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574 lines
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<a href="basis__representation_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_BASIS_REPRESENTATION_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_BASIS_REPRESENTATION_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="base_2logging_8h.html">ortools/base/logging.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="lu__factorization_8h.html">ortools/glop/lu_factorization.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 "ortools/glop/parameters.pb.h"</span></div>
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<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#include "<a class="code" href="rank__one__update_8h.html">ortools/glop/rank_one_update.h</a>"</span></div>
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<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#include "<a class="code" href="status_8h.html">ortools/glop/status.h</a>"</span></div>
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<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</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="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="preprocessor">#include "<a class="code" href="lp__data_2permutation_8h.html">ortools/lp_data/permutation.h</a>"</span></div>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="preprocessor">#include "<a class="code" href="scattered__vector_8h.html">ortools/lp_data/scattered_vector.h</a>"</span></div>
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<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</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="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="preprocessor">#include "<a class="code" href="stats_8h.html">ortools/util/stats.h</a>"</span></div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> </div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</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="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="keyword">namespace </span>glop {</div>
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<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> </div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="comment">// An eta matrix E corresponds to the identity matrix except for one column e of</span></div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="comment">// index j. In particular, B.E is the matrix of the new basis obtained from B by</span></div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="comment">// replacing the j-th vector of B by B.e, note that this is exactly what happens</span></div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="comment">// during a "pivot" of the current basis in the simplex algorithm.</span></div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span><span class="comment">//</span></div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="comment">// E = [ 1 ... 0 e_0 0 ... 0</span></div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span><span class="comment">// ... ... ... ... ... ... ...</span></div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="comment">// 0 ... 1 e_{j-1} 0 ... 0</span></div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="comment">// 0 ... 0 e_j 0 ... 0</span></div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="comment">// 0 ... 0 e_{j+1} 1 ... 0</span></div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="comment">// ... ... ... ... ... ... ...</span></div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="comment">// 0 ... 0 e_{n-1} 0 ... 1 ]</span></div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span><span class="comment">//</span></div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="comment">// The inverse of the eta matrix is:</span></div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span><span class="comment">// E^{-1} = [ 1 ... 0 -e_0/e_j 0 ... 0</span></div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span><span class="comment">// ... ... ... ... ... ... ...</span></div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span><span class="comment">// 0 ... 1 -e_{j-1}/e_j 0 ... 0</span></div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span><span class="comment">// 0 ... 0 1/e_j 0 ... 0</span></div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span><span class="comment">// 0 ... 0 -e_{j+1}/e_j 1 ... 0</span></div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="comment">// ... ... ... ... ... ... ...</span></div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span><span class="comment">// 0 ... 0 -e_{n-1}/e_j 0 ... 1 ]</span></div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_eta_matrix.html"> 52</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1glop_1_1_eta_matrix.html">EtaMatrix</a> {</div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_eta_matrix.html#a7b76b8753b814ba45ef9be10454230d9">EtaMatrix</a>(ColIndex eta_col, <span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_column.html">ScatteredColumn</a>& direction);</div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="keyword">virtual</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_eta_matrix.html#a4975f6e9d308a97737d76519e0b773d5">~EtaMatrix</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">// Solves the system y.E = c, 'c' beeing the initial value of 'y'.</span></div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="comment">// Then y = c.E^{-1}, so y is equal to c except for</span></div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="comment">// y_j = (c_j - \sum_{i != j}{c_i * e_i}) / e_j.</span></div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_eta_matrix.html#a6b5f31c4068711b8e6823f4888f410ce">LeftSolve</a>(<a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseRow</a>* y) <span class="keyword">const</span>;</div>
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<div class="line"><a id="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">// Same as LeftSolve(), but 'pos' contains the non-zero positions of c. The</span></div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="comment">// order of the positions is not important, but there must be no duplicates.</span></div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="comment">// The values not in 'pos' are not used. If eta_col_ was not already in 'pos',</span></div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="comment">// it is added.</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_eta_matrix.html#ad1e32061321d5cc422c6f18a8ed6d33d">SparseLeftSolve</a>(<a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseRow</a>* y, <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a2b83a25cb4fd203c57a7155699fab246">ColIndexVector</a>* pos) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> </div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="comment">// Solves the system E.d = a, 'a' beeing the initial value of 'd'.</span></div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="comment">// Then d = E^{-1}.a = [ a_0 - e_0 * a_j / e_j</span></div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="comment">// ...</span></div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="comment">// a_{j-1} - e_{j-1} * a_j / e_j</span></div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="comment">// a_j / e_j</span></div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="comment">// a_{j+1} - e_{j+1} * a_j / e_j</span></div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="comment">// ...</span></div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="comment">// a_{n-1} - e_{n-1} * a_j / e_j ]</span></div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_eta_matrix.html#a3cb026dc900190c13b208d24134755ed">RightSolve</a>(<a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* d) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> </div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="keyword">private</span>:</div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="comment">// Internal RightSolve() and LeftSolve() implementations using either the</span></div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="comment">// dense or the sparse representation of the eta vector.</span></div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="keywordtype">void</span> LeftSolveWithDenseEta(<a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseRow</a>* y) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="keywordtype">void</span> LeftSolveWithSparseEta(<a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseRow</a>* y) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="keywordtype">void</span> RightSolveWithDenseEta(<a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* d) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <span class="keywordtype">void</span> RightSolveWithSparseEta(<a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* d) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> </div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="comment">// If an eta vector density is smaller than this threshold, we use the</span></div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="comment">// sparse version of the Solve() functions rather than the dense version.</span></div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <span class="comment">// TODO(user): Detect automatically a good parameter? 0.5 is a good value on</span></div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="comment">// the Netlib (I only did a few experiments though). Note that in the future</span></div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="comment">// we may not even keep the dense representation at all.</span></div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="keyword">static</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> kSparseThreshold;</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="keyword">const</span> ColIndex eta_col_;</div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> eta_col_coefficient_;</div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> </div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="comment">// Note that to optimize solves, the position eta_col_ is set to 0.0 and</span></div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="comment">// stored in eta_col_coefficient_ instead.</span></div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a> eta_coeff_;</div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_sparse_column.html">SparseColumn</a> sparse_eta_coeff_;</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> DISALLOW_COPY_AND_ASSIGN(<a class="code hl_class" href="classoperations__research_1_1glop_1_1_eta_matrix.html">EtaMatrix</a>);</div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span>};</div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> </div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span><span class="comment">// An eta factorization corresponds to the product of k eta matrices,</span></div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span><span class="comment">// i.e. E = E_0.E_1. ... .E_{k-1}</span></div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span><span class="comment">// It is used to solve two systems:</span></div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span><span class="comment">// - E.d = a (where a is usually the entering column).</span></div>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span><span class="comment">// - y.E = c (where c is usually the objective row).</span></div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_eta_factorization.html"> 109</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1glop_1_1_eta_factorization.html">EtaFactorization</a> {</div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_eta_factorization.html#acddc81707ff8e60f4ab42b3c21939be6">EtaFactorization</a>();</div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> <span class="keyword">virtual</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_eta_factorization.html#aa4714584196a160a394ec3345b30ec03">~EtaFactorization</a>();</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">// Deletes all eta matrices.</span></div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_eta_factorization.html#aa71d36872f416feaa853788a7a7a7ef8">Clear</a>();</div>
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<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> </div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="comment">// Updates the eta factorization, i.e. adds the new eta matrix defined by</span></div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <span class="comment">// the leaving variable and the corresponding eta column.</span></div>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_eta_factorization.html#ae3aaa0f52a29f8a7b3f4550f97ca915d">Update</a>(ColIndex entering_col, RowIndex leaving_variable_row,</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_struct" href="structoperations__research_1_1glop_1_1_scattered_column.html">ScatteredColumn</a>& direction);</div>
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> </div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <span class="comment">// Left solves all systems from right to left, i.e. y_i = y_{i+1}.(E_i)^{-1}</span></div>
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_eta_factorization.html#a6b5f31c4068711b8e6823f4888f410ce">LeftSolve</a>(<a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseRow</a>* y) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> </div>
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<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> <span class="comment">// Same as LeftSolve(), but 'pos' contains the non-zero positions of c. The</span></div>
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <span class="comment">// order of the positions is not important, but there must be no duplicates.</span></div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <span class="comment">// The values not in 'pos' are not used. If eta_col_ was not already in 'pos',</span></div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> <span class="comment">// it is added.</span></div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_eta_factorization.html#ad1e32061321d5cc422c6f18a8ed6d33d">SparseLeftSolve</a>(<a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseRow</a>* y, <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a2b83a25cb4fd203c57a7155699fab246">ColIndexVector</a>* pos) <span class="keyword">const</span>;</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> <span class="comment">// Right solves all systems from left to right, i.e. E_i.d_{i+1} = d_i</span></div>
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_eta_factorization.html#a3cb026dc900190c13b208d24134755ed">RightSolve</a>(<a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>* d) <span class="keyword">const</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="keyword">private</span>:</div>
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<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> std::vector<EtaMatrix*> eta_matrix_;</div>
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<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> </div>
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> DISALLOW_COPY_AND_ASSIGN(<a class="code hl_class" href="classoperations__research_1_1glop_1_1_eta_factorization.html">EtaFactorization</a>);</div>
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<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span>};</div>
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<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> </div>
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<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span><span class="comment">// A basis factorization is the product of an eta factorization and</span></div>
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<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span><span class="comment">// a L.U decomposition, i.e. B = L.U.E_0.E_1. ... .E_{k-1}</span></div>
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<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span><span class="comment">// It is used to solve two systems:</span></div>
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<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span><span class="comment">// - B.d = a where a is the entering column.</span></div>
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<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span><span class="comment">// - y.B = c where c is the objective row.</span></div>
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<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span><span class="comment">//</span></div>
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<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span><span class="comment">// To speed-up and improve stability the factorization is refactorized at least</span></div>
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<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span><span class="comment">// every 'refactorization_period' updates.</span></div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span><span class="comment">//</span></div>
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span><span class="comment">// This class does not take ownership of the underlying matrix and basis, and</span></div>
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<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span><span class="comment">// thus they must outlive this class (and keep the same address in memory).</span></div>
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<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_basis_factorization.html"> 151</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1glop_1_1_basis_factorization.html">BasisFactorization</a> {</div>
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<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#a278dfa01552170d8e781c1b7e613479e">BasisFactorization</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="l00154" name="l00154"></a><span class="lineno"> 154</span> <span class="keyword">const</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="l00155" name="l00155"></a><span class="lineno"> 155</span> <span class="keyword">virtual</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#a90c2785b56a02a7d2e87b72cef43db9e">~BasisFactorization</a>();</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="comment">// Sets the parameters for this component.</span></div>
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<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_basis_factorization.html#ae7202d055b6b172a8a1da4f5b136f9ea"> 158</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#ae7202d055b6b172a8a1da4f5b136f9ea">SetParameters</a>(<span class="keyword">const</span> GlopParameters& <a class="code hl_variable" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>) {</div>
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<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> max_num_updates_ = <a class="code hl_variable" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>.basis_refactorization_period();</div>
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<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> use_middle_product_form_update_ =</div>
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<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> <a class="code hl_variable" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>.use_middle_product_form_update();</div>
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<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> parameters_ = <a class="code hl_variable" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>;</div>
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<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> lu_factorization_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#ae7202d055b6b172a8a1da4f5b136f9ea">SetParameters</a>(<a class="code hl_variable" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>);</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> </div>
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<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> <span class="comment">// Returns the column permutation used by the LU factorization.</span></div>
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<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> <span class="comment">// This call only makes sense if the basis was just refactorized.</span></div>
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<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_basis_factorization.html#a5a3deeb8998f541c08d96dc079591a54"> 168</a></span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_permutation.html">ColumnPermutation</a>& <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#a5a3deeb8998f541c08d96dc079591a54">GetColumnPermutation</a>()<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(<a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#a6e2a232672ee1580b9144f558662a77c">IsRefactorized</a>());</div>
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<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> <span class="keywordflow">return</span> lu_factorization_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#a5a3deeb8998f541c08d96dc079591a54">GetColumnPermutation</a>();</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> </div>
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<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> <span class="comment">// Sets the column permutation used by the LU factorization to the identity.</span></div>
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<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> <span class="comment">// Hense the Solve() results will be computed without this permutation.</span></div>
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<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> <span class="comment">// This call only makes sense if the basis was just refactorized.</span></div>
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<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_basis_factorization.html#ad91a397910de30b87b9fb45298fa5c58"> 176</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#ad91a397910de30b87b9fb45298fa5c58">SetColumnPermutationToIdentity</a>() {</div>
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<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(<a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#a6e2a232672ee1580b9144f558662a77c">IsRefactorized</a>());</div>
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<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> lu_factorization_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#ad91a397910de30b87b9fb45298fa5c58">SetColumnPermutationToIdentity</a>();</div>
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<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> }</div>
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<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> </div>
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<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> <span class="comment">// Clears the factorization and resets it to an identity matrix of size given</span></div>
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<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> <span class="comment">// by matrix_.num_rows().</span></div>
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<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#aa71d36872f416feaa853788a7a7a7ef8">Clear</a>();</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="comment">// Clears the factorization and initializes the class using the current</span></div>
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<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> <span class="comment">// matrix_ and basis_. This is fast if IsIdentityBasis() is true, otherwise</span></div>
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<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> <span class="comment">// it will trigger a refactorization and will return an error if the matrix</span></div>
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<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> <span class="comment">// could not be factorized.</span></div>
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<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> ABSL_MUST_USE_RESULT <a class="code hl_class" href="classoperations__research_1_1glop_1_1_status.html">Status</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#a697f638cbd5a2dab2977b24e550bd7f9">Initialize</a>();</div>
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<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> </div>
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<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> <span class="comment">// This mainly forward the call to LuFactorization::ComputeInitialBasis().</span></div>
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<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> <span class="comment">// Note that once this is called, one would need to call Initialize() to</span></div>
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<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> <span class="comment">// actually create the factorization. The only side effect of this is to</span></div>
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<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> <span class="comment">// update the deterministic time.</span></div>
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<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> <span class="comment">// TODO(user): This "double" factorization is a bit inefficient, and we should</span></div>
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<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> <span class="comment">// probably Initialize() right away the factorization with the new basis, but</span></div>
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<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> <span class="comment">// more code is needed for that. It is also not that easy also because we want</span></div>
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<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> <span class="comment">// to permute all the added slack first.</span></div>
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<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">RowToColMapping</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#aac85dc71bb2e4980043fd2da3b8ee8cf">ComputeInitialBasis</a>(<span class="keyword">const</span> std::vector<ColIndex>& candidates);</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="comment">// Return the number of rows in the basis.</span></div>
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<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_basis_factorization.html#ae1d8c3228cb8e036c1d8ab67336a7d2f"> 204</a></span> RowIndex <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#ae1d8c3228cb8e036c1d8ab67336a7d2f">GetNumberOfRows</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> 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="l00205" name="l00205"></a><span class="lineno"> 205</span> </div>
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<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> <span class="comment">// Clears eta factorization and refactorizes LU.</span></div>
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<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> <span class="comment">// Nothing happens if this is called on an already refactorized basis.</span></div>
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<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> <span class="comment">// Returns an error if the matrix could not be factorized: i.e. not a basis.</span></div>
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<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> ABSL_MUST_USE_RESULT <a class="code hl_class" href="classoperations__research_1_1glop_1_1_status.html">Status</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#a39b7e347f32f4024a988cb93f5e81a2d">Refactorize</a>();</div>
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<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> </div>
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<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> <span class="comment">// Like Refactorize(), but do it even if IsRefactorized() is true.</span></div>
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<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> <span class="comment">// Call this if the underlying basis_ changed and Update() wasn't called.</span></div>
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<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> ABSL_MUST_USE_RESULT <a class="code hl_class" href="classoperations__research_1_1glop_1_1_status.html">Status</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#aedf255db8741ebb2011757ff37dfc02e">ForceRefactorization</a>();</div>
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<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> </div>
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<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> <span class="comment">// Returns true if the factorization was just recomputed.</span></div>
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<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> <span class="keywordtype">bool</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#a6e2a232672ee1580b9144f558662a77c">IsRefactorized</a>() <span class="keyword">const</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> <span class="comment">// Updates the factorization. The 'eta' column will be modified with a swap to</span></div>
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<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> <span class="comment">// avoid a copy (only if the standard eta update is used). Returns an error if</span></div>
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<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> <span class="comment">// the matrix could not be factorized: i.e. not a basis.</span></div>
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<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> ABSL_MUST_USE_RESULT <a class="code hl_class" href="classoperations__research_1_1glop_1_1_status.html">Status</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#a87e6110ce2612a27f85e9036afef1599">Update</a>(ColIndex entering_col,</div>
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<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> RowIndex leaving_variable_row,</div>
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<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span> <span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_column.html">ScatteredColumn</a>& direction);</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="comment">// Left solves the system y.B = rhs, where y initially contains rhs.</span></div>
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<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#aacdbeb58ac2d391f6586ad88db99ad61">LeftSolve</a>(<a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_row.html">ScatteredRow</a>* y) <span class="keyword">const</span>;</div>
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<div class="line"><a id="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="comment">// Left solves the system y.B = e_j, where e_j has only 1 non-zero</span></div>
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<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> <span class="comment">// coefficient of value 1.0 at position 'j'.</span></div>
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<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#a41b0509864e6eb62f0415975a914ba4b">LeftSolveForUnitRow</a>(ColIndex j, <a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_row.html">ScatteredRow</a>* y) <span class="keyword">const</span>;</div>
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<div class="line"><a id="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">// Same as LeftSolveForUnitRow() but does not update any internal data.</span></div>
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<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#a781d7728c278ae44bf265cf222479b98">TemporaryLeftSolveForUnitRow</a>(ColIndex j, <a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_row.html">ScatteredRow</a>* y) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span> </div>
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<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> <span class="comment">// Right solves the system B.d = a where the input is the initial value of d.</span></div>
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<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#aeaeb43840844cc69a88dc924b282b4c7">RightSolve</a>(<a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_column.html">ScatteredColumn</a>* d) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span> </div>
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<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span> <span class="comment">// Same as RightSolve() for matrix.column(col). This also exploits its</span></div>
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<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> <span class="comment">// sparsity.</span></div>
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<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#ab9de0c21968ffad6320a44a010e33e07">RightSolveForProblemColumn</a>(ColIndex <a class="code hl_variable" href="markowitz_8cc.html#aa9d6c98fdf8d89b0e2321fda02adc82c">col</a>, <a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_column.html">ScatteredColumn</a>* d) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> </div>
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<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span> <span class="comment">// Specialized version for ComputeTau() in DualEdgeNorms. This reuses an</span></div>
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<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span> <span class="comment">// intermediate result of the last LeftSolveForUnitRow() in order to save a</span></div>
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<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span> <span class="comment">// permutation if it is available. Note that the input 'a' should always be</span></div>
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<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> <span class="comment">// equal to the last result of LeftSolveForUnitRow() and will be used for a</span></div>
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<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> <span class="comment">// DCHECK() or if the intermediate result wasn't kept.</span></div>
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<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">DenseColumn</a>& <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#a405547c96cca2eded0c29941a3ff7f22">RightSolveForTau</a>(<span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_column.html">ScatteredColumn</a>& <a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>) <span class="keyword">const</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="comment">// Returns the norm of B^{-1}.a, this is a specific function because</span></div>
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<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> <span class="comment">// it is a bit faster and it avoids polluting the stats of RightSolve().</span></div>
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<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> <span class="comment">// It can be called only when IsRefactorized() is true.</span></div>
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<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#a4bf241af6b1844669171d6e170ef991d">RightSolveSquaredNorm</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_column_view.html">ColumnView</a>& <a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>) <span class="keyword">const</span>;</div>
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<div class="line"><a id="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> <span class="comment">// Returns the norm of (B^T)^{-1}.e_row where e is an unit vector.</span></div>
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<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> <span class="comment">// This is a bit faster and avoids polluting the stats of LeftSolve().</span></div>
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<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> <span class="comment">// It can be called only when IsRefactorized() is true.</span></div>
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<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#a9b738f6b485a4d4ef866b8d82ac07876">DualEdgeSquaredNorm</a>(RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> </div>
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<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> <span class="comment">// Computes the condition number of B.</span></div>
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<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span> <span class="comment">// For a given norm, this is the matrix norm times the norm of its inverse.</span></div>
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<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> <span class="comment">// A condition number greater than 1E7 will lead to precision problems.</span></div>
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<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#a6748ce52d80c6013d4edfc77d56b96f8">ComputeOneNormConditionNumber</a>() <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#abcfadeef96ab0ef83b82cf0046a45dd7">ComputeInfinityNormConditionNumber</a>() <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#a2ac7d8b80f20a8442138b0673aa0158c">ComputeInfinityNormConditionNumberUpperBound</a>() <span class="keyword">const</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">// Computes the 1-norm of B.</span></div>
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<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span> <span class="comment">// The 1-norm |A| is defined as max_j sum_i |a_ij|</span></div>
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<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span> <span class="comment">// http://en.wikipedia.org/wiki/Matrix_norm</span></div>
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<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#a64fea3282d498f3eb2d4af70692bb117">ComputeOneNorm</a>() <span class="keyword">const</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> <span class="comment">// Computes the infinity-norm of B.</span></div>
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<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span> <span class="comment">// The infinity-norm |A| is defined as max_i sum_j |a_ij|</span></div>
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<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> <span class="comment">// http://en.wikipedia.org/wiki/Matrix_norm</span></div>
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<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#a3f219a081f88c22ae282ada4f0bdddd3">ComputeInfinityNorm</a>() <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span> </div>
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<div class="line"><a id="l00276" name="l00276"></a><span class="lineno"> 276</span> <span class="comment">// Computes the 1-norm of the inverse of B.</span></div>
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<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span> <span class="comment">// For this we iteratively solve B.x = e_j, where e_j is the jth unit vector.</span></div>
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<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span> <span class="comment">// The result of this computation is the jth column of B^-1.</span></div>
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<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"> 279</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#a05d6979828b99ac719553f75335a1937">ComputeInverseOneNorm</a>() <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"> 280</span> </div>
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<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</span> <span class="comment">// Computes the infinity-norm of the inverse of B.</span></div>
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<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#a3a6bb95b9009b1c578a27e6139d52696">ComputeInverseInfinityNorm</a>() <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span> </div>
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<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span> <span class="comment">// Stats related function.</span></div>
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<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span> <span class="comment">// Note that ResetStats() could be const, but until needed it is not to</span></div>
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<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</span> <span class="comment">// prevent anyone holding a const BasisFactorization& to call it.</span></div>
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<div class="line"><a id="l00287" name="l00287"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_basis_factorization.html#af9bc435481ae9e6e60d66a65d5394a7f"> 287</a></span> std::string <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#af9bc435481ae9e6e60d66a65d5394a7f">StatString</a>()<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00288" name="l00288"></a><span class="lineno"> 288</span> <span class="keywordflow">return</span> stats_.StatString() + lu_factorization_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_lu_factorization.html#af9bc435481ae9e6e60d66a65d5394a7f">StatString</a>();</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"><a class="line" href="classoperations__research_1_1glop_1_1_basis_factorization.html#aecf3e3d1e43ed7f9b67b3a919d24f17f"> 290</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#aecf3e3d1e43ed7f9b67b3a919d24f17f">ResetStats</a>() { stats_.Reset(); }</div>
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<div class="line"><a id="l00291" name="l00291"></a><span class="lineno"> 291</span> </div>
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<div class="line"><a id="l00292" name="l00292"></a><span class="lineno"> 292</span> <span class="comment">// The deterministic time used by this class. It is incremented for each</span></div>
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<div class="line"><a id="l00293" name="l00293"></a><span class="lineno"> 293</span> <span class="comment">// solve and each factorization.</span></div>
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<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#aeccc8138b268e621d96d105e0ddd474a">DeterministicTime</a>() <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00295" name="l00295"></a><span class="lineno"> 295</span> </div>
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<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span> <span class="keyword">private</span>:</div>
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<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span> <span class="comment">// Called by ForceRefactorization() or Refactorize() or Initialize().</span></div>
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<div class="line"><a id="l00298" name="l00298"></a><span class="lineno"> 298</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_status.html">Status</a> ComputeFactorization();</div>
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<div class="line"><a id="l00299" name="l00299"></a><span class="lineno"> 299</span> </div>
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<div class="line"><a id="l00300" name="l00300"></a><span class="lineno"> 300</span> <span class="comment">// Return true if the submatrix of matrix_ given by basis_ is exactly the</span></div>
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<div class="line"><a id="l00301" name="l00301"></a><span class="lineno"> 301</span> <span class="comment">// identity (without permutation).</span></div>
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<div class="line"><a id="l00302" name="l00302"></a><span class="lineno"> 302</span> <span class="keywordtype">bool</span> IsIdentityBasis() <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00303" name="l00303"></a><span class="lineno"> 303</span> </div>
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<div class="line"><a id="l00304" name="l00304"></a><span class="lineno"> 304</span> <span class="comment">// Updates the factorization using the middle product form update.</span></div>
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<div class="line"><a id="l00305" name="l00305"></a><span class="lineno"> 305</span> <span class="comment">// Qi Huangfu, J. A. Julian Hall, "Novel update techniques for the revised</span></div>
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<div class="line"><a id="l00306" name="l00306"></a><span class="lineno"> 306</span> <span class="comment">// simplex method", 28 january 2013, Technical Report ERGO-13-0001</span></div>
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<div class="line"><a id="l00307" name="l00307"></a><span class="lineno"> 307</span> ABSL_MUST_USE_RESULT <a class="code hl_class" href="classoperations__research_1_1glop_1_1_status.html">Status</a></div>
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<div class="line"><a id="l00308" name="l00308"></a><span class="lineno"> 308</span> MiddleProductFormUpdate(ColIndex entering_col, RowIndex leaving_variable_row);</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="comment">// Increases the deterministic time for a solve operation with a vector having</span></div>
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<div class="line"><a id="l00311" name="l00311"></a><span class="lineno"> 311</span> <span class="comment">// this number of non-zero entries (it can be an approximation).</span></div>
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<div class="line"><a id="l00312" name="l00312"></a><span class="lineno"> 312</span> <span class="keywordtype">void</span> BumpDeterministicTimeForSolve(<span class="keywordtype">int</span> <a class="code hl_variable" href="preprocessor_8cc.html#a2babe18010525bbf13c2fa5a959971e4">num_entries</a>) <span class="keyword">const</span>;</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> <span class="comment">// Stats about this class.</span></div>
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<div class="line"><a id="l00315" name="l00315"></a><span class="lineno"> 315</span> <span class="keyword">struct </span>Stats : <span class="keyword">public</span> <a class="code hl_class" href="classoperations__research_1_1_stats_group.html">StatsGroup</a> {</div>
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<div class="line"><a id="l00316" name="l00316"></a><span class="lineno"> 316</span> Stats()</div>
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<div class="line"><a id="l00317" name="l00317"></a><span class="lineno"> 317</span> : <a class="code hl_class" href="classoperations__research_1_1_stats_group.html">StatsGroup</a>(<span class="stringliteral">"BasisFactorization"</span>),</div>
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<div class="line"><a id="l00318" name="l00318"></a><span class="lineno"> 318</span> refactorization_interval(<span class="stringliteral">"refactorization_interval"</span>, this) {}</div>
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<div class="line"><a id="l00319" name="l00319"></a><span class="lineno"> 319</span> <a class="code hl_class" href="classoperations__research_1_1_integer_distribution.html">IntegerDistribution</a> refactorization_interval;</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">// Mutable because we track the running time of const method like</span></div>
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<div class="line"><a id="l00323" name="l00323"></a><span class="lineno"> 323</span> <span class="comment">// RightSolve() and LeftSolve().</span></div>
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<div class="line"><a id="l00324" name="l00324"></a><span class="lineno"> 324</span> <span class="keyword">mutable</span> Stats stats_;</div>
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<div class="line"><a id="l00325" name="l00325"></a><span class="lineno"> 325</span> GlopParameters parameters_;</div>
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<div class="line"><a id="l00326" name="l00326"></a><span class="lineno"> 326</span> </div>
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<div class="line"><a id="l00327" name="l00327"></a><span class="lineno"> 327</span> <span class="comment">// References to the basis subpart of the linear program matrix.</span></div>
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<div class="line"><a id="l00328" name="l00328"></a><span class="lineno"> 328</span> <span class="keyword">const</span> CompactSparseMatrix& compact_matrix_;</div>
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<div class="line"><a id="l00329" name="l00329"></a><span class="lineno"> 329</span> <span class="keyword">const</span> <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="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> <span class="comment">// Middle form product update factorization and scratchpad_ used to construct</span></div>
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<div class="line"><a id="l00332" name="l00332"></a><span class="lineno"> 332</span> <span class="comment">// new rank one matrices.</span></div>
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<div class="line"><a id="l00333" name="l00333"></a><span class="lineno"> 333</span> RankOneUpdateFactorization rank_one_factorization_;</div>
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<div class="line"><a id="l00334" name="l00334"></a><span class="lineno"> 334</span> <span class="keyword">mutable</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#ae5fa9e57c2d31b294195ed8a9e17bfac">DenseColumn</a> scratchpad_;</div>
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<div class="line"><a id="l00335" name="l00335"></a><span class="lineno"> 335</span> <span class="keyword">mutable</span> std::vector<RowIndex> scratchpad_non_zeros_;</div>
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<div class="line"><a id="l00336" name="l00336"></a><span class="lineno"> 336</span> </div>
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<div class="line"><a id="l00337" name="l00337"></a><span class="lineno"> 337</span> <span class="comment">// This is used by RightSolveForTau(). It holds an intermediate result from</span></div>
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<div class="line"><a id="l00338" name="l00338"></a><span class="lineno"> 338</span> <span class="comment">// the last LeftSolveForUnitRow() and also the final result of</span></div>
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<div class="line"><a id="l00339" name="l00339"></a><span class="lineno"> 339</span> <span class="comment">// RightSolveForTau().</span></div>
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<div class="line"><a id="l00340" name="l00340"></a><span class="lineno"> 340</span> <span class="keyword">mutable</span> ScatteredColumn tau_;</div>
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<div class="line"><a id="l00341" name="l00341"></a><span class="lineno"> 341</span> </div>
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<div class="line"><a id="l00342" name="l00342"></a><span class="lineno"> 342</span> <span class="comment">// Booleans controlling the interaction between LeftSolveForUnitRow() that may</span></div>
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<div class="line"><a id="l00343" name="l00343"></a><span class="lineno"> 343</span> <span class="comment">// or may not keep its intermediate results for the optimized</span></div>
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<div class="line"><a id="l00344" name="l00344"></a><span class="lineno"> 344</span> <span class="comment">// RightSolveForTau().</span></div>
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<div class="line"><a id="l00345" name="l00345"></a><span class="lineno"> 345</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00346" name="l00346"></a><span class="lineno"> 346</span> <span class="comment">// tau_computation_can_be_optimized_ will be true iff LeftSolveForUnitRow()</span></div>
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<div class="line"><a id="l00347" name="l00347"></a><span class="lineno"> 347</span> <span class="comment">// kept its intermediate result when it was called and the factorization</span></div>
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<div class="line"><a id="l00348" name="l00348"></a><span class="lineno"> 348</span> <span class="comment">// didn't change since then. If it is true, then RightSolveForTau() can use</span></div>
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<div class="line"><a id="l00349" name="l00349"></a><span class="lineno"> 349</span> <span class="comment">// this result for a faster computation.</span></div>
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<div class="line"><a id="l00350" name="l00350"></a><span class="lineno"> 350</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00351" name="l00351"></a><span class="lineno"> 351</span> <span class="comment">// tau_is_computed_ is used as an heuristic by LeftSolveForUnitRow() to decide</span></div>
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<div class="line"><a id="l00352" name="l00352"></a><span class="lineno"> 352</span> <span class="comment">// if it is worth keeping its intermediate result (which is sligthly slower).</span></div>
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<div class="line"><a id="l00353" name="l00353"></a><span class="lineno"> 353</span> <span class="comment">// It is simply set to true by RightSolveForTau() and to false by</span></div>
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<div class="line"><a id="l00354" name="l00354"></a><span class="lineno"> 354</span> <span class="comment">// LeftSolveForUnitRow(), this way the optimization will automatically switch</span></div>
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<div class="line"><a id="l00355" name="l00355"></a><span class="lineno"> 355</span> <span class="comment">// itself on when switching from the primal simplex (where RightSolveForTau()</span></div>
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<div class="line"><a id="l00356" name="l00356"></a><span class="lineno"> 356</span> <span class="comment">// is never called) to the dual where it is called after each</span></div>
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<div class="line"><a id="l00357" name="l00357"></a><span class="lineno"> 357</span> <span class="comment">// LeftSolveForUnitRow(), and back off again in the other direction.</span></div>
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<div class="line"><a id="l00358" name="l00358"></a><span class="lineno"> 358</span> <span class="keyword">mutable</span> <span class="keywordtype">bool</span> tau_computation_can_be_optimized_;</div>
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<div class="line"><a id="l00359" name="l00359"></a><span class="lineno"> 359</span> <span class="keyword">mutable</span> <span class="keywordtype">bool</span> tau_is_computed_;</div>
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<div class="line"><a id="l00360" name="l00360"></a><span class="lineno"> 360</span> </div>
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<div class="line"><a id="l00361" name="l00361"></a><span class="lineno"> 361</span> <span class="comment">// Data structure to store partial solve results for the middle form product</span></div>
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<div class="line"><a id="l00362" name="l00362"></a><span class="lineno"> 362</span> <span class="comment">// update. See LeftSolveForUnitRow() and RightSolveForProblemColumn(). We use</span></div>
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<div class="line"><a id="l00363" name="l00363"></a><span class="lineno"> 363</span> <span class="comment">// two CompactSparseMatrix to have a better cache behavior when solving with</span></div>
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<div class="line"><a id="l00364" name="l00364"></a><span class="lineno"> 364</span> <span class="comment">// the rank_one_factorization_.</span></div>
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<div class="line"><a id="l00365" name="l00365"></a><span class="lineno"> 365</span> <span class="keyword">mutable</span> CompactSparseMatrix storage_;</div>
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<div class="line"><a id="l00366" name="l00366"></a><span class="lineno"> 366</span> <span class="keyword">mutable</span> CompactSparseMatrix right_storage_;</div>
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<div class="line"><a id="l00367" name="l00367"></a><span class="lineno"> 367</span> <span class="keyword">mutable</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#afa7534bb8eff64b643c6079dc82e5e3c">ColMapping</a> left_pool_mapping_;</div>
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<div class="line"><a id="l00368" name="l00368"></a><span class="lineno"> 368</span> <span class="keyword">mutable</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#afa7534bb8eff64b643c6079dc82e5e3c">ColMapping</a> right_pool_mapping_;</div>
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<div class="line"><a id="l00369" name="l00369"></a><span class="lineno"> 369</span> </div>
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<div class="line"><a id="l00370" name="l00370"></a><span class="lineno"> 370</span> <span class="keywordtype">bool</span> use_middle_product_form_update_;</div>
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<div class="line"><a id="l00371" name="l00371"></a><span class="lineno"> 371</span> <span class="keywordtype">int</span> max_num_updates_;</div>
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<div class="line"><a id="l00372" name="l00372"></a><span class="lineno"> 372</span> <span class="keywordtype">int</span> num_updates_;</div>
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<div class="line"><a id="l00373" name="l00373"></a><span class="lineno"> 373</span> EtaFactorization eta_factorization_;</div>
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<div class="line"><a id="l00374" name="l00374"></a><span class="lineno"> 374</span> LuFactorization lu_factorization_;</div>
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<div class="line"><a id="l00375" name="l00375"></a><span class="lineno"> 375</span> </div>
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<div class="line"><a id="l00376" name="l00376"></a><span class="lineno"> 376</span> <span class="comment">// mutable because the Solve() functions are const but need to update this.</span></div>
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<div class="line"><a id="l00377" name="l00377"></a><span class="lineno"> 377</span> <span class="keywordtype">double</span> last_factorization_deterministic_time_ = 0.0;</div>
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<div class="line"><a id="l00378" name="l00378"></a><span class="lineno"> 378</span> <span class="keyword">mutable</span> <span class="keywordtype">double</span> deterministic_time_;</div>
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<div class="line"><a id="l00379" name="l00379"></a><span class="lineno"> 379</span> </div>
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<div class="line"><a id="l00380" name="l00380"></a><span class="lineno"> 380</span> DISALLOW_COPY_AND_ASSIGN(<a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#a278dfa01552170d8e781c1b7e613479e">BasisFactorization</a>);</div>
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<div class="line"><a id="l00381" name="l00381"></a><span class="lineno"> 381</span>};</div>
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<div class="line"><a id="l00382" name="l00382"></a><span class="lineno"> 382</span> </div>
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<div class="line"><a id="l00383" name="l00383"></a><span class="lineno"> 383</span>} <span class="comment">// namespace glop</span></div>
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<div class="line"><a id="l00384" name="l00384"></a><span class="lineno"> 384</span>} <span class="comment">// namespace operations_research</span></div>
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<div class="line"><a id="l00385" name="l00385"></a><span class="lineno"> 385</span> </div>
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<div class="line"><a id="l00386" name="l00386"></a><span class="lineno"> 386</span><span class="preprocessor">#endif </span><span class="comment">// OR_TOOLS_GLOP_BASIS_REPRESENTATION_H_</span></div>
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<div class="ttc" id="abase_2logging_8h_html"><div class="ttname"><a href="base_2logging_8h.html">logging.h</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_ae17f8119c108cf3070bad3449c7e0006"><div class="ttname"><a href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a></div><div class="ttdeci">#define DCHECK(condition)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00890">base/logging.h:890</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_integer_distribution_html"><div class="ttname"><a href="classoperations__research_1_1_integer_distribution.html">operations_research::IntegerDistribution</a></div><div class="ttdef"><b>Definition:</b> <a href="stats_8h_source.html#l00287">stats.h:287</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_stats_group_html"><div class="ttname"><a href="classoperations__research_1_1_stats_group.html">operations_research::StatsGroup</a></div><div class="ttdef"><b>Definition:</b> <a href="stats_8h_source.html#l00131">stats.h:131</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html">operations_research::glop::BasisFactorization</a></div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8h_source.html#l00151">basis_representation.h:151</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_a05d6979828b99ac719553f75335a1937"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#a05d6979828b99ac719553f75335a1937">operations_research::glop::BasisFactorization::ComputeInverseOneNorm</a></div><div class="ttdeci">Fractional ComputeInverseOneNorm() const</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00540">basis_representation.cc:540</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_a278dfa01552170d8e781c1b7e613479e"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#a278dfa01552170d8e781c1b7e613479e">operations_research::glop::BasisFactorization::BasisFactorization</a></div><div class="ttdeci">BasisFactorization(const CompactSparseMatrix *compact_matrix, const RowToColMapping *basis)</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00177">basis_representation.cc:177</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_a2ac7d8b80f20a8442138b0673aa0158c"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#a2ac7d8b80f20a8442138b0673aa0158c">operations_research::glop::BasisFactorization::ComputeInfinityNormConditionNumberUpperBound</a></div><div class="ttdeci">Fractional ComputeInfinityNormConditionNumberUpperBound() const</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00596">basis_representation.cc:596</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_a39b7e347f32f4024a988cb93f5e81a2d"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#a39b7e347f32f4024a988cb93f5e81a2d">operations_research::glop::BasisFactorization::Refactorize</a></div><div class="ttdeci">ABSL_MUST_USE_RESULT Status Refactorize()</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00224">basis_representation.cc:224</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_a3a6bb95b9009b1c578a27e6139d52696"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#a3a6bb95b9009b1c578a27e6139d52696">operations_research::glop::BasisFactorization::ComputeInverseInfinityNorm</a></div><div class="ttdeci">Fractional ComputeInverseInfinityNorm() const</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00562">basis_representation.cc:562</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_a3f219a081f88c22ae282ada4f0bdddd3"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#a3f219a081f88c22ae282ada4f0bdddd3">operations_research::glop::BasisFactorization::ComputeInfinityNorm</a></div><div class="ttdeci">Fractional ComputeInfinityNorm() const</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00531">basis_representation.cc:531</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_a405547c96cca2eded0c29941a3ff7f22"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#a405547c96cca2eded0c29941a3ff7f22">operations_research::glop::BasisFactorization::RightSolveForTau</a></div><div class="ttdeci">const DenseColumn & RightSolveForTau(const ScatteredColumn &a) const</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00369">basis_representation.cc:369</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_a41b0509864e6eb62f0415975a914ba4b"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#a41b0509864e6eb62f0415975a914ba4b">operations_research::glop::BasisFactorization::LeftSolveForUnitRow</a></div><div class="ttdeci">void LeftSolveForUnitRow(ColIndex j, ScatteredRow *y) const</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00395">basis_representation.cc:395</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_a4bf241af6b1844669171d6e170ef991d"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#a4bf241af6b1844669171d6e170ef991d">operations_research::glop::BasisFactorization::RightSolveSquaredNorm</a></div><div class="ttdeci">Fractional RightSolveSquaredNorm(const ColumnView &a) const</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00498">basis_representation.cc:498</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_a5a3deeb8998f541c08d96dc079591a54"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#a5a3deeb8998f541c08d96dc079591a54">operations_research::glop::BasisFactorization::GetColumnPermutation</a></div><div class="ttdeci">const ColumnPermutation & GetColumnPermutation() const</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8h_source.html#l00168">basis_representation.h:168</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_a64fea3282d498f3eb2d4af70692bb117"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#a64fea3282d498f3eb2d4af70692bb117">operations_research::glop::BasisFactorization::ComputeOneNorm</a></div><div class="ttdeci">Fractional ComputeOneNorm() const</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00525">basis_representation.cc:525</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_a6748ce52d80c6013d4edfc77d56b96f8"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#a6748ce52d80c6013d4edfc77d56b96f8">operations_research::glop::BasisFactorization::ComputeOneNormConditionNumber</a></div><div class="ttdeci">Fractional ComputeOneNormConditionNumber() const</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00586">basis_representation.cc:586</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_a697f638cbd5a2dab2977b24e550bd7f9"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#a697f638cbd5a2dab2977b24e550bd7f9">operations_research::glop::BasisFactorization::Initialize</a></div><div class="ttdeci">ABSL_MUST_USE_RESULT Status Initialize()</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00206">basis_representation.cc:206</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_a6e2a232672ee1580b9144f558662a77c"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#a6e2a232672ee1580b9144f558662a77c">operations_research::glop::BasisFactorization::IsRefactorized</a></div><div class="ttdeci">bool IsRefactorized() const</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00222">basis_representation.cc:222</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_a781d7728c278ae44bf265cf222479b98"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#a781d7728c278ae44bf265cf222479b98">operations_research::glop::BasisFactorization::TemporaryLeftSolveForUnitRow</a></div><div class="ttdeci">void TemporaryLeftSolveForUnitRow(ColIndex j, ScatteredRow *y) const</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00450">basis_representation.cc:450</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_a87e6110ce2612a27f85e9036afef1599"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#a87e6110ce2612a27f85e9036afef1599">operations_research::glop::BasisFactorization::Update</a></div><div class="ttdeci">ABSL_MUST_USE_RESULT Status Update(ColIndex entering_col, RowIndex leaving_variable_row, const ScatteredColumn &direction)</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00299">basis_representation.cc:299</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_a90c2785b56a02a7d2e87b72cef43db9e"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#a90c2785b56a02a7d2e87b72cef43db9e">operations_research::glop::BasisFactorization::~BasisFactorization</a></div><div class="ttdeci">virtual ~BasisFactorization()</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00191">basis_representation.cc:191</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_a9b738f6b485a4d4ef866b8d82ac07876"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#a9b738f6b485a4d4ef866b8d82ac07876">operations_research::glop::BasisFactorization::DualEdgeSquaredNorm</a></div><div class="ttdeci">Fractional DualEdgeSquaredNorm(RowIndex row) const</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00506">basis_representation.cc:506</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_aa71d36872f416feaa853788a7a7a7ef8"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#aa71d36872f416feaa853788a7a7a7ef8">operations_research::glop::BasisFactorization::Clear</a></div><div class="ttdeci">void Clear()</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00193">basis_representation.cc:193</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_aac85dc71bb2e4980043fd2da3b8ee8cf"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#aac85dc71bb2e4980043fd2da3b8ee8cf">operations_research::glop::BasisFactorization::ComputeInitialBasis</a></div><div class="ttdeci">RowToColMapping ComputeInitialBasis(const std::vector< ColIndex > &candidates)</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00213">basis_representation.cc:213</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_aacdbeb58ac2d391f6586ad88db99ad61"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#aacdbeb58ac2d391f6586ad88db99ad61">operations_research::glop::BasisFactorization::LeftSolve</a></div><div class="ttdeci">void LeftSolve(ScatteredRow *y) const</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00337">basis_representation.cc:337</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_ab9de0c21968ffad6320a44a010e33e07"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#ab9de0c21968ffad6320a44a010e33e07">operations_research::glop::BasisFactorization::RightSolveForProblemColumn</a></div><div class="ttdeci">void RightSolveForProblemColumn(ColIndex col, ScatteredColumn *d) const</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00463">basis_representation.cc:463</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_abcfadeef96ab0ef83b82cf0046a45dd7"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#abcfadeef96ab0ef83b82cf0046a45dd7">operations_research::glop::BasisFactorization::ComputeInfinityNormConditionNumber</a></div><div class="ttdeci">Fractional ComputeInfinityNormConditionNumber() const</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00591">basis_representation.cc:591</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_ad91a397910de30b87b9fb45298fa5c58"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#ad91a397910de30b87b9fb45298fa5c58">operations_research::glop::BasisFactorization::SetColumnPermutationToIdentity</a></div><div class="ttdeci">void SetColumnPermutationToIdentity()</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8h_source.html#l00176">basis_representation.h:176</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_ae1d8c3228cb8e036c1d8ab67336a7d2f"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#ae1d8c3228cb8e036c1d8ab67336a7d2f">operations_research::glop::BasisFactorization::GetNumberOfRows</a></div><div class="ttdeci">RowIndex GetNumberOfRows() const</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8h_source.html#l00204">basis_representation.h:204</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_ae7202d055b6b172a8a1da4f5b136f9ea"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#ae7202d055b6b172a8a1da4f5b136f9ea">operations_research::glop::BasisFactorization::SetParameters</a></div><div class="ttdeci">void SetParameters(const GlopParameters &parameters)</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8h_source.html#l00158">basis_representation.h:158</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_aeaeb43840844cc69a88dc924b282b4c7"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#aeaeb43840844cc69a88dc924b282b4c7">operations_research::glop::BasisFactorization::RightSolve</a></div><div class="ttdeci">void RightSolve(ScatteredColumn *d) const</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00353">basis_representation.cc:353</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_aeccc8138b268e621d96d105e0ddd474a"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#aeccc8138b268e621d96d105e0ddd474a">operations_research::glop::BasisFactorization::DeterministicTime</a></div><div class="ttdeci">double DeterministicTime() const</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00604">basis_representation.cc:604</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_aecf3e3d1e43ed7f9b67b3a919d24f17f"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#aecf3e3d1e43ed7f9b67b3a919d24f17f">operations_research::glop::BasisFactorization::ResetStats</a></div><div class="ttdeci">void ResetStats()</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8h_source.html#l00290">basis_representation.h:290</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_aedf255db8741ebb2011757ff37dfc02e"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#aedf255db8741ebb2011757ff37dfc02e">operations_research::glop::BasisFactorization::ForceRefactorization</a></div><div class="ttdeci">ABSL_MUST_USE_RESULT Status ForceRefactorization()</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00229">basis_representation.cc:229</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_basis_factorization_html_af9bc435481ae9e6e60d66a65d5394a7f"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_basis_factorization.html#af9bc435481ae9e6e60d66a65d5394a7f">operations_research::glop::BasisFactorization::StatString</a></div><div class="ttdeci">std::string StatString() const</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8h_source.html#l00287">basis_representation.h:287</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_column_view_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_column_view.html">operations_research::glop::ColumnView</a></div><div class="ttdef"><b>Definition:</b> <a href="sparse__column_8h_source.html#l00065">sparse_column.h:65</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_compact_sparse_matrix.html">operations_research::glop::CompactSparseMatrix</a></div><div class="ttdef"><b>Definition:</b> <a href="sparse_8h_source.html#l00289">sparse.h:289</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_compact_sparse_matrix_html_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_eta_factorization_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_eta_factorization.html">operations_research::glop::EtaFactorization</a></div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8h_source.html#l00109">basis_representation.h:109</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_eta_factorization_html_a3cb026dc900190c13b208d24134755ed"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_eta_factorization.html#a3cb026dc900190c13b208d24134755ed">operations_research::glop::EtaFactorization::RightSolve</a></div><div class="ttdeci">void RightSolve(DenseColumn *d) const</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00166">basis_representation.cc:166</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_eta_factorization_html_a6b5f31c4068711b8e6823f4888f410ce"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_eta_factorization.html#a6b5f31c4068711b8e6823f4888f410ce">operations_research::glop::EtaFactorization::LeftSolve</a></div><div class="ttdeci">void LeftSolve(DenseRow *y) const</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00152">basis_representation.cc:152</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_eta_factorization_html_aa4714584196a160a394ec3345b30ec03"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_eta_factorization.html#aa4714584196a160a394ec3345b30ec03">operations_research::glop::EtaFactorization::~EtaFactorization</a></div><div class="ttdeci">virtual ~EtaFactorization()</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00139">basis_representation.cc:139</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_eta_factorization_html_aa71d36872f416feaa853788a7a7a7ef8"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_eta_factorization.html#aa71d36872f416feaa853788a7a7a7ef8">operations_research::glop::EtaFactorization::Clear</a></div><div class="ttdeci">void Clear()</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00141">basis_representation.cc:141</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_eta_factorization_html_acddc81707ff8e60f4ab42b3c21939be6"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_eta_factorization.html#acddc81707ff8e60f4ab42b3c21939be6">operations_research::glop::EtaFactorization::EtaFactorization</a></div><div class="ttdeci">EtaFactorization()</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00137">basis_representation.cc:137</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_eta_factorization_html_ad1e32061321d5cc422c6f18a8ed6d33d"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_eta_factorization.html#ad1e32061321d5cc422c6f18a8ed6d33d">operations_research::glop::EtaFactorization::SparseLeftSolve</a></div><div class="ttdeci">void SparseLeftSolve(DenseRow *y, ColIndexVector *pos) const</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00159">basis_representation.cc:159</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_eta_factorization_html_ae3aaa0f52a29f8a7b3f4550f97ca915d"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_eta_factorization.html#ae3aaa0f52a29f8a7b3f4550f97ca915d">operations_research::glop::EtaFactorization::Update</a></div><div class="ttdeci">void Update(ColIndex entering_col, RowIndex leaving_variable_row, const ScatteredColumn &direction)</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00143">basis_representation.cc:143</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_eta_matrix_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_eta_matrix.html">operations_research::glop::EtaMatrix</a></div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8h_source.html#l00052">basis_representation.h:52</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_eta_matrix_html_a3cb026dc900190c13b208d24134755ed"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_eta_matrix.html#a3cb026dc900190c13b208d24134755ed">operations_research::glop::EtaMatrix::RightSolve</a></div><div class="ttdeci">void RightSolve(DenseColumn *d) const</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00061">basis_representation.cc:61</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_eta_matrix_html_a4975f6e9d308a97737d76519e0b773d5"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_eta_matrix.html#a4975f6e9d308a97737d76519e0b773d5">operations_research::glop::EtaMatrix::~EtaMatrix</a></div><div class="ttdeci">virtual ~EtaMatrix()</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00049">basis_representation.cc:49</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_eta_matrix_html_a6b5f31c4068711b8e6823f4888f410ce"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_eta_matrix.html#a6b5f31c4068711b8e6823f4888f410ce">operations_research::glop::EtaMatrix::LeftSolve</a></div><div class="ttdeci">void LeftSolve(DenseRow *y) const</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00051">basis_representation.cc:51</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_eta_matrix_html_a7b76b8753b814ba45ef9be10454230d9"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_eta_matrix.html#a7b76b8753b814ba45ef9be10454230d9">operations_research::glop::EtaMatrix::EtaMatrix</a></div><div class="ttdeci">EtaMatrix(ColIndex eta_col, const ScatteredColumn &direction)</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00029">basis_representation.cc:29</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_eta_matrix_html_ad1e32061321d5cc422c6f18a8ed6d33d"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_eta_matrix.html#ad1e32061321d5cc422c6f18a8ed6d33d">operations_research::glop::EtaMatrix::SparseLeftSolve</a></div><div class="ttdeci">void SparseLeftSolve(DenseRow *y, ColIndexVector *pos) const</div><div class="ttdef"><b>Definition:</b> <a href="basis__representation_8cc_source.html#l00075">basis_representation.cc:75</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_a5a3deeb8998f541c08d96dc079591a54"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#a5a3deeb8998f541c08d96dc079591a54">operations_research::glop::LuFactorization::GetColumnPermutation</a></div><div class="ttdeci">const ColumnPermutation & GetColumnPermutation() const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8h_source.html#l00066">lu_factorization.h:66</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_ad91a397910de30b87b9fb45298fa5c58"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#ad91a397910de30b87b9fb45298fa5c58">operations_research::glop::LuFactorization::SetColumnPermutationToIdentity</a></div><div class="ttdeci">void SetColumnPermutationToIdentity()</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8h_source.html#l00072">lu_factorization.h:72</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_ae7202d055b6b172a8a1da4f5b136f9ea"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#ae7202d055b6b172a8a1da4f5b136f9ea">operations_research::glop::LuFactorization::SetParameters</a></div><div class="ttdeci">void SetParameters(const GlopParameters &parameters)</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8h_source.html#l00196">lu_factorization.h:196</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_lu_factorization_html_af9bc435481ae9e6e60d66a65d5394a7f"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_lu_factorization.html#af9bc435481ae9e6e60d66a65d5394a7f">operations_research::glop::LuFactorization::StatString</a></div><div class="ttdeci">std::string StatString() const</div><div class="ttdef"><b>Definition:</b> <a href="lu__factorization_8h_source.html#l00202">lu_factorization.h:202</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_permutation_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_permutation.html">operations_research::glop::Permutation< ColIndex ></a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_sparse_column_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_sparse_column.html">operations_research::glop::SparseColumn</a></div><div class="ttdef"><b>Definition:</b> <a href="sparse__column_8h_source.html#l00044">sparse_column.h:44</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_status_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_status.html">operations_research::glop::Status</a></div><div class="ttdef"><b>Definition:</b> <a href="status_8h_source.html#l00026">status.h:26</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_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="aconstraint__solver_2table_8cc_html_acb18315d548212835cd8ed4287e6c0b6"><div class="ttname"><a href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a></div><div class="ttdeci">int64_t a</div><div class="ttdef"><b>Definition:</b> <a href="constraint__solver_2table_8cc_source.html#l00046">constraint_solver/table.cc:46</a></div></div>
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<div class="ttc" id="acp__model__fz__solver_8cc_html_a10a1eab179b472c030bdc2a2efef7219"><div class="ttname"><a href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a></div><div class="ttdeci">SatParameters parameters</div><div class="ttdef"><b>Definition:</b> <a href="cp__model__fz__solver_8cc_source.html#l00119">cp_model_fz_solver.cc:119</a></div></div>
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<div class="ttc" id="alp__data_2permutation_8h_html"><div class="ttname"><a href="lp__data_2permutation_8h.html">permutation.h</a></div></div>
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<div class="ttc" id="alp__types_8h_html"><div class="ttname"><a href="lp__types_8h.html">lp_types.h</a></div></div>
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<div class="ttc" id="alu__factorization_8h_html"><div class="ttname"><a href="lu__factorization_8h.html">lu_factorization.h</a></div></div>
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<div class="ttc" id="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_a2b83a25cb4fd203c57a7155699fab246"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a2b83a25cb4fd203c57a7155699fab246">operations_research::glop::ColIndexVector</a></div><div class="ttdeci">std::vector< ColIndex > ColIndexVector</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00312">lp_types.h:312</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a733947145e3e1631165b618b05c9ccb7"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">operations_research::glop::Fractional</a></div><div class="ttdeci">double Fractional</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00078">lp_types.h:78</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_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_ae5fa9e57c2d31b294195ed8a9e17bfac"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#ae5fa9e57c2d31b294195ed8a9e17bfac">operations_research::glop::DenseColumn</a></div><div class="ttdeci">StrictITIVector< RowIndex, Fractional > DenseColumn</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00332">lp_types.h:332</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_afa7534bb8eff64b643c6079dc82e5e3c"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#afa7534bb8eff64b643c6079dc82e5e3c">operations_research::glop::ColMapping</a></div><div class="ttdeci">StrictITIVector< ColIndex, ColIndex > ColMapping</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00309">lp_types.h:309</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="apreprocessor_8cc_html_a2babe18010525bbf13c2fa5a959971e4"><div class="ttname"><a href="preprocessor_8cc.html#a2babe18010525bbf13c2fa5a959971e4">num_entries</a></div><div class="ttdeci">EntryIndex num_entries</div><div class="ttdef"><b>Definition:</b> <a href="preprocessor_8cc_source.html#l01370">preprocessor.cc:1370</a></div></div>
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<div class="ttc" id="arank__one__update_8h_html"><div class="ttname"><a href="rank__one__update_8h.html">rank_one_update.h</a></div></div>
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<div class="ttc" id="ascattered__vector_8h_html"><div class="ttname"><a href="scattered__vector_8h.html">scattered_vector.h</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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<div class="ttc" id="astats_8h_html"><div class="ttname"><a href="stats_8h.html">stats.h</a></div></div>
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<div class="ttc" id="astatus_8h_html"><div class="ttname"><a href="status_8h.html">status.h</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1glop_1_1_scattered_column_html"><div class="ttname"><a href="structoperations__research_1_1glop_1_1_scattered_column.html">operations_research::glop::ScatteredColumn</a></div><div class="ttdef"><b>Definition:</b> <a href="scattered__vector_8h_source.html#l00195">scattered_vector.h:196</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1glop_1_1_scattered_row_html"><div class="ttname"><a href="structoperations__research_1_1glop_1_1_scattered_row.html">operations_research::glop::ScatteredRow</a></div><div class="ttdef"><b>Definition:</b> <a href="scattered__vector_8h_source.html#l00197">scattered_vector.h:197</a></div></div>
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