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260 lines
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<a href="initial__basis_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">// Copyright 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">#ifndef OR_TOOLS_GLOP_INITIAL_BASIS_H_</span></div>
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<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="preprocessor">#define OR_TOOLS_GLOP_INITIAL_BASIS_H_</span></div>
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<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span> </div>
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<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include "<a class="code" href="lp__data_8h.html">ortools/lp_data/lp_data.h</a>"</span></div>
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<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#include "<a class="code" href="lp__types_8h.html">ortools/lp_data/lp_types.h</a>"</span></div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="preprocessor">#include "<a class="code" href="sparse_8h.html">ortools/lp_data/sparse.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"> 24</span><span class="comment">// This class implements two initial basis algorithms. The idea is to replace as</span></div>
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<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="comment">// much as possible the columns of B that correspond to fixed slack variables</span></div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="comment">// with some column of A in order to have more freedom in the values the basic</span></div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="comment">// variables can take.</span></div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="comment">//</span></div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="comment">// The first algorithm is Bixby's initial basis algorithm, described in the</span></div>
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<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="comment">// paper below. It considers the columns of A in a particular order (the ones</span></div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="comment">// with more freedom first) and adds the current column to the basis if it keeps</span></div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="comment">// B almost triangular and with coefficients close to 1.0 on the diagonal for</span></div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="comment">// good numerical stability.</span></div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="comment">//</span></div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span><span class="comment">// Robert E. Bixby, "Implementing the Simplex Method: The Initial Basis"</span></div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="comment">// ORSA Jounal on Computing, Vol. 4, No. 3, Summer 1992.</span></div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span><span class="comment">// http://joc.journal.informs.org/content/4/3/267.abstract</span></div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="comment">//</span></div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="comment">// The second algorithm is is similar to the "advanced initial basis" that GLPK</span></div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="comment">// uses by default. It adds columns one by one to the basis B while keeping it</span></div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="comment">// triangular (not almost triangular as in Bixby's algorithm). The next</span></div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="comment">// column to add is chosen amongst the set of possible candidates using a</span></div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span><span class="comment">// heuristic similar to the one used by Bixby.</span></div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_initial_basis.html"> 44</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1glop_1_1_initial_basis.html">InitialBasis</a> {</div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <span class="comment">// Takes references to the linear program data we need.</span></div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_initial_basis.html#a438d4b4af9e16ef2e33252a47d2cbdcc">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="l00048" name="l00048"></a><span class="lineno"> 48</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, <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="l00049" name="l00049"></a><span class="lineno"> 49</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="l00050" name="l00050"></a><span class="lineno"> 50</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="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> <span class="comment">// Completes the entries of the given basis that are equal to kInvalidCol with</span></div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="comment">// one of the first num_cols columns of A using Bixby's algorithm.</span></div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="comment">// Important: For this function, the matrix must be scaled such that the</span></div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="comment">// maximum absolute value in each column is 1.0.</span></div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_initial_basis.html#a5131899a6d009ae005c0ed3bdc610bc2">CompleteBixbyBasis</a>(ColIndex num_cols, <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="l00058" name="l00058"></a><span class="lineno"> 58</span> </div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="comment">// Similar to CompleteBixbyBasis() but completes the basis into a triangular</span></div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="comment">// one. This function usually produces better initial bases. The dual version</span></div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="comment">// just restricts the possible entering columns to the ones with a cost of 0.0</span></div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="comment">// in order to always start with the all-zeros vector of dual values.</span></div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="comment">// Returns false if an error occurred during the algorithm (numerically</span></div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="comment">// instable basis).</span></div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_initial_basis.html#a32936088b1bad8c16018509688635b92">CompleteTriangularPrimalBasis</a>(ColIndex num_cols, <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="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_initial_basis.html#a3d28502c22b7bcc6a65a04a97aee3ac5">CompleteTriangularDualBasis</a>(ColIndex num_cols, <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="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">// Use Maros's LTSF crash from the book "Computational Techniques of the</span></div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="comment">// Simplex Method". Unlike the other crashes this does not use the initial</span></div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="comment">// content of the basis parameter.</span></div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_initial_basis.html#a7cba4815d55cf1ab1e2f9258dae8b3b2">GetPrimalMarosBasis</a>(ColIndex num_cols, <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="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_initial_basis.html#a76876ba077b64a095c15770aea40d6c9">GetDualMarosBasis</a>(ColIndex num_cols, <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="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> <span class="comment">// Visible for testing. Computes a list of candidate column indices out of the</span></div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="comment">// fist num_candidate_columns of A and sorts them using the</span></div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="comment">// bixby_column_comparator_. This also fills max_scaled_abs_cost_.</span></div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_initial_basis.html#aed74a869cec0e008dc81b453176426f6">ComputeCandidates</a>(ColIndex num_cols, std::vector<ColIndex>* candidates);</div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> </div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="keyword">private</span>:</div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="comment">// Internal implementation of the Primal/Dual CompleteTriangularBasis().</span></div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</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="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="keywordtype">void</span> CompleteTriangularBasis(ColIndex num_cols, <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="l00084" name="l00084"></a><span class="lineno"> 84</span> </div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</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="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="keywordtype">void</span> GetMarosBasis(ColIndex num_cols, <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="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> <span class="comment">// Returns an integer representing the order (the lower the better)</span></div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="comment">// between column categories (known as C2, C3 or C4 in the paper).</span></div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="comment">// Also returns a greater index for fixed columns.</span></div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="keywordtype">int</span> 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="l00092" name="l00092"></a><span class="lineno"> 92</span> </div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="comment">// Row and column priorities for Maros crash.</span></div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="keywordtype">int</span> 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="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="keywordtype">int</span> 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="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> <span class="comment">// Returns the penalty (the lower the better) of a column. This is 'q_j' for a</span></div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="comment">// column 'j' in the paper.</span></div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> 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="l00100" name="l00100"></a><span class="lineno"> 100</span> </div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="comment">// Maximum scaled absolute value of the objective for the columns which are</span></div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="comment">// entering candidates. This is used by GetColumnPenalty().</span></div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> max_scaled_abs_cost_;</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"> 105</span> <span class="comment">// Comparator used to sort column indices according to their penalty.</span></div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> <span class="comment">// Lower is better.</span></div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> <span class="keyword">struct </span>BixbyColumnComparator {</div>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> <span class="keyword">explicit</span> BixbyColumnComparator(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_initial_basis.html">InitialBasis</a>& initial_basis)</div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> : initial_basis_(initial_basis) {}</div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <span class="keywordtype">bool</span> operator()(ColIndex col_a, ColIndex col_b) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_initial_basis.html">InitialBasis</a>& initial_basis_;</div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> } bixby_column_comparator_;</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> <span class="comment">// Comparator used by CompleteTriangularBasis(). Note that this one is meant</span></div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="comment">// to be used by a priority queue, so higher is better.</span></div>
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<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <span class="keyword">struct </span>TriangularColumnComparator {</div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="keyword">explicit</span> TriangularColumnComparator(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_initial_basis.html">InitialBasis</a>& initial_basis)</div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> : initial_basis_(initial_basis) {}</div>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <span class="keywordtype">bool</span> operator()(ColIndex col_a, ColIndex col_b) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_initial_basis.html">InitialBasis</a>& initial_basis_;</div>
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> } triangular_column_comparator_;</div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> </div>
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <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="l00124" name="l00124"></a><span class="lineno"> 124</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="l00125" name="l00125"></a><span class="lineno"> 125</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>& lower_bound_;</div>
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</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>& upper_bound_;</div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</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="l00128" name="l00128"></a><span class="lineno"> 128</span> </div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> DISALLOW_COPY_AND_ASSIGN(<a class="code hl_class" href="classoperations__research_1_1glop_1_1_initial_basis.html">InitialBasis</a>);</div>
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</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>} <span class="comment">// namespace glop</span></div>
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<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span>} <span class="comment">// namespace operations_research</span></div>
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<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> </div>
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<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span><span class="preprocessor">#endif </span><span class="comment">// OR_TOOLS_GLOP_INITIAL_BASIS_H_</span></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_initial_basis_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_initial_basis.html">operations_research::glop::InitialBasis</a></div><div class="ttdef"><b>Definition:</b> <a href="initial__basis_8h_source.html#l00044">initial_basis.h:44</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_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="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#l00137">gscip_solver.cc:137</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#l00136">gscip_solver.cc:136</a></div></div>
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<div class="ttc" id="alp__data_8h_html"><div class="ttname"><a href="lp__data_8h.html">lp_data.h</a></div></div>
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<div class="ttc" id="alp__types_8h_html"><div class="ttname"><a href="lp__types_8h.html">lp_types.h</a></div></div>
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<div class="ttc" id="amarkowitz_8cc_html_aa9d6c98fdf8d89b0e2321fda02adc82c"><div class="ttname"><a href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a></div><div class="ttdeci">ColIndex col</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00183">markowitz.cc:183</a></div></div>
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<div class="ttc" id="amarkowitz_8cc_html_aea35f36ba98d5bbd8d033382f50c9e52"><div class="ttname"><a href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a></div><div class="ttdeci">RowIndex row</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00182">markowitz.cc:182</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_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_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="asparse_8h_html"><div class="ttname"><a href="sparse_8h.html">sparse.h</a></div></div>
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