426f6">ComputeCandidates</a>(num_cols, &candidates);</div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> </div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="comment">// Loop over the candidate columns, and add them to the basis if the</span></div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="comment">// heuristics are satisfied.</span></div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < candidates.size(); ++i) {</div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="keywordtype">bool</span> enter_basis = <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="keyword">const</span> ColIndex candidate_col_index = candidates[i];</div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="keyword">const</span> <span class="keyword">auto</span>& candidate_col = compact_matrix_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#afbe7c81d6b4066bf7874299a0f7c0d59">column</a>(candidate_col_index);</div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> </div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="comment">// Bixby's heuristic only works with scaled columns. This should be the</span></div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="comment">// case by default since we only use this when the matrix is scaled, but</span></div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="comment">// it is not the case for our tests... The overhead for computing the</span></div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="comment">// infinity norm for each column should be minimal.</span></div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a2ad7ea612bc859f5b637d5029fb875fb">InfinityNorm</a>(candidate_col) != 1.0) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> </div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> RowIndex candidate_row;</div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> candidate_coeff = <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#ad8019bac1bde0ead6ff32980cd5bff52">RestrictedInfinityNorm</a>(</div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> candidate_col, has_zero_coefficient, &candidate_row);</div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> kBixbyHighThreshold = 0.99;</div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="keywordflow">if</span> (candidate_coeff > kBixbyHighThreshold) {</div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> enter_basis = <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a9a9b90bb0105347953a41ae1d6f4dce3">IsDominated</a>(candidate_col, scaled_diagonal_abs)) {</div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> candidate_coeff = <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#ad8019bac1bde0ead6ff32980cd5bff52">RestrictedInfinityNorm</a>(candidate_col, can_be_replaced,</div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> &candidate_row);</div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <span class="keywordflow">if</span> (candidate_coeff != 0.0) {</div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> enter_basis = <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> }</div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> }</div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> </div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="keywordflow">if</span> (enter_basis) {</div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> can_be_replaced[candidate_row] = <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a82b6c13b99cf0a0c7c92f4f1e44eda29">SetSupportToFalse</a>(candidate_col, &has_zero_coefficient);</div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> kBixbyLowThreshold = 0.01;</div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> scaled_diagonal_abs[candidate_row] =</div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> kBixbyLowThreshold * std::abs(candidate_coeff);</div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> (*basis)[candidate_row] = candidate_col_index;</div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> }</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"> 99</span> </div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_initial_basis.html#a7cba4815d55cf1ab1e2f9258dae8b3b2"> 100</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_initial_basis.html#a7cba4815d55cf1ab1e2f9258dae8b3b2">InitialBasis::GetPrimalMarosBasis</a>(ColIndex num_cols,</div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</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="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="keywordflow">return</span> GetMarosBasis<false>(num_cols, basis);</div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span>}</div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> </div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_initial_basis.html#a76876ba077b64a095c15770aea40d6c9"> 105</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_initial_basis.html#a76876ba077b64a095c15770aea40d6c9">InitialBasis::GetDualMarosBasis</a>(ColIndex num_cols,</div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</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="l00107" name="l00107"></a><span class="lineno"> 107</span> <span class="keywordflow">return</span> GetMarosBasis<true>(num_cols, basis);</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"> 109</span> </div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_initial_basis.html#a32936088b1bad8c16018509688635b92"> 110</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_initial_basis.html#a32936088b1bad8c16018509688635b92">InitialBasis::CompleteTriangularPrimalBasis</a>(ColIndex num_cols,</div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</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="l00112" name="l00112"></a><span class="lineno"> 112</span> <span class="keywordflow">return</span> CompleteTriangularBasis<false>(num_cols, basis);</div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span>}</div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> </div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_initial_basis.html#a3d28502c22b7bcc6a65a04a97aee3ac5"> 115</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_initial_basis.html#a3d28502c22b7bcc6a65a04a97aee3ac5">InitialBasis::CompleteTriangularDualBasis</a>(ColIndex num_cols,</div>
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<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</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="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="keywordflow">return</span> CompleteTriangularBasis<true>(num_cols, basis);</div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span>}</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><span class="keyword">template</span> <<span class="keywordtype">bool</span> only_allow_zero_cost_column></div>
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span><span class="keywordtype">void</span> InitialBasis::CompleteTriangularBasis(ColIndex num_cols,</div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</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="l00123" name="l00123"></a><span class="lineno"> 123</span> <span class="comment">// Initialize can_be_replaced.</span></div>
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> <span class="keyword">const</span> RowIndex num_rows = compact_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="l00125" name="l00125"></a><span class="lineno"> 125</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseBooleanColumn</a> can_be_replaced(num_rows, <span class="keyword">false</span>);</div>
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <a class="code hl_define" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(num_rows, basis-><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="l00127" name="l00127"></a><span class="lineno"> 127</span> basis-><a class="code hl_function" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a64b6b04f3a519d2c61d49daaa88bf06e">resize</a>(num_rows, <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>);</div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</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="l00129" name="l00129"></a><span class="lineno"> 129</span> <span class="keywordflow">if</span> ((*basis)[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] == <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>) {</div>
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> can_be_replaced[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] = <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> }</div>
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> }</div>
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<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> </div>
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<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <span class="comment">// Initialize the residual non-zero pattern for the rows that can be replaced.</span></div>
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<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> MatrixNonZeroPattern residual_pattern;</div>
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<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> residual_pattern.Reset(num_rows, num_cols);</div>
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</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="l00138" name="l00138"></a><span class="lineno"> 138</span> <span class="keywordflow">if</span> (only_allow_zero_cost_column && objective_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] != 0.0) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</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 : compact_matrix_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#afbe7c81d6b4066bf7874299a0f7c0d59">column</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)) {</div>
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<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> <span class="keywordflow">if</span> (can_be_replaced[e.row()]) {</div>
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<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> residual_pattern.AddEntry(e.row(), <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> }</div>
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<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> }</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> </div>
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<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <span class="comment">// Initialize a priority queue of residual singleton columns.</span></div>
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<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> <span class="comment">// Also compute max_scaled_abs_cost_ for GetColumnPenalty().</span></div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> std::vector<ColIndex> residual_singleton_column;</div>
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> max_scaled_abs_cost_ = 0.0;</div>
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<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</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="l00151" name="l00151"></a><span class="lineno"> 151</span> max_scaled_abs_cost_ =</div>
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<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(max_scaled_abs_cost_, std::abs(objective_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]));</div>
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<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> <span class="keywordflow">if</span> (residual_pattern.ColDegree(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) == 1) {</div>
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<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> residual_singleton_column.push_back(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> }</div>
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<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> }</div>
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<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> kBixbyWeight = 1000.0;</div>
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<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> max_scaled_abs_cost_ =</div>
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<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> (max_scaled_abs_cost_ == 0.0) ? 1.0 : kBixbyWeight * max_scaled_abs_cost_;</div>
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<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> std::priority_queue<ColIndex, std::vector<ColIndex>,</div>
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<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> InitialBasis::TriangularColumnComparator></div>
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<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> queue(residual_singleton_column.begin(), residual_singleton_column.end(),</div>
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<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> triangular_column_comparator_);</div>
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<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> </div>
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<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> <span class="comment">// Process the residual singleton columns by priority and add them to the</span></div>
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<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> <span class="comment">// basis if their "diagonal" coefficient is not too small.</span></div>
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<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> <span class="keywordflow">while</span> (!queue.empty()) {</div>
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<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> <span class="keyword">const</span> ColIndex candidate = queue.top();</div>
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<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> queue.pop();</div>
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<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> <span class="keywordflow">if</span> (residual_pattern.ColDegree(candidate) != 1) <span class="keywordflow">continue</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"> 172</span> <span class="comment">// Find the position of the singleton and compute the infinity norm of</span></div>
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<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> <span class="comment">// the column (note that this is always 1.0 if the problem was scaled).</span></div>
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<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> RowIndex <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="l00175" name="l00175"></a><span class="lineno"> 175</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> coeff = 0.0;</div>
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<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> max_magnitude = 0.0;</div>
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<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</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 : compact_matrix_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#afbe7c81d6b4066bf7874299a0f7c0d59">column</a>(candidate)) {</div>
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<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> max_magnitude = <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(max_magnitude, std::abs(e.coefficient()));</div>
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<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> <span class="keywordflow">if</span> (can_be_replaced[e.row()]) {</div>
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<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> = e.row();</div>
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<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> coeff = e.coefficient();</div>
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<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> <span class="keywordflow">break</span>;</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> }</div>
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<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> kStabilityThreshold = 0.01;</div>
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<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> <span class="keywordflow">if</span> (std::abs(coeff) < kStabilityThreshold * max_magnitude) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> <a class="code hl_define" href="base_2logging_8h.html#a46e69120fbd3b36e6960e096d23b66f0">DCHECK_NE</a>(<a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a31ee82f6ef05c3da492c0376f910d015">kInvalidRow</a>, <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>);</div>
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<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> </div>
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<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> <span class="comment">// Use this candidate column in the basis.</span></div>
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<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> (*basis)[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] = candidate;</div>
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<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> can_be_replaced[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] = <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> residual_pattern.DeleteRowAndColumn(<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>, candidate);</div>
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<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> : residual_pattern.RowNonZero(<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>)) {</div>
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<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> == candidate) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> residual_pattern.DecreaseColDegree(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> <span class="keywordflow">if</span> (residual_pattern.ColDegree(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) == 1) {</div>
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<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> queue.push(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> }</div>
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<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> }</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> </div>
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<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span><span class="keywordtype">int</span> InitialBasis::GetMarosPriority(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="l00204" name="l00204"></a><span class="lineno"> 204</span> <span class="comment">// Priority values for columns as defined in Maros's book.</span></div>
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<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> <span class="keywordflow">switch</span> (variable_type_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]) {</div>
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<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> <span class="keywordflow">case</span> <a class="code hl_enumvalue" href="namespaceoperations__research_1_1glop.html#a4452e21ffb34da40470f1e0791800027a2882f30bbca588e5d0e88be217ce75c1">VariableType::UNCONSTRAINED</a>:</div>
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<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> <span class="keywordflow">return</span> 3;</div>
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<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> <span class="keywordflow">case</span> <a class="code hl_enumvalue" href="namespaceoperations__research_1_1glop.html#a4452e21ffb34da40470f1e0791800027a9972b9c8a6068625d6cf1f789f3fd872">VariableType::LOWER_BOUNDED</a>:</div>
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<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> <span class="keywordflow">return</span> 2;</div>
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<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> <span class="keywordflow">case</span> <a class="code hl_enumvalue" href="namespaceoperations__research_1_1glop.html#a4452e21ffb34da40470f1e0791800027ae7243c883ff6508ee41b3b1339a7e8f1">VariableType::UPPER_BOUNDED</a>:</div>
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<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> <span class="keywordflow">return</span> 2;</div>
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<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> <span class="keywordflow">case</span> <a class="code hl_enumvalue" href="namespaceoperations__research_1_1glop.html#a4452e21ffb34da40470f1e0791800027a62e32b9a6efb029208f576ee123b459f">VariableType::UPPER_AND_LOWER_BOUNDED</a>:</div>
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<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> <span class="keywordflow">return</span> 1;</div>
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<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> <span class="keywordflow">case</span> <a class="code hl_enumvalue" href="namespaceoperations__research_1_1glop.html#a4452e21ffb34da40470f1e0791800027aaa56837dd3f2917e1e13f3173b596103">VariableType::FIXED_VARIABLE</a>:</div>
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<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> }</div>
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<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span>}</div>
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<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> </div>
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<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span><span class="keywordtype">int</span> InitialBasis::GetMarosPriority(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="l00220" name="l00220"></a><span class="lineno"> 220</span> <span class="comment">// Priority values for rows are equal to</span></div>
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<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> <span class="comment">// 3 - row priority values as defined in Maros's book</span></div>
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<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> ColIndex slack_index(<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>) + compact_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="l00223" name="l00223"></a><span class="lineno"> 223</span> <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a8fbc9efd86a3cc862a9079d86ab8b524">RowToColIndex</a>(compact_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="l00224" name="l00224"></a><span class="lineno"> 224</span> </div>
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<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> <span class="keywordflow">return</span> GetMarosPriority(slack_index);</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><span class="keyword">template</span> <<span class="keywordtype">bool</span> only_allow_zero_cost_column></div>
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<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span><span class="keywordtype">void</span> InitialBasis::GetMarosBasis(ColIndex num_cols, <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#ad73165f71f932e8ccc240d4db5097803">RowToColMapping</a>* basis) {</div>
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<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> <a class="code hl_define" href="base_2logging_8h.html#afcaa7cadd41741bb855c2ada1d2ef927">VLOG</a>(1) << <span class="stringliteral">"Starting Maros crash procedure."</span>;</div>
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<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> </div>
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<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> <span class="comment">// Initialize basis to the all-slack basis.</span></div>
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<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> <span class="keyword">const</span> RowIndex num_rows = compact_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="l00234" name="l00234"></a><span class="lineno"> 234</span> <span class="keyword">const</span> ColIndex first_slack = num_cols - <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a8fbc9efd86a3cc862a9079d86ab8b524">RowToColIndex</a>(num_rows);</div>
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<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> <a class="code hl_define" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(num_rows, basis->size());</div>
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<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> basis->resize(num_rows);</div>
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<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</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="l00238" name="l00238"></a><span class="lineno"> 238</span> (*basis)[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] = first_slack + <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="l00239" name="l00239"></a><span class="lineno"> 239</span> }</div>
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<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span> </div>
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<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> <span class="comment">// Initialize the set of available rows and columns.</span></div>
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<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#ac053cc327ce11b0008e2030fcdc467f9">DenseBooleanRow</a> available(num_cols, <span class="keyword">true</span>);</div>
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<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</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> < first_slack; ++<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span> <span class="keywordflow">if</span> (variable_type_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] == <a class="code hl_enumvalue" href="namespaceoperations__research_1_1glop.html#a4452e21ffb34da40470f1e0791800027aaa56837dd3f2917e1e13f3173b596103">VariableType::FIXED_VARIABLE</a> ||</div>
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<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> (only_allow_zero_cost_column && objective_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] != 0.0)) {</div>
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<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> available[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> }</div>
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<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> }</div>
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<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> <span class="keywordflow">for</span> (ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> = first_slack; <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="l00250" name="l00250"></a><span class="lineno"> 250</span> <span class="keywordflow">if</span> (variable_type_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] == <a class="code hl_enumvalue" href="namespaceoperations__research_1_1glop.html#a4452e21ffb34da40470f1e0791800027a2882f30bbca588e5d0e88be217ce75c1">VariableType::UNCONSTRAINED</a>) {</div>
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<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> available[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> }</div>
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<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> }</div>
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<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> </div>
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<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> <span class="comment">// Initialize the residual non-zero pattern for the active part of the matrix.</span></div>
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<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> MatrixNonZeroPattern residual_pattern;</div>
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<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> residual_pattern.Reset(num_rows, num_cols);</div>
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<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</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> < first_slack; ++<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) {</div>
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<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</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 : compact_matrix_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#afbe7c81d6b4066bf7874299a0f7c0d59">column</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>)) {</div>
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<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span> <span class="keywordflow">if</span> (available[<a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a8fbc9efd86a3cc862a9079d86ab8b524">RowToColIndex</a>(e.row())] && available[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]) {</div>
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<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> residual_pattern.AddEntry(e.row(), <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<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"> 263</span> }</div>
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<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span> }</div>
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<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span> </div>
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<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span> <span class="comment">// Go over residual pattern and mark rows as unavailable.</span></div>
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<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</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="l00268" name="l00268"></a><span class="lineno"> 268</span> <span class="keywordflow">if</span> (residual_pattern.RowDegree(<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) == 0) {</div>
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<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span> available[<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>) + first_slack] = <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span> }</div>
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<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> }</div>
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<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span> </div>
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<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> <span class="keywordflow">for</span> (;;) {</div>
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<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> <span class="comment">// Make row selection by the Row Priority Function (RPF) from Maros's</span></div>
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<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span> <span class="comment">// book.</span></div>
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<div class="line"><a id="l00276" name="l00276"></a><span class="lineno"> 276</span> <span class="keywordtype">int</span> max_row_priority_function = <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::numeric_limits<int>::min</a>();</div>
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<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span> RowIndex max_rpf_row = <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a31ee82f6ef05c3da492c0376f910d015">kInvalidRow</a>;</div>
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<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</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="l00279" name="l00279"></a><span class="lineno"> 279</span> <span class="keywordflow">if</span> (available[<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>) + first_slack]) {</div>
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<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"> 280</span> <span class="keyword">const</span> <span class="keywordtype">int</span> rpf =</div>
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<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</span> 10 * (3 - GetMarosPriority(<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>)) - residual_pattern.RowDegree(<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>);</div>
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<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span> <span class="keywordflow">if</span> (rpf > max_row_priority_function) {</div>
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<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span> max_row_priority_function = rpf;</div>
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<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span> max_rpf_row = <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>;</div>
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<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span> }</div>
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<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</span> }</div>
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<div class="line"><a id="l00287" name="l00287"></a><span class="lineno"> 287</span> }</div>
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<div class="line"><a id="l00288" name="l00288"></a><span class="lineno"> 288</span> <span class="keywordflow">if</span> (max_rpf_row == <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a31ee82f6ef05c3da492c0376f910d015">kInvalidRow</a>) <span class="keywordflow">break</span>;</div>
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<div class="line"><a id="l00289" name="l00289"></a><span class="lineno"> 289</span> </div>
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<div class="line"><a id="l00290" name="l00290"></a><span class="lineno"> 290</span> <span class="comment">// Trace row for nonzero entries and pick one with best Column Priority</span></div>
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<div class="line"><a id="l00291" name="l00291"></a><span class="lineno"> 291</span> <span class="comment">// Function (cpf).</span></div>
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<div class="line"><a id="l00292" name="l00292"></a><span class="lineno"> 292</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> kStabilityThreshold = 1e-3;</div>
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<div class="line"><a id="l00293" name="l00293"></a><span class="lineno"> 293</span> ColIndex max_cpf_col(<a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>);</div>
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<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span> <span class="keywordtype">int</span> max_col_priority_function(<a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::numeric_limits<int>::min</a>());</div>
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<div class="line"><a id="l00295" name="l00295"></a><span class="lineno"> 295</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> pivot_absolute_value = 0.0;</div>
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<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> : residual_pattern.RowNonZero(max_rpf_row)) {</div>
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<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span> <span class="keywordflow">if</span> (!available[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00298" name="l00298"></a><span class="lineno"> 298</span> <span class="keyword">const</span> <span class="keywordtype">int</span> cpf =</div>
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<div class="line"><a id="l00299" name="l00299"></a><span class="lineno"> 299</span> 10 * GetMarosPriority(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>) - residual_pattern.ColDegree(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00300" name="l00300"></a><span class="lineno"> 300</span> <span class="keywordflow">if</span> (cpf > max_col_priority_function) {</div>
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<div class="line"><a id="l00301" name="l00301"></a><span class="lineno"> 301</span> <span class="comment">// Make sure that the pivotal entry is not too small in magnitude.</span></div>
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<div class="line"><a id="l00302" name="l00302"></a><span class="lineno"> 302</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> max_magnitude = 0;</div>
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<div class="line"><a id="l00303" name="l00303"></a><span class="lineno"> 303</span> pivot_absolute_value = 0.0;</div>
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<div class="line"><a id="l00304" name="l00304"></a><span class="lineno"> 304</span> <span class="keyword">const</span> <span class="keyword">auto</span>& column_values = compact_matrix_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#afbe7c81d6b4066bf7874299a0f7c0d59">column</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00305" name="l00305"></a><span class="lineno"> 305</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 : column_values) {</div>
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<div class="line"><a id="l00306" name="l00306"></a><span class="lineno"> 306</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> absolute_value = std::fabs(e.coefficient());</div>
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<div class="line"><a id="l00307" name="l00307"></a><span class="lineno"> 307</span> <span class="keywordflow">if</span> (e.row() == max_rpf_row) pivot_absolute_value = absolute_value;</div>
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<div class="line"><a id="l00308" name="l00308"></a><span class="lineno"> 308</span> max_magnitude = <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(max_magnitude, absolute_value);</div>
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<div class="line"><a id="l00309" name="l00309"></a><span class="lineno"> 309</span> }</div>
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<div class="line"><a id="l00310" name="l00310"></a><span class="lineno"> 310</span> <span class="keywordflow">if</span> (pivot_absolute_value >= kStabilityThreshold * max_magnitude) {</div>
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<div class="line"><a id="l00311" name="l00311"></a><span class="lineno"> 311</span> max_col_priority_function = cpf;</div>
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<div class="line"><a id="l00312" name="l00312"></a><span class="lineno"> 312</span> max_cpf_col = <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>;</div>
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<div class="line"><a id="l00313" name="l00313"></a><span class="lineno"> 313</span> }</div>
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<div class="line"><a id="l00314" name="l00314"></a><span class="lineno"> 314</span> }</div>
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<div class="line"><a id="l00315" name="l00315"></a><span class="lineno"> 315</span> }</div>
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<div class="line"><a id="l00316" name="l00316"></a><span class="lineno"> 316</span> </div>
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<div class="line"><a id="l00317" name="l00317"></a><span class="lineno"> 317</span> <span class="keywordflow">if</span> (max_cpf_col == <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#afb755b7934d8679476e2f05a89739bcd">kInvalidCol</a>) {</div>
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<div class="line"><a id="l00318" name="l00318"></a><span class="lineno"> 318</span> available[<a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a8fbc9efd86a3cc862a9079d86ab8b524">RowToColIndex</a>(max_rpf_row) + first_slack] = <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00319" name="l00319"></a><span class="lineno"> 319</span> <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00320" name="l00320"></a><span class="lineno"> 320</span> }</div>
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<div class="line"><a id="l00321" name="l00321"></a><span class="lineno"> 321</span> </div>
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<div class="line"><a id="l00322" name="l00322"></a><span class="lineno"> 322</span> <span class="comment">// Ensure that the row leaving the basis has a lower priority than the</span></div>
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<div class="line"><a id="l00323" name="l00323"></a><span class="lineno"> 323</span> <span class="comment">// column entering the basis. If the best column is not good enough mark</span></div>
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<div class="line"><a id="l00324" name="l00324"></a><span class="lineno"> 324</span> <span class="comment">// row as unavailable and choose another one.</span></div>
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<div class="line"><a id="l00325" name="l00325"></a><span class="lineno"> 325</span> <span class="keyword">const</span> <span class="keywordtype">int</span> row_priority = GetMarosPriority(max_rpf_row);</div>
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<div class="line"><a id="l00326" name="l00326"></a><span class="lineno"> 326</span> <span class="keyword">const</span> <span class="keywordtype">int</span> column_priority = GetMarosPriority(max_cpf_col);</div>
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<div class="line"><a id="l00327" name="l00327"></a><span class="lineno"> 327</span> <span class="keywordflow">if</span> (row_priority >= column_priority) {</div>
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<div class="line"><a id="l00328" name="l00328"></a><span class="lineno"> 328</span> available[<a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a8fbc9efd86a3cc862a9079d86ab8b524">RowToColIndex</a>(max_rpf_row) + first_slack] = <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00329" name="l00329"></a><span class="lineno"> 329</span> <span class="keywordflow">continue</span>;</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> <span class="comment">// Use this candidate column in the basis. Update residual pattern and row</span></div>
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<div class="line"><a id="l00333" name="l00333"></a><span class="lineno"> 333</span> <span class="comment">// counts list.</span></div>
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<div class="line"><a id="l00334" name="l00334"></a><span class="lineno"> 334</span> (*basis)[max_rpf_row] = max_cpf_col;</div>
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<div class="line"><a id="l00335" name="l00335"></a><span class="lineno"> 335</span> </div>
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<div class="line"><a id="l00336" name="l00336"></a><span class="lineno"> 336</span> <a class="code hl_define" href="base_2logging_8h.html#afcaa7cadd41741bb855c2ada1d2ef927">VLOG</a>(2) << <span class="stringliteral">"Slack variable "</span> << max_rpf_row << <span class="stringliteral">" replaced by column "</span></div>
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<div class="line"><a id="l00337" name="l00337"></a><span class="lineno"> 337</span> << max_cpf_col</div>
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<div class="line"><a id="l00338" name="l00338"></a><span class="lineno"> 338</span> << <span class="stringliteral">". Pivot coefficient magnitude: "</span> << pivot_absolute_value << <span class="stringliteral">"."</span>;</div>
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<div class="line"><a id="l00339" name="l00339"></a><span class="lineno"> 339</span> </div>
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<div class="line"><a id="l00340" name="l00340"></a><span class="lineno"> 340</span> available[max_cpf_col] = <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00341" name="l00341"></a><span class="lineno"> 341</span> available[first_slack + <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a8fbc9efd86a3cc862a9079d86ab8b524">RowToColIndex</a>(max_rpf_row)] = <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00342" name="l00342"></a><span class="lineno"> 342</span> </div>
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<div class="line"><a id="l00343" name="l00343"></a><span class="lineno"> 343</span> <span class="comment">// Maintain the invariant that all the still available columns will have</span></div>
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<div class="line"><a id="l00344" name="l00344"></a><span class="lineno"> 344</span> <span class="comment">// zeros on the rows we already replaced. This ensures the lower-triangular</span></div>
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<div class="line"><a id="l00345" name="l00345"></a><span class="lineno"> 345</span> <span class="comment">// nature (after permutation) of the returned basis.</span></div>
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<div class="line"><a id="l00346" name="l00346"></a><span class="lineno"> 346</span> residual_pattern.DeleteRowAndColumn(max_rpf_row, max_cpf_col);</div>
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<div class="line"><a id="l00347" name="l00347"></a><span class="lineno"> 347</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a> : residual_pattern.RowNonZero(max_rpf_row)) {</div>
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<div class="line"><a id="l00348" name="l00348"></a><span class="lineno"> 348</span> available[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] = <span class="keyword">false</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"> 351</span>}</div>
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<div class="line"><a id="l00352" name="l00352"></a><span class="lineno"> 352</span> </div>
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<div class="line"><a id="l00353" name="l00353"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_initial_basis.html#aed74a869cec0e008dc81b453176426f6"> 353</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_initial_basis.html#aed74a869cec0e008dc81b453176426f6">InitialBasis::ComputeCandidates</a>(ColIndex num_cols,</div>
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<div class="line"><a id="l00354" name="l00354"></a><span class="lineno"> 354</span> std::vector<ColIndex>* candidates) {</div>
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<div class="line"><a id="l00355" name="l00355"></a><span class="lineno"> 355</span> candidates->clear();</div>
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<div class="line"><a id="l00356" name="l00356"></a><span class="lineno"> 356</span> max_scaled_abs_cost_ = 0.0;</div>
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<div class="line"><a id="l00357" name="l00357"></a><span class="lineno"> 357</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="l00358" name="l00358"></a><span class="lineno"> 358</span> <span class="keywordflow">if</span> (variable_type_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] != <a class="code hl_enumvalue" href="namespaceoperations__research_1_1glop.html#a4452e21ffb34da40470f1e0791800027aaa56837dd3f2917e1e13f3173b596103">VariableType::FIXED_VARIABLE</a> &&</div>
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<div class="line"><a id="l00359" name="l00359"></a><span class="lineno"> 359</span> compact_matrix_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#afbe7c81d6b4066bf7874299a0f7c0d59">column</a>(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>).<a class="code hl_function" href="classoperations__research_1_1glop_1_1_column_view.html#af69d9b7065a8f31604a8134be4307749">num_entries</a>() > 0) {</div>
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<div class="line"><a id="l00360" name="l00360"></a><span class="lineno"> 360</span> candidates->push_back(<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>);</div>
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<div class="line"><a id="l00361" name="l00361"></a><span class="lineno"> 361</span> max_scaled_abs_cost_ =</div>
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<div class="line"><a id="l00362" name="l00362"></a><span class="lineno"> 362</span> <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(max_scaled_abs_cost_, std::abs(objective_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]));</div>
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<div class="line"><a id="l00363" name="l00363"></a><span class="lineno"> 363</span> }</div>
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<div class="line"><a id="l00364" name="l00364"></a><span class="lineno"> 364</span> }</div>
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<div class="line"><a id="l00365" name="l00365"></a><span class="lineno"> 365</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> kBixbyWeight = 1000.0;</div>
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<div class="line"><a id="l00366" name="l00366"></a><span class="lineno"> 366</span> max_scaled_abs_cost_ =</div>
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<div class="line"><a id="l00367" name="l00367"></a><span class="lineno"> 367</span> (max_scaled_abs_cost_ == 0.0) ? 1.0 : kBixbyWeight * max_scaled_abs_cost_;</div>
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<div class="line"><a id="l00368" name="l00368"></a><span class="lineno"> 368</span> std::sort(candidates->begin(), candidates->end(), bixby_column_comparator_);</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> </div>
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<div class="line"><a id="l00371" name="l00371"></a><span class="lineno"> 371</span><span class="keywordtype">int</span> InitialBasis::GetColumnCategory(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="l00372" name="l00372"></a><span class="lineno"> 372</span> <span class="comment">// Only the relative position of the returned number is important, so we use</span></div>
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<div class="line"><a id="l00373" name="l00373"></a><span class="lineno"> 373</span> <span class="comment">// 2 for the category C2 in Bixby's paper and so on.</span></div>
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<div class="line"><a id="l00374" name="l00374"></a><span class="lineno"> 374</span> <span class="keywordflow">switch</span> (variable_type_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]) {</div>
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<div class="line"><a id="l00375" name="l00375"></a><span class="lineno"> 375</span> <span class="keywordflow">case</span> <a class="code hl_enumvalue" href="namespaceoperations__research_1_1glop.html#a4452e21ffb34da40470f1e0791800027a2882f30bbca588e5d0e88be217ce75c1">VariableType::UNCONSTRAINED</a>:</div>
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<div class="line"><a id="l00376" name="l00376"></a><span class="lineno"> 376</span> <span class="keywordflow">return</span> 2;</div>
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<div class="line"><a id="l00377" name="l00377"></a><span class="lineno"> 377</span> <span class="keywordflow">case</span> <a class="code hl_enumvalue" href="namespaceoperations__research_1_1glop.html#a4452e21ffb34da40470f1e0791800027a9972b9c8a6068625d6cf1f789f3fd872">VariableType::LOWER_BOUNDED</a>:</div>
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<div class="line"><a id="l00378" name="l00378"></a><span class="lineno"> 378</span> <span class="keywordflow">return</span> 3;</div>
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<div class="line"><a id="l00379" name="l00379"></a><span class="lineno"> 379</span> <span class="keywordflow">case</span> <a class="code hl_enumvalue" href="namespaceoperations__research_1_1glop.html#a4452e21ffb34da40470f1e0791800027ae7243c883ff6508ee41b3b1339a7e8f1">VariableType::UPPER_BOUNDED</a>:</div>
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<div class="line"><a id="l00380" name="l00380"></a><span class="lineno"> 380</span> <span class="keywordflow">return</span> 3;</div>
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<div class="line"><a id="l00381" name="l00381"></a><span class="lineno"> 381</span> <span class="keywordflow">case</span> <a class="code hl_enumvalue" href="namespaceoperations__research_1_1glop.html#a4452e21ffb34da40470f1e0791800027a62e32b9a6efb029208f576ee123b459f">VariableType::UPPER_AND_LOWER_BOUNDED</a>:</div>
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<div class="line"><a id="l00382" name="l00382"></a><span class="lineno"> 382</span> <span class="keywordflow">return</span> 4;</div>
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<div class="line"><a id="l00383" name="l00383"></a><span class="lineno"> 383</span> <span class="keywordflow">case</span> <a class="code hl_enumvalue" href="namespaceoperations__research_1_1glop.html#a4452e21ffb34da40470f1e0791800027aaa56837dd3f2917e1e13f3173b596103">VariableType::FIXED_VARIABLE</a>:</div>
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<div class="line"><a id="l00384" name="l00384"></a><span class="lineno"> 384</span> <span class="keywordflow">return</span> 5;</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>}</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><a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> InitialBasis::GetColumnPenalty(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="l00389" name="l00389"></a><span class="lineno"> 389</span> <span class="keyword">const</span> <a class="code hl_enumeration" href="namespaceoperations__research_1_1glop.html#a4452e21ffb34da40470f1e0791800027">VariableType</a> type = variable_type_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>];</div>
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<div class="line"><a id="l00390" name="l00390"></a><span class="lineno"> 390</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> penalty = 0.0;</div>
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<div class="line"><a id="l00391" name="l00391"></a><span class="lineno"> 391</span> <span class="keywordflow">if</span> (type == <a class="code hl_enumvalue" href="namespaceoperations__research_1_1glop.html#a4452e21ffb34da40470f1e0791800027a9972b9c8a6068625d6cf1f789f3fd872">VariableType::LOWER_BOUNDED</a>) {</div>
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<div class="line"><a id="l00392" name="l00392"></a><span class="lineno"> 392</span> penalty = lower_bound_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>];</div>
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<div class="line"><a id="l00393" name="l00393"></a><span class="lineno"> 393</span> }</div>
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<div class="line"><a id="l00394" name="l00394"></a><span class="lineno"> 394</span> <span class="keywordflow">if</span> (type == <a class="code hl_enumvalue" href="namespaceoperations__research_1_1glop.html#a4452e21ffb34da40470f1e0791800027ae7243c883ff6508ee41b3b1339a7e8f1">VariableType::UPPER_BOUNDED</a>) {</div>
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<div class="line"><a id="l00395" name="l00395"></a><span class="lineno"> 395</span> penalty = -upper_bound_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>];</div>
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<div class="line"><a id="l00396" name="l00396"></a><span class="lineno"> 396</span> }</div>
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<div class="line"><a id="l00397" name="l00397"></a><span class="lineno"> 397</span> <span class="keywordflow">if</span> (type == <a class="code hl_enumvalue" href="namespaceoperations__research_1_1glop.html#a4452e21ffb34da40470f1e0791800027a62e32b9a6efb029208f576ee123b459f">VariableType::UPPER_AND_LOWER_BOUNDED</a>) {</div>
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<div class="line"><a id="l00398" name="l00398"></a><span class="lineno"> 398</span> penalty = lower_bound_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>] - upper_bound_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>];</div>
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<div class="line"><a id="l00399" name="l00399"></a><span class="lineno"> 399</span> }</div>
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<div class="line"><a id="l00400" name="l00400"></a><span class="lineno"> 400</span> <span class="keywordflow">return</span> penalty + std::abs(objective_[<a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>]) / max_scaled_abs_cost_;</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> </div>
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<div class="line"><a id="l00403" name="l00403"></a><span class="lineno"> 403</span><span class="keywordtype">bool</span> InitialBasis::BixbyColumnComparator::operator()(ColIndex col_a,</div>
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<div class="line"><a id="l00404" name="l00404"></a><span class="lineno"> 404</span> ColIndex col_b)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00405" name="l00405"></a><span class="lineno"> 405</span> <span class="keywordflow">if</span> (col_a == col_b) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00406" name="l00406"></a><span class="lineno"> 406</span> <span class="keyword">const</span> <span class="keywordtype">int</span> category_a = initial_basis_.GetColumnCategory(col_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> <span class="keywordtype">int</span> category_b = initial_basis_.GetColumnCategory(col_b);</div>
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<div class="line"><a id="l00408" name="l00408"></a><span class="lineno"> 408</span> <span class="keywordflow">if</span> (category_a != category_b) {</div>
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<div class="line"><a id="l00409" name="l00409"></a><span class="lineno"> 409</span> <span class="keywordflow">return</span> category_a < category_b;</div>
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<div class="line"><a id="l00410" name="l00410"></a><span class="lineno"> 410</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00411" name="l00411"></a><span class="lineno"> 411</span> <span class="keywordflow">return</span> initial_basis_.GetColumnPenalty(col_a) <</div>
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<div class="line"><a id="l00412" name="l00412"></a><span class="lineno"> 412</span> initial_basis_.GetColumnPenalty(col_b);</div>
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<div class="line"><a id="l00413" name="l00413"></a><span class="lineno"> 413</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"> 416</span><span class="keywordtype">bool</span> InitialBasis::TriangularColumnComparator::operator()(</div>
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<div class="line"><a id="l00417" name="l00417"></a><span class="lineno"> 417</span> ColIndex col_a, ColIndex col_b)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00418" name="l00418"></a><span class="lineno"> 418</span> <span class="keywordflow">if</span> (col_a == col_b) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00419" name="l00419"></a><span class="lineno"> 419</span> <span class="keyword">const</span> <span class="keywordtype">int</span> category_a = initial_basis_.GetColumnCategory(col_a);</div>
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<div class="line"><a id="l00420" name="l00420"></a><span class="lineno"> 420</span> <span class="keyword">const</span> <span class="keywordtype">int</span> category_b = initial_basis_.GetColumnCategory(col_b);</div>
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<div class="line"><a id="l00421" name="l00421"></a><span class="lineno"> 421</span> <span class="keywordflow">if</span> (category_a != category_b) {</div>
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<div class="line"><a id="l00422" name="l00422"></a><span class="lineno"> 422</span> <span class="keywordflow">return</span> category_a > category_b;</div>
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<div class="line"><a id="l00423" name="l00423"></a><span class="lineno"> 423</span> }</div>
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<div class="line"><a id="l00424" name="l00424"></a><span class="lineno"> 424</span> </div>
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<div class="line"><a id="l00425" name="l00425"></a><span class="lineno"> 425</span> <span class="comment">// The nonzero is not in the original Bixby paper, but experiment shows it is</span></div>
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<div class="line"><a id="l00426" name="l00426"></a><span class="lineno"> 426</span> <span class="comment">// important. It leads to sparser solves, but also sparser direction, which</span></div>
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<div class="line"><a id="l00427" name="l00427"></a><span class="lineno"> 427</span> <span class="comment">// mean potentially less blocking variables on each pivot...</span></div>
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<div class="line"><a id="l00428" name="l00428"></a><span class="lineno"> 428</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00429" name="l00429"></a><span class="lineno"> 429</span> <span class="comment">// TODO(user): Experiments more with this comparator or the</span></div>
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<div class="line"><a id="l00430" name="l00430"></a><span class="lineno"> 430</span> <span class="comment">// BixbyColumnComparator.</span></div>
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<div class="line"><a id="l00431" name="l00431"></a><span class="lineno"> 431</span> <span class="keywordflow">if</span> (initial_basis_.compact_matrix_.column(col_a).num_entries() !=</div>
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<div class="line"><a id="l00432" name="l00432"></a><span class="lineno"> 432</span> initial_basis_.compact_matrix_.column(col_b).num_entries()) {</div>
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<div class="line"><a id="l00433" name="l00433"></a><span class="lineno"> 433</span> <span class="keywordflow">return</span> initial_basis_.compact_matrix_.column(col_a).num_entries() ></div>
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<div class="line"><a id="l00434" name="l00434"></a><span class="lineno"> 434</span> initial_basis_.compact_matrix_.column(col_b).num_entries();</div>
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<div class="line"><a id="l00435" name="l00435"></a><span class="lineno"> 435</span> }</div>
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<div class="line"><a id="l00436" name="l00436"></a><span class="lineno"> 436</span> <span class="keywordflow">return</span> initial_basis_.GetColumnPenalty(col_a) ></div>
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<div class="line"><a id="l00437" name="l00437"></a><span class="lineno"> 437</span> initial_basis_.GetColumnPenalty(col_b);</div>
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<div class="line"><a id="l00438" name="l00438"></a><span class="lineno"> 438</span>}</div>
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<div class="line"><a id="l00439" name="l00439"></a><span class="lineno"> 439</span> </div>
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<div class="line"><a id="l00440" name="l00440"></a><span class="lineno"> 440</span>} <span class="comment">// namespace glop</span></div>
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<div class="line"><a id="l00441" name="l00441"></a><span class="lineno"> 441</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_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#l00888">base/logging.h:888</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#l00887">base/logging.h:887</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#l00980">base/logging.h:980</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_column_view_html_af69d9b7065a8f31604a8134be4307749"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_column_view.html#af69d9b7065a8f31604a8134be4307749">operations_research::glop::ColumnView::num_entries</a></div><div class="ttdeci">EntryIndex num_entries() const</div><div class="ttdef"><b>Definition:</b> <a href="sparse__column_8h_source.html#l00082">sparse_column.h:82</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_html_afbe7c81d6b4066bf7874299a0f7c0d59"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html#afbe7c81d6b4066bf7874299a0f7c0d59">operations_research::glop::CompactSparseMatrix::column</a></div><div class="ttdeci">ColumnView column(ColIndex col) const</div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00369">sparse.h:369</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_initial_basis_html_a32936088b1bad8c16018509688635b92"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_initial_basis.html#a32936088b1bad8c16018509688635b92">operations_research::glop::InitialBasis::CompleteTriangularPrimalBasis</a></div><div class="ttdeci">void CompleteTriangularPrimalBasis(ColIndex num_cols, RowToColMapping *basis)</div><div class="ttdef"><b>Definition:</b> <a href="initial__basis_8cc_source.html#l00110">initial_basis.cc:110</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_initial_basis_html_a3d28502c22b7bcc6a65a04a97aee3ac5"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_initial_basis.html#a3d28502c22b7bcc6a65a04a97aee3ac5">operations_research::glop::InitialBasis::CompleteTriangularDualBasis</a></div><div class="ttdeci">void CompleteTriangularDualBasis(ColIndex num_cols, RowToColMapping *basis)</div><div class="ttdef"><b>Definition:</b> <a href="initial__basis_8cc_source.html#l00115">initial_basis.cc:115</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_initial_basis_html_a438d4b4af9e16ef2e33252a47d2cbdcc"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_initial_basis.html#a438d4b4af9e16ef2e33252a47d2cbdcc">operations_research::glop::InitialBasis::InitialBasis</a></div><div class="ttdeci">InitialBasis(const CompactSparseMatrix &compact_matrix, const DenseRow &objective, const DenseRow &lower_bound, const DenseRow &upper_bound, const VariableTypeRow &variable_type)</div><div class="ttdef"><b>Definition:</b> <a href="initial__basis_8cc_source.html#l00024">initial_basis.cc:24</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_initial_basis_html_a5131899a6d009ae005c0ed3bdc610bc2"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_initial_basis.html#a5131899a6d009ae005c0ed3bdc610bc2">operations_research::glop::InitialBasis::CompleteBixbyBasis</a></div><div class="ttdeci">void CompleteBixbyBasis(ColIndex num_cols, RowToColMapping *basis)</div><div class="ttdef"><b>Definition:</b> <a href="initial__basis_8cc_source.html#l00038">initial_basis.cc:38</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_initial_basis_html_a76876ba077b64a095c15770aea40d6c9"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_initial_basis.html#a76876ba077b64a095c15770aea40d6c9">operations_research::glop::InitialBasis::GetDualMarosBasis</a></div><div class="ttdeci">void GetDualMarosBasis(ColIndex num_cols, RowToColMapping *basis)</div><div class="ttdef"><b>Definition:</b> <a href="initial__basis_8cc_source.html#l00105">initial_basis.cc:105</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_initial_basis_html_a7cba4815d55cf1ab1e2f9258dae8b3b2"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_initial_basis.html#a7cba4815d55cf1ab1e2f9258dae8b3b2">operations_research::glop::InitialBasis::GetPrimalMarosBasis</a></div><div class="ttdeci">void GetPrimalMarosBasis(ColIndex num_cols, RowToColMapping *basis)</div><div class="ttdef"><b>Definition:</b> <a href="initial__basis_8cc_source.html#l00100">initial_basis.cc:100</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_initial_basis_html_aed74a869cec0e008dc81b453176426f6"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_initial_basis.html#aed74a869cec0e008dc81b453176426f6">operations_research::glop::InitialBasis::ComputeCandidates</a></div><div class="ttdeci">void ComputeCandidates(ColIndex num_cols, std::vector< ColIndex > *candidates)</div><div class="ttdef"><b>Definition:</b> <a href="initial__basis_8cc_source.html#l00353">initial_basis.cc:353</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="sparse__vector_8h_source.html#l00091">sparse_vector.h:91</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< ColIndex, Fractional ></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="agscip__solver_8cc_html_a1ba5ca0f61f2fa13bd23bf0f89004f35"><div class="ttname"><a href="gscip__solver_8cc.html#a1ba5ca0f61f2fa13bd23bf0f89004f35">upper_bound</a></div><div class="ttdeci">double upper_bound</div><div class="ttdef"><b>Definition:</b> <a href="gscip__solver_8cc_source.html#l00126">gscip_solver.cc:126</a></div></div>
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<div class="ttc" id="agscip__solver_8cc_html_a1e2f9a2352c1d9a6cada9544898fceec"><div class="ttname"><a href="gscip__solver_8cc.html#a1e2f9a2352c1d9a6cada9544898fceec">lower_bound</a></div><div class="ttdeci">double lower_bound</div><div class="ttdef"><b>Definition:</b> <a href="gscip__solver_8cc_source.html#l00125">gscip_solver.cc:125</a></div></div>
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<div class="ttc" id="ainitial__basis_8h_html"><div class="ttname"><a href="initial__basis_8h.html">initial_basis.h</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="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="amarkowitz_8h_html"><div class="ttname"><a href="markowitz_8h.html">markowitz.h</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a2ad7ea612bc859f5b637d5029fb875fb"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a2ad7ea612bc859f5b637d5029fb875fb">operations_research::glop::InfinityNorm</a></div><div class="ttdeci">Fractional InfinityNorm(const DenseColumn &v)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2lp__utils_8cc_source.html#l00081">lp_data/lp_utils.cc:81</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_a4452e21ffb34da40470f1e0791800027"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a4452e21ffb34da40470f1e0791800027">operations_research::glop::VariableType</a></div><div class="ttdeci">VariableType</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00175">lp_types.h:175</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a4452e21ffb34da40470f1e0791800027a2882f30bbca588e5d0e88be217ce75c1"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a4452e21ffb34da40470f1e0791800027a2882f30bbca588e5d0e88be217ce75c1">operations_research::glop::VariableType::UNCONSTRAINED</a></div><div class="ttdeci">@ UNCONSTRAINED</div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a4452e21ffb34da40470f1e0791800027a62e32b9a6efb029208f576ee123b459f"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a4452e21ffb34da40470f1e0791800027a62e32b9a6efb029208f576ee123b459f">operations_research::glop::VariableType::UPPER_AND_LOWER_BOUNDED</a></div><div class="ttdeci">@ UPPER_AND_LOWER_BOUNDED</div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a4452e21ffb34da40470f1e0791800027a9972b9c8a6068625d6cf1f789f3fd872"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a4452e21ffb34da40470f1e0791800027a9972b9c8a6068625d6cf1f789f3fd872">operations_research::glop::VariableType::LOWER_BOUNDED</a></div><div class="ttdeci">@ LOWER_BOUNDED</div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a4452e21ffb34da40470f1e0791800027aaa56837dd3f2917e1e13f3173b596103"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a4452e21ffb34da40470f1e0791800027aaa56837dd3f2917e1e13f3173b596103">operations_research::glop::VariableType::FIXED_VARIABLE</a></div><div class="ttdeci">@ FIXED_VARIABLE</div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a4452e21ffb34da40470f1e0791800027ae7243c883ff6508ee41b3b1339a7e8f1"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a4452e21ffb34da40470f1e0791800027ae7243c883ff6508ee41b3b1339a7e8f1">operations_research::glop::VariableType::UPPER_BOUNDED</a></div><div class="ttdeci">@ UPPER_BOUNDED</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_a82b6c13b99cf0a0c7c92f4f1e44eda29"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a82b6c13b99cf0a0c7c92f4f1e44eda29">operations_research::glop::SetSupportToFalse</a></div><div class="ttdeci">void SetSupportToFalse(const ColumnView &column, DenseBooleanColumn *b)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2lp__utils_8cc_source.html#l00146">lp_data/lp_utils.cc:146</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_a9a9b90bb0105347953a41ae1d6f4dce3"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a9a9b90bb0105347953a41ae1d6f4dce3">operations_research::glop::IsDominated</a></div><div class="ttdeci">bool IsDominated(const ColumnView &column, const DenseColumn &radius)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2lp__utils_8cc_source.html#l00154">lp_data/lp_utils.cc:154</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_ac053cc327ce11b0008e2030fcdc467f9"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#ac053cc327ce11b0008e2030fcdc467f9">operations_research::glop::DenseBooleanRow</a></div><div class="ttdeci">StrictITIVector< ColIndex, bool > DenseBooleanRow</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00306">lp_types.h:306</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_ad73165f71f932e8ccc240d4db5097803"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#ad73165f71f932e8ccc240d4db5097803">operations_research::glop::RowToColMapping</a></div><div class="ttdeci">StrictITIVector< RowIndex, ColIndex > RowToColMapping</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00346">lp_types.h:346</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_ad8019bac1bde0ead6ff32980cd5bff52"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#ad8019bac1bde0ead6ff32980cd5bff52">operations_research::glop::RestrictedInfinityNorm</a></div><div class="ttdeci">Fractional RestrictedInfinityNorm(const ColumnView &column, const DenseBooleanColumn &rows_to_consider, RowIndex *row_index)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2lp__utils_8cc_source.html#l00133">lp_data/lp_utils.cc:133</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_af9a790b7e8c5b0c6d55b336177378e78"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#af9a790b7e8c5b0c6d55b336177378e78">operations_research::glop::kInfinity</a></div><div class="ttdeci">const double kInfinity</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00084">lp_types.h:84</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="asearch_8cc_html_a9c6d2505b571d11bc113813060f465a3"><div class="ttname"><a href="search_8cc.html#a9c6d2505b571d11bc113813060f465a3">objective_</a></div><div class="ttdeci">IntVar *const objective_</div><div class="ttdef"><b>Definition:</b> <a href="search_8cc_source.html#l03017">search.cc:3017</a></div></div>
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