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<a href="dual__edge__norms_8cc.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">// Copyright 2010-2021 Google LLC</span></div>
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<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
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<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment">// you may not use this file except in compliance with the License.</span></div>
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<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment">// You may obtain a copy of the License at</span></div>
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<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">//</span></div>
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<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
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<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">//</span></div>
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<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
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<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
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<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
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<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment">// See the License for the specific language governing permissions and</span></div>
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<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment">// limitations under the License.</span></div>
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<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
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<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#include "<a class="code" href="dual__edge__norms_8h.html">ortools/glop/dual_edge_norms.h</a>"</span></div>
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<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span> </div>
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<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="preprocessor">#include "<a class="code" href="lp__data_2lp__utils_8h.html">ortools/lp_data/lp_utils.h</a>"</span></div>
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<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span> </div>
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<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="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="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="keyword">namespace </span>glop {</div>
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<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span> </div>
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<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_dual_edge_norms.html#aae480c260ae0af4e638f918eb7deaaf4"> 21</a></span><a class="code hl_function" href="classoperations__research_1_1glop_1_1_dual_edge_norms.html#aae480c260ae0af4e638f918eb7deaaf4">DualEdgeNorms::DualEdgeNorms</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_basis_factorization.html">BasisFactorization</a>& basis_factorization)</div>
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<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span> : basis_factorization_(basis_factorization),</div>
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<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> recompute_edge_squared_norms_(true) {}</div>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> </div>
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<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_dual_edge_norms.html#af507437729fd1e93677772e748ca1cfc"> 25</a></span><span class="keywordtype">bool</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_dual_edge_norms.html#af507437729fd1e93677772e748ca1cfc">DualEdgeNorms::NeedsBasisRefactorization</a>()<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> <span class="keywordflow">return</span> recompute_edge_squared_norms_;</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> </div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_dual_edge_norms.html#aa71d36872f416feaa853788a7a7a7ef8"> 29</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_dual_edge_norms.html#aa71d36872f416feaa853788a7a7a7ef8">DualEdgeNorms::Clear</a>() { recompute_edge_squared_norms_ = <span class="keyword">true</span>; }</div>
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<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> </div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_dual_edge_norms.html#aa1eaa31ee29b8635d194762c1eb80962"> 31</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_dual_edge_norms.html#aa1eaa31ee29b8635d194762c1eb80962">DualEdgeNorms::ResizeOnNewRows</a>(RowIndex new_size) {</div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> edge_squared_norms_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a64b6b04f3a519d2c61d49daaa88bf06e">resize</a>(new_size, 1.0);</div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span>}</div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> </div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_dual_edge_norms.html#a1f1a686f26843ecfeb36e71f7626c330"> 35</a></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_dual_edge_norms.html#a1f1a686f26843ecfeb36e71f7626c330">DualEdgeNorms::GetEdgeSquaredNorms</a>() {</div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <span class="keywordflow">if</span> (recompute_edge_squared_norms_) ComputeEdgeSquaredNorms();</div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <span class="keywordflow">return</span> edge_squared_norms_;</div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span>}</div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> </div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_dual_edge_norms.html#a0c2c64e7a26487661db464cb20d4ddfe"> 40</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_dual_edge_norms.html#a0c2c64e7a26487661db464cb20d4ddfe">DualEdgeNorms::UpdateDataOnBasisPermutation</a>(</div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1glop_1_1_permutation.html">ColumnPermutation</a>& col_perm) {</div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <span class="keywordflow">if</span> (recompute_edge_squared_norms_) <span class="keywordflow">return</span>;</div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#ae436c0f61edb4f16608010c8bd75a1da">ApplyColumnPermutationToRowIndexedVector</a>(col_perm, &edge_squared_norms_);</div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span>}</div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> </div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_dual_edge_norms.html#a07ecfa8dabb00a7f680dc64efe1127d1"> 46</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1glop_1_1_dual_edge_norms.html#a07ecfa8dabb00a7f680dc64efe1127d1">DualEdgeNorms::UpdateBeforeBasisPivot</a>(</div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> ColIndex entering_col, RowIndex leaving_row,</div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_column.html">ScatteredColumn</a>& direction,</div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1glop_1_1_scattered_row.html">ScatteredRow</a>& unit_row_left_inverse) {</div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="comment">// No need to update if we will recompute it from scratch later.</span></div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="keywordflow">if</span> (recompute_edge_squared_norms_) <span class="keywordflow">return</span>;</div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</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>& tau = ComputeTau(<a class="code hl_function" href="namespaceoperations__research_1_1glop.html#af6375d177c0b120cebef16673060d132">TransposedView</a>(unit_row_left_inverse));</div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <a class="code hl_define" href="stats_8h.html#a9995704aaaf45fc21e08c847551a8d04">SCOPED_TIME_STAT</a>(&stats_);</div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> </div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="comment">// ||unit_row_left_inverse||^2 is the same as</span></div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="comment">// edge_squared_norms_[leaving_row], but with a better precision. If the</span></div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="comment">// difference between the two is too large, we trigger a full recomputation.</span></div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="comment">// Note that we use the PreciseSquaredNorms() because it is a small price to</span></div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="comment">// pay for more precise update below.</span></div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> leaving_squared_norm =</div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a1faa927dd93b43b3dea3eb2a993e30a1">PreciseSquaredNorm</a>(<a class="code hl_function" href="namespaceoperations__research_1_1glop.html#af6375d177c0b120cebef16673060d132">TransposedView</a>(unit_row_left_inverse));</div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> old_squared_norm = edge_squared_norms_[leaving_row];</div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> estimated_edge_norms_accuracy =</div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> (sqrt(leaving_squared_norm) - sqrt(old_squared_norm)) /</div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> sqrt(leaving_squared_norm);</div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> stats_.edge_norms_accuracy.Add(estimated_edge_norms_accuracy);</div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="keywordflow">if</span> (std::abs(estimated_edge_norms_accuracy) ></div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> parameters_.recompute_edges_norm_threshold()) {</div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <a class="code hl_define" href="base_2logging_8h.html#afcaa7cadd41741bb855c2ada1d2ef927">VLOG</a>(1) << <span class="stringliteral">"Recomputing edge norms: "</span> << sqrt(leaving_squared_norm)</div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> << <span class="stringliteral">" vs "</span> << sqrt(old_squared_norm);</div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> recompute_edge_squared_norms_ = <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="keywordflow">return</span>;</div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> }</div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> </div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> pivot = direction[leaving_row];</div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> new_leaving_squared_norm =</div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> leaving_squared_norm / <a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a1dcd08b0f6c19cd4a302bb5a3a6ea06e">Square</a>(pivot);</div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> </div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="comment">// Update the norm.</span></div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="keywordtype">int</span> stat_lower_bounded_norms = 0;</div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> e : direction) {</div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="comment">// Note that the update formula used is important to maximize the precision.</span></div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <span class="comment">// See Koberstein's PhD section 8.2.2.1.</span></div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> edge_squared_norms_[e.row()] +=</div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> e.coefficient() * (e.coefficient() * new_leaving_squared_norm -</div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> 2.0 / pivot * tau[e.row()]);</div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> </div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="comment">// Avoid 0.0 norms (The 1e-4 is the value used by Koberstein).</span></div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="comment">// TODO(user): use a more precise lower bound depending on the column norm?</span></div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="comment">// We can do that with Cauchy-Swartz inequality:</span></div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="comment">// (edge . leaving_column)^2 = 1.0 < ||edge||^2 * ||leaving_column||^2</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> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> kLowerBound = 1e-4;</div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="keywordflow">if</span> (edge_squared_norms_[e.row()] < kLowerBound) {</div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="keywordflow">if</span> (e.row() == leaving_row) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> edge_squared_norms_[e.row()] = kLowerBound;</div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> ++stat_lower_bounded_norms;</div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> }</div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> }</div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> edge_squared_norms_[leaving_row] = new_leaving_squared_norm;</div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <a class="code hl_define" href="stats_8h.html#a3c3e6b102f0d91c523099325c98e1887">IF_STATS_ENABLED</a>(stats_.lower_bounded_norms.Add(stat_lower_bounded_norms));</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="keywordtype">void</span> DualEdgeNorms::ComputeEdgeSquaredNorms() {</div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <a class="code hl_define" href="stats_8h.html#a9995704aaaf45fc21e08c847551a8d04">SCOPED_TIME_STAT</a>(&stats_);</div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> </div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> <span class="comment">// Since we will do a lot of inversions, it is better to be as efficient and</span></div>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> <span class="comment">// precise as possible by having a refactorized basis.</span></div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <a class="code hl_define" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(basis_factorization_.<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="l00110" name="l00110"></a><span class="lineno"> 110</span> <span class="keyword">const</span> RowIndex num_rows = basis_factorization_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#ae1d8c3228cb8e036c1d8ab67336a7d2f">GetNumberOfRows</a>();</div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> edge_squared_norms_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a64b6b04f3a519d2c61d49daaa88bf06e">resize</a>(num_rows, 0.0);</div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> <span class="keywordflow">for</span> (RowIndex <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>(0); <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> < num_rows; ++<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>) {</div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> edge_squared_norms_[<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>] = basis_factorization_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#a9b738f6b485a4d4ef866b8d82ac07876">DualEdgeSquaredNorm</a>(<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>);</div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> }</div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> recompute_edge_squared_norms_ = <span class="keyword">false</span>;</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> </div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span><span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#ae5fa9e57c2d31b294195ed8a9e17bfac">DenseColumn</a>& DualEdgeNorms::ComputeTau(</div>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <span class="keyword">const</span> ScatteredColumn& unit_row_left_inverse) {</div>
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<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <a class="code hl_define" href="stats_8h.html#a9995704aaaf45fc21e08c847551a8d04">SCOPED_TIME_STAT</a>(&stats_);</div>
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#ae5fa9e57c2d31b294195ed8a9e17bfac">DenseColumn</a>& result =</div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> basis_factorization_.<a class="code hl_function" href="classoperations__research_1_1glop_1_1_basis_factorization.html#a405547c96cca2eded0c29941a3ff7f22">RightSolveForTau</a>(unit_row_left_inverse);</div>
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <a class="code hl_define" href="stats_8h.html#a3c3e6b102f0d91c523099325c98e1887">IF_STATS_ENABLED</a>(stats_.tau_density.Add(<a class="code hl_function" href="namespaceoperations__research_1_1glop.html#a6b36bbbcd695191600dab9b88487ff18">Density</a>(<a class="code hl_function" href="namespaceoperations__research_1_1glop.html#aaa803ce9366dca251925e0bdde517430">Transpose</a>(result))));</div>
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> <span class="keywordflow">return</span> result;</div>
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<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span>}</div>
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> </div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span>} <span class="comment">// namespace glop</span></div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span>} <span class="comment">// namespace operations_research</span></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="abase_2logging_8h_html_afcaa7cadd41741bb855c2ada1d2ef927"><div class="ttname"><a href="base_2logging_8h.html#afcaa7cadd41741bb855c2ada1d2ef927">VLOG</a></div><div class="ttdeci">#define VLOG(verboselevel)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00984">base/logging.h:984</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_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_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_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_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_dual_edge_norms_html_a07ecfa8dabb00a7f680dc64efe1127d1"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_dual_edge_norms.html#a07ecfa8dabb00a7f680dc64efe1127d1">operations_research::glop::DualEdgeNorms::UpdateBeforeBasisPivot</a></div><div class="ttdeci">void UpdateBeforeBasisPivot(ColIndex entering_col, RowIndex leaving_row, const ScatteredColumn &direction, const ScatteredRow &unit_row_left_inverse)</div><div class="ttdef"><b>Definition:</b> <a href="dual__edge__norms_8cc_source.html#l00046">dual_edge_norms.cc:46</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_dual_edge_norms_html_a0c2c64e7a26487661db464cb20d4ddfe"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_dual_edge_norms.html#a0c2c64e7a26487661db464cb20d4ddfe">operations_research::glop::DualEdgeNorms::UpdateDataOnBasisPermutation</a></div><div class="ttdeci">void UpdateDataOnBasisPermutation(const ColumnPermutation &col_perm)</div><div class="ttdef"><b>Definition:</b> <a href="dual__edge__norms_8cc_source.html#l00040">dual_edge_norms.cc:40</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_dual_edge_norms_html_a1f1a686f26843ecfeb36e71f7626c330"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_dual_edge_norms.html#a1f1a686f26843ecfeb36e71f7626c330">operations_research::glop::DualEdgeNorms::GetEdgeSquaredNorms</a></div><div class="ttdeci">const DenseColumn & GetEdgeSquaredNorms()</div><div class="ttdef"><b>Definition:</b> <a href="dual__edge__norms_8cc_source.html#l00035">dual_edge_norms.cc:35</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_dual_edge_norms_html_aa1eaa31ee29b8635d194762c1eb80962"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_dual_edge_norms.html#aa1eaa31ee29b8635d194762c1eb80962">operations_research::glop::DualEdgeNorms::ResizeOnNewRows</a></div><div class="ttdeci">void ResizeOnNewRows(RowIndex new_size)</div><div class="ttdef"><b>Definition:</b> <a href="dual__edge__norms_8cc_source.html#l00031">dual_edge_norms.cc:31</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_dual_edge_norms_html_aa71d36872f416feaa853788a7a7a7ef8"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_dual_edge_norms.html#aa71d36872f416feaa853788a7a7a7ef8">operations_research::glop::DualEdgeNorms::Clear</a></div><div class="ttdeci">void Clear()</div><div class="ttdef"><b>Definition:</b> <a href="dual__edge__norms_8cc_source.html#l00029">dual_edge_norms.cc:29</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_dual_edge_norms_html_aae480c260ae0af4e638f918eb7deaaf4"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_dual_edge_norms.html#aae480c260ae0af4e638f918eb7deaaf4">operations_research::glop::DualEdgeNorms::DualEdgeNorms</a></div><div class="ttdeci">DualEdgeNorms(const BasisFactorization &basis_factorization)</div><div class="ttdef"><b>Definition:</b> <a href="dual__edge__norms_8cc_source.html#l00021">dual_edge_norms.cc:21</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_dual_edge_norms_html_af507437729fd1e93677772e748ca1cfc"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_dual_edge_norms.html#af507437729fd1e93677772e748ca1cfc">operations_research::glop::DualEdgeNorms::NeedsBasisRefactorization</a></div><div class="ttdeci">bool NeedsBasisRefactorization() const</div><div class="ttdef"><b>Definition:</b> <a href="dual__edge__norms_8cc_source.html#l00025">dual_edge_norms.cc:25</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_strict_i_t_i_vector_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">operations_research::glop::StrictITIVector< RowIndex, Fractional ></a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1glop_1_1_strict_i_t_i_vector_html_a64b6b04f3a519d2c61d49daaa88bf06e"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a64b6b04f3a519d2c61d49daaa88bf06e">operations_research::glop::StrictITIVector::resize</a></div><div class="ttdeci">void resize(IntType size)</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00273">lp_types.h:273</a></div></div>
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<div class="ttc" id="adual__edge__norms_8h_html"><div class="ttname"><a href="dual__edge__norms_8h.html">dual_edge_norms.h</a></div></div>
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<div class="ttc" id="alp__data_2lp__utils_8h_html"><div class="ttname"><a href="lp__data_2lp__utils_8h.html">lp_utils.h</a></div></div>
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<div class="ttc" id="amarkowitz_8cc_html_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_a1dcd08b0f6c19cd4a302bb5a3a6ea06e"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a1dcd08b0f6c19cd4a302bb5a3a6ea06e">operations_research::glop::Square</a></div><div class="ttdeci">Fractional Square(Fractional f)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2lp__utils_8h_source.html#l00036">lp_data/lp_utils.h:36</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a1faa927dd93b43b3dea3eb2a993e30a1"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a1faa927dd93b43b3dea3eb2a993e30a1">operations_research::glop::PreciseSquaredNorm</a></div><div class="ttdeci">Fractional PreciseSquaredNorm(const SparseColumn &v)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2lp__utils_8cc_source.html#l00038">lp_data/lp_utils.cc:38</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_a6b36bbbcd695191600dab9b88487ff18"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a6b36bbbcd695191600dab9b88487ff18">operations_research::glop::Density</a></div><div class="ttdeci">double Density(const DenseRow &row)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2lp__utils_8cc_source.html#l00106">lp_data/lp_utils.cc:106</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_aaa803ce9366dca251925e0bdde517430"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#aaa803ce9366dca251925e0bdde517430">operations_research::glop::Transpose</a></div><div class="ttdeci">const DenseRow & Transpose(const DenseColumn &col)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2lp__utils_8h_source.html#l00192">lp_data/lp_utils.h:192</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_ae436c0f61edb4f16608010c8bd75a1da"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#ae436c0f61edb4f16608010c8bd75a1da">operations_research::glop::ApplyColumnPermutationToRowIndexedVector</a></div><div class="ttdeci">void ApplyColumnPermutationToRowIndexedVector(const Permutation< ColIndex > &col_perm, RowIndexedVector *v)</div><div class="ttdef"><b>Definition:</b> <a href="lp__data_2permutation_8h_source.html#l00116">lp_data/permutation.h:116</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_af6375d177c0b120cebef16673060d132"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#af6375d177c0b120cebef16673060d132">operations_research::glop::TransposedView</a></div><div class="ttdeci">const ScatteredRow & TransposedView(const ScatteredColumn &c)</div><div class="ttdef"><b>Definition:</b> <a href="scattered__vector_8h_source.html#l00199">scattered_vector.h:199</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="astats_8h_html_a3c3e6b102f0d91c523099325c98e1887"><div class="ttname"><a href="stats_8h.html#a3c3e6b102f0d91c523099325c98e1887">IF_STATS_ENABLED</a></div><div class="ttdeci">#define IF_STATS_ENABLED(instructions)</div><div class="ttdef"><b>Definition:</b> <a href="stats_8h_source.html#l00437">stats.h:437</a></div></div>
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<div class="ttc" id="astats_8h_html_a9995704aaaf45fc21e08c847551a8d04"><div class="ttname"><a href="stats_8h.html#a9995704aaaf45fc21e08c847551a8d04">SCOPED_TIME_STAT</a></div><div class="ttdeci">#define SCOPED_TIME_STAT(stats)</div><div class="ttdef"><b>Definition:</b> <a href="stats_8h_source.html#l00438">stats.h:438</a></div></div>
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<div class="ttc" id="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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